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.

A linear-correction method is developed for source position and velocity estimation using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The proposed technique first obtains an initial source location estimate using the first-step processing of an existing algebraic algorithm. It then refines the initial localization result by estimating via weighted least-squares (WLS) optimization and subtracting out its estimation error. The new solution is shown to be able to achieve the Cramer-Rao lower bound (CRLB) accuracy and it has better accuracy over several benchmark methods at relatively high noise levels.

In this paper, we propose a simple method to find the optimal rational function, with a fixed denominator, which minimizes an integral of polynomially weighted squared error to given analytic function. Firstly, we present a generalization of the Walsh's theorem. By using the knowledge on the zeros of the fixed denominator, this theorem characterizes the optimal rational function with a system of linear equations on the coefficients of its numerator polynomial. Moreover when the analytic function is specially given as a polynomial, we show that the optimal numerator can be derived without using any numerical integration or any root finding technique. Numerical examples demonstrate the practical applicability of the proposed method.