This paper proposes an improved closed-form method for moving source localization using time difference of arrival (TDOA), frequency difference of arrival (FDOA) and differential Doppler rate measurements. After linearizing the measurement equations by introducing three additional parameters, a rough estimate is obtained by using the weighted least-square (WLS) estimator. To further refine the estimate, the relationship between additional parameters and source location is utilized. The proposed method gives a final closed-form solution without iteration or the extra mathematics operations used in existing methods by employing the basic idea of WLS processing. Numerical examples show that the proposed method exhibits better robustness and performance compared with several existing methods.

This paper proposes a moving source localization method that combines TDOA, FDOA and doppler rate measurements. First, the observation equations are linearized by introducing nuisance variables and an initial solution of all the variables is acquired using the weighted least squares method. Then, the Taylor expression and gradient method is applied to eliminate the correlation between the elements in the initial solution and obtain the final estimation of the source position and velocity. The proposed method achieves CRLB derived using TDOA, FDOA and doppler rate and is much more accurate than the conventional TDOA/FDOA based method. In addition, it can avoid the rank-deficiency problem and is more robust than the conventional method. Simulations are conducted to examine the algorithm's performance and compare it with conventional TDOA/FDOA based method.