A closed-form weighted least squares method for finding a target position in the presence of multiple transmitters and multiple receivers from time difference of arrival (TDOA) measurements is proposed. The method is based on the intersection of the ellipsoids defined by bistatic range (BR) measurements from a number of transmitters and receivers. The localization formula is derived from the minimization of the weighted equation error energy. To produce a substantial improvement in the performance of the method, a weighting matrix is derived in two different conditions, which one of them leads to an approximate maximum likelihood (ML) and the other one results in a best linear unbiased estimator (BLUE). Numerical simulations are included to support and corroborate the theoretical developments.