Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements

By utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of signals received at a number of receivers, a constrained least-square (CLS) algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of convolute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time implementation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square (WLS) approach especially for higher measurement noise level.