Passive Multisource Tracking via Distributed Sparse Arrays: Homogeneous Data Fusion and Multivariate Adaptation

The global navigation satellite systems (GNSS) are crucial for applications such as traffic monitoring, intelligent transportation systems and advanced driver assistance systems; however, they are prone to large deviations or even failures in hidden scenarios such as urban canyons and tunnels. In this paper, we investigate a system based on distributed arrays for positioning and tracking of multiple vehicles as a supplement to the GNSS. Conventional tracking methods often assume a constant signal-to-noise ratio (SNR) across arrays; however, this assumption does not hold in dynamic, dense traffic or signal-obstructed areas where variable SNR conditions frequently arise. To address this, this paper proposes two adaptive passive position tracking methods utilizing distributed sparse arrays, which are robust to variations in SNR and capable of maintaining reliable tracking performance. The first method relies on the extended Kalman filter (EKF) algorithm, while the second employs the unscented Kalman filter (UKF) algorithm. A novel tracking system model is developed, including a multi-target state transfer equation and a fused signal equation. The unknown noise covariance and signal covariance of the fused signal are estimated using vectorization and least squares methods, respectively. Prior state information and minimum mean square error estimation are incorporated to address unknown signal challenges within the EKF and UKF frameworks. Additionally, the posterior Cramér-Rao bound provides a performance benchmark, underscoring the robustness of the proposed methods. Computer simulation studies and practical tests show that the proposed methods significantly improve computational efficiency and tracking performance in vehicle tracking, demonstrating high adaptability to noise variations compared to traditional methods.