JPDA Probability Data Association and Kalman Filter Implementation for Target Tracking

This implementation demonstrates JPDA (Joint Probabilistic Data Association) combined with Kalman filtering for tracking two targets performing constant velocity linear motion in the x-y plane, with added noise to motion positions. The targets start from initial positions (4000,1200) and (300,1500) with respective velocities of (200,200) and (400,200). The sensor measures position states with a sampling interval T=1 for n=80 data points. The system configuration includes a detection probability of 1, where correct measurements fall within the tracking gate with probability 0.99. Clutter is modeled with uniform distribution density of 2/km², generated using the RAND function producing uniformly distributed random variables in the range [0,1]. The tracking gate threshold is maintained at 9.21 to ensure accurate and reliable target tracking performance. Key implementation aspects include: - Kalman filter implementation for state prediction and update cycles - JPDA algorithm for handling measurement-to-track association probabilities - Gate validation using Mahalanobis distance with the 9.21 threshold - Clutter generation and management using uniform random variables - Constant velocity motion model implementation for state transition - Measurement noise modeling and covariance management - Track maintenance and data association probability calculations The code structure typically involves initialization of target states, prediction steps using state transition matrices, measurement validation gating, JPDA probability calculations, and Kalman filter update steps incorporating associated measurements.