Adaptive measurement design for direction of arrival estimation and target tracking

Abstract

Compressive sensing theory states that a sparse vector x in dictionary A can be recovered from measurements y = WAx. For recovery of x, the measurement matrix W is generally chosen as random since a random W is sufficiently incoherent with a given basis A with high probability. Although Gaussian or Bernoulli random measurement matrices satisfy recovery requirements, they do not necessarily yield the best performance in terms of minimal mutual coherence or best parameter estimation. In literature several studies focused on measurement matrix design mainly to minimize some form of coherence between W and A to minimize measurement numbers while exact reconstruction is guaranteed. On the other hand, for enhanced parameter estimation W can be designed to minimize the Cramer Rao Lower Bound (CRLB). In this study, we propose direct and sequential measurement designs that minimizes the CRLB for the application of direction of arrival (DoA) estimation. Based on our results an adaptive target tracking procedure for single and multiple target scenarios is also proposed. Initial simulations show that measurement design solutions provide enhanced parameter estimation and target tracking performance compared to widely used random matrices in compressive sensing.