Kalman Filter Design with MATLAB Implementation

The Kalman filter is an efficient recursive state estimation algorithm widely applied in signal processing and control systems. This article demonstrates the complete design process and MATLAB implementation approach through a practical room temperature control case study.

The Kalman filter consists of two main phases: prediction and update. In room temperature control applications, the first step involves establishing a state-space model comprising state equations and observation equations. The state variable typically represents room temperature, while control input may correspond to heater power. Code implementation requires defining system matrices (A, B, C, D) that mathematically describe the thermal dynamics.

During the prediction phase, the filter estimates the current state based on the previous state estimate and system model. Accounting for real-world process noise, the algorithm simultaneously computes the covariance matrix of the predicted state. MATLAB implementation involves matrix operations for state prediction: x_pred = A*x_prev + B*u and covariance prediction: P_pred = A*P_prev*A' + Q, where Q represents the process noise covariance.

In the update phase, the filter combines the predicted state with new temperature measurements using the Kalman gain to balance confidence between predictions and measurements. This gain matrix determines whether to trust model predictions or actual sensor readings more heavily. The MATLAB calculation involves: K = P_pred*C'/(C*P_pred*C' + R), where R denotes measurement noise covariance, followed by state update: x_update = x_pred + K*(z - C*x_pred) and covariance update: P_update = (I - K*C)*P_pred.

Key MATLAB implementation considerations include proper initialization of state vectors and covariance matrices, along with accurate modeling of process and measurement noise statistics. In room temperature control, process noise may stem from heater power fluctuations, while measurement noise arises from temperature sensor accuracy limitations. Developers should use empirical data or system specifications to determine appropriate Q and R matrices.

Through this practical example, learners can deeply understand how Kalman filters achieve optimal estimation through iterative computations and their application to real engineering problems. The room temperature control case proves particularly suitable for beginners due to its intuitive physical meaning and relatively straightforward parameter configuration.