Sparse representation discretization errors in multi-sensor radar target motion estimation

In a multi-sensor radar for the estimation of the targets motion states, more than one module of transmitter and receiver are utilized to estimate the positions and velocities of targets, also known as motion states. By applying the compressed sensing (CS) reconstruction algorithms, the surveillance space needs to be discretized. The effect of the additive errors due to the discretization are studied in this paper. The errors are considered as an additive noise in the well-known under-determined CS problem. By employing properties of these errors, analytical models for its average and variance are derived. Numerous simulations are carried out to verify the analytical model empirically. Furthermore, the probability density functions of discretization errors are estimated. The analytical model is useful for the optimization of the performance, the efficiency and the success rate in CS reconstruction for radar as well as many other applications.