Principles of Classical One-Dimensional Kalman Filtering

This program introduces the fundamental principles of classical one-dimensional Kalman filtering. Kalman filtering represents a linear time-invariant algorithmic approach that compares observed measurements with predictions generated by mathematical models (such as physical systems). The algorithm effectively filters observational data by removing unwanted noise, thereby enhancing both data accuracy and reliability. A critical application of Kalman filtering occurs in missile guidance systems, where it demonstrates exceptional capability in target tracking and trajectory prediction. The implementation typically involves two main phases: prediction and update. During the prediction phase, the algorithm projects the current state estimate forward using system dynamics models, while the update phase incorporates new measurements to refine these predictions. Key mathematical components include state transition matrices, observation matrices, and covariance calculations for both process and measurement noise. The recursive nature of the algorithm allows for efficient real-time processing with minimal computational overhead. This program provides practical MATLAB/Octave code examples demonstrating how to initialize filter parameters, implement prediction-update cycles, and visualize filtering results. Through this hands-on approach, you'll gain insights into tuning parameters like process noise covariance (Q) and measurement noise covariance (R) for optimal performance. We hope this implementation inspires you to apply these techniques effectively in your practical engineering applications.