Urban target tracking using sparse representations

In this chapter, we propose a novel sparsity-based algorithm for multiple-target tracking in a time-varying multipath environment. A sparse measurement model for the received signal is obtained by considering a finite-dimensional representation of the time-varying system function that characterizes the transmission channel. This sparse measurement model allows us to exploit the joint delay-Doppler diversity offered by the environment. We reformulate the problem of multiple-target tracking as a block support recovery problem and derive an upper bound on the overall error probability of wrongly identifying the support of the sparse signal. Using this bound, we prove that spread-spectrum waveforms are ideal candidates for signaling. In addition, under spread-spectrum signaling, the dictionary of the sparse measurement model exhibits a special structure. We exploit this for structure to develop a computationally inexpensive support recovery algorithm by projecting the received signal on to the row space of the dictionary. Numerical simulations show that tracking using proposed algorithm for support recovery performs better when compared with tracking using other sparse reconstruction algorithms. The proposed algorithm takes significantly less time when compared with the time taken by other methods.