Weighted least squares target location estimation in multi-transmitter multi-receiver passive radar using bistatic range measurements

This study proposes a weighted least squares method to determine the position of an individual target in the presence of multiple transmitters and multiple receivers from time difference of arrival measurements. The method is based on the intersection of the ellipsoids defined by bistatic range measurements from a number of transmitters and receivers. The solution is derived from the minimisation of the weighted equation error energy. In addition, the method requires no initial guess of the solution to find the target location. A weighting matrix is obtained in two different conditions in order to generate a substantial improvement in the performance of the method, which one of them leads to an approximate maximum-likelihood estimator and the other one results in a best linear unbiased estimator. A detailed theoretical error analysis associated with this method is presented and the Cramer-Rao lower bound is also derived. Simulations are included to examine the algorithm's performance and corroborate the theoretical developments.