A low-complexity multi-target tracking algorithm in urban environments using sparse modeling

We propose a novel sparsity-based algorithm for multiple-target tracking in a time-varying multipath environment. We develop a sparse measurement model for the received signal, by considering a finite dimensional representation of the time-varying system function which characterizes the transmission channel. The 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 we 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. We also prove that under spread-spectrum signaling, the dictionary of the sparse measurement model exhibits a special structure. We exploit this 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 to tracking using other sparse reconstruction algorithms and tracking using a particle filter. The proposed algorithm takes significantly less time when compared to the time taken by other methods.