MATLAB Implementation of Extended Kalman Filter Algorithm

In this section, I will provide a detailed explanation of implementing an Extended Kalman Filter program. First, let's revisit the fundamental concepts of the Kalman Filter. The Kalman Filter is an algorithm used for estimating system states based on dynamic models and sensor measurements. The Extended Kalman Filter extends this approach to handle nonlinear systems and non-Gaussian noise conditions. It utilizes Taylor series approximations to linearize nonlinear systems and employs Gaussian approximations to manage non-Gaussian noise distributions.

The implementation of an Extended Kalman Filter program typically involves the following key steps:

1. System Modeling: Define the system's dynamic equations and measurement equations. In MATLAB, this involves creating state transition functions (f) and measurement functions (h) that describe how states evolve over time and how measurements relate to states.

2. Prediction Step: Based on the system's dynamic model, predict the posterior distribution of the current state. This includes calculating the predicted state estimate using the state transition function and updating the error covariance matrix through the Jacobian matrix computation (using MATLAB's jacobian function or numerical differentiation).

3. Update Step: Compare measurement results with predictions and update the posterior distribution of the state. This involves computing the Kalman gain, updating the state estimate using innovation (measurement residual), and refining the error covariance matrix.

In practical applications, the Extended Kalman Filter is widely used in robotics navigation, flight control systems, and target tracking scenarios. When implementing in MATLAB, key functions include ode solvers for state propagation, matrix operations for covariance updates, and optimization techniques for handling numerical stability. This article aims to help developers better understand and apply Extended Kalman Filter programs through practical code implementation insights.