Constrained Weighted Least-Squares Algorithms for 3-D AOA-Based Hybrid Localization

Source localization with time-of-arrival (TOA), time-difference-of-arrival (TDOA), time-delay (TD), received-signal-strength (RSS), or angle-of-arrival (AOA) measurements from several spatially distributed sensors is commonly used in practice. Existing analysis of the Cram $\acute{\text{e}}$ r-Rao lower bounds (CRLB) shows that a hybrid of two or more independent kinds of measurement has a lower CRLB than one individual type of measurement. This paper develops a unified constrained weighted-least squares (CWLS) algorithm for five types of hybrid localization systems: AOA and TOA (AOA/TOA), AOA and TDOA (AOA/TDOA), AOA and TD (AOA/TD), AOA and RSS (AOA/RSS), AOA, TOA, and RSS (AOA/TOA/RSS). These formulated CWLS problems only have one quadratic constraint, which can be effectively solved by the Lagrange multiplier method and root-finding algorithm. Extensive simulation results show that the proposed CWLS algorithms are superior to state-of-the-art algorithms and reach the CRLB.