Extended Kalman Filter (EKF) Implementation

This document presents an implementation of the Extended Kalman Filter (EKF) algorithm. The EKF is a fundamental nonlinear state estimation technique widely employed in robotics, navigation systems, and flight control applications. This implementation includes core components such as: - State prediction using nonlinear motion models - Measurement update with Jacobian matrix calculations - Covariance propagation for uncertainty management The code structure demonstrates practical implementation aspects including: 1. System initialization with state vectors and noise parameters 2. Prediction step handling nonlinear dynamics through Taylor series approximation 3. Update step incorporating sensor measurements with partial derivatives 4. Numerical stability considerations for covariance matrices Through this implementation, users can examine how EKF linearizes nonlinear systems at each operating point using Jacobian matrices. The code provides educational value for understanding: - How to handle nonlinear state transitions and observation models - The role of process noise and measurement noise covariance matrices - Techniques for maintaining positive semi-definite covariance matrices This resource serves as both a learning tool and practical foundation for implementing EKF in projects requiring state estimation. Users are encouraged to modify parameters, test with different system models, and share improvements with the community.