Kalman Filter Design and MATLAB Implementation with Room Temperature Control Example

This article presents the design methodology of Kalman Filter and its implementation using MATLAB programming language. The Kalman Filter is a recursive filter based on Bayesian probability theory, widely applied in signal processing, control systems, navigation systems, and related fields. The article elaborates on the algorithmic principles of Kalman Filter, demonstrating the specific design process through a practical room temperature control example. Key implementation aspects include state-space modeling using MATLAB's matrix operations, recursive prediction-correction cycles through functions like 'predict' and 'update', and covariance matrix management for noise handling. Furthermore, the article discusses both the advantages and limitations of Kalman Filter, helping readers better understand and apply this filtering technique. The MATLAB code implementation covers essential components such as state transition matrices, measurement models, and optimal gain calculation using built-in functions for matrix inversion and multiplication. Overall, this serves as an excellent learning routine for Kalman Filter, providing significant reference value for research and practical applications in related domains. The code structure demonstrates proper initialization of state vectors, real-time filtering loops, and performance evaluation through innovation sequences and residual analysis.