Optimization Based Sensor Placement for Multi-Target Localization With Coupling Sensor Clusters

Since the Cramér-Rao lower bounds (CRLB) of target localization depends on the sensor geometry explicitly, sensor placement becomes a crucial issue in many target or source localization applications. In the context of simultaneous time-of-arrival (TOA) based multi-target localization, we consider the sensor placement for multiple sensor clusters in the presence of shared sensors. To minimize the mean squared error (MSE) of target localization, we formulate the sensor placement problem as a minimization of the trace of the Cramér-Rao lower bound (CRLB) matrix (i.e., $A$ -optimal design), subject to the coupling constraints corresponding to the freely-placed shared sensors. For the formulated nonconvex problem, we propose an optimization approach based on the combination of alternating minimization (AM), alternating direction method of multipliers (ADMM) and majorization-minimization (MM), in which the AM alternates between sensor clusters and the integrated ADMM and MM are employed to solve the subproblems. The proposed algorithm monotonically minimizes the joint design criterion and converges to a stationary point of the objective. Unlike the state-of-the-art analytical approaches in the literature, the proposed algorithm can handle both the non-uniform and correlated measurement noise in the simultaneous multi-target case. Through various numerical simulations under different scenario settings, we show the efficiency of the proposed method to design the optimal sensor geometry.