Improved least-squares algorithm for TDOA/AOA-based localization

The two-stage weighted least squares (TSWLS) and constrained weighted least squares (CWLS) are used to locate mobile station with TDOA/AOA hybrid model, and they both have the same measurement matrix that become ill-conditioned when base-station present circular array distribution and Mobile-Station is close to the array center. An improved constrained weighted least square algorithm is proposed to circumvent this problem. The main strategy is to separate the mobile station coordinates and the additional variable to different sides of the linear equations, the additional variable is first solved via a quadratic equation in order to avoid the inverse operation of ill-conditioned matrix. Under the zero mean Gaussian white noise environment and the mobile station is located in or near the array center, the simulation results evaluate its localization accuracy by comparing with the existing TSWLS and CWLS algorithms as well as the Cramér-Rao lower bound.