Estimation and Kalman Filter (KC-1): Extended Kalman Filter for Navigation Systems

This article provides an in-depth exploration of estimation theory and Kalman filtering with a focus on their practical applications in navigation systems. We begin by introducing fundamental concepts of estimation and Kalman filtering, followed by a detailed demonstration of the Extended Kalman Filter (EKF) implemented in a navigation system context. The example showcases how to apply EKF for navigation system implementation, featuring step-by-step procedures and practical code considerations.

Through comprehensive examples, we illustrate the implementation approach including state vector initialization, nonlinear system modeling using Jacobian matrices, and the recursive prediction-update cycle characteristic of Kalman filters. The discussion covers practical challenges such as handling nonlinear system dynamics through linearization techniques, managing sensor noise covariance matrices, and ensuring numerical stability during matrix operations.

Key algorithmic components addressed include the EKF's two-phase process: prediction phase (using system dynamics model) and update phase (incorporating sensor measurements). We examine critical functions for calculating state transitions, measurement predictions, and Kalman gain optimization. Readers will gain understanding of estimation principles, Kalman filter mechanics, and practical techniques for solving real-world navigation system problems, along with implementation insights for managing computational efficiency and accuracy trade-offs.