Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) for Bearing-Only Target Tracking

This article provides an in-depth exploration of Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) implementations for Bearing-Only Target Tracking systems. This technology is widely applied in target tracking applications where only angular measurements are available. Both EKF and UKF are sophisticated filtering methods that recursively estimate target position and velocity states through prediction and update cycles. Bearing-Only Tracking represents a specialized tracking approach that utilizes only the azimuth/elevation angle measurements from sensors while excluding distance information. This methodology proves particularly valuable in scenarios including: autonomous target tracking, navigation systems, and robotic applications where range data may be unavailable or unreliable. The EKF implementation typically involves linearizing nonlinear measurement models using Jacobian matrices, while the UKF employs a deterministic sampling approach (sigma points) to better handle nonlinearities without requiring derivative calculations. Key algorithmic components include state transition models, measurement functions, and covariance propagation. We will examine implementation details for both filters, including initialization procedures (x0, P0), measurement update steps, and state prediction mechanisms. Practical considerations such as observability analysis, consistency checks, and tuning parameters (Q, R matrices) will be discussed to ensure robust performance across various operational scenarios including underwater tracking, airborne surveillance, and mobile robotics applications.