Efficient Closed-Form Solution for Moving Target Localization in MIMO Radars With Minimum Number of Antennas

This paper deals with the moving target localization problem from time delay and Doppler shift measurements in a distributed multiple-input multiple-output radar system. An algebraic closed-form two-stage weighted least squares solution is presented to locate the target position and velocity. In the first stage, a set of pseudo-linear equations is established by introducing and decreasing the nuisance parameters. Then, two quadratic equations are obtained in terms of the nuisance parameters by considering relationships among them and the target position and velocity. By applying the elimination method that gives the nuisance parameters and substituting them into the localization problem, the target position and velocity are determined in the first stage. In the second stage, the error in the initial solution is estimated to improve the localization performance. The proposed estimator is shown to achieve the Cramer-Rao lower bound performance under Gaussian noise conditions, when the measurement error is small. The great advantage of the proposed method is that it can give the solution with fewer sensors (transmitters or receivers) in comparison with the state-of-the-art algorithms. Simulation results show that when there are one transmitter and three receivers or two transmitters and two receivers, the method can find the solution with a good accuracy whereas the state-of-the-art ones cannot determine the target position and velocity.