By utilizing time delay (TD) and angle of arrival (AOA) measurements, three dimensional (3D) target localization based on multi-input and multi-output (MIMO) radar systems is studied in this letter. For such a positioning problem, the typical closed-form solution firstly establishes pseudolinear equation and then applies the weighted least squares (WLS) to determine the final position.However, the WLS solution often suffers performance degradation when the noise is large. To alleviate this problem, the cost function of the WLS is re-represented and a quadratic constraint is imposed such that the expectation of the cost function can attain the minimum value at the true position. Moreover, simulation experiments show that the proposed method performs better than the state-of art algorithms.
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