Timely Remote Estimation and Applications to Situational Awareness

Abstract

In real-time monitoring and networked control systems, sensor observations from vehicles, robots, UAVs, or stock markets, are transmitted to a monitoring or controlling unit, which could be any kind of decision-making device. Real-time services often require fresh and timely data which are usually in the form of a signal. A key performance metric characterizing data freshness is the Age of Information (AoI). However, data signals can exhibit diverse behavior, sometimes evolving slowly and later on evolving very quickly. Therefore, only considering the time difference is insufficient to characterize the variation of a signal. In this dissertation, we investigate the performance of a remote estimation system by considering both the data signal value and its timeliness.

First, we consider the sampling problem for the remote estimation of a scalar Gauss-Markov process. The optimal sampling problem is a constrained continuous-time Markov Decision Process (MDP) with an uncountable state space. Our analysis reveals that the optimal sampling policy is a threshold policy on instantaneous estimation error and the threshold is found. If the sampler has no knowledge of the process, the optimal sampling problem reduces to an MDP for minimizing nonlinear age functions. In both problems, the optimal sampling policies can be computed by low-complexity algorithms.

Next, We generalize this study from single-source, single-channel to multiple-source, multiple-channel and formulate a scheduling problem for the remote estimation of multiple Gauss-Markov processes. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) with a continuous state space. We prove that all bandits are indexable and derive an exact expression of the Whittle index. Our results unite two theoretical frameworks that are used for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In these investigations, the numerical evidence shows that our proposed policy achieves high-performance gain over existing policies.

Finally, we study a scheduling problem for maximizing situational awareness in safety-critical systems where a centralized monitor pulls updates from multiple agents monitoring several safety-critical situations. Based on the received updates, multiple estimators determine the current safety-critical situations. We provide a novel framework that quantifies the loss due to the unawareness of potential danger which depends on the AoI and the observed signal value. To minimize the penalty, we study an RMAB problem and provide a low-complexity scheduling algorithm that is asymptotically optimal. Numerical evidence shows that our scheduling policy can achieve up to 100 times performance gain over periodic updating and up to 10 times over randomized policy.