A closed-form solution for moving source localization using LBI changing rate of phase difference only

Due to the deficiencies in the conventional multiple-receiver localization systems based on direction of arrival (DOA) such as system complexity of interferometer or array and amplitude/phase unbalance between multiple receiving channels and constraint on antenna configuration, a new radiated source localization method using the changing rate of phase difference (CRPD) measured by a long baseline interferometer (LBI) only is studied. To solve the strictly nonlinear problem, a two-stage closed-form solution is proposed. In the first stage, the DOA and its changing rate are estimated from the CRPD of each observer by the pseudolinear least square (PLS) method, and then in the second stage, the source position and velocity are found by another PLS minimization. The bias of the algorithm caused by the correlation between the measurement matrix and the noise in the second stage is analyzed. To reduce this bias, an instrumental variable (IV) method is derived. A weighted IV estimator is given in order to reduce the estimation variance. The proposed method does not need any initial guess and the computation is small. The Cramer–Rao lower bound (CRLB) and mean square error (MSE) are also analyzed. Simulation results show that the proposed method can be close to the CRLB with moderate Gaussian measurement noise.