Underwater multi-sensor passive tracking faces two critical challenges: the strong nonlinearity of Doppler–bearing measurements and underwater acoustic propagation delays. To address these issues, this paper proposes a distributed fusion filtering method based on extended measurement space modeling and delay compensation. First, an extended measurement space comprising range, Doppler frequency, bearing, and bearing rate is constructed to transform the nonlinear measurements into a linear framework. Within this space, linear prediction equations for constant velocity (CV) motion are derived to facilitate linearized local filtering. Furthermore, a closed-form linear solution for propagation delay is established within the constructed state space. To resolve the incompatibility of multi-node estimates caused by local coordinate frame discrepancies, a distributed architecture based on the Unscented Transform (UT) is designed. In this architecture, local states are transformed into a unified Cartesian coordinate system for temporal compensation and fast Covariance Intersection (FCI) fusion, followed by an inverse mapping back to the local space. Simulation results demonstrate that, compared with traditional nonlinear methods based on mixed coordinate systems, the proposed method significantly reduces nonlinear approximation errors, thereby enhancing tracking accuracy and robustness.
Zhang et al. (2026) studied this question.