Initial Relative-Orbit Determination Using Second-Order Dynamics and Line-of-Sight Measurements

Abstract

This thesis addresses the problem of determining the initial relative-orbit state between a chief and a deputy satellite using line-of-sight unit vectors. An analytical solution is investigated for estimating the deputy satellite’s initial states relative to the chief satellite, assuming circular chief orbit. The line-of-sight measurements and the relative motion of the deputy satellite, captured with a closed-form second-order solution of relative motion, leads to the nonlinear measurements equation. The measurement equations are transformed using the new proposed formulation which solves directly for the unknown ranges. The new formulation is applied to two solution procedures to solve the relative-orbit determination problem. Within the first solution method, the new formulation is computationally faster and requires fewer measurements, than the previous formulation. The second solution method requires the minimal number of measurements, but the new formulation provides reduced algebraic complexity in comparison to the previously published formulation.