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GPSSatellites summationtext Multipath/Spoofing (2.3,2.4) VehicleGPSReceiver AmbiguityKF(3.1.1)PositionSolution (AppendixA) SingleDiffer-ence(3.1.1) FixAmbigu-ities(3.1.2) ComputeGPSAttitude(3.3)CalculateRPVs(3.1.3) AttitudeEKF(4.1) IMU(4.2) Check/Reject(5) ImprovedPositioning ?ephemeris ?,? C/N0 ? ?XY Z ? ? ??, ?? Nk1,2 (float) Nk,l1,2 (fix) ? ??X?Y ?Z ? ? ? ??? ? ? ? gx,gy,gz ? ??? ? ? ? a70a105a103a117a114a101 a49a46a49a58 a66a108a111a99a107 a100a105a97a103a114a97a109 a111a118a101a114a118a105a101a119 a111a102 a116a104a101 a115a105a103a110a97a108 a114a101a106a101a99a116a105a111a110 a115a121a115a116a101a109a46 a84a101a120a116 a105a110 a112a97a114a101a110a116a104a101a115a101a115 a100a101a110a111a116a101a115 a116a104a101 a97a112a112a101a110a100a105a120 a111a114 a99a104a97a112a116a101a114 a97a110a100 a115a101a99a116a105a111a110 a119a104a105a99a104 a99a111a110a116a97a105a110a115 a105a110a102a111a114a109a97a116a105a111a110 a97a98a111a117a116 a101a97a99a104 a98a108a111a99a107a46 a53 a67a104a97a112a116a101a114 a50 a84a104a101 a71a108a111a98a97a108 a80a111a115a105a116a105a111a110a105a110a103 a83a121a115a116a101a109 a50a46a49 a83a105a103a110a97a108 a83a116a114a117a99a116a117a114a101 a84a104a101 a71a80a83 a115a105a103a110a97a108 a105a115 a109a97a100a101 a117a112 a111a102 a116a104a114a101a101 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a102a114a101a113a117a101a110a99a105a101a115a44 a116a104a101 a76a49 a97a110a100 a76a50 a102a114a101a113a117a101a110a99a105a101a115a44 a105a110 a117a115a101 a111a110 a97a108a108 a71a80a83 a115a97a116a101a108a108a105a116a101a115a46 a65a100a100a105a116a105a111a110a97a108a108a121a44 a97a110 a76a53 a115a105a103a110a97a108 a105a115 a112a108a97a110a110a101a100 a102a111a114 a102a117a116a117a114a101 a117a115a101a46 a84a104a101 a76a49a44 a76a50a44 a97a110a100 a76a53 a102a114a101a113a117a101a110a99a105a101a115 a97a114a101 a97a108a108 a115a99a97a108a97a114 a109a117a108a116a105a112a108a101a115 a111a102 a97 a99a111a109a109a111a110 a102a114a101a113a117a101a110a99a121a44 foa58 f0 = 10:23 a77a72a122 a40a50a46a49a41 fL1 = 154f0 = 1575:42 a77a72a122 a40a50a46a50a41 fL2 = 120f0 = 1227:60 a77a72a122 a40a50a46a51a41 fL5 = 115f0 = 1176:54 a77a72a122 a40a50a46a52a41 a54 a70a105a103a117a114a101 a50a46a49a58 a67a111a109a112a111a110a101a110a116a115 a111a102 a97 a71a80a83 a115a105a103a110a97a108 a84a104a101 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a116a101a114a109a115a58 ki = (ex)ki (ey)ki (ez)ki 1 2 66 66 66 64 xk xi yk yi zk zi cdti 3 77 77 77 75 +cdtk +Tki +Iki + ki a40a51a46a49a41 a49a52 ki = (ex)ki (ey)ki (ez)ki 1 2 66 66 66 64 xk xi yk yi zk zi cdti 3 77 77 77 75 +cdtk +Tki Iki + L1Nki + ki a40a51a46a50a41 a119a104a101a114a101 (ex)ki (ey)ki (ez)ki a105a115 a116a104a101 a117a110a105a116 a118a101a99a116a111a114 a102a114a111a109 a114a101a99a101a105a118a101a114 i a116a111 a115a97a116a101a108a108a105a116a101 k a97a110a100 (xk xi) (yk yi) (zk zi) T a105a115 a116a104a101 a118a101a99a116a111a114 a102a114a111a109 a116a104a101 a71a80a83 a114a101a99a101a105a118a101a114 a116a111 a116a104a101 a71a80a83 a115a97a116a101a108a108a105a116a101 a105a110 a69a67a69a70 a99a111a111a114a100a105a110a97a116a101a115a46 a66a101a102a111a114a101 a116a104a101 a110a101a120a116 a115a116a101a112a44 a105a116 a105a115 a105a109a112a111a114a116a97a110a116 a116a111 a110a111a116a101 a116a119a111 a105a109a112a111a114a116a97a110a116 a102a97a99a116a115 a97a98a111a117a116 a69a113a117a97a116a105a111a110a115 a40a51a46a49a41 a97a110a100 a40a51a46a50a41a46 a70a105a114a115a116a44 (ex)ki (ey)ki (ez)ki (ex)kj (ey)kj (ez)kj a102a111a114 a116a119a111 a114a101a99a101a105a118a101a114a115 a116a104a97a116 a97a114a101 a99a108a111a115a101 a116a111 a101a97a99a104 a111a116a104a101a114a46 a73a110 a102a97a99a116a44 a98a101a99a97a117a115a101 a116a104a101 a100a105a115a116a97a110a99a101 a116a111 a97 a71a80a83 a115a97a116a101a108a108a105a116a101 a102a114a111a109 a101a105a116a104a101a114 a114a101a99a101a105a118a101a114 a105a115 a115a101a118a101a114a97a108 a111a114a100a101a114a115 a111a102 a109a97a103a110a105a116a117a100a101 a108a111a110a103a101a114 a116a104a97a110 a116a104a101 a100a105a115a116a97a110a99a101 a98a101a116a119a101a101a110 a116a119a111 a114a101a99a101a105a118a101a114a115 a40a102a111a114 a116a104a105a115 a119a111a114a107a41a44 a116a104a101 a116a119a111 a117a110a105a116 a118a101a99a116a111a114a115 a109a97a121 a98a101 a99a111a110a115a105a100a101a114a101a100 a101a113a117a97a108a46 a84a104a101 a115a101a99a111a110a100 a105a109a112a111a114a116a97a110a116 a102a97a99a116 a105a115 a116a104a97a116 a116a104a101 a116a119a111 a97a116a109a111a115a112a104a101a114a105a99 a101a114a114a111a114a115 a97a114a101 a115a116a114a111a110a103a108a121 a99a111a114a114a101a108a97a116a101a100 a98a121 a112a111a115a105a116a105a111a110a59 a116a104a97a116 a105a115a44 a116a104a101a121 a97a114a101 a110a101a97a114a108a121 a116a104a101 a115a97a109a101 a102a111a114 a116a119a111 a114a101a99a101a105a118a101a114a115 a116a104a97a116 a97a114a101 a99a108a111a115a101 a116a111 a101a97a99a104 a111a116a104a101a114a46 a70a111a114 a114a101a99a101a105a118a101a114a115 a111a110a108a121 a97 a102a101a119 a109a101a116a101a114a115 a97a112a97a114a116a44 a116a104a101 a101a114a114a111a114a115 a119a105a108a108 a98a101 a110a101a97a114a108a121 a105a100a101a110a116a105a99a97a108 a105a110 a116a104a101 a109a101a97a115a117a114a101a109a101a110a116a115 a111a102 a101a97a99a104 a114a101a99a101a105a118a101a114a46 a84a104a101a110a44 a116a104a101 a112a115a101a117a100a111a114a97a110a103a101a115 a97a110a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115 a102a114a111a109 a114a101a99a101a105a118a101a114a115 i a97a110a100 j a102a111a114 a115a97a116a101a108a108a105a116a101 k a97a114a101 a115a117a98a116a114a97a99a116a101a100a44 a111a114 a100a105a27a101a114a101a110a99a101a100a46 a84a104a101 a100a105a27a101a114a101a110a99a101a100 a109a101a97a115a117a114a101a109a101a110a116a115 a121a105a101a108a100a58 k1 k2 = k1;2 = (ex)k1 (ey)k1 (ez)k1 1 2 66 66 66 64 x1;2 y1;2 z1;2 cdt1;2 3 77 77 77 75 + k1;2 a40a51a46a51a41 k1 k2 = k1;2 = (ex)k1 (ey)k1 (ez)k1 1 2 66 66 66 64 x1;2 y1;2 z1;2 cdt12 3 77 77 77 75 + (Nk1;2) + k1;2 a40a51a46a52a41 a49a53 a119a104a101a114a101 x1;2 y1;2 z1;2 a105a115 a116a104a101 a82a80a86 a102a114a111a109 a97a110a116a101a110a110a97 a49 a116a111 a97a110a116a101a110a110a97 a50a44 cdt1;2 = cdt1 cdt2 a97a110a100 k1;2 = k1 k2a46 a69a113a117a97a116a105a111a110a115 a40a51a46a51a41 a97a110a100 a40a51a46a52a41 a103a105a118a101 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101a115 a97a110a100 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115a44 a114a101a115a112a101a99a116a105a118a101a108a121a46 a87a104a105a108a101 a109a97a110a121 a111a102 a116a104a101 a101a114a114a111a114a115 a104a97a118a101 a98a101a101a110 a114a101a109a111a118a101a100 a102a114a111a109 a116a104a101 a109a101a97a115a117a114a101a109a101a110a116a115a44 a116a104a101 a114a101a108a97a116a105a118a101 a99a108a111a99a107 a98a105a97a115 a115a116a105a108a108 a114a101a109a97a105a110a115a46 a84a104a101 a110a101a120a116 a115a116a101a112 a105a115 a116a111 a99a104a111a111a115a101 a111a110a101 a115a97a116a101a108a108a105a116a101 l a45 a103a101a110a101a114a97a108a108a121 a116a104a101 a115a97a116a101a108a108a105a116a101 a102a97a114a116a104a101a115a116 a102a114a111a109 a116a104a101 a104a111a114a105a122a111a110 a45 a97a110a100 a115a117a98a116a114a97a99a116 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a97a110a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115 a97a115a115a111a99a105a97a116a101a100 a119a105a116a104 a116a104a97a116 a115a97a116a101a108a108a105a116a101 a102a114a111a109 a116a104a101 a111a116a104a101a114 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a109a101a97a115a117a114a101a109a101a110a116a115a44 a121a105a101a108a100a105a110a103 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101a115 a97a110a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115a58 r k;l1;2 = (ex)k;l1 (ey)k;l1 (ez)k;l1 2 66 66 4 x1;2 y1;2 z1;2 3 77 77 5 + k;l1;2 a40a51a46a53a41 r k;l1;2 = (ex)k;l1 (ey)k;l1 (ez)k;l1 2 66 66 4 x1;2 y1;2 z1;2 3 77 77 5 + L1(Nk;l1;2) + k;l1;2 a40a51a46a54a41 a119a104a101a114a101 (ex)k;l1 (ey)k;l1 (ez)k;l1 = (ex)k1 (ey)k1 (ez)k1 (ex)l1 (ey)l1 (ez)l1 a44 Nk;l1;2 = Nk1;2 Nl1;2a44 a97a110a100 k;11;2 = k1;2 l1;2a46 a84a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a97a110a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a45 a109a101a110a116a115 a109a97a121 a98a101 a99a111a109a112a117a116a101a100 a102a111a114 k = 1;:::;n a119a104a101a114a101 n a105a115 a116a104a101 a110a117a109a98a101a114 a111a102 a111a98a115a101a114a118a101a100 a115a97a116a101a108a108a105a116a101a115 a97a110a100 k 6= la46 a87a104a105a108a101 a116a104a101 a111a110a108a121 a101a114a114a111a114 a108a101a102a116 a105a110 a69a113a117a97a116a105a111a110 a40a51a46a53a41 a105a115 a116a104a101 a114a97a110a100a111a109 a101a114a114a111a114a44 a105a116a115 a118a97a114a105a97a110a99a101 a104a97a115 a110a111a119 a113a117a97a100a114a117a112a108a101a100 a102a114a111a109 a116a104a97a116 a111a102 a116a104a101 ki a116a101a114a109 a105a110 a69a113a117a97a116a105a111a110 a40a50a46a53a41a44 a119a104a105a99a104 a112a114a101a118a101a110a116a115 a116a104a101 a103a117a97a114a97a110a45 a116a101a101a100 a112a114a101a99a105a115a105a111a110 a100a101a115a105a114a101a100 a102a111a114 a97a116a116a105a116a117a100a101 a100a101a116a101a114a109a105a110a97a116a105a111a110a46 a69a113a117a97a116a105a111a110 a40a51a46a54a41 a115a116a105a108a108 a109a97a105a110a116a97a105a110a115 a97 a104a105a103a104 a100a101a103a114a101a101 a111a102 a112a114a101a99a105a115a105a111a110a44 a115a105a110a99a101 a116a104a101 ki a116a101a114a109 a105a110 a69a113a117a97a116a105a111a110 a40a50a46a54a41 a104a97a100 a97 a118a101a114a121 a115a109a97a108a108 a118a97a114a105a97a110a99a101 a111a114a105a103a105a110a97a108a108a121a46 a72a111a119a101a118a101a114a44 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a109a117a115a116 a98a101 a99a97a108a99a117a108a97a116a101a100 a98a101a102a111a114a101 a116a104a101 a100a111a117a98a108a101a45 a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115 a109a97a121 a98a101 a117a115a101a100 a116a111 a99a97a108a99a117a108a97a116a101 a97a110 a82a80a86a46 a67a97a108a99a117a108a97a116a105a110a103 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a105a115 a97 a116a119a111 a115a116a97a103a101 a112a114a111a99a101a115a115a46 a70a105a114a115a116a44 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115 a109a117a115a116 a98a101 a97a112a112a114a111a120a105a109a97a116a101a100a44 a121a105a101a108a100a105a110a103 a110a111a110a45a105a110a116a101a103a101a114 a40a16a29a111a97a116a17a41 a97a112a112a114a111a120a105a109a97a116a105a111a110a115 a111a102 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115a46 a84a104a101 a29a111a97a116 a49a54 a97a109a98a105a103a117a105a116a105a101a115 a97a114a101 a99a111a109a112a117a116a101a100 a117a115a105a110a103 a97 a75a97a108a109a97a110 a28a108a116a101a114a44 a119a104a105a99a104 a107a101a101a112a115 a97 a114a117a110a110a105a110a103 a97a112a112a114a111a120a105a109a97a116a105a111a110 a111a102 a116a104a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115a46 a65a102a116a101a114 a101a97a99a104 a105a116a101a114a97a116a105a111a110 a111a102 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114a44 a97a110 a97a116a116a101a109a112a116 a105a115 a109a97a100a101 a116a111 a16a28a120a17a44 a111a114 a114a111a117a110a100a44 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115 a116a111 a105a110a116a101a103a101a114a115a46 a70a105a120a105a110a103 a116a104a101 a105a110a116a101a103a101a114a115 a105a115 a97a116a116a101a109a112a116a101a100 a117a115a105a110a103 a116a104a101 a108a101a97a115a116a45a115a113a117a97a114a101a115 a97a109a98a105a103a117a105a116a121 a100a101a99a111a114a114a101a108a97a116a105a111a110 a97a100a106a117a115a116a109a101a110a116 a40a76a65a77a66a68a65a41 a109a101a116a104a111a100a44 a119a104a105a99a104 a117a115a101a115 a116a104a101 a115a116a97a116a101 a101a115a116a105a109a97a116a101 a99a111a45 a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a102a114a111a109 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114 a116a111 a114a111a117a110a100 a116a104a101 a105a110a116a101a103a101a114a115 a16a105a110a116a101a108a108a105a103a101a110a116a108a121a44a17 a105a110 a111a114a100a101a114 a102a114a111a109 a108a101a97a115a116 a118a97a114a105a97a110a99a101 a116a111 a109a111a115a116 a118a97a114a105a97a110a99a101a46 a51a46a49a46a49 a67a97a108a99a117a108a97a116a105a110a103 a70a108a111a97a116 a65a109a98a105a103a117a105a116a105a101a115 a65a115 a97 a28a114a115a116 a115a116a101a112a44 a116a104a101 a107a110a111a119a110 a105a110a102a111a114a109a97a116a105a111a110 a109a117a115a116 a98a101 a112a117a116 a105a110a116a111 a97 a102a111a114a109 a116a104a97a116 a97a108a108a111a119a115 a116a104a101 a97a109a98a105a103a117a45 a105a116a105a101a115 a116a111 a98a101 a101a115a116a105a109a97a116a101a100a46 a84a104a101 a115a105a110a103a108a101a100a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a97a110a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115 a109a97a121 a98a101 a114a101a112a114a101a115a101a110a116a101a100 a97a115a58 2 66 66 66 64 k1;2 a46a46a46 k1;2 a46a46a46 3 77 77 77 75 = 2 66 66 66 64 (ex)k1 (ey)k1 (ez)k1 1 a46a46a46 a46a46a46 a46a46a46 a46a46a46 (ex)k1 (ey)k1 (ez)k1 1 a46a46a46 a46a46a46 a46a46a46 a46a46a46 3 77 77 77 75 2 66 66 66 64 x1;2 y1;2 z1;2 cdt1;2 3 77 77 77 75 + L1 2 66 66 66 64 0 a46a46a46 Nk1;2 a46a46a46 3 77 77 77 75 +w a40a51a46a55a41 a84a111 a101a115a116a105a109a97a116a101 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115a44 a105a116 a105a115 a110a101a99a101a115a115a97a114a121 a116a111 a104a97a118a101 a97 a109a111a100a101a108 a111a102 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115 a116a104a97a116 a119a105a108a108 a28a116 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114a46 a84a104a101 a101a113a117a97a116a105a111a110a115 a102a111a114 a105a109a112a108a101a109a101a110a116a105a110a103 a97 a75a97a108a109a97a110 a28a108a116a101a114 a97a110a100 a115a111a109a101 a98a97a99a107a103a114a111a117a110a100 a105a110a102a111a114a109a97a116a105a111a110 a111a110 a116a104a101 a28a108a116a101a114 a109a97a121 a98a101 a102a111a117a110a100 a105a110 a65a112a112a101a110a100a105a120 a66a46 a51a46a49a46a49a46a49 a84a105a109a101 a85a112a100a97a116a101 a70a111a114 a116a104a101 a116a105a109a101 a117a112a100a97a116a101 a115a116a101a112 a111a102 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114a44 a105a116 a105a115 a110a101a99a101a115a115a97a114a121 a116a111 a104a97a118a101 a97 a109a111a100a101a108 a100a101a115a99a114a105a98a105a110a103 a116a104a101 a115a116a97a116a101 a116a114a97a110a115a105a116a105a111a110 a116a104a97a116 a28a116a115 a116a104a101 a102a111a114a109 a111a102 a69a113a117a97a116a105a111a110 a40a66a46a49a41a46 a79a110a99a101 a97 a71a80a83 a115a105a103a110a97a108 a105a115 a98a101a105a110a103 a116a114a97a99a107a101a100a44 a116a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121 a115a104a111a117a108a100 a110a111a116 a99a104a97a110a103a101a46 a84a104a101a114a101a102a111a114a101a44 Ak a105a115 a103a105a118a101a110 a98a121 a97a110 m m a105a100a101a110a116a105a116a121 a109a97a116a114a105a120a44 a119a104a101a114a101 m a105a115 a116a104a101 a110a117a109a98a101a114 a111a102 a97a109a98a105a103a117a105a116a105a101a115a58 Ak = Im m a40a51a46a56a41 a49a55 a65a108a115a111a44 a115a105a110a99a101 a116a104a101a114a101 a105a115 a110a111 a105a110a112a117a116 a105a110a116a111 a116a104a101 a16a115a121a115a116a101a109a17 a111a102 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115a44 a116a104a101 Bkuk a116a101a114a109 a111a102 a69a113a117a97a116a105a111a110 a40a66a46a49a41 a109a97a121 a98a101 a111a109a105a116a116a101a100 a99a111a109a112a108a101a116a101a108a121a46 a83a116a114a105a99a116a108a121 a115a112a101a97a107a105a110a103a44 a115a105a110a99a101 a116a104a101a114a101 a115a104a111a117a108a100 a98a101 a110a111 a118a97a114a105a97a98a105a108a105a116a121 a105a110 a97a110a121 a111a102 a116a104a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115a44 Qk a115a104a111a117a108a100 a98a101 a97a110 m m a109a97a116a114a105a120 a111a102 a122a101a114a111a101a115a59 a104a111a119a101a118a101a114a44 a104a97a118a105a110a103 a97 a16a112a101a114a102a101a99a116a17 a109a111a100a101a108 a112a117a116a115 a116a104a101 a28a108a116a101a114 a97a116 a114a105a115a107 a111a102 a103a111a105a110a103 a116a111 a115a108a101a101a112a44 a97a115 a101a120a112a108a97a105a110a101a100 a105a110 a83a101a99a116a105a111a110 a66a46a51a46 a84a111 a112a114a101a118a101a110a116 a116a104a101 a28a108a116a101a114 a102a114a111a109 a103a111a105a110a103 a116a111 a115a108a101a101a112a44 Qk a109a97a121 a98a101 a97a114a116a105a28a99a105a97a108a108a121 a105a110a29a97a116a101a100 a116a111 a101a110a115a117a114a101 a116a104a97a116 a110a101a119 a109a101a97a115a117a114a101a109a101a110a116a115 a119a105a108a108 a97a108a119a97a121a115 a98a101 a116a97a107a101a110 a105a110a116a111 a97a99a99a111a117a110a116a46 a70a111a114 a116a104a105a115 a119a111a114a107a44 Qk a119a97a115 a99a104a111a115a101a110 a116a111 a98a101a58 Qk = Im m 10 6 a40a51a46a57a41 a73a116 a105a115 a105a109a112a111a114a116a97a110a116 a116a111 a110a111a116a101 a116a104a97a116 a98a101a99a97a117a115a101 Qk a114a101a29a101a99a116a115 a112a114a111a99a101a115a115 a100a105a115a116a117a114a98a97a110a99a101 a101a114a114a111a114 a116a104a97a116 a105a115 a110a111a116 a97a99a116a117a97a108a108a121 a112a114a101a115a101a110a116 a105a110 a116a104a101 a115a121a115a116a101a109a44 Pk a119a105a108a108 a110a111a116 a114a101a112a114a101a115a101a110a116 a116a104a101 a114a101a97a108 a99a111a118a97a114a105a97a110a99a101 a111a102 a116a104a101 a105a110a116a101a103a101a114 a97a109a45 a98a105a103a117a105a116a121 a109a101a97a115a117a114a101a109a101a110a116a115a46 a84a104a101 a115a116a97a116a101 a101a115a116a105a109a97a116a105a111a110 a101a114a114a111a114 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120a44 Pka44 a105a115 a115a116a105a108a108 a117a115a101a102a117a108 a97a115 a97 a114a101a108a97a116a105a118a101 a99a111a109a112a97a114a105a115a111a110 a111a102 a116a104a101 a118a97a114a105a97a110a99a101 a98a101a116a119a101a101a110 a116a104a101 a105a110a100a105a118a105a100a117a97a108 a97a109a98a105a103a117a105a116a105a101a115a46 a51a46a49a46a49a46a50 a77a101a97a115a117a114a101a109a101a110a116 a85a112a100a97a116a101 a84a111 a109a97a107a101 a69a113a117a97a116a105a111a110 a40a51a46a55a41 a28a116 a116a104a101 a102a111a114a109 a111a102 a69a113a117a97a116a105a111a110 a40a66a46a50a41a44 a105a116 a105a115 a110a101a99a101a115a115a97a114a121 a116a111 a114a101a109a111a118a101 a116a104a101 a109a97a116a114a105a120 a111a102 a117a110a105a116 a118a101a99a116a111a114a115a44 a99a97a108a108a101a100 a116a104a101 a103a101a111a109a101a116a114a121 a109a97a116a114a105a120a44 a97a110a100 a116a104a101 a82a80a86a46 a73a116 a105a115 a112a111a115a115a105a98a108a101 a116a111 a114a101a109a111a118a101 a116a104a101 a103a101a111a109a101a116a114a121 a109a97a116a114a105a120 a116a101a114a109 a98a121 a109a117a108a116a105a112a108a121a105a110a103 a69a113a117a97a116a105a111a110 a40a51a46a55a41 a98a121 a116a104a101 a108a101a102a116 a110a117a108a108 a115a112a97a99a101a44 La44 a111a102 a116a104a101 a103a101a111a109a101a116a114a121 a109a97a116a114a105a120a59 a116a104a97a116 a105a115a44 a97 a109a97a116a114a105a120 L a115a117a99a104 a116a104a97a116a58 L 2 66 66 66 64 (ex)k1 (ey)k1 (ez)k1 1 a46a46a46 a46a46a46 a46a46a46 a46a46a46 (ex)k1 (ey)k1 (ez)k1 1 a46a46a46 a46a46a46 a46a46a46 a46a46a46 3 77 77 77 75 = 0 a40a51a46a49a48a41 a77a117a108a116a105a112a108a121a105a110a103 a69a113a117a97a116a105a111a110 a40a51a46a55a41 a98a121 L a119a105a108a108 a121a105a101a108a100a58 a49a56 L 2 66 66 66 64 k1;2 a46a46a46 k1;2 a46a46a46 3 77 77 77 75 = L 2 64 0m m L1Im m 3 75 2 64Nk1;2 a46a46a46 3 75+w a40a51a46a49a49a41 a84a104a105a115 a28a116a115 a116a104a101 a102a111a114a109a97a116 a111a102 a69a113a117a97a116a105a111a110 a40a66a46a50a41a44 a103a105a118a105a110a103a58 yk = L 2 66 66 66 64 k1;2 a46a46a46 k1;2 a46a46a46 3 77 77 77 75 a40a51a46a49a50a41 Ck = L 2 64 0m m L1Im m 3 75 a40a51a46a49a51a41 xk = 2 64Nk1;2 a46a46a46 3 75 a40a51a46a49a52a41 a84a104a101 a99a111a109a112a117a116a97a116a105a111a110 a111a102 a116a104a101 a109a101a97a115a117a114a101a109a101a110a116 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120a44 Rka44 a105a115 a116a97a107a101a110 a102a114a111a109 a91a57a93a46 Rk a105a115 a103a105a118a101a110 a98a121a58 Rk = L 2 66 66 66 64 2 ;1 + 2 ;2 0 0 0 0 a46a46a46 0 0 0 0 2 ;1 + 2 ;2 0 0 0 0 a46a46a46 3 77 77 77 75 LT a40a51a46a49a53a41 a119a104a101a114a101 a97a110a100 a97a114a101 a103a105a118a101a110 a98a121 a116a104a101 a84a97a98a108a101 a51a46a49 a97a110a100 a116a104a101 a101a113a117a97a116a105a111a110a115a58 2 = 2 atm + 2DLL a40a51a46a49a54a41 a49a57 DLL = c s 4d2Bn C=N0 (2(1 d) + 4d TC=N0) a40a51a46a49a55a41 2 = 2 atm + 2PLL a40a51a46a49a56a41 PLL = L12 s Bn C=N0(1 + 1 TC=N0) a40a51a46a49a57a41 a73a116 a105a115 a105a109a112a111a114a116a97a110a116 a116a111 a110a111a116a101 a116a104a97a116 a116a104a101 C=N0 a109a101a97a115a117a114a101a109a101a110a116 a105a115 a103a101a110a101a114a97a108a108a121 a114a101a112a111a114a116a101a100 a105a110 a100a101a99a105a98a101a108a115a44 a98a117a116 a115a104a111a117a108a100 a98a101 a99a111a110a118a101a114a116a101a100 a116a111 a116a104a101 a97a98a115a111a108a117a116a101 C=N0 a98a101a102a111a114a101 a117a115a101 a105a110 a69a113a117a97a116a105a111a110a115 a40a51a46a49a55a41 a97a110a100 a40a51a46a49a57a41 a84a97a98a108a101 a51a46a49a58 a80a97a114a97a109a101a116a101a114a115 a102a111a114 a117a115a101 a105a110 a69a113a117a97a116a105a111a110a115 a40a51a46a49a54a41 a116a104a114a111a117a103a104 a40a51a46a49a57a41 a80a97a114a97a109a101a116a101a114 a68a101a115a99a114a105a112a116a105a111a110 a86a97a108a117a101 a40a117a110a105a116a115a41 2 atm a86a97a114a105a97a110a99a101 a100a117a101 a116a111 a97a116a109a111a115a112a104a101a114a105a99 a99a111a100a101 a100a101a108a97a121 a53a46a50a50 a40a109a41 c a67a111a100a101 a99a104a105a112 a119a105a100a116a104 a50a57a51a46a48a53 a40a109a41 d a67a111a114a114a101a108a97a116a111a114 a115a112a97a99a105a110a103 a48a46a53 a40a99a104a105a112a115a41 Bnp a67a111a100a101 a108a111a111a112 a110a111a105a115a101 a98a97a110a100a119a105a100a116a104 a50 a40a72a122a41 T a80a114a101a100a105a99a116a105a111a110 a105a110a116a101a103a114a97a116a105a111a110 a116a105a109a101 a50 a40a109a115a41 2 atm a86a97a114a105a97a110a99a101 a100a117a101 a116a111 a97a116a109a111a115a112a104a101a114a105a99 a99a97a114a114a105a101a114 a100a101a108a97a121 a48a46a48a51 a40a109a41 L1 a67a97a114a114a105a101a114 a119a97a118a101a108a101a110a103a116a104 a49a57a46a48a51 a40a99a109a41 Bn a67a97a114a114a105a101a114 a108a111a111a112 a110a111a105a115a101 a98a97a110a100a119a105a100a116a104 a49a56 a40a72a122a41 a51a46a49a46a49a46a51 a73a109a112a108a101a109a101a110a116a97a116a105a111a110 a84a111 a105a110a105a116a105a97a108a105a122a101 a116a104a101 a28a108a116a101a114a44 a97a110 a101a115a116a105a109a97a116a101 a111a102 a116a104a101 a116a104a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a109a117a115a116 a28a114a115a116 a98a101 a99a97a108a99a117a108a97a116a101a100a46 a73a116 a105a115 a111a98a115a101a114a118a101a100 a116a104a97a116 a115a117a98a116a114a97a99a116a105a110a103 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a102a114a111a109 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a112a114a111a118a105a100a101a115 a97 a103a111a111a100 a99a97a110a100a105a100a97a116a101a58 k1;2 k1;2 = ~e 2 66 66 66 64 x1;2 y1;2 z1;2 cdt1;2 3 77 77 77 75 + (Nk1;2) ~e 2 66 66 66 64 x1;2 y1;2 z1;2 cdt1;2 3 77 77 77 75 = L1(Nk1;2) a40a51a46a50a48a41 a50a48 a119a104a101a114a101 ~ek1 = (ex)k1 (ey)k1 (ez)k1 1 a78a111a116a101 a116a104a97a116 a116a104a101 a101a114a114a111a114 a116a101a114a109a115 a104a97a118a101 a98a101 a111a109a105a116a116a101a100 a102a111a114 a99a108a97a114a105a116a121a46 a69a113a117a97a116a105a111a110 a40a51a46a50a48a41 a109a97a121 a98a101 a115a105a109a112a108a105a28a101a100 a116a111 a121a105a101a108a100 a116a104a101 a105a110a105a116a105a97a108 a101a115a116a105a109a97a116a101 a111a102 Nk1;2a58 Nk1;2 = k 1;2 k 1;2 L1 a40a51a46a50a49a41 a84a104a101 a105a110a105a116a105a97a108 a115a116a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a105a115 a115a111a109a101a119a104a97a116 a97a114a98a105a116a114a97a114a121 a98a97a115a101a100 a111a110 a100a101a115a105a114a101a100 a28a108a116a101a114 a112a101a114a102a111a114a109a97a110a99a101a44 a115a112a101a99a105a28a99a97a108a108a121 a104a111a119 a113a117a105a99a107a108a121 a105a116 a105a115 a100a101a115a105a114a101a100 a116a104a97a116 Pk a115a104a111a117a108a100 a99a111a110a118a101a114a103a101a46 a70a114a111a109 a91a57a93a44 a105a116 a119a97a115 a100a101a99a105a100a101a100 a116a104a97a116 a116a104a101 a115a116a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a119a111a117a108a100 a98a101 a105a110a105a116a105a97a108a105a122a101a100 a97a115a58 P0 = 12 Im m a40a51a46a50a50a41 a65a102a116a101a114 a105a110a105a116a105a97a108a105a122a97a116a105a111a110a44 a117a112a100a97a116a105a110a103 a116a104a101 a28a108a116a101a114 a105a115 a102a97a105a114a108a121 a115a116a114a97a105a103a104a116a102a111a114a119a97a114a100 a117a115a105a110a103 a116a104a101 a115a116a101a112a115 a111a117a116a108a105a110a101a100 a102a111a114 a97 a75a97a108a109a97a110 a28a108a116a101a114a46 a51a46a49a46a50 a76a65a77a66a68a65 a109a101a116a104a111a100 a79a110a99a101 a29a111a97a116 a101a115a116a105a109a97a116a101a115 a111a102 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115 a104a97a118a101 a98a101a101a110 a99a97a108a99a117a108a97a116a101a100a44 a116a104a101 a110a101a120a116 a115a116a101a112 a105a115 a97a116a116a101a109a112a116a45 a105a110a103 a116a111 a103a101a116 a97 a115a101a116 a111a102 a28a120a101a100 a97a109a98a105a103a117a105a116a105a101a115a46 a84a104a101 a109a111a115a116 a115a116a114a97a105a103a104a116a102a111a114a119a97a114a100 a109a101a116a104a111a100 a111a102 a111a98a116a97a105a110a105a110a103 a28a120a101a100 a97a109a98a105a103a117a105a116a105a101a115 a119a111a117a108a100 a98a101 a116a111 a109a101a114a101a108a121 a114a111a117a110a100 a116a104a101 a29a111a97a116 a97a109a98a105a103a117a105a116a105a101a115a59 a104a111a119a101a118a101a114a44 a115a105a109a112a108a101 a114a111a117a110a100a105a110a103 a100a111a101a115 a110a111a116 a97a99a99a111a117a110a116 a102a111a114 a116a104a101 a105a110a102a111a114a109a97a116a105a111a110 a99a111a110a116a97a105a110a101a100 a105a110 a116a104a101 a115a116a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a97a115a115a111a99a105a97a116a101a100 a119a105a116a104 a116a104a101 a29a111a97a116 a97a109a98a105a103a117a105a116a105a101a115a46 a65 a112a111a112a117a108a97a114 a109a101a116a104a111a100 a116a104a97a116 a100a111a101a115 a105a110a99a108a117a100a101 a116a104a101 a115a116a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a105a115 a116a104a101 a76a65a77a66a68a65 a109a101a116a104a111a100a91a63a93a46 a65a115 a116a104a101 a110a97a109a101 a105a109a112a108a105a101a115a44 a116a104a101 a76a65a77a66a68a65 a109a101a116a104a111a100 a117a115a101a115 a97 a100a101a99a111a114a114a101a108a97a116a105a111a110 a116a114a97a110a115a102a111a114a109a97a116a105a111a110 a116a111 a100a101a99a111a114a114a101a108a97a116a101 a116a104a101 a101a114a114a111a114 a105a110 a116a104a101 a97a109a98a105a103a117a105a116a105a101a115 a115a111 a116a104a97a116 a116a104a101a121 a109a97a121 a98a101 a115a101a108a101a99a116a101a100 a109a111a114a101 a99a97a114a101a102a117a108a108a121a46 a77a111a114a101 a115a112a101a99a105a28a99a97a108a108a121a44 a116a104a101 a116a114a97a110a115a102a111a114a109a97a116a105a111a110 a99a101a110a116a101a114a115 a97a114a111a117a110a100 a97 a116a114a97a110a115a102a111a114a109a97a116a105a111a110 a109a97a116a114a105a120 Z a115a117a99a104 a116a104a97a116 z = Z a a40a51a46a50a51a41 Qz = Z QaZ a40a51a46a50a52a41 a50a49 a119a104a101a114a101aa114a101a112a114a101a115a101a110a116a115 a116a104a101 a29a111a97a116 a99a121a99a108a101 a97a109a98a105a103a117a105a116a105a101a115a44z a114a101a112a114a101a115a101a110a116a115 a116a104a101 a116a114a97a110a115a102a111a114a109a101a100 a29a111a97a116 a97a109a98a105a103a117a105a116a105a101a115a44 Qa a114a101a112a114a101a115a101a110a116a115 a116a104a101 a115a116a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a111a102 a116a104a101 a116a114a117a101 a99a121a99a108a101 a97a109a98a105a103a117a105a116a105a101a115a44 Qz a114a101a112a114a101a115a101a110a116a115 a116a104a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a111a102 a116a104a101 a116a114a97a110a115a102a111a114a109a101a100 a97a109a98a105a103a117a105a116a105a101a115a44 a97a110a100 Z a100a101a110a111a116a101a115 a116a104a101 a99a111a110a106a117a103a97a116a101 a116a114a97a110a115a112a111a115a101 a111a102 Za46 a73a100a101a97a108a108a121a44 a116a104a101 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a111a110a101a115 a97a108a111a110a103 a116a104a101 a109a97a105a110 a100a105a97a103a111a110a97a108a44 a97a110a100 D a105a115 a97 a100a105a97a103a111a110a97a108 a109a97a116a114a105a120a46 Z a119a105a108a108 a98a101 a97 a109a97a116a114a105a120 a111a102 a105a110a116a101a103a101a114a115 a97a110a100 a105a115 a105a110a116a101a110a100a101a100 a116a111 a97a112a112a114a111a120a105a109a97a116a101 La59 a105a102 Z = La58 Qz = Z QaZ = Z L D 1L 1Z = D 1 a40a51a46a50a55a41 a119a104a105a99a104 a103a105a118a101a115 a116a104a101 a105a110a116a101a110a100a101a100 a114a101a115a117a108a116 a111a102Qz a98a101a105a110a103 a100a105a97a103a111a110a97a108a46 a84a104a101 a105a110a116a101a103a101a114 a114a101a115a116a114a105a99a116a105a111a110 a111a110La109a101a97a110a115 a116a104a97a116 a117a115a117a97a108a108a121 Z6= L a97a110a100 a116a104a101 a116a114a97a110a115a102a111a114a109a101a100 a97a109a98a105a103a117a105a116a105a101a115 a119a105a108a108 a110a111a116 a98a101 a112a101a114a102a101a99a116a108a121 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a109a97a116a114a105a120 a102a111a114 ^za44 a97a110a100 2 a105a115 a97 a113a117a97a110a116a105a116a121 a117a115a101a100 a116a111 a99a111a110a116a114a111a108 a116a104a101 a118a111a108a117a109a101 a111a102 a116a104a101 a115a101a97a114a99a104 a115a112a97a99a101 a102a111a114 a116a104a101 a105a110a116a101a103a101a114a115a46 a73a102 Q 1^z a119a101a114a101 a100a105a97a103a111a110a97a108 a40a97a109a98a105a103a117a105a116a105a101a115 a112a101a114a102a101a99a116a108a121 a100a101a99a111a114a114a101a108a97a116a101a100a41a44 a116a104a101 a102a117a110a99a116a105a111a110 a119a111a117a108a100 a101a115a115a101a110a116a105a97a108a108a121 a98a101a58 nX i=1 (^zi zi)2 qi;i < 2 a40a51a46a50a57a41 a119a104a101a114a101qi;i a105a115 a116a104a101 a101a108a101a109a101a110a116 a105a110 a116a104a101ith a114a111a119 a97a110a100ith a99a111a108a117a109a110 a111a102Q^za46 a69a113a117a97a116a105a111a110 a40a51a46a50a57a41 a115a104a111a119a115 a116a104a101 a101a115a115a101a110a99a101 a111a102 a116a104a101 a105a100a101a97 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a115a101a116 a111a102 a105a110a116a101a103a101a114a115 a91a52a93a46 a79a110a99a101 a97 a115a101a116 a111a102 a105a110a116a101a103a101a114a115 a104a97a115 a98a101a101a110 a99a104a111a115a101a110a44 a116a104a101a121 a109a117a115a116 a98a101 a116a114a97a110a115a102a111a114a109a101a100 a98a97a99a107 a105a110a116a111 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a102a111a114 a116a104a101 a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a101a113a117a97a116a105a111a110a115a46 a82a101a99a97a108a108 a116a104a97a116a58 z = Z a a40a51a46a51a48a41 a83a111 a116a104a101 a28a120a101a100 a105a110a116a101a103a101a114 a115a101a116 a a109a97a121 a98a101 a99a97a108a99a117a108a97a116a101a100 a98a121 a109a117a108a116a105a112a108a121a105a110a103 z a111a110 a116a104a101 a108a101a102a116 a115a105a100a101 a98a121 a116a104a101 a105a110a118a101a114a115a101 a111a102 Z a46 a50a51 a51a46a49a46a51 a67a97a108a99a117a108a97a116a105a110a103 a82a80a86a115 a79a110a99a101 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a104a97a118a101 a98a101a101a110 a111a98a116a97a105a110a101a100 a116a104a114a111a117a103a104 a116a104a101 a76a65a77a66a68a65 a109a101a116a104a111a100a44 a116a104a101 a82a80a86a115 a109a97a121 a98a101 a99a97a108a99a117a108a97a116a101a100a46 a82a101a97a114a114a97a110a103a105a110a103 a69a113a117a97a116a105a111a110 a40a51a46a54a41a44 a105a116 a105a115 a115a101a101a110 a116a104a97a116a58 r k;l1;2 L1(Nk;l1;2) = (ex)k;l1 (ey)k;l1 (ez)k;l1 2 66 66 4 x1;2 y1;2 z1;2 3 77 77 5 + k;l1;2 a40a51a46a51a49a41 a83a105a110a99a101 a116a104a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a97a114a101 a110a111a119 a107a110a111a119a110a44 a99a97a108a99a117a108a97a116a105a110a103 a116a104a101 a114a101a108a97a116a105a118a101 a112a111a115a105a116a105a111a110a105a110a103 a118a101a99a116a111a114 a105a115 a103a105a118a101a110 a98a121 a97 a108a101a97a115a116 a115a113a117a97a114a101a115 a115a111a108a117a116a105a111a110a58 (HTH) 1HT(r k;l1;2 L1(Nk;l1;2)) = 2 66 66 4 x1;2 y1;2 z1;2 3 77 77 5 a40a51a46a51a50a41 H = 2 64(ex)k;l1 (ey)k;l1 (ez)k;l1 a46a46a46 a46a46a46 a46a46a46 3 75 a40a51a46a51a51a41 a51a46a49a46a52 a83a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a121a99a108a101 a97a109a98a105a103a117a105a116a105a101a115 a84a104a101 a109a111a115a116 a105a100a101a97a108 a115a105a116a117a97a116a105a111a110 a102a111a114 a116a104a101 a116a97a115a107 a97a116 a104a97a110a100 a119a111a117a108a100 a98a101 a116a111 a107a110a111a119 a116a104a101 a114a101a108a97a116a105a118a101 a99a108a111a99a107 a101a114a114a111a114 a98a101a116a119a101a101a110 a116a104a101 a116a119a111 a114a101a99a101a105a118a101a114a115 a97a110a100 a116a104a101 a105a110a116a101a103a101a114 a99a121a99a108a101 a97a109a98a105a103a117a105a116a105a101a115 a102a111a114 a116a104a101 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a99a97a108a99a117a108a97a116a101a100a44 a69a113a117a97a116a105a111a110 a40a51a46a51a41 a109a97a121 a98a101 a117a116a105a108a105a122a101a100 a116a111 a99a97a108a99a117a108a97a116a101 a97 a110a111a105a115a121 a101a115a116a105a109a97a116a101 a111a102 a116a104a101 a99a108a111a99a107 a101a114a114a111a114a46 a82a101a97a114a114a97a110a103a105a110a103 a69a113a117a97a116a105a111a110 a40a51a46a51a41 a116a111 a103a105a118a101 a116a104a101 a110a111a105a115a121 a99a108a111a99a107 a101a114a114a111a114 a101a115a116a105a109a97a116a101 a121a105a101a108a100a115a58 k1;2 (ex)k1 (ey)k1 (ez)k1 2 66 66 4 x1;2 y1;2 z1;2 3 77 77 5 = cdt1;2 +ek1;2 a40a51a46a51a52a41 a65a115 a115a101a101a110 a105a110 a69a113a117a97a116a105a111a110 a40a51a46a51a52a41a44 a97 a109a101a97a115a117a114a101a109a101a110a116 a111a102 a116a104a101 a99a108a111a99a107 a101a114a114a111a114 a109a97a121 a98a101 a111a98a116a97a105a110a101a100 a98a121 a99a97a108a45 a99a117a108a97a116a105a110a103 a116a104a101 a100a111a116 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a114a101a103a117a108a97a114 a75a70a46 a84a104a101 a112a114a105a109a97a114a121 a100a105a27a101a114a101a110a99a101a115 a98a101a116a119a101a101a110 a116a104a101 a69a75a70 a97a110a100 a97 a115a116a97a110a100a97a114a100 a75a70 a97a114a101a58 a49a46 a83a105a110a99a101 a116a104a101 a115a116a97a116a101a115 a97a114a101 a110a111a110a45a108a105a110a101a97a114a44 a116a104a101 a115a116a97a116a101 a116a114a97a110a115a105a116a105a111a110 a109a111a100a101a108 a105a115 a108a105a110a101a97a114a105a122a101a100 a97a98a111a117a116 a97a110 a111a112a101a114a45 a97a116a105a110a103 a112a111a105a110a116a46 a50a46 a84a104a101 a115a116a97a116a101 a101a115a116a105a109a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a105a115 a117a112a100a97a116a101a100 a97 a108a105a116a116a108a101 a100a105a27a101a114a101a110a116a108a121 a116a104a97a110 a119a105a116a104 a97 a115a116a97a110a100a97a114a100 a75a70a46 a51a51 a84a111 a99a97a108a99a117a108a97a116a101 a116a104a101 a115a116a97a116a101 a115a112a97a99a101 a109a97a116a114a105a99a101a115 a110a101a101a100a101a100 a102a111a114 a116a104a101 a69a75a70a44 a116a104a101 a100a105a27a101a114a101a110a116a105a97a108 a101a113a117a97a116a105a111a110a115 a100a101a115a99a114a105a98a105a110a103 a116a104a101 a99a104a97a110a103a101 a119a105a116a104 a114a101a115a112a101a99a116 a116a111 a116a105a109a101 a97a114a101 a110a101a101a100a101a100a46 a84a104a101a121 a97a114a101a58 _ = (gx bx) sin sin + (gy by) cos (gz bz) cos sin a40a52a46a49a41 _ = (gx bx) cos + (gz bz) sin a40a52a46a50a41 _ = (gx bx) sin cos (gy by) sin (gz bz) cos sin a40a52a46a51a41 a119a104a101a114a101 _ a44 _ a44 a97a110a100 _ a97a114a101 a116a104a101 a99a104a97a110a103a101a115 a105a110 a116a104a101 a97a116a116a105a116a117a100a101 a115a116a97a116a101a115 a119a105a116a104 a114a101a115a112a101a99a116 a116a111 a116a105a109a101a44 gxa44 gya44 a97a110a100 gz a97a114a101 a103a121a114a111 a109a101a97a115a117a114a101a109a101a110a116a115a44 a97a110a100 bxa44 bya44 a97a110a100 bz a97a114a101 a103a121a114a111 a98a105a97a115a101a115a46 a84a104a101 a116a104a114a101a101 a97a116a116a105a116a117a100a101 a97a110a103a108a101a115 a97a110a100 a116a104a114a101a101 a98a105a97a115 a115a116a97a116a101a115 a119a105a108a108 a99a111a109a112a114a105a115a101 a116a104a101 a115a105a120 a115a116a97a116a101a115 a111a102 a116a104a101 a28a108a116a101a114a46 a84a104a101 a109a111a100a101a108 a105a115 a103a105a118a101a110 a98a121a58 _x = Ax+Buu+Bww a40a52a46a52a41 _x = _ _ _ _bx _by _bz T a40a52a46a53a41 x = bx by bz a40a52a46a54a41 A = 2 64A1;1 A1;2 A2;1 A2;2 3 75 a40a52a46a55a41 A1;2 = 2 66 66 4 sin sin cos cos sin cos 0 sin sin cos sin cos cos 3 77 77 5 a40a52a46a56a41 a51a52 A1;1 = A2;1 = A2;2 = 03 3 a40a52a46a57a41 Bu = 2 64 A1;2 03 3 3 75 a40a52a46a49a48a41 u = gx gy gz T a40a52a46a49a49a41 Bw = 2 64 A1;2 03 3 03 3 I3 3 3 75 a40a52a46a49a50a41 y = Cx+ a40a52a46a49a51a41 C = 2 66 66 4 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 3 77 77 5 a40a52a46a49a52a41 a119a104a101a114a101wa105a115 a97 a54a45a98a121a45a49 a112a114a111a99a101a115a115 a110a111a105a115a101 a118a101a99a116a111a114 a97a110a100 a105a115 a97 a51a45a98a121a45a49 a109a101a97a115a117a114a101a109a101a110a116 a110a111a105a115a101 a118a101a99a116a111a114a46 a83a105a110a99a101 a116a104a101 a110a111a105a115a101 a99a104a97a114a97a99a116a101a114a105a115a116a105a99a115 a97a114a101 a101a115a116a105a109a97a116a101a100 a102a114a111a109 a115a101a110a115a111a114 a100a97a116a97a44 a116a104a101a121 a119a105a108a108 a98a101 a100a101a28a110a101a100 a119a105a116a104 a116a104a101 a100a105a115a99a114a101a116a101a45 a116a105a109a101 a109a111a100a101a108a46 a84a104a101 a109a111a100a101a108 a105a115 a100a105a115a99a114a101a116a105a122a101a100 a117a115a105a110a103 a97 a122a101a114a111a45a111a114a100a101a114 a104a111a108a100 a40a90a79a72a41 a109a111a100a101a108 a119a105a116a104 a97 a115a97a109a112a108a105a110a103 a114a97a116a101 a111a102 a56a48 a72a122 a40a116a104a101 a109a101a97a115a117a114a101a109a101a110a116 a114a97a116a101 a111a102 a116a104a101 a73a77a85a44 a100a105a115a99a117a115a115a101a100 a108a97a116a101a114a41a44 a103a105a118a105a110a103 a116a104a101 a100a105a115a99a114a101a116a101a45a116a105a109a101 a115a116a97a116a101 a115a112a97a99a101 a109a111a100a101a108a58 xk+1 = Adxk +Buduk +Bwdwk a40a52a46a49a53a41 Ad = I6 6 + 180A a40a52a46a49a54a41 a51a53 Bud = 180Bu a40a52a46a49a55a41 Bwd = 180Bw a40a52a46a49a56a41 yk = Cxk + k a40a52a46a49a57a41 wk N 0; 2 64(4 10 5)I3 3 03 3 03 3 (10 8)I3 3 3 75 a40a52a46a50a48a41 k N 0;(2 10 6)I3 3 a40a52a46a50a49a41 a84a104a101 a118a97a108a117a101a115 a102a111a114 a116a104a101 a103a121a114a111 a110a111a105a115a101 a97a110a100 a71a80a83 a97a116a116a105a116a117a100a101 a110a111a105a115a101 a119a101a114a101 a116a97a107a101a110 a102a114a111a109 a103a121a114a111 a97a110a100 a71a80a83 a109a101a97a45 a115a117a114a101a109a101a110a116a115a44 a119a104a105a108a101 a116a104a101 a117a110a99a101a114a116a97a105a110a116a121 a97a115a115a111a99a105a97a116a101a100 a119a105a116a104 a116a104a101 a98a105a97a115 a116a101a114a109a115 a105a115 a99a104a111a115a101a110 a102a111a114 a100a101a115a105a114a101a100 a28a108a116a101a114 a112a101a114a102a111a114a109a97a110a99a101a46 a68a101a116a97a105a108a101a100 a105a110a102a111a114a109a97a116a105a111a110 a97a98a111a117a116 a116a104a101 a69a75a70 a97a110a100 a116a104a101 a100a105a27a101a114a101a110a99a101a115 a98a101a116a119a101a101a110 a97a110 a69a75a70 a97a110a100 a97 a75a70 a109a97a121 a98a101 a102a111a117a110a100 a105a110 a91a49a54a93a46 a52a46a50 a73a77a85 a69a114a114a111a114a115 a84a104a101 a73a77a85 a117a115a101a100 a105a110 a116a104a105a115 a119a111a114a107 a105a115 a116a104a101 a67a114a111a115a115a98a111a119 a73a77a85a52a48a48a45a67a67 a115a101a114a105a101a115a46 a73a116 a105a115 a97 a54a45a68a79a70 a109a105a99a114a111a45 a101a108a101a99a116a114a111a109a101a99a104a97a110a105a99a97a108 a115a121a115a116a101a109 a40a77a69a77a83a41 a73a77a85a44 a103a105a118a105a110a103 a97a99a99a101a108a101a114a111a109a101a116a101a114 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= r +cr +br +wgyro a40a52a46a50a50a41 a51a54 a119a104a101a114a101 gr a105a115 a116a104a101 a103a121a114a111 a111a117a116a112a117a116a44 r a105a115 a116a104a101 a116a114a117a101 a114a111a116a97a116a105a111a110 a114a97a116a101 a111a102 a116a104a101 a103a121a114a111a44 cr a105a115 a97 a99a111a110a115a116a97a110a116 a98a105a97a115a44 br a105a115 a97 a109a111a118a105a110a103 a111a114 a119a97a108a107a105a110a103 a98a105a97a115a44 a97a110a100 wgyro a105a115 a114a97a110a100a111a109 a115a101a110a115a111a114 a110a111a105a115a101a44 a97a115a115a117a109a101a100 a116a111 a98a101 a110a111a114a109a97a108a108a121 a100a105a115a116a114a105a98a117a116a101a100 a119a105a116a104 a122a101a114a111 a109a101a97a110a46 a73a116 a105a115 a100a101a115a105a114a97a98a108a101 a116a111 a114a101a109a111a118a101 a97a115 a109a117a99a104 a101a114a114a111a114 a97a115 a112a111a115a115a105a98a108a101a44 a97a115 a105a110a116a101a103a114a97a116a105a110a103 a114a111a116a97a116a105a111a110 a114a97a116a101 a98a105a97a115 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a114a101a113a117a105a114a101a115 a111a110a108a121 a115a111a109a101 a101a108a101a109a101a110a116a97a114a121 a103a101a111a109a101a116a114a121a46 a84a104a101 a114a101a97a100a101a114 a119a105a108a108 a110a111a116a105a99a101 a102a114a111a109 a70a105a103a117a114a101 a53a46a49 a116a104a97a116 a116a104a101 a118a101a99a116a111a114~r a98a101a116a119a101a101a110 a116a104a101 a116a119a111 a97a110a116a101a110a110a97a115 a97a110a100 a116a104a101 a100a105a27a101a114a101a110a99a101 L a105a110 a100a105a115a116a97a110a99a101 a116a111 a116a104a101 a115a97a116a101a108a108a105a116a101 a102a114a111a109 a116a104a101 a116a119a111 a97a110a116a101a110a110a97a115 a102a111a114a109 a116a119a111 a108a101a103a115 a111a102 a97 a114a105a103a104a116 a116a114a105a97a110a103a108a101a46 a87a101 a109a97a121 a116a104a101a110 a99a111a110a99a108a117a100a101 a116a104a97a116 a116a104a101 a65a79a65a44 a44 a109a97a121 a98a101 a111a98a116a97a105a110a101a100 a98a121 a97 a112a114a111a112a101a114a116a121 a111a102 a116a104a101 a114a105a103a104a116 a116a114a105a97a110a103a108a101a58 a52a52 a70a105a103a117a114a101 a53a46a49a58 a50a45a68 a101a120a97a109a112a108a101 a111a102 a65a79a65a46 a83a111a108a105a100 a114a101a100 a108a105a110a101a115 a100a101a112a105a99a116 a76a79a83 a116a111 a71a80a83 a115a97a116a101a108a108a105a116a101a46 cos = Lj~rj! = cos 1 L j~rj a40a53a46a54a41 a84a104a101 a108a101a110a103a116a104 L a105a115 a115a105a109a112a108a101 a116a111 a111a98a116a97a105a110 a105a102 a116a104a101 a114a101a108a97a116a105a118a101 a114a101a99a101a105a118a101a114 a99a108a111a99a107 a101a114a114a111a114 a97a110a100 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a109a98a105a103a117a105a116a105a101a115 a97a114a101 a107a110a111a119a110a46 a65a110 a101a115a116a105a109a97a116a101 a111a102 L a109a97a121 a98a101 a99a111a109a112a117a116a101a100 a102a111a114 a101a97a99a104 a115a105a103a110a97a108 a102a114a111a109 a116a104a101 a115a105a110a103a108a101a45 a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a58 ^L = k1;2 L1(Nk1;2) (cdt2 cdt1) a40a53a46a55a41 a73a102 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a109a98a105a103a117a105a116a105a101a115 a111a114 a114a101a108a97a116a105a118a101 a114a101a99a101a105a118a101a114 a99a108a111a99a107 a98a105a97a115 a97a114a101 a117a110a107a110a111a119a110a44 a116a104a101a114a101 a105a115 a110a111 a119a97a121 a116a111 a100a105a114a101a99a116a108a121 a99a111a109a112a117a116a101 La46 a72a111a119a101a118a101a114a44 a105a116 a105a115 a112a111a115a115a105a98a108a101 a116a111 a99a97a108a99a117a108a97a116a101 a97 a114a101a108a97a116a101a100 a113a117a97a110a116a105a116a121a44 L0; a119a104a105a99a104 a109a97a121 a98a101 a99a111a109a112a117a116a101a100 a102a114a111a109 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a84a104a101 a105a100a101a97a108 L0 a109a97a121 a98a101 a99a111a109a112a117a116a101a100 a98a121a58 a52a53 L0 = (^xk1 ^xl1) (^yk1 ^yl1) (^zk1 ^zl1) 2 66 66 4 x2 x1 y2 y1 z2 z1 3 77 77 5 a40a53a46a56a41 a84a104a105a115 a113a117a97a110a116a105a116a121 a109a97a121 a98a101 a99a104a101a99a107a101a100 a98a121 a115a117a98a116a114a97a99a116a105a110a103 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a109a98a105a103a117a105a116a121 a116a101a114a109 a102a114a111a109 a101a97a99a104 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a58 ^L0 =r k;l1;2 L1(Nk;l1;2) a40a53a46a57a41 a84a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a112a112a114a111a97a99a104 a105a115 a108a101a115a115 a114a111a98a117a115a116 a116a104a97a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a112a112a114a111a97a99a104 a97a115 a97a108a108 a111a102 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a105a101a115 a114a101a108a121 a111a110 a97 a99a111a109a109a111a110 a115a97a116a101a108a108a105a116a101a46 a73a110 a97a100a100a105a116a105a111a110a44 ^L0 a100a111a101a115 a110a111a116 a112a114a111a118a105a100a101 a97a110 a65a79a65a44 a115a111 a105a116 a105a115 a97 a108a105a116a116a108a101 a109a111a114a101 a100a105a30a99a117a108a116 a116a111 a100a101a99a105a100a101 a111a110 a97a110 a97a112a112a114a111a112a114a105a97a116a101 a101a114a114a111a114 a116a111a108a101a114a97a110a99a101a46 a72a111a119a101a118a101a114a44 a101a118a101a110 a119a105a116a104 a116a104a101 a100a111a119a110a115a105a100a101a115a44 a117a115a105a110a103 a116a104a101 a100a111a117a98a108a101a45a100a105a27a101a114a101a110a99a101a100 a97a109a98a105a103a117a105a116a105a101a115 a105a115 a98a101a116a116a101a114 a116a104a97a110 a104a97a118a105a110a103 a110a111 a101a114a114a111a114 a100a101a116a101a99a116a105a111a110 a97a116 a97a108a108a46 a84a111 a101a115a116a97a98a108a105a115a104 a97 a116a104a114a101a115a104a111a108a100 a111a110 a97a99a99a101a112a116a97a98a108a101 a65a79a65 a99a97a108a99a117a108a97a116a105a111a110a115a44 a116a119a111 a99a111a110a116a114a105a98a117a116a105a110a103 a102a97a99a116a111a114a115 a109a117a115a116 a98a101 a99a111a110a115a105a100a101a114a101a100a46 a84a104a101 a28a114a115a116a44 a97a110a100 a109a111a115a116 a111a98a118a105a111a117a115a44 a105a115 a116a104a101 a97a99a99a117a114a97a99a121 a111a102 a116a104a101 a97a116a116a105a116a117a100a101 a101a115a116a105a109a97a116a101a46 a83a105a110a99a101 a116a104a101 a82a80a86 a117a115a101a100 a105a110 a99a104a101a99a107a105a110a103 a110a101a119 a71a80a83 a115a105a103a110a97a108a115 a105a115 a103a101a110a101a114a97a116a101a100 a98a121 a116a104a101 a97a116a116a105a116a117a100a101 a101a115a116a105a109a97a116a101a44 a105a116 a109a97a107a101a115 a115a101a110a115a101 a116a104a97a116 a116a104a101 a101a115a116a105a109a97a116a101a100 a65a79a65 a119a105a108a108 a98a101 a97a27a101a99a116a101a100 a98a121 a116a104a101 a101a114a114a111a114 a105a110 a116a104a101 a82a80a86 a116a104a97a116 a105a115 a99a97a117a115a101a100 a98a121 a97a116a116a105a116a117a100a101 a101a114a114a111a114a46 a84a104a101 a115a101a99a111a110a100 a99a111a110a116a114a105a98a117a116a105a110a103 a102a97a99a116a111a114 a116a111 a98a101 a99a111a110a115a105a100a101a114a101a100 a105a115 a116a104a101 a110a111a105a115a101 a111a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a83a105a110a99a101 ^L a105a115 a103a101a110a101a114a97a116a101a100 a102a114a111a109 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a44 a97a110a121 a101a114a114a111a114 a111a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a119a105a108a108 a99a97a117a115a101 a101a114a114a111a114 a105a110 a116a104a101 a101a115a116a105a109a97a116a101a100 a65a79a65 a111a102 a97 a115a105a103a110a97a108a46 a70a111a114 a101a120a97a109a112a108a101a44 a115a117a112a112a111a115a101 a97a110 a101a120a112a101a99a116a101a100 a118a97a108a117a101 a111a102 L = 0:8 a109a101a116a101a114a115 a102a111a114 a97 a111a110a101a45a109a101a116a101a114 a98a97a115a101a108a105a110a101a46 a73a110 a116a104a97a116 a99a97a115a101a58 = cos 1(:81 ) = 36:9 a40a53a46a49a48a41 a83a117a112a112a111a115a101 a116a104a101a110 a116a104a97a116 a116a104a101a114a101 a105a115 a97a110 a101a114a114a111a114 a111a102 a46a48a50 a109a101a116a101a114a115 a111a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a87a105a116a104 a116a104a101 a46a48a50 a109a101a116a101a114 a101a114a114a111a114a44 a116a104a101 a101a115a116a105a109a97a116a101a100 a65a79a65 a105a115a58 a52a54 0 20 40 60 80 100 120 140 160 1800 5 10 15 20 Expected AOA (deg) Apparent AOA error 0.94m Baseline .01 m error on ?? .02 m error on ??.03 m error on ?? .04 m error on ??.05 m error on ?? 0 20 40 60 80 100 120 140 160 1800 1 2 3 4 5 6 7 8 Expected AOA (deg) Apparent AOA error 1.91m Baseline .01 m error on ?? .02 m error on ??.03 m error on ?? .04 m error on ??.05 m error on ?? a70a105a103a117a114a101 a53a46a50a58 a69a120a112a101a99a116a101a100 a65a79a65 a118a115a46 a97a112a112a97a114a101a110a116 a65a79a65 a101a114a114a111a114 a102a111a114 a97 a103a105a118a101a110 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a101a114a114a111a114a46 a78a111a116a101 a116a104a97a116 a101a97a99a104 a99a117a114a118a101 a105a115 a101a118a97a108a117a97a116a101a100 a117a112 a117a110a116a105a108 a116a104a101 a112a111a105a110a116 a97a116 a119a104a105a99a104 a116a104a101 a97a114a103a117a109a101a110a116 a102a111a114 a105a110a118a101a114a115a101 a99a111a115a105a110a101 a100a111a101a115 a110a111a116 a121a105a101a108a100 a97 a114a101a97a108 a97a110a103a108a101a46 = cos 1(:821 ) = 34:9 a111a114 = cos 1(:781 ) = 38:7 a40a53a46a49a49a41 a87a105a116a104 a97a110 a101a114a114a111a114 a111a102 a97 a108a105a116a116a108a101 a109a111a114a101 a116a104a97a110 a46a49 a99a97a114a114a105a101a114 a112a104a97a115a101 a99a121a99a108a101a44 a116a104a101 a109a101a97a115a117a114a101a100 a65a79a65 a105a115 a116a104a114a111a119a110 a111a27 a98a121 a97a115 a109a117a99a104 a97a115 a116a119a111 a100a101a103a114a101a101a115a46 a70a105a103a117a114a101 a53a46a50 a115a104a111a119a115 a97a112a112a97a114a101a110a116 a65a79a65 a101a114a114a111a114 a97a115 a97 a102a117a110a99a116a105a111a110 a111a102 a101a120a112a101a99a116a101a100 a65a79a65 a97a110a100 a118a97a114a105a111a117a115 a97a109a111a117a110a116a115 a111a102 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a101a114a114a111a114a46 a71a101a110a101a114a97a108a108a121 a115a112a101a97a107a105a110a103a44 a97 a108a111a110a103a101a114 a98a97a115a101a108a105a110a101 a119a105a108a108 a98a101 a108a101a115a115 a97a27a101a99a116a101a100 a98a121 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a101a114a114a111a114a44 a97a110a100 a115a105a103a110a97a108a115 a119a105a116a104 a97 a108a111a119 a111a114 a104a105a103a104 a101a120a112a101a99a116a101a100 a65a79a65 a119a105a108a108 a114a101a113a117a105a114a101 a97 a119a105a100a101a114 a116a104a114a101a115a104a111a108a100 a116a104a97a110 a116a104a111a115a101 a119a105a116a104 a97a110 a101a120a112a101a99a116a101a100 a65a79a65 a99a108a111a115a101a114 a116a111 a57a48 a100a101a103a114a101a101a115a46 a52a55 a53a46a50a46a50 a65a108a116a101a114a110a97a116a101 a65a79a65 a67a104a101a99a107a105a110a103 a83a116a114a97a116a101a103a105a101a115 a84a104a101 a109a101a116a104a111a100 a102a111a114 a99a97a108a99a117a108a97a116a105a110a103 a116a104a101 a65a79a65 a105a110 a83a101a99a116a105a111a110 a53a46a50a46a49 a105a115 a97 a103a111a111a100 a111a110a101a44 a98a117a116 a116a104a101 a109a101a116a104a111a100 a114a101a108a105a101a115 a111a110 a107a110a111a119a105a110a103 a116a104a101 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121a44 a119a104a105a99a104 a105a115 a110a111a116 a97a108a119a97a121a115 a107a110a111a119a110a46 a83a112a101a99a105a28a99a97a108a108a121a44 a116a104a101 a97a109a98a105a103a117a105a116a121 a119a105a108a108 a110a111a116 a98a101 a107a110a111a119a110 a102a111a114 a116a104a101 a99a97a115a101 a111a102 a97 a110a101a119a108a121 a97a99a113a117a105a114a101a100 a115a97a116a101a108a108a105a116a101 a111a114 a111a110a101 a116a104a97a116 a104a97a115 a114a101a99a101a110a116a108a121 a98a101a101a110 a114a101a106a101a99a116a101a100a44 a109a97a107a105a110a103 a116a104a101 a65a79a65 a99a97a108a99a117a108a97a116a105a111a110 a105a110 a83a101a99a116a105a111a110 a53a46a50a46a49 a105a109a112a111a115a115a105a98a108a101a46 a73a116 a105a115 a115a116a105a108a108 a100a101a115a105a114a97a98a108a101 a116a111 a104a97a118a101 a115a111a109a101 a105a100a101a97 a111a102 a116a104a101 a65a79a65 a111a102 a97 a115a105a103a110a97a108 a116a104a111a117a103a104a44 a115a111 a116a104a101a114a101 a97a114a101 a116a119a111 a109a111a114a101 a97a112a112a114a111a97a99a104a101a115 a116a104a97a116 a111a27a101a114 a97 a114a101a100a117a99a101a100 a108a101a118a101a108 a111a102 a100a101a116a101a99a116a105a111a110 a111a102 a65a79a65 a117a115a105a110a103 a108a101a115a115 a105a110a102a111a114a109a97a116a105a111a110a46 a53a46a50a46a50a46a49 a83a105a110a103a108a101a45a68a105a27a101a114a101a110a99a101a100 a80a115a101a117a100a111a114a97a110a103a101 a84a104a101 a28a114a115a116 a97a108a116a101a114a110a97a116a101 a97a112a112a114a111a97a99a104 a117a115a101a115 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a109a101a97a115a117a114a101a109a101a110a116a115 a105a110 a112a108a97a99a101 a111a102 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115a46 a84a104a101 a114a101a97a100a101a114 a119a105a108a108 a114a101a99a97a108a108 a102a114a111a109 a69a113a117a97a45 a116a105a111a110a115 a40a51a46a51a41 a97a110a100 a40a51a46a52a41 a116a104a97a116 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a97a110a100 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115 a119a105a108a108 a103a105a118a101 a116a104a101 a115a97a109a101 a113a117a97a110a116a105a116a121 a105a102 a116a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a109a97a121 a98a101 a99a111a114a114a101a99a116a101a100 a119a105a116a104 a116a104a101 a99a121a99a108a101 a97a109a98a105a103a117a105a116a121a44 a101a120a99a101a112a116 a116a104a97a116 a116a104a101 a112a115a101a117a100a111a114a97a110a103a101 a109a101a97a115a117a114a101a109a101a110a116 a105a115 a109a117a99a104 a109a111a114a101 a110a111a105a115a121a46 a84a104a101a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a97a110a100 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121 a116a101a114a109a115 a105a110 a69a113a117a97a116a105a111a110 a40a53a46a55a41 a109a97a121 a98a101 a114a101a112a108a97a99a101a100 a98a121 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a109a101a97a115a117a114a101a109a101a110a116a44 a121a105a101a108a100a105a110a103a58 ^L = k1;2 (cdt2 cdt1) a40a53a46a49a50a41 a84a104a105a115 a97a112a112a114a111a97a99a104 a100a111a101a115 a104a97a118a101 a116a104a101 a100a114a97a119a98a97a99a107 a111a102 a116a104a101 a114a101a108a97a116a105a118a101a108a121 a104a105a103a104 a110a111a105a115a101 a111a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a73a116 a105a115 a110a111a116 a117a110a99a111a109a109a111a110 a102a111a114 a116a104a101 a101a114a114a111a114 a105a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a45 a100a111a114a97a110a103a101 a116a111 a98a101 a105a110 a101a120a99a101a115a115 a111a102 a97 a109a101a116a101a114a44 a109a97a107a105a110a103 a116a104a105a115 a97a112a112a114a111a97a99a104 a108a101a115a115 a101a27a101a99a116a105a118a101 a102a111a114 a115a104a111a114a116a101a114 a98a97a115a101a108a105a110a101a115a46 a65a115 a97a110 a101a120a97a109a112a108a101a44 a97 a111a110a101a45a109a101a116a101a114 a98a97a115a101a108a105a110a101 a99a97a110 a104a97a118a101 a118a97a108a117a101a115 a111a102La98a101a116a119a101a101a110 a45a49 a97a110a100 a49 a109a101a116a101a114a46 a73a102 a116a104a101 a105a100a101a97a108 L a102a111a114 a97 a103a105a118a101a110 a115a97a116a101a108a108a105a116a101 a105a115 a46a55a53 a109a101a116a101a114a115a44 a116a104a101a110 a118a97a108a117a101a115 a111a102 :25 a116a111 a49a46a55a53 a109a101a116a101a114 a109a117a115a116 a98a101 a97a99a99a101a112a116a101a100 a102a111a114 ^L a116a111 a97a99a99a111a117a110a116 a102a111a114 a116a104a101 a112a111a116a101a110a116a105a97a108 a101a114a114a111a114 a111a110 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a115a46 a73a110 a116a104a105a115 a112a97a114a116a105a99a117a108a97a114 a101a120a97a109a112a108a101a44 a116a104a101 a119a105a100a101 a116a104a114a101a115a104a111a108a100 a104a97a115 a116a104a101 a112a111a116a101a110a116a105a97a108 a116a111 a97a108a108a111a119 a65a79a65a115 a115a112a97a110a110a105a110a103 a111a118a101a114 a49a48a48 a100a101a103a114a101a101a115 a116a111 a98a101 a97a108a108a111a119a101a100a46 a70a111a114 a116a104a101 a98a97a115a101a108a105a110a101a115 a117a115a101a100 a105a110 a116a104a105a115 a119a111a114a107 a40a46a57a52 a109a101a116a101a114a115 a97a110a100 a49a46a57a49 a109a101a116a101a114a115a41a44 a52a56 a111a114 a97a110a121 a98a97a115a101a108a105a110a101a115 a97a98a108a101 a116a111 a98a101 a105a109a112a108a101a109a101a110a116a101a100 a111a110 a97 a99a97a114a44 a116a104a105a115 a109a101a116a104a111a100 a105a115 a110a111a116 a114a101a108a105a97a98a108a101 a101a110a111a117a103a104 a116a111 a98a101 a117a115a101a100 a97a115 a116a104a101 a112a114a105a109a97a114a121 a109a117a108a116a105a112a97a116a104a47a115a112a111a111a28a110a103 a114a101a106a101a99a116a105a111a110 a97a108a103a111a114a105a116a104a109a46 a53a46a50a46a50a46a50 a83a105a110a103a108a101a45a68a105a27a101a114a101a110a99a101a100 a67a97a114a114a105a101a114 a80a104a97a115a101 a84a104a101 a115a101a99a111a110a100 a97a108a116a101a114a110a97a116a101 a97a112a112a114a111a97a99a104 a117a116a105a108a105a122a101a115 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116 a119a105a116a104a111a117a116 a116a104a101 a107a110a111a119a108a101a100a103a101 a111a102 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a97a109a98a105a103a117a105a116a105a101a115a46 a73a102 a69a113a117a97a116a105a111a110 a40a53a46a55a41 a105a115 a100a105a118a105a100a101a100 a98a121 L1 a97a110a100 a111a110a108a121 a116a104a101 a114a101a109a97a105a110a100a101a114 a105a115 a107a101a112a116a44 a105a116 a105a115 a115a101a101a110 a116a104a97a116a58 rem( ^L L1) = rem( k1;2 L1(Nk1;2) (cdt2 cdt1) L1 ) = rem( k1;2 (cdt2 cdt1) L1 ) a40a53a46a49a51a41 a65a110 a101a115a116a105a109a97a116a101 a111a102 ^L a109a97a121 a98a101 a99a97a108a99a117a108a97a116a101a100 a117a115a105a110a103 a69a113a117a97a116a105a111a110a115 a40a53a46a50a41 a97a110a100 a40a53a46a54a41a46 a83a105a110a99a101 a116a104a105a115 a101a115a116a105a109a97a116a101 a105a115 a98a97a115a101a100 a111a110 a116a104a101 a82a80a86 a99a97a108a99a117a108a97a116a101a100 a102a114a111a109 a116a104a101 a73a77a85 a97a116a116a105a116a117a100a101 a115a111a108a117a116a105a111a110a44 a98a111a117a110a100a115 a109a97a121 a98a101 a115a101a116 a111a110 a97a99a99a101a112a116a97a98a108a101 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a104a97a118a105a110a103 a109a111a114a101 a116a104a97a110 a97 a102a101a119 a112a111a116a101a110a116a105a97a108 a65a79a65a115a44 a101a118a101a110 a97 a115a109a97a108a108 a97a116a116a105a116a117a100a101 a101a114a114a111a114 a99a111a117a108a100 a109a97a107a101 a116a104a101 a100a101a116a101a99a116a105a111a110 a111a102 a102a97a117a108a116a121 a115a105a103a110a97a108a115 a100a105a30a99a117a108a116a46 a84a104a101 a114a97a110a103a101 a111a102 R a116a104a97a116 a105a115 a97a99a99a101a112a116a97a98a108a101 a100a101a112a101a110a100a115 a110a111a116 a111a110a108a121 a97a116a116a105a116a117a100a101 a101a114a114a111a114 a98a117a116 a111a110 a116a104a101 a101a120a112a101a99a116a101a100 a97a110a103a108a101 a111a102 a97a114a114a105a118a97a108a46 a71a101a110a101a114a97a108a108a121 a115a112a101a97a107a105a110a103a44 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 R a97a114a101 a119a111a114a115a116 a97a116 a57a48 a100a101a103a114a101a101a115 a102a111a114 a97 a103a105a118a101a110 a97a116a116a105a116a117a100a101 a101a114a114a111a114 a97a110a100 a97a114a101 a109a105a110a105a109a105a122a101a100 a110a101a97a114a105a110a103 a122a101a114a111 a97a110a100 a49a56a48 a100a101a103a114a101a101a115a46 a70a111a114 a101a120a97a109a112a108a101a44 a115a117a112a112a111a115a101 a102a111a114 a97 a111a110a101a45a109a101a116a101a114 a98a97a115a101a108a105a110a101 a116a104a97a116 a116a104a114a101a115a104a111a108a100a115 a111a110 R a115a104a111a117a108a100 a98a101 a99a111a109a112a117a116a101a100 a116a111 a116a97a107a101 a105a110a116a111 a97a99a99a111a117a110a116 a116a119a111 a100a101a103a114a101a101a115 a111a102 a101a114a114a111a114a46 a84a104a101a110a58 L = 1 cos(90 ) = 0 a40a53a46a49a56a41 a65a99a99a111a117a110a116a105a110a103 a102a111a114 a116a119a111 a100a101a103a114a101a101a115 a111a102 a101a114a114a111a114a58 L = 1 cos(88 ) = :0349 a109 = :183 a99a121a99a108a101a115 a40a53a46a49a57a41 a73a110 a116a104a105a115 a99a97a115a101a44 a97a110 a97a108a108a111a119a97a110a99a101 a109a117a115a116 a98a101 a109a97a100a101 a102a111a114 :0349 a109a44 a111a114 :183 a99a97a114a114a105a101a114 a99a121a99a108a101a115a44 a102a111a114 a97 a116a111a116a97a108 a114a97a110a103a101 a111a102 a46a51a54a54 a99a121a99a108a101a115a46 a83a105a110a99a101 R a114a101a112a114a101a115a101a110a116a115 a116a104a101 a112a97a114a116 a111a102 a97 a119a104a111a108a101 a99a121a99a108a101a44 a114a111a117a103a104a108a121 a97 a116a104a105a114a100 a111a102 a97a108a108 a115a105a103a110a97a108a115 a99a111a117a108a100 a112a111a116a101a110a116a105a97a108a108a121 a98a101 a97a99a99a101a112a116a101a100a46 a67a111a110a118a101a114a115a101a108a121a44 a115a117a112a112a111a115a101 a116a104a101 a99a97a115a101 a102a111a114 a97a110 a65a79a65 a111a102 a52a53 a100a101a103a114a101a101a115 a105a115 a101a120a112a108a111a114a101a100a46 a84a104a101a110a58 a53a49 0 0.5 1 1.5 2 2.50 1 2 3 4 5 6 Baseline Length (?L1 cycles) Max Potential AOAs Baseline length vs. Potential AOAs a70a105a103a117a114a101 a53a46a51a58 a80a108a111a116 a111a102 a98a97a115a101a108a105a110a101 a108a101a110a103a116a104 a118a115a46 a110a117a109a98a101a114 a111a102 a112a111a116a101a110a116a105a97a108 a65a79a65a115a46 a53a50 0 2 4 6 8 100 1 2 3 4 5 6 Baseline Length (meters) Attitude Error (deg) Baseline Length vs. Attitude Error a70a105a103a117a114a101 a53a46a52a58 a65a116a116a105a116a117a100a101 a97a99a99a117a114a97a99a121 a97a115 a97 a102a117a110a99a116a105a111a110 a111a102 a98a97a115a101a108a105a110a101 a108a101a110a103a116a104a46 a53a51 a70a105a103a117a114a101 a53a46a53a58 a71a114a97a112a104a105a99a97a108 a114a101a112a114a101a115a101a110a116a97a116a105a111a110 a111a102 a109a117a108a116a105a112a108a101 a65a79a65a115 a116a104a97a116 a102a117a108a28a108a108 a116a104a101 a114a101a109a97a105a110a100a101a114 a114a101a113a117a105a114a101a109a101a110a116 a111a102 a69a113a117a97a116a105a111a110a115 a40a53a46a49a53a41 a97a110a100 a40a53a46a49a54a41a46 a84a104a101 a101a120a112a101a99a116a101a100 a65a79a65 a105a115 a115a104a111a119a110 a97a115 a97 a98a108a117a101 a115a111a108a105a100 a108a105a110a101a44 a119a104a105a108a101 a105a110a99a111a114a114a101a99a116 a65a79a65a115 a97a114a101 a115a104a111a119a110 a97a115 a114a101a100 a115a111a108a105a100 a108a105a110a101a115a46 a82a101a100 a97a110a100 a98a108a117a101 a100a97a115a104a101a100 a108a105a110a101a115 a114a101a112a114a101a115a101a110a116 a101a114a114a111a114 a98a111a117a110a100a115 a98a97a115a101a100 a111a110 a97a116a116a105a116a117a100a101 a101a115a116a105a109a97a116a105a111a110 a101a114a114a111a114 a102a114a111a109 a97a116a116a105a116a117a100a101 a28a108a116a101a114a46 a53a52 L = 1 cos(45 ) = :707 a40a53a46a50a48a41 a65a99a99a111a117a110a116a105a110a103 a102a111a114 a116a119a111 a100a101a103a114a101a101a115 a111a102 a101a114a114a111a114a58 L = 1 cos(47 ) = :682 a40a53a46a50a49a41 a73a110 a116a104a105a115 a115a101a99a111a110a100 a99a97a115a101a44 a97a110 a97a108a108a111a119a97a110a99a101 a109a117a115a116 a111a110a108a121 a98a101 a109a97a100a101 a102a111a114 :025 a109a44 a111a114 :131 a99a97a114a114a105a101a114 a99a121a99a108a101a115a44 a102a111a114 a97 a116a111a116a97a108 a114a97a110a103a101 a111a102 a46a50a54a50 a99a121a99a108a101a115a46 a84a104a105a115 a114a101a112a114a101a115a101a110a116a115 a97a110 a105a109a112a114a111a118a101a109a101a110a116 a111a118a101a114 a116a104a101 a57a48 a100a101a103a114a101a101 a99a97a115a101a44 a97a115 a114a111a117a103a104a108a121 a55a52 a112a101a114a99a101a110a116 a111a102 a115a105a103a110a97a108a115 a109a97a121 a98a101 a114a101a106a101a99a116a101a100a44 a105a110a115a116a101a97a100 a111a102 a54a51 a112a101a114a99a101a110a116 a119a105a116a104 a116a104a101 a57a48 a100a101a103a114a101a101 a99a97a115a101a46 a70a105a103a117a114a101 a53a46a54 a115a104a111a119a115 a116a104a101 a114a101a108a97a116a105a111a110a115a104a105a112 a98a101a116a119a101a101a110 a101a120a112a101a99a116a101a100 a65a79a65a44 a101a114a114a111a114 a98a111a117a110a100a115 a102a111a114 Ra44 a97a110a100 a97a116a116a105a116a117a100a101 a101a114a114a111a114 a102a111a114 a116a104a101 a116a119a111 a98a97a115a101a108a105a110a101a115 a117a115a101a100 a105a110 a116a104a105a115 a119a111a114a107a46 a84a104a101 a118a101a114a116a105a99a97a108 a98a108a97a99a107 a108a105a110a101a115 a114a101a112a114a101a115a101a110a116 a112a114a97a99a116a105a99a97a108 a98a111a117a110a100a97a114a105a101a115 a111a102 a65a79a65a44 a97a115 a109a111a115a116 a115a97a116a101a108a108a105a116a101a115 a119a105a116a104a105a110 a49a53 a100a101a103a114a101a101a115 a111a102 a101a108a101a118a97a116a105a111a110 a102a114a111a109 a116a104a101 a104a111a114a105a122a111a110 a97a114a101 a103a101a110a101a114a97a108a108a121 a110a111a116 a118a105a115a105a98a108a101 a111a114 a105a103a110a111a114a101a100 a100a117a101 a116a111 a104a105a103a104a101a114 a108a101a118a101a108a115 a111a102 a97a116a109a111a115a112a104a101a114a105a99 a101a114a114a111a114a46 a84a104a101 a104a111a114a105a122a111a110a116a97a108 a98a108a97a99a107 a100a97a115a104a101a100 a108a105a110a101 a114a101a112a114a101a115a101a110a116a115 :5 a99a121a99a108a101a115a44 a97a116 a119a104a105a99a104 a112a111a105a110a116 a110a111 a115a105a103a110a97a108a115 a99a97a110 a98a101 a114a101a106a101a99a116a101a100a46 a67a111a109a112a97a114a105a110a103 a116a104a101 a116a119a111 a112a108a111a116a115a44 a116a104a101 a115a104a111a114a116a101a114 a98a97a115a101a108a105a110a101 a104a97a115 a97 a99a108a101a97a114 a97a100a118a97a110a116a97a103a101 a111a118a101a114 a116a104a101 a108a97a114a103a101a114 a98a97a115a101a108a105a110a101 a105a110 a116a101a114a109a115 a111a102 a97a108a108a111a119a97a98a108a101 a101a114a114a111a114a46 a84a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a114a101a115a105a100a117a97a108 a97a112a112a114a111a97a99a104 a105a115 a115a116a114a101a110a103a116a104a101a110a101a100 a98a121 a116a104a101 a112a114a101a115a101a110a99a101 a111a102 a116a119a111 a112a97a105a114a115 a111a102 a97a110a45 a116a101a110a110a97a115 a116a104a97a116 a97a114a101 a111a114a116a104a111a103a111a110a97a108 a116a111 a101a97a99a104 a111a116a104a101a114a46 a70a105a103a117a114a101 a53a46a53 a105a115 a98a101a115a116 a101a120a112a97a110a100a101a100 a116a111 a97 a116a104a114a101a101a45a100a105a109a101a110a115a105a111a110a97a108 a114a101a112a114a101a115a101a110a116a97a116a105a111a110 a98a121 a112a114a111a106a101a99a116a105a110a103 a116a104a101 a65a79a65 a98a111a117a110a100a115 a111a110a116a111 a97 a104a101a109a105a115a112a104a101a114a101 a97a114a111a117a110a100 a116a104a101 a98a97a115a101a108a105a110a101a46 a84a104a101 a65a79a65 a98a111a117a110a100a115 a119a105a108a108 a102a111a114a109 a99a111a110a99a101a110a116a114a105a99 a98a97a110a100a115 a97a98a111a117a116 a116a104a101 a82a80a86 a111a102 a116a104a101 a97a110a116a101a110a110a97a44 a115a105a109a105a108a97a114 a116a111 a108a97a116a105a116a117a100a101 a108a105a110a101a115 a111a110 a97 a103a108a111a98a101a46 a84a104a101 a51a45a68 a114a101a112a114a101a115a101a110a116a97a116a105a111a110 a111a102 a116a104a101 a65a79a65 a101a114a114a111a114 a98a111a117a110a100a115 a109a97a121 a98a101 a115a101a101a110 a105a110 a70a105a103a117a114a101 a53a46a55a46 a84a104a101 a98a108a117a101 a108a105a110a101a115 a105a110 a70a105a103a117a114a101 a53a46a55 a114a101a112a114a101a115a101a110a116 a97 a115a101a116 a111a102 a98a111a117a110a100a115 a102a111a114 a119a104a105a99a104 a97 a115a105a103a110a97a108 a119a111a117a108a100 a98a101 a97a99a99a101a112a116a101a100 a98a121 a97a110a116a101a110a110a97 a112a97a105a114 a49a44 a119a104a105a108a101 a116a104a101 a114a101a100 a108a105a110a101a115 a114a101a112a114a101a115a101a110a116 a97 a115a101a116 a111a102 a98a111a117a110a100a115 a102a111a114 a119a104a105a99a104 a97 a115a105a103a110a97a108 a119a111a117a108a100 a98a101 a97a99a99a101a112a116a101a100 a98a121 a97a110a116a101a110a110a97 a112a97a105a114 a50a46 a83a105a110a99a101 a114a101a106a101a99a116a105a111a110 a111a102 a97 a102a97a117a108a116a121 a115a105a103a110a97a108 a111a110a108a121 a114a101a113a117a105a114a101a115 a116a104a101 a115a105a103a110a97a108 a116a111 a98a101 a100a101a116a101a99a116a101a100 a98a121 a111a110a101 a112a97a105a114 a111a102 a97a110a116a101a110a110a97a115a44 a97 a102a97a117a108a116a121 a115a105a103a110a97a108 a109a117a115a116 a102a97a108a108 a105a110a116a111 a111a110a101 a111a102 a116a104a101 a105a110a116a101a114a115a101a99a116a105a111a110a115 a111a102 a116a104a101 a98a111a117a110a100a115 a111a102 a97a110a116a101a110a110a97 a112a97a105a114a115 a49 a97a110a100 a50 a116a111 a101a115a99a97a112a101 a100a101a116a101a99a116a105a111a110 a98a121 a98a111a116a104 a97a110a116a101a110a110a97a115a46 a53a53 0 20 40 60 80 100 120 140 160 1800 0.1 0.2 0.3 0.4 0.5 Expected AOA (deg) Expected length error ( ? L1 cycles) .94 m Baseline 0 20 40 60 80 100 120 140 160 1800 0.2 0.4 0.6 0.8 1 Expected AOA (deg) Expected length error ( ? L1 cycles) 1.91 m Baseline 1? error 2? error 3? error 4? error 5? error 1? error 2? error 3? error 4? error 5? error a70a105a103a117a114a101 a53a46a54a58 a69a120a112a101a99a116a101a100 a65a79a65 a118a115a46 a101a120a112a101a99a116a101a100 a101a114a114a111a114 a105a110 La44 a112a108a111a116a116a101a100 a102a111a114 a109a117a108a116a105a112a108a101 a118a97a108a117a101a115 a116a111a116a97a108 a97a110a103a108a101 a101a114a114a111a114a46 a78a111a116a105a99a101 a116a104a97a116 a111a110a99a101 a116a104a101 a101a114a114a111a114 a114a101a97a99a104a101a115 :5 a99a121a99a108a101a115a44 a110a111 a115a105a103a110a97a108a115 a99a97a110 a98a101 a114a101a106a101a99a116a101a100a46 a53a54 a70a105a103a117a114a101 a53a46a55 a97a108a115a111 a115a101a114a118a101a115 a116a111 a99a111a109a112a97a114a101 a115a101a118a101a114a97a108 a99a111a111a114a100a105a110a97a116a101 a115a121a115a116a101a109a115 a116a104a97a116 a119a105a108a108 a98a101 a117a115a101a102a117a108 a105a110 a100a101a116a101a114a109a105a110a105a110a103 a116a104a101 a112a114a111a98a97a98a105a108a105a116a121 a111a102 a97a99a99a101a112a116a105a110a103 a97 a102a97a108a115a101 a115a105a103a110a97a108 a97a115 a103a101a110a117a105a110a101a46 a70a105a114a115a116a44 a97 a115a116a97a110a100a97a114a100 a67a97a114a116a101a115a105a97a110 a99a111a111a114a100a105a110a97a116a101 a102a114a97a109a101 a105a115 a100a101a28a110a101a100 a119a105a116a104 a98a97a115a101a108a105a110a101 a49 a101a120a116a101a110a100a105a110a103 a105a110 a116a104a101 a100a105a114a101a99a116a105a111a110 a111a102 a116a104a101 a112a111a115a105a116a105a118a101 a88a45a97a120a105a115 a97a110a100 a98a97a115a101a108a105a110a101 a50 a101a120a116a101a110a100a105a110a103 a105a110 a116a104a101 a100a105a114a101a99a116a105a111a110 a111a102 a116a104a101 a112a111a115a105a116a105a118a101 a89a45a97a120a105a115a46 a84a104a101 a88 a97a110a100 a89 a97a120a101a115 a97a114a101 a105a110 a116a104a101 a104a111a114a105a122a111a110a116a97a108 a112a108a97a110a101 a119a105a116a104 a116a104a101 a90a45a97a120a105a115 a112a111a105a110a116a105a110a103 a117a112a46 a78a101a120a116a44 a105a116 a105a115 a104a101a108a112a102a117a108 a116a111 a100a101a28a110a101 a115a112a104a101a114a105a99a97a108 a99a111a111a114a100a105a110a97a116a101 a115a121a115a116a101a109a115 a97a98a111a117a116 a116a104a101 a97a110a116a101a110a110a97 a98a97a115a101a108a105a110a101a115a46 1 a105a115 a116a104a101 a65a79a65 a102a111a114 a98a97a115a101a108a105a110a101 a49 a97a110a100 a100a101a110a111a116a101a115 a116a104a101 a97a110a103a108a101 a98a101a116a119a101a101a110 a116a104a101 a112a111a115a105a116a105a118a101 a88a45a97a120a105a115 a97a110a100 a97 a118a101a99a116a111a114 a101a120a116a101a110a100a105a110a103 a97a119a97a121 a102a114a111a109 a116a104a101 a111a114a105a103a105a110a46 2 a115a101a114a118a101a115 a116a104a101 a115a97a109a101 a112a117a114a112a111a115a101 a102a111a114 a116a104a101 a89a45a97a120a105a115 a111a114 a98a97a115a101a108a105a110a101 a50a46 a70a111a114 a97 a118a101a99a116a111a114 a101a120a116a101a110a100a105a110a103 a111a117a116a119a97a114a100 a102a114a111a109 a116a104a101 a111a114a105a103a105a110a44 1 a105a115 a116a104a101 a114a105a103a104a116a45a104a97a110a100a101a100 a114a111a116a97a116a105a111a110 a111a102 a116a104a101 a118a101a99a116a111a114 a97a98a111a117a116 a116a104a101 a88a45a97a120a105a115a46 a73a102 a97 a118a101a99a116a111a114 a105a115 a112a114a111a106a101a99a116a101a100 a105a110a116a111 a116a104a101 a89a90a45a112a108a97a110a101a44 1 = 0 a99a111a114a114a101a115a112a111a110a100a115 a116a111 a97 a118a101a99a116a111a114 a112a114a111a106a101a99a116a101a100 a111a110a116a111 a116a104a101 a89a45a97a120a105a115 a111a110a108a121 a119a104a105a108a101 1 = 2 a99a111a114a114a101a115a112a111a110a100a115 a116a111 a97 a118a101a99a116a111a114 a112a114a111a106a101a99a116a101a100 a111a110a116a111 a116a104a101 a122 a97a120a105a115 a111a110a108a121a46 2 a100a101a110a111a116a101a115 a97 a118a101a99a116a111a114 a112a114a111a106a101a99a116a101a100 a105a110 a116a104a101 a115a97a109a101 a109a97a110a110a101a114 a111a110a116a111 a116a104a101 a88a90 a112a108a97a110a101a44 a119a105a116a104 2 = 0 a111a110 a116a104a101 a110a101a103a97a116a105a118a101 a88a45a97a120a105a115 a111a110a108a121 a97a110a100 2 = 2 a111a110 a116a104a101 a90a45a97a120a105a115 a111a110a108a121a46 a70a105a110a97a108a108a121a44 rh a100a101a110a111a116a101a115 a100a105a115a116a97a110a99a101 a102a114a111a109 a116a104a101 a111a114a105a103a105a110 a97a110a100 a105a115 a116a104a101 a115a97a109a101 a102a111a114 a98a111a116a104 a115a101a116a115 a111a102 a99a111a111a114a100a105a110a97a116a101a115a46 a78a111a116a101 a116a104a97a116 a97a115 a105a116 a105a115 a117a115a101a100 a104a101a114a101 a97a115 a97 a118a97a114a105a97a98a108a101 a102a111a114 a115a112a104a101a114a105a99a97a108 a99a111a111a114a100a105a110a97a116a101a115 a115a104a111a117a108a100 a110a111a116 a98a101 a99a111a110a102a117a115a101a100 a119a105a116a104 a116a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a70a111a114 a97a110 a65a79a65 i a103a105a118a101a110 a98a121 Li a116a104a97a116 a102a117a108a28a108a108a115 a116a104a101 a114a101a109a97a105a110a100a101a114 a114a101a113a117a105a114a101a109a101a110a116a44 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 i a119a105a108a108 a98a101 a100a101a116a101a114a109a105a110a101a100 a98a121 a115a105a103a110a97a108 a110a111a105a115a101 a97a110a100 a97a116a116a105a116a117a100a101 a101a114a114a111a114a46 a84a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a109a97a121 a98a101 a101a120a112a114a101a115a115a101a100 a97a115 a97a110a103a108a101a115 i;1 a97a110a100 i;2 a111a114 a97a115 a108a101a110a103a116a104a115 Li;1 a97a110a100 Li;2a44 a98a111a116a104 a111a102 a119a104a105a99a104 a109a97a121 a98a101 a117a115a101a100 a116a111 a99a97a108a99a117a108a97a116a101 a116a104a101 a115a117a114a102a97a99a101 a97a114a101a97 a111a102 a116a104a101 a104a101a109a105a115a112a104a101a114a101 a102a111a114 a119a104a105a99a104 a115a105a103a110a97a108a115 a119a105a108a108 a98a101 a97a99a99a101a112a116a101a100a46 a84a111 a28a110a100 a116a104a101 a115a117a114a102a97a99a101 a97a114a101a97 a111a102 a116a104a101 a104a101a109a105a115a112a104a101a114a101 a102a111a114 a119a104a105a99a104 a105a110a99a111a109a105a110a103 a115a105a103a110a97a108a115 a119a105a108a108 a98a101 a97a99a99a101a112a116a101a100 a98a121 a97 a115a105a110a103a108a101 a98a97a115a101a108a105a110a101a44 a116a104a101 a115a117a114a102a97a99a101 a97a114a101a97 a101a110a99a111a109a112a97a115a115a101a100 a98a121 a101a97a99a104 a112a97a105a114 a111a102 a98a111a117a110a100a115 a109a117a115a116 a98a101 a99a97a108a99a117a108a97a116a101a100 a28a114a115a116a46 a84a104a101a110 a116a104a101 a105a110a100a105a118a105a100a117a97a108 a115a117a114a102a97a99a101 a97a114a101a97a115 a119a105a108a108 a98a101 a115a117a109a109a101a100 a116a111 a103a105a118a101 a116a104a101 a116a111a116a97a108 a115a117a114a102a97a99a101 a97a114a101a97 a111a102 a116a104a101 a104a101a109a105a115a112a104a101a114a101 a101a110a99a111a109a112a97a115a115a101a100 a98a121 a116a104a101 a114a101a115a105a100a117a97a108 a98a111a117a110a100a115a46 a70a111a114 n a97a110a103a108a101a115 a111a102 a97a114a114a105a118a97a108 a116a104a97a116 a115a97a116a105a115a102a121 a116a104a101 a114a101a109a97a105a110a100a101a114 a114a101a113a117a105a114a101a109a101a110a116a44 a116a104a101 a116a111a116a97a108 a115a117a114a102a97a99a101 a97a114a101a97 a111a102 a116a104a101 a104a101a109a105a115a112a104a101a114a101 a101a110a99a111a109a112a97a115a115a101a100 a98a121 a116a104a101 a114a101a115a105a100a117a97a108 a98a111a117a110a100a115 a105a115 a103a105a118a101a110 a98a121a58 nX i=1 0 i;2 i;1 r2h sin d d = r2h nX i=1 (cos i;1 cos i;2) = r2h nX i=1 r2h Li;2 Li;1j~rj a40a53a46a50a50a41 a53a55 a70a105a103a117a114a101 a53a46a55a58 a82a101a112a114a101a115a101a110a116a97a116a105a111a110 a111a102 a65a79a65 a101a114a114a111a114 a98a111a117a110a100a115 a112a114a111a106a101a99a116a101a100 a111a110a116a111 a97 a104a101a109a105a115a112a104a101a114a101 a102a111a114 a116a119a111 a111a114a45 a116a104a111a103a111a110a97a108 a98a97a115a101a108a105a110a101a115a46 a65a110a116a101a110a110a97 a98a97a115a101a108a105a110a101 a49 a101a120a116a101a110a100a115 a102a114a111a109 a116a104a101 a111a114a105a103a105a110 a111a117a116a119a97a114a100 a97a108a111a110a103 a116a104a101 a88a45a97a120a105a115 a119a104a105a108a101 a98a97a115a101a108a105a110a101 a50 a101a120a116a101a110a100a115 a102a114a111a109 a116a104a101 a111a114a105a103a105a110 a111a117a116a119a97a114a100 a97a108a111a110a103 a116a104a101 a89 a97a120a105a115a46 a84a104a101 a112a97a105a114 a111a102 a98a108a117a101 a98a97a110a100a115 a114a101a112a114a101a115a101a110a116 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 a97a110 a65a79a65 a102a111a114 a98a97a115a101a108a105a110a101 a49 a119a104a105a108a101 a116a104a101 a114a101a100 a98a97a110a100a115 a114a101a112a114a101a115a101a110a116 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 a97a110 a65a79a65 a102a111a114 a98a97a115a101a108a105a110a101 a50a46 a84a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a119a105a108a108 a98a101 a117a115a101a100 a116a111 a100a101a116a101a114a109a105a110a101 a116a104a101 a112a114a111a98a97a98a105a108a105a116a121 a111a102 a97a99a99a101a112a116a105a110a103 a97 a102a97a108a115a101 a115a105a103a110a97a108a46 a53a56 a119a104a101a114a101 a105a115 a116a104a101 a65a79a65a44 a105a115 a114a111a116a97a116a105a111a110 a97a98a111a117a116 a116a104a101 a97a110a116a101a110a110a97 a98a97a115a101a108a105a110a101a44 rh a105a115 a116a104a101 a114a97a100a105a117a115 a111a102 a116a104a101 a104a101a109a105a45 a115a112a104a101a114a101a44 a97a110a100j~rja105a115 a116a104a101 a97a110a116a101a110a110a97 a98a97a115a101a108a105a110a101 a108a101a110a103a116a104a46 a65a108a115a111a44 Li;2 >Li;1 a115a111 a116a104a97a116 a116a104a101 a113a117a97a110a116a105a116a121Li;2 Li;1 a119a105a108a108 a98a101 a112a111a115a105a116a105a118a101 a97a110a100 a121a105a101a108a100 a97 a112a111a115a105a116a105a118a101 a115a117a114a102a97a99a101 a97a114a101a97 a99a97a108a99a117a108a97a116a105a111a110a46 a84a104a101a114a101 a105a115 a110a111 a110a101a101a100 a116a111 a101a115a116a97a98a108a105a115a104 a97 a118a97a108a117a101 a102a111a114 rh a97a115 a105a116 a119a105a108a108 a99a97a110a99a101a108 a111a117a116 a105a110 a69a113a117a97a116a105a111a110 a40a53a46a50a53a41a46 a66a111a117a110a100a115 a111a110 i;1a44 i;2a44 Li;1a44 a97a110a100 Li;2 a97a114a101a58 0 < i;1; i;2 < a40a53a46a50a51a41 j~rj j~rja102a111a114 a97a108a108 Lka46 a84a104a101 a98a97a115a101a108a105a110a101 a108a101a110a103a116a104 a109a97a121 a97a108a115a111 a98a101 a101a120a112a114a101a115a115a101a100 a105a110 a116a101a114a109a115 a111a102 a99a97a114a114a105a101a114 a119a97a118a101a108a101a110a103a116a104a115a58 j~rj = b L1 a119a104a101a114a101 n 12 < b n2a46 a69a113a117a97a116a105a111a110 a40a53a46a50a53a41 a109a97a121 a116a104a101a110 a98a101 a114a101a119a114a105a116a116a101a110 a105a110 a97 a109a117a99a104 a109a111a114a101 a99a111a109a112a97a99a116 a102a111a114a109a97a116a58 a53a57 a105a109a97a103a101 a111a102 a70a105a103a117a114a101 a53a46a56a58 a68a105a27a101a114a101a110a116a105a97a108 a115a117a114a102a97a99a101 a97a114a101a97 dA a97a115 a105a116 a114a101a108a97a116a101a115 a116a111 d 1 a97a110a100 d 2a46 Pfalse = 2na L12b L1 = nab a40a53a46a50a55a41 a73a110 a99a97a115a101a115 a119a104a101a114a101 b a97a112a112a114a111a97a99a104a101a115 n2 a111a114 b a105a115 a108a97a114a103a101 a40n 1a41a44 Pfalse a114a101a100a117a99a101a115 a102a117a114a116a104a101a114 a116a111 Pfalse 2a a40a53a46a50a56a41 a65a115 a97a110 a101a120a97a109a112a108a101a44 a115a117a112a112a111a115a101 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 Lk a97a114a101 a100a101a116a101a114a109a105a110a101a100 a116a111 a98a101 :1 L1a46 a73a102 a116a104a101 a114a101a113a117a105a114a101a45 a109a101a110a116a115 a102a111a114 a69a113a117a97a116a105a111a110 a40a53a46a50a56a41 a97a114a101 a109a101a116a44 Pfalse :2a44 a111a114 a50a48a37a46 a65a115 a119a97a115 a109a101a110a116a105a111a110a101a100 a101a97a114a108a105a101a114a44 a116a104a101 a114a101a97a108 a115a116a114a101a110a103a116a104 a111a102 a116a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a114a101a115a105a100a117a97a108 a97a112a112a114a111a97a99a104 a108a105a101a115 a105a110 a117a115a105a110a103 a116a119a111 a111a114a116a104a111a103a111a110a97a108 a97a110a116a101a110a110a97 a98a97a115a101a108a105a110a101a115a46 a73a102 a116a119a111 a115a101a116a115 a111a102 a97a110a116a101a110a110a97a115 a97a114a101 a117a115a101a100 a116a111 a99a104a101a99a107 a105a110a99a111a109a45 a105a110a103 a71a80a83 a109a101a97a115a117a114a101a109a101a110a116a115a44 a116a104a101 a105a110a99a111a109a105a110a103 a115a105a103a110a97a108a115 a109a117a115a116 a112a97a115a115 a116a104a101 a114a101a115a105a100a117a97a108 a116a101a115a116 a102a111a114 a98a111a116a104 a97a110a116a101a110a110a97a115 a115a105a109a117a108a116a97a110a101a111a117a115a108a121 a105a110 a111a114a100a101a114 a116a111 a98a101 a97a99a99a101a112a116a101a100a46 a73a110 a70a105a103a117a114a101 a53a46a55a44 a112a97a115a115a105a110a103 a116a104a101 a116a104a101 a114a101a115a105a100a117a97a108 a116a101a115a116 a102a111a114 a98a111a116a104 a97a110a116a101a110a110a97a115 a97a116 a111a110a99a101 a105a115 a114a101a112a114a101a115a101a110a116a101a100 a98a121 a116a104a101 a105a110a116a101a114a115a101a99a116a105a111a110 a111a102 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a102a114a111a109 a116a104a101 a116a119a111 a111a114a116a104a111a103a45 a111a110a97a108 a115a101a116a115 a111a102 a97a110a116a101a110a110a97a115a46 a84a111 a99a97a108a99a117a108a97a116a101 a116a104a101 a99a117a109a117a108a97a116a105a118a101 a97a114a101a97 a101a110a99a111a109a112a97a115a115a101a100 a98a121 a116a104a101a115a101 a105a110a116a101a114a115a101a99a116a105a111a110a115a44 a105a116 a105a115 a105a109a112a111a114a116a97a110a116 a116a111 a100a101a28a110a101 dA a105a110 a116a101a114a109a115 a111a102 1 a97a110a100 2a46 a73a110 a103a101a110a101a114a97a108a44 dA a119a105a108a108 a98a101 a105a110 a116a104a101 a115a104a97a112a101 a111a102 a97 a116a114a97a112a101a122a111a105a100 a97a115 a115a101a101a110 a105a110 a70a105a103a117a114a101 a53a46a56a46 a70a114a111a109 a116a104a101 a28a103a117a114a101a44 a105a116 a99a97a110 a98a101 a115a101a101a110 a116a104a97a116 a116a104a101 a97a114a101a97 dA a105a115 a103a105a118a101a110 a98a121a58 dA = (rhd 1)(rhd 2) 1sin s = (rhd 1)(rhd 2) 1p1 cos2 s a40a53a46a50a57a41 a119a104a101a114a101 s a105a115 a111a110a101 a111a102 a116a104a101 a105a110a116a101a114a105a111a114 a97a110a103a108a101a115 a111a102 a116a104a101 a116a114a97a112a101a122a111a105a100a46 a54a48 a66a101a102a111a114a101 a97a116a116a101a109a112a116a105a110a103 a116a111 a115a111a108a118a101 a102a111a114 sa44 a105a116 a105a115 a104a101a108a112a102a117a108 a104a97a118a101 a101a120a112a114a101a115a115a105a111a110a115 a102a111a114 a116a104a101 a88 a97a110a100 a89 a99a111a111a114a100a105a45 a110a97a116a101a115 a105a110 a116a101a114a109a115 a111a102 1a44 1a44 2a44 a97a110a100 2 a58 X = rh cos 1 = rh sin 2 cos 2 a40a53a46a51a48a41 Y = rh cos 2 = rh sin 1 cos 1 a40a53a46a51a49a41 a73a116 a105a115 a107a110a111a119a110 a116a104a97a116 ^ 1 a105a115 a112a97a114a97a108a108a101a108 a116a111 a108a105a110a101a115 a100a101a110a111a116a105a110a103 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a102a111a114 1a46 a76a105a107a101a119a105a115a101a44 ^ 2 a105a115 a112a97a114a97a108a108a101a108 a116a111 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a102a111a114 2a46 a65a115 a115a117a99a104a44 a116a104a101 a97a110a103a108a101 a98a101a116a119a101a101a110 a116a104a101 a115a105a100a101a115 a109a97a121 a98a101 a102a111a117a110a100 a98a121 a116a104a101 a100a111a116 a112a114a111a100a117a99a116 a111a102 ^ 1 a97a110a100 ^ 2a46 a69a113a117a97a116a105a111a110a115 a102a111a114 ^ 1 a97a110a100 ^ 2 a97a114a101 a103a105a118a101a110 a98a121a58 ^ 1 = sin 1^y + cos 1^z a40a53a46a51a50a41 ^ 2 = sin 2^x+ cos 2^z a40a53a46a51a51a41 a84a97a107a105a110a103 a116a104a101 a97a114a99a99a111a115a105a110a101 a111a102 a116a104a101 a100a111a116 a112a114a111a100a117a99a116 a100a105a118a105a100a101a100 a98a121 a116a104a101 a112a114a111a100a117a99a116 a111a102 a116a104a101 a109a97a103a110a105a116a117a100a101 a111a102 a116a104a101 a118a101a99a116a111a114a115 a103a105a118a101a115a58 s = arccos( ^ 1 ^ 2 j^ 1jj^ 2j) = arccos(cos 1 cos 2) a40a53a46a51a52a41 a83a117a98a115a116a105a116a117a116a105a110a103 a69a113a117a97a116a105a111a110 a40a53a46a51a52a41 a105a110a116a111 a69a113a117a97a116a105a111a110 a40a53a46a50a57a41 a121a105a101a108a100a115a58 dA = (rhd 1)(rhd 2) 1p1 cos2(arccos(cos 1 cos 2))) a40a53a46a51a53a41 = (rhd 1)(rhd 2) 1p1 (cos 1 cos 2)2 a84a104a101 (cos 1 cos 2) a116a101a114a109 a99a97a110 a98a101 a101a120a112a114a101a115a115a101a100 a105a110 a116a101a114a109a115 a111a102 1 a97a110a100 2 a102a114a111a109 a69a113a117a97a116a105a111a110a115 a40a53a46a51a48a41 a97a110a100 a40a53a46a51a49a41a44 a103a105a118a105a110a103a58 a54a49 da = r 2 hp 1 (cot 1 cot 2)2d 1d 2 a40a53a46a51a54a41 a84a104a101 a112a114a111a98a97a98a105a108a105a116a121 a111a102 a97a99a99a101a112a116a105a110a103 a97 a102a97a108a115a101 a115a105a103a110a97a108 a109a97a121 a116a104a101a110 a98a101 a99a111a109a112a117a116a101a100 a98a121 a105a110a116a101a103a114a97a116a105a110a103 a111a118a101a114 a116a104a101 a105a110a100a105a118a105a100a117a97a108 a105a110a116a101a114a115a101a99a116a105a111a110a115 a111a102 a65a79a65 a101a114a114a111a114 a98a111a117a110a100a115a44 a115a117a109a109a105a110a103 a116a104a101 a114a101a115a117a108a116a115a44 a97a110a100 a100a105a118a105a100a105a110a103 a98a121 a116a104a101 a116a111a116a97a108 a115a117a114a102a97a99a101 a97a114a101a97 a111a102 a97 a104a101a109a105a115a112a104a101a114a101a58 Pfalse = 12 mX i=1 nX j=1 i;2 i;1 j;2 j;1 1p 1 (cot 1 cot 2)2d 1d 2 a40a53a46a51a55a41 = 16 mX i=1 nX j=1 (1 (cot 1 cot 2)2)32 sin 1 sin 2 cos 1 cos 2j i;2 i;1 j i;2 i;1 a102a111a114 cos2 1 + cos2 2 1: a84a104a101 a99a111a110a115a116a114a97a105a110a116 a111a110 1 a97a110a100 2 a115a101a114a118a101a115 a116a111 a101a110a115a117a114a101 a116a104a97a116 a116a104a101 a65a79a65a115 a97a114a101 a105a110a116a101a103a114a97a116a101a100 a111a110a108a121 a119a104a101a114a101 a116a104a101a121 a105a110a116a101a114a115a101a99a116a46 a70a111a114 a101a120a97a109a112a108a101a44 a115a117a112a112a111a115a101 1 = 2 = 6a46 a84a104a101a110 cos2( 6) + cos2( 6) = 32a44 a105a110a100a105a99a97a116a105a110a103 1 a97a110a100 2 a100a111 a110a111a116 a105a110a116a101a114a115a101a99a116a46 a65a110a111a116a104a101a114 a115a116a114a101a110a103a116a104 a111a102 a116a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a114a101a115a105a100a117a97a108 a109a101a116a104a111a100 a99a111a109a101a115 a102a114a111a109 a116a104a101 a108a111a119 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a111a117a116a108a105a101a114a115a46 a65a110a111a116a104a101a114 a112a111a116a101a110a116a105a97a108 a99a97a117a115a101 a102a111a114 a116a104a101 a119a111a114a115a101 a112a101a114a102a111a114a109a97a110a99a101 a99a111a117a108a100 a98a101 a116a104a101 a115a111a117a114a99a101 a111a102 a109a117a108a116a105a112a97a116a104 a115a105a103a110a97a108a115 a105a110 a101a97a99a104 a111a102 a116a104a101 a100a97a116a97 a115a101a116a115a46 a73a110 a116a104a101 a116a114a97a99a107 a100a97a116a97a44 a116a104a101 a109a117a108a116a105a112a97a116a104 a111a99a99a117a114a114a101a100 a114a97a110a100a111a109a108a121 a97a115 a97 a114a101a115a117a108a116 a111a102 a116a114a101a101a115 a98a111a114a100a101a114a105a110a103 a98a111a116a104 a115a105a100a101a115 a111a102 a116a104a101 a116a114a97a99a107 a97a110a100 a116a104a101a114a101a102a111a114a101 a119a101a114a101 a110a111a116 a108a105a107a101a108a121 a116a111 a103a101a110a101a114a97a116a101 a116a104a101 a115a97a109a101 a109a117a108a116a105a45 a112a97a116a104 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a115a105a103a110a97a108 a105a115 a114a101a106a101a99a116a101a100a44 a105a116a115 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121 a109a117a115a116 a98a101 a114a101a115a101a116 a97a110a100 a116a104a117a115 a116a104a101 a65a79a65 a99a97a110 a110a111a116 a98a101 a99a97a108a99a117a108a97a116a101a100 a117a110a116a105a108 a97 a110a101a119 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121 a105a115 a28a120a101a100a46 a84a104a101 a108a111a115a115 a111a102 a105a110a116a101a103a101a114 a97a109a98a105a103a117a105a116a121 a109a101a97a110a115 a116a104a97a116 a116a104a101 a65a79a65 a99a97a110 a110a111a116 a98a101 a99a111a109a112a117a116a101a100 a97a110a100 a116a104a117a115 a101a120a112a108a97a105a110a115 a97a116 a108a101a97a115a116 a115a111a109a101 a111a102 a116a104a101 a112a111a111a114 a112a101a114a102a111a114a109a97a110a99a101a46 a70a105a103a117a114a101 a54a46a50 a115a104a111a119a115 a116a104a101 a112a101a114a99a101a105a118a101a100 a65a79a65 a101a114a114a111a114 a102a111a114 a97 a115a101a112a97a114a97a116a101 a100a97a116a97 a114a117a110 a119a105a116a104 a104a105a103a104 a100a121a110a97a109a105a99a115a44 a98a117a116 a110a111 a109a117a108a116a105a112a97a116a104a46 a84a104a101 a98a108a97a99a107 a99a105a114a99a108a101a115 a100a101a112a105a99a116 a101a114a114a111a114 a98a97a115a101a100 a111a110 a116a104a101 a82a80a86a115 a103a101a110a101a114a97a116a101a100 a98a121 a116a104a101 a97a116a116a105a116a117a100a101 a101a115a116a105a109a97a116a101a115 a116a111 a99a104a101a99a107 a105a110a99a111a109a105a110a103 a115a105a103a110a97a108a115a44 a119a104a105a108a101 a116a104a101 a114a101a100 a99a105a114a99a108a101a115 a100a101a112a105a99a116 a101a114a114a111a114 a98a97a115a101a100 a111a110 a116a104a101 a99a97a108a99a117a108a97a116a101a100 a82a80a86a115a46 a65a115 a99a97a110 a98a101 a115a101a101a110 a102a114a111a109 a116a104a101 a28a103a117a114a101a44 a116a104a101 a101a114a114a111a114 a111a110 a116a104a101 a115a105a103a110a97a108a115 a54a57 0 20 40 60 80 100 120 140 160 1800 1 2 3 4 5 6 7 8 9 10 Expected AOA (deg) Apparent AOA error(deg) 0.94m Baseline .01 m error on ?? .02 m error on ??.03 m error on ?? .04 m error on ??.05 m error on ?? a70a105a103a117a114a101 a54a46a50a58 a80a101a114a99a101a105a118a101a100 a65a79a65 a101a114a114a111a114 a102a111a114 a97 a100a97a116a97 a114a117a110a46 a66a108a97a99a107 a99a105a114a99a108a101a115 a100a101a112a105a99a116 a65a79a65 a101a114a114a111a114 a102a114a111a109 a116a104a101 a112a114a101a100a105a99a116a101a100 a82a80a86 a119a104a105a108a101 a114a101a100 a99a105a114a99a108a101a115 a100a101a112a105a99a116 a65a79a65 a101a114a114a111a114 a102a114a111a109 a116a104a101 a99a97a108a99a117a108a97a116a101a100 a82a80a86a46 a102a114a111a109 a116a104a101 a114a101a97a108 a82a80a86 a105a115 a99a111a110a115a105a115a116a101a110a116a108a121 a108a111a119a101a114 a116a104a97a110 a116a104a97a116 a111a110 a116a104a101 a82a80a86 a103a101a110a101a114a97a116a101a100 a98a121 a97a116a116a105a116a117a100a101 a101a115a116a105a45 a109a97a116a101a115a46 a84a104a101 a117a112a112a101a114 a98a111a117a110a100a115 a111a102 a98a111a116a104 a101a114a114a111a114a115 a97a112a112a101a97a114 a116a111 a98a101 a115a104a105a102a116a101a100 a98a121 a97a98a111a117a116 a97 a100a101a103a114a101a101a44 a119a104a105a99a104 a105a115 a114a101a97a115a111a110a97a98a108a101 a99a111a110a115a105a100a101a114a105a110a103 a116a104a101 a97a116a116a105a116a117a100a101 a101a114a114a111a114 a111a110 a116a104a101 a112a114a101a100a105a99a116a101a100 a82a80a86a115a46 a73a100a101a97a108a108a121a44 a116a104a101 a112a101a114a102a111a114a109a97a110a99a101 a111a102 a116a104a101 a97a116a116a105a116a117a100a101a45a103a101a110a101a114a97a116a101a100 a82a80a86 a119a105a108a108 a97a112a112a114a111a97a99a104 a116a104a101 a112a101a114a102a111a114a109a97a110a99a101 a111a102 a116a104a101 a114a101a97a108 a82a80a86 a119a105a116a104 a109a111a114a101 a97a99a99a117a114a97a116a101 a97a116a116a105a116a117a100a101 a101a115a116a105a109a97a116a105a111a110a46 a54a46a51a46a50 a83a105a110a103a108a101a45a68a105a27a101a114a101a110a99a101a100 a80a115a101a117a100a111a114a97a110a103a101 a68a101a116a101a99a116a105a111a110 a111a102 a109a117a108a116a105a112a97a116a104 a115a105a103a110a97a108a115 a117a115a105a110a103 a116a104a101 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a109a101a97a115a117a114a101a109a101a110a116a115 a112a114a111a118a101a100 a116a111 a98a101 a118a101a114a121 a117a110a114a101a108a105a97a98a108a101a46 a65a115 a105a115 a115a116a97a116a101a100 a105a110 a83a101a99a116a105a111a110 a53a46a50a46a50a46a49a44 a116a104a101 a101a114a114a111a114 a98a111a117a110a100a115 a111a110 a97 a115a105a110a103a108a101a45 a100a105a27a101a114a101a110a99a101a100 a112a115a101a117a100a111a114a97a110a103a101 a109a101a97a115a117a114a101a109a101a110a116 a97a114a101 a102a97a114 a116a111a111 a108a97a114a103a101 a116a111 a98a101 a117a115a101a102a117a108 a102a111a114 a100a101a116a101a99a116a105a110a103 a112a115a101a117a100a111a114a45 a97a110a103a101a115 a102a111a114 a116a104a101 a97a110a116a101a110a110a97 a98a97a115a101a108a105a110a101a115 a105a110 a116a104a105a115 a119a111a114a107a46 a55a48 20 40 60 80 100 120 140 160 1800 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Expected AOA (deg) Expected length error ( ? L1 cycles) 1.905m Baseline 1? error 2? error3? error 4? error5? error a70a105a103a117a114a101 a54a46a51a58 a82a101a109a97a105a110a100a101a114a115 a111a102 a115a105a110a103a108a101a45a100a105a27a101a114a101a110a99a101a100 a99a97a114a114a105a101a114 a112a104a97a115a101 a109a101a97a115a117a114a101a109a101a110a116a46 a82a101a100 a99a105a114a99a108a101a115 a114a101a112a45 a114a101a115a101a110a116 a114a101a115a105a100a117a97a108a115 a103a101a110a101a114a97a116a101a100 a102a114a111a109 a99a97a108a99a117a108a97a116a101a100 a82a80a86a44 a98a108a97a99a107 a99a105a114a99a108a101a115 a114a101a112a114a101a115a101a110a116 a114a101a115a105a100a117a97a108a115 a103a101a110a101a114a97a116a101a100 a102a114a111a109 a112a114a101a100a105a99a116a101a100 a82a80a86a46 a54a46a51a46a51 a67a97a114a114a105a101a114 a80a104a97a115a101 a82a101a115a105a100a117a97a108 a84a104a101 a99a97a114a114a105a101a114 a112a104a97a115a101 a114a101a115a105a100a117a97a108 a109a101a116a104a111a100a44 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Residual ( ? 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a110a111a105a115a101a46 a73a116 a105a115 a97a115a115a117a109a101a100 a116a104a97a116 w a97a110a100 v a97a114a101 a117a110a107a110a111a119a110 a97a110a100 a114a97a110a100a111a109a44 a98a117a116 a116a104a101a105a114 a115a116a97a116a105a115a116a105a99a97a108 a112a114a111a112a101a114a116a105a101a115 a97a114a101 a107a110a111a119a110a46 a66a46a50 a84a105a109a101 a85a112a100a97a116a101 a84a104a101 a116a105a109a101 a117a112a100a97a116a101 a111a102 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114 a105a115 a97 a16a112a114a101a100a105a99a116a105a111a110a17 a111a102 a115a111a114a116a115a44 a117a115a105a110a103 a116a104a101 a115a121a115a116a101a109 a109a111a100a101a108a44 a115a121a115a116a101a109 a115a116a97a116a101a115a44 a97a110a100 a107a110a111a119a110 a105a110a112a117a116a115 a116a111 a116a104a101 a115a121a115a116a101a109 a116a111 a112a114a111a118a105a100a101 a97a110 a101a115a116a105a109a97a116a101 a111a102 a116a104a101 a115a116a97a116a101a115 a111a102 a116a104a101 a115a121a115a116a101a109 a97a116 a116a104a101 a110a101a120a116 a116a105a109a101 a115a116a101a112a46 a84a104a101 a116a105a109a101 a117a112a100a97a116a101 a111a102 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114 a105a115 a105a109a112a108a101a109a101a110a116a101a100 a116a104a114a111a117a103a104 a116a104a101 a102a111a108a108a111a119a105a110a103 a101a113a117a97a116a105a111a110a115a58 ^x k = Ak 1^xk 1 +Bk 1uk 1 a40a66a46a51a41 P k = Ak 1P+k 1ATk 1 +Qk 1 a40a66a46a52a41 a69a113a117a97a116a105a111a110 a40a66a46a51a41 a103a105a118a101a115 a119a104a97a116 a105a115 a107a110a111a119a110 a97a115 a116a104a101 a97 a112a114a105a111a114a105 a101a115a116a105a109a97a116a101a44 a97a110 a101a115a116a105a109a97a116a101 a116a104a97a116 a112a114a111a112a97a103a97a116a101a115 a116a104a101 a115a116a97a116a101 a101a115a116a105a109a97a116a101 a102a111a114a119a97a114a100 a117a115a105a110a103 a116a104a101 a115a121a115a116a101a109 a109a111a100a101a108a46 a67a111a109a112a97a114a105a110a103 a69a113a117a97a116a105a111a110a115 a40a66a46a49a41 a97a110a100 a40a66a46a51a41a44 a105a116 a105a115 a99a108a101a97a114 a116a104a97a116 a116a104a101a121 a97a114a101 a110a101a97a114a108a121 a116a104a101 a115a97a109a101 a101a113a117a97a116a105a111a110a44 a101a120a99a101a112a116 a69a113a117a97a116a105a111a110 a40a66a46a51a41 a100a111a101a115 a110a111a116 a105a110a99a108a117a100a101 a116a104a101 a112a114a111a99a101a115a115 a100a105a115a116a117a114a98a97a110a99a101 a116a101a114a109a46 a84a104a101 a111a109a105a115a115a105a111a110 a111a102 a116a104a101 a100a105a115a116a117a114a98a97a110a99a101 a116a101a114a109 a109a97a107a101a115 a115a101a110a115a101 a105a110a116a117a105a116a105a118a101a108a121a44 a97a115 a116a104a101 a100a105a115a116a117a114a98a97a110a99a101 a105a115 a114a97a110a100a111a109 a97a110a100 a117a110a107a110a111a119a110a59 a116a104a101a114a101a102a111a114a101a44 a116a104a101 a97 a112a114a105a111a114a105 a101a115a116a105a109a97a116a101 a105a115 a116a104a101 a16a98a101a115a116 a103a117a101a115a115a17 a111a102 a116a104a101 a115a116a97a116a101a115 a97a116 a116a104a101 a110a101a120a116 a116a105a109a101 a115a116a101a112a44 a103a105a118a101a110 a116a104a101 a115a121a115a116a101a109 a109a111a100a101a108a46 a69a113a117a97a116a105a111a110 a40a66a46a52a41 a103a105a118a101a115 a116a104a101 a97 a112a114a105a111a114a105 a101a115a116a105a109a97a116a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120a44 a97 a109a101a97a115a117a114a101 a111a102 a116a104a101 a117a110a99a101a114a45 a116a97a105a110a116a121 a105a110 a116a104a101 a101a115a116a105a109a97a116a101a115a46 P k a119a105a108a108 a98a101 n n a102a111a114 a97 a115a121a115a116a101a109 a119a105a116a104 n a115a116a97a116a101a115a44 a119a105a116a104 a101a97a99a104 a100a105a97a103a111a110a97a108 a56a54 a116a101a114a109 a114a101a112a114a101a115a101a110a116a105a110a103 a116a104a101 a101a120a112a101a99a116a101a100 a118a97a114a105a97a110a99a101 a111a102 a101a97a99a104 a115a116a97a116a101a46 a69a97a99a104 a111a27 a100a105a97a103a111a110a97a108 a116a101a114a109 a119a105a108a108 a98a101 a111a102 a116a104a101 a102a111a114a109 i j a44 a119a104a101a114a101 i a105a115 a116a104a101 a101a120a112a101a99a116a101a100 a115a116a97a110a100a97a114a100 a100a101a118a105a97a116a105a111a110 a111a102 a115a116a97a116a101 ia44 j a105a115 a116a104a101 a101a120a112a101a99a116a101a100 a115a116a97a110a100a97a114a100 a100a101a118a105a97a116a105a111a110 a111a102 a115a116a97a116a101 j; a105a115 a116a104a101 a115a116a97a116a105a115a116a105a99a97a108 a99a111a114a114a101a108a97a116a105a111a110 a111a102 a116a104a101 a116a119a111 a115a116a97a116a101a115a44 a97a110a100 i6= ja46 a73a116 a105a115 a105a109a112a111a114a116a97a110a116 a116a111 a101a109a112a104a97a115a105a122a101 a116a104a97a116 P k a114a101a112a114a101a115a101a110a116a115 a116a104a101 a101a120a112a101a99a116a101a100 a118a97a114a105a97a110a99a101a115 a97a110a100 a99a111a118a97a114a105a97a110a99a101a115 a111a102 a116a104a101 a115a116a97a116a101a115a46 a73a102 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a112a114a105a111a114a105 a101a115a116a105a109a97a116a101 a117a115a105a110a103 a109a101a97a115a117a114a101a109a101a110a116a115 a111a102 a116a104a101 a115a116a97a116a101a115a46 a84a104a101 a109a101a97a115a117a114a101a109a101a110a116 a117a112a100a97a116a101 a111a102 a116a104a101 a75a97a108a109a97a110 a28a108a116a101a114 a105a115 a105a109a112a108a101a109a101a110a116a101a100 a116a104a114a111a117a103a104 a116a104a101 a102a111a108a108a111a119a105a110a103 a101a113a117a97a116a105a111a110a115a58 Lk = P k CTk (CkP k CTk +Rk) 1 a40a66a46a53a41 ^x+k = ^x k +Lk(yk Ck^x k ) a40a66a46a54a41 P+k = (I LkCk)P k (I LkCk)T +LkRkLTk a40a66a46a55a41 a69a113a117a97a116a105a111a110 a40a66a46a53a41 a103a105a118a101a115 a116a104a101 a75a97a108a109a97a110 a103a97a105a110a44 a117a115a101a100 a105a110 a69a113a117a97a116a105a111a110 a40a66a46a54a41a46 a85a110a108a105a107a101 a116a104a101 a103a97a105a110a115 a117a115a101a100 a105a110 a99a108a97a115a115a105a99a97a108 a101a115a116a105a109a97a116a111a114a115a44 a119a104a105a99a104 a97a114a101 a103a101a110a101a114a97a108a108a121 a99a104a111a115a101a110 a98a97a115a101a100 a111a110 a114a105a115a101 a116a105a109a101a44 a115a101a116a116a108a105a110a103 a116a105a109a101a44 a97a110a100 a111a116a104a101a114 a99a104a97a114a97a99a116a101a114a105a115a116a105a99a115a44 a116a104a101 a75a97a108a109a97a110 a103a97a105a110 a105a115 a114a101a99a97a108a99a117a108a97a116a101a100 a119a105a116a104 a101a97a99a104 a105a116a101a114a97a116a105a111a110 a116a111 a103a105a118a101 a97a110 a111a112a116a105a109a97a108 a101a115a116a105a45 a109a97a116a101 a119a105a116a104 a109a105a110a105a109a97a108 a101a120a112a101a99a116a101a100 a101a114a114a111a114a46 a73a110a115a112a101a99a116a105a110a103 a69a113a117a97a116a105a111a110 a40a66a46a53a41a44 a116a104a101 a75a97a108a109a97a110 a103a97a105a110 a105a115 a99a97a108a99a117a108a97a116a101a100 a98a97a115a101a100 a111a110 a116a104a101 a109a101a97a115a117a114a101a109a101a110a116 a110a111a105a115a101 a99a111a118a97a114a105a97a110a99a101 a109a97a116a114a105a120 a40Rka41a44 P k a44 a97a110a100 Cka46 a73a116 a105a115 a104a101a108a112a102a117a108 a116a111 a105a110a115a112a101a99a116 a69a113a117a97a116a105a111a110 a40a66a46a53a41 a102a111a114 a97 a115a105a110a103a108a101 a115a116a97a116a101a44 a115a105a110a103a108a101 a109a101a97a115a117a114a101a109a101a110a116 a115a121a115a116a101a109a44 a105a110 a119a104a105a99a104 a99a97a115a101 a105a116 a98a101a99a111a109a101a115a58 a56a55 Lk = P k P k +Rk a40a66a46a56a41 a78a111a116a105a99a101 a116a104a97a116 a98a101a99a97a117a115a101 a116a104a101 a115a121a115a116a101a109 a119a111a117a108a100 a104a97a118a101 a97 a115a105a110a103a108a101 a115a116a97a116a101 a97a110a100 a97 a115a105a110a103a108a101 a109a101a97a115a117a114a101a109a101a110a116a44 a97a108a108 a116a101a114a109a115 a105a110 a69a113a117a97a116a105a111a110 a40a66a46a56a41 a97a114a101 a115a99a97a108a97a114a115a46 a69a113a117a97a116a105a111a110 a40a66a46a56a41 a99a97a112a116a117a114a101a115 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a97a112a112a114a111a97a99a104a101a115 1 a97a110a100 a116a104a101 a115a116a97a116a101 a101a115a116a105a109a97a116a101 a119a105a108a108 a98a101 a99a111a114a114a101a99a116a101a100 a104a101a97a118a105a108a121 a116a111a119a97a114a100 a116a104a101 a110a101a119 a109a101a97a115a117a114a101a109a101a110a116a46 a77a97a107a105a110a103 a116a104a101 a108a97a114a103a101 a99a111a114a114a101a99a116a105a111a110 a109a97a107a101a115 a105a110a116a117a105a116a105a118a101 a115a101a110a115a101a44 a99a111a110a115a105a100a101a114a105a110a103 a116a104a101 a109a101a97a115a117a114a101a109a101a110a116 a105a115 a97 a109a117a99a104 a98a101a116a116a101a114 a114a101a112a114a101a115a101a110a116a97a116a105a111a110 a111a102 a116a104a101 a115a116a97a116a101 a116a104a97a110 a116a104a101 a99a117a114a114a101a110a116 a115a116a97a116a101 a101a115a116a105a109a97a116a101a46 a65a115 a119a111a117a108a100 a98a101 a101a120a112a101a99a116a101a100a44 Lk a119a111a117a108a100 a97a112a112a114a111a97a99a104 a122a101a114a111 a105a102 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