Particle Filter in Target Tracking with 100 Monte Carlo Simulations

Particle filter is a probability-based nonlinear filtering method widely used in target tracking applications, particularly effective in non-Gaussian noise environments. Conducting 100 Monte Carlo simulations helps validate the algorithm's stability and robustness. Implementation Approach Particle Initialization: Randomly distribute particles within the target's potential occurrence area using uniform sampling. Each particle represents a potential target state (e.g., position, velocity) initialized through random number generation. State Prediction: Update particle states using motion models (constant velocity or constant acceleration models) with added process noise to simulate uncertainty. Code implementation typically involves state transition matrices and noise covariance matrices. Weight Calculation: Compute likelihood probabilities for each particle based on observation data (e.g., sensor measurements). Weight update utilizes measurement models and probability density functions, where higher weights indicate better alignment with the true state. Resampling: Reselect particles proportionally to their weights using algorithms like systematic resampling or multinomial resampling to prevent particle degeneracy (where most particles have negligible weights). State Estimation: Output tracking results by calculating the weighted average of all particle states or selecting the particle with maximum weight. Simulation Analysis Trajectory Plot: Compare the estimated trajectory (particle mean or maximum-weight particle) against the ground truth trajectory to visually assess tracking performance. Implementation involves plotting functions and trajectory overlay comparisons. Error Curve: Statistical analysis of position errors (e.g., Euclidean distance) per simulation, plotting Mean Squared Error (MSE) curves or cumulative error distributions to quantify algorithm accuracy. Code implementation requires error calculation and statistical visualization libraries. Extension Considerations If error curves show high volatility, adjust particle numbers or resampling strategies (e.g., implement systematic resampling). For nonlinear observation models, incorporate Unscented Transform (UKF) to improve particle proposal distributions through sigma point propagation.