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We study two sensor assignment problems for multi-target tracking with thegoal of improving the observability of the underlying estimator. We considervarious measures of the observability matrix as the assignment value function.We first study the general version where the sensors must form teams to trackindividual targets. If the value function is monotonically increasing andsubmodular then a greedy algorithm yields a 1/2-approximation. We then study arestricted version where exactly two sensors must be assigned to each target.We present a 1/3-approximation algorithm for this problem which holds forarbitrary value functions (not necessarily submodular or monotone). In additionto approximation algorithms, we also present various properties ofobservability measures. We show that the inverse of the condition number of theobservability matrix is neither monotone nor submodular, but present othermeasures which are. Specifically, we show that the trace and rank of thesymmetric observability matrix are monotone and submodular and the logdeterminant of the symmetric observability matrix is monotone and submodularwhen the matrix is non-singular. If the target's motion model is not known, theinverse cannot be computed exactly. Instead, we present a lower bound fordistance sensors. In addition to theoretical results, we evaluate our resultsempirically through simulations.

Sensor Assignment Algorithms to Improve Observability while Tracking Targets