MATLAB Implementation of Kalman Filter Algorithm with Recursive Code

This article provides a detailed guide on implementing Kalman filter recursive algorithm using MATLAB. The Kalman filter is an optimal estimation algorithm that combines system models with measurement data to estimate dynamic system states. We will explain both the theoretical foundation and practical MATLAB implementation with code examples. First, we introduce the fundamental principles of Kalman filtering. As a recursive algorithm, it utilizes previous state estimates and new measurements to compute current state estimates. Based on Bayesian theory, the algorithm optimally combines predictive models with observational data. Key implementation steps include state prediction using system dynamics equations and measurement update incorporating sensor data. The filter finds extensive applications in navigation systems, control engineering, and signal processing. Next, we demonstrate MATLAB implementation techniques. MATLAB provides powerful numerical computation capabilities and specialized toolboxes (such as Control System Toolbox) that simplify Kalman filter development. We will explain key MATLAB functions including: - kalman(): For designing discrete-time Kalman filters - predict(): For state prediction step implementation - correct(): For measurement update operations The implementation involves defining system matrices (A, B, C), covariance matrices (Q, R), and handling recursive loops for real-time processing. In summary, this article comprehensively covers Kalman filter theory and MATLAB implementation methodology. Readers will gain understanding of core concepts like state-space modeling, covariance propagation, and recursive estimation, enabling them to develop functional Kalman filter algorithms in MATLAB for various engineering applications.