Group Sparsity Based Multi-Target Tracking in Passive Multi-Static Radar Systems Using Doppler-Only Measurements

In this paper, we consider the problem of tracking multiple targets in a passive multi-static radar system using Doppler-only measurements. The number of targets is assumed unknown and time-varying. The Doppler measurements are subject to additive noise, clutter, and missed detections. Doppler-only measurements from a single sensor provide incomplete information about the target state, commonly referred to as single-sensor unobservability. In a passive multi-static radar system, the availability of multiple bistatic links naturally lends itself to the fusion of measurements from spatially distributed sensors. However, data fusion emerges as a computationally intensive problem in multi-sensor multi-target tracking algorithms. We propose a two-step sequential approach to solve the underlying problem. We first cast the underlying problem as a group sparse problem in a discretized position-velocity space. A group sparsity based algorithm is applied to simultaneously exploit the multi-static Doppler frequency measurements to directly obtain the instantaneous target state estimates in the Cartesian coordinate system. These estimates are then fed as inputs to the linear Gaussian mixture probability hypothesis density (GMPHD) filter, which removes the false measurements, compensates for missed detections and reduces the localization error. The optimal sub-pattern assignment metric, which jointly comprises a weighted contribution of cardinality error and localization error, is used to evaluate the performance of the proposed method. Simulation results show that the proposed method successfully handles the multi-target tracking problem and outperforms the existing random receiver selection based multi-sensor implementation of the GMPHD filter.