Abstract: To address the limitations of conventional multi-station time difference of arrival (TDOA) and frequency difference of arrival (FDOA) passive localization, which require high time-frequency synchronization accuracy and large data transmission bandwidth, making them difficult to adapt to ultra-low sidelobe emitters, as well as the drawbacks of multi-station direction of arrival (DOA) passive localization, which demands high channel consistency in direction-finding systems and involves complex system structures, this paper proposes a passive localization system using multiple-baseline interferometer phase difference rate with multiple moving observers. By exploiting the mathematical characteristics of the phase difference rate measured by multiple-baseline interferometers, a four-stage closed-form localization method is developed. In Stage 1, the phase difference rate measurements obtained from the multiple-baseline interferometer of each observer are used to obtain intermediate variables related to azimuth and its rate of change via weighted least squares (WLS). In Stage 2, the azimuth and its rate of change are derived through nonlinear transformation. In Stage 3, a weighted pseudo-linear least squares (WPLS) approach is employed to obtain the position estimate of each observer. To mitigate the estimation degradation caused by the correlation between the pseudo-linear observation matrix and the observation vector, a weighted instrumental variable (WIV) is introduced to enhance estimation performance. In the final Stage 4, the position estimates from all observers are fused with weights to obtain the final emitter location estimate. The proposed method requires no initial value, exhibits high robustness, and has low risk of convergence failure. Through mean square error (MSE) analysis, it is shown that under Gaussian observation noise, the proposed method can approach the Cramér-Rao lower bound (CRLB) of localization error. Simulation results validate the effectiveness of the proposed method.

Key words: passive localization, multiple-baseline interferometer, phase difference rate, pseudo-linear least squares, weighted instrumental variable