Target Localization and Tracking Using Single Sensor: EKF and UKF Algorithms with CA and IMM Models

This article explores methodologies for target localization and tracking using a single sensor. We introduce two widely adopted filtering algorithms: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), implemented under both Constant Acceleration (CA) and Interacting Multiple Model (IMM) dynamic models. The EKF algorithm linearizes nonlinear systems using first-order Taylor expansion, while UKF employs sigma point transformation for more accurate nonlinear state estimation without derivative calculations. The IMM framework enhances adaptability by probabilistically switching between multiple motion models (e.g., CA, CV). We analyze the trade-offs between computational complexity and estimation accuracy, providing practical examples with MATLAB/Python code snippets demonstrating state prediction, measurement update, and covariance management. Performance optimization techniques include adaptive noise tuning and model probability initialization. Implementation guidelines cover crucial functions like ukf_predict for sigma point propagation and imm_update for model transition logic, aiding engineers in real-time sensor fusion applications.