Detailed Simulation and Comparison of EKF, UKF, and PF Algorithms

This algorithm implements comprehensive simulations of three prominent filtering techniques: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF). The implementation includes detailed comparisons of their performance characteristics through parametric studies. By simply adjusting parameters such as process noise covariance, measurement noise covariance, or particle count (for PF), users can observe filtering performance variations across different operational conditions. The code structure typically includes modular implementations for each filter type, with core functions handling prediction and update steps. The EKF implementation utilizes Jacobian matrices for linearization, while UKF employs sigma points to capture nonlinear transformations. The PF algorithm incorporates importance sampling and resampling mechanisms to maintain particle diversity. This comparative analysis helps researchers better understand the relative strengths and limitations of each filtering approach under various scenarios. The algorithm demonstrates practical applications across multiple domains including robotic navigation, signal processing, and sensor fusion, showcasing significant real-world implementation value through configurable simulation environments.