Three Advanced Nonlinear Filtering Methods: Detailed EKF, UKF, and PF Simulation

In the domain of state estimation and filtering, Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) represent three widely adopted nonlinear filtering methodologies. This simulation experiment demonstrates their performance variations under different conditions through parameter adjustments, providing users with intuitive insights into their respective application scenarios, strengths, and limitations.

EKF operates by linearizing nonlinear systems through first-order Taylor series approximations, making it suitable for mildly nonlinear systems. The implementation typically involves calculating Jacobian matrices for state transition and observation models. However, its performance may degrade under highly nonlinear systems or strong noise conditions due to linearization errors.

UKF employs unscented transformation to handle nonlinearities more accurately, using carefully selected sigma points to propagate system states through nonlinear functions. This approach eliminates Jacobian matrix calculations while maintaining second-order estimation accuracy. The core implementation involves sigma point generation, nonlinear propagation, and weighted mean/covariance reconstruction.

PF utilizes Monte Carlo methods with sequential importance sampling, representing probability distributions through numerous particles. Each particle carries a weight updated through resampling techniques like systematic resampling or stratified sampling. This method excels in highly nonlinear or non-Gaussian systems but requires substantial computational resources for effective particle management and weight normalization.

The simulation allows users to adjust parameters including noise intensity, system nonlinearity degree, and particle count (for PF). Users can observe comparative performance in convergence speed, estimation accuracy, and robustness. The flexible comparison framework assists engineers and researchers in selecting appropriate filtering algorithms for practical applications, with code modules demonstrating parameter tuning interfaces and real-time performance metrics visualization.