Bayesian target location and velocity estimation for multiple-input multiple-output radar

For a non-coherent multiple-input multiple-output radar system, the minimum mean square error (MMSE) estimator and maximum a posteriori (MAP) estimator of the target location and velocity, considered random unknown parameters, are formulated and the corresponding posterior Cramér-Rao lower bound (PCRLB) is derived. Moreover, numerical solutions for the proposed MMSE estimator and the PCRLB are obtained by using Monte-Carlo methods because of the absence of closed-form solutions. The numerical results show that the mean square errors (MSEs) of the MMSE estimate and the MAP estimate converge to the corresponding PCRLB as the signal-to-noise ratio (SNR) increases when the number of transmit and receive antennas is sufficiently large. A linear approximation can be used to simplify the MMSE estimation. It is shown in some simulations that the linear approximation of the MMSE estimate is accurate at high SNR values and the SNR needed for accurate approximation can be reduced by increasing the number of antennas employed.