In this article, a constrained weighted least-squares (CWLS) problem with two quadratic constraints for hybrid angle of arrival (AOA), time difference of arrival (TDOA), and received signal strength (RSS) localization is formulated. The Lagrange multiplier method cannot be efficiently used in this situation, so we provide four methods to solve the CWLS problem: 1) weighted least-squares (WLS); 2) iterative CWLS (ICWLS); 3) Lagrange multiplier method combined with Newton’s method (LMM+NM); and 4) semidefinite programming (SDP). Furthermore, to obtain a good balance between accuracy and computational burden, we develop a fixed point iteration (FPI)-based algorithm that is derived from an approximate maximum likelihood estimator (MLE). Simulation results show that the accuracy of the proposed FPI method is better than the other four methods; besides, its computational burden is one in ten of the SDP algorithm.