EKF and UKF for Bearing-Only Target Tracking

In the field of target tracking, bearing-only tracking represents a classic passive localization problem. The core challenge lies in estimating a target's motion state using limited angular observation data (such as azimuth measurements from radar/sonar systems). Since the observation model exhibits strong nonlinear characteristics, traditional Kalman Filter (KF) cannot be directly applied, making Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) the mainstream solutions. EKF performs local linearization of nonlinear models through first-order Taylor expansion, making it suitable for weakly nonlinear scenarios. The implementation typically involves these key steps: state prediction using the process model, linearization of the observation model through Jacobian matrix calculation, and Kalman gain computation for state update. However, linearization errors in highly nonlinear systems (such as scenarios with low observation frequency or large bearing change rates) can lead to estimation bias or even filter divergence. UKF employs the Unscented Transform to directly approximate nonlinear distributions by propagating carefully selected sigma points through the nonlinear functions. This deterministic sampling approach avoids Jacobian matrix calculations and demonstrates better robustness for strongly nonlinear systems (like close-range target maneuvers). The UKF implementation involves: generating sigma points around the current state estimate, propagating these points through both process and observation models, and reconstructing the Gaussian distribution from the transformed points. While more computationally intensive than EKF, UKF typically provides superior performance for severe nonlinearities. Practical implementation considerations include: Observability issues - Single-station bearing-only tracking suffers from range-velocity ambiguity, which can be mitigated through multi-station cooperation or motion constraints; Initialization strategies - Due to missing range information, initialization typically requires multiple time-step observations or assumed initial range distributions; Maneuvering target handling - Integration with Interactive Multiple Model (IMM) framework can enhance adaptability to abrupt motion changes. The IMM implementation would involve multiple model filters running in parallel with mode transition probabilities. Code implementation typically requires careful attention to coordinate transformations, numerical stability in covariance matrix operations, and proper tuning of process and measurement noise parameters for optimal performance.