Sensor Assignment Algorithms to Improve Observability While Tracking Targets

In this paper, we study two sensor assignment problems for multitarget tracking with the goal of improving the observability of the underlying estimator. We consider various measures of the observability matrix as the assignment value function. We first study the general version where the sensors must form teams to track individual targets. If the value function is monotonically increasing and submodular, then a greedy algorithm yields a $1/2$–approximation. We then study a restricted version where exactly two sensors must be assigned to each target. We present a $1/3$–approximation algorithm for this problem, which holds for arbitrary value functions (not necessarily submodular or monotone). In addition to approximation algorithms, we also present various properties of observability measures. We show that the inverse of the condition number of the observability matrix is neither monotone nor submodular, but present other measures that are. Specifically, we show that the trace and rank of the symmetric observability matrix are monotone and submodular and the log determinant of the symmetric observability matrix is monotone and submodular when the matrix is nonsingular. If the target's motion model is not known, the inverse cannot be computed exactly. Instead, we present a lower bound for distance sensors. In addition to theoretical results, we evaluate our results empirically through simulations.