Multi-Target Tracking with MM-GMPHD Algorithm

The MM-GMPHD algorithm is an efficient method for multi-target tracking, particularly suitable for dynamically estimating target counts and observations in complex scenarios. Based on the Gaussian Mixture Probability Hypothesis Density (GMPHD) filter and combined with Multiple Model (MM) concepts, this algorithm can handle variations in target motion patterns.

In the given scenario, five targets generated at different time instances are tracked through the following MM-GMPHD implementation steps:

Target Model Initialization: For each potential target motion pattern (e.g., constant velocity, acceleration, or turning maneuvers), assign corresponding dynamic models and initialize Gaussian mixture components. Code implementation typically involves defining model transition probabilities and initializing covariance matrices for each motion mode.

Prediction Phase: Using prior states, predict future target positions through multiple models. Each Gaussian component undergoes state and covariance prediction according to its associated motion model, while incorporating target survival probabilities. The prediction step can be implemented using Kalman filter equations for each model branch.

Update Phase: Correct predictions using current observations (e.g., sensor measurements). Through data association and likelihood computation, update weights for each Gaussian component while pruning low-probability false targets. This involves gating techniques and probabilistic data association to handle measurement uncertainty.

Target Count Estimation: Calculate the current target count based on the total weight of updated Gaussian mixture components, extracting high-weight components as valid targets. The expected number of targets is computed as the sum of all mixture weights, with thresholding applied for target extraction.

Model Switching and Merging: Dynamically adjust target motion models and merge similar Gaussian components to reduce computational complexity while maintaining tracking continuity. Implementation requires model probability updates and mixture component management using distance metrics like Mahalanobis distance.

The MM-GMPHD algorithm's advantages include computational efficiency and adaptability to changing target counts, making it suitable for cluttered environments with missed detections. For the five targets at different time instances, the algorithm effectively estimates their states and maintains stable tracking trajectories through probabilistic multi-model handling.