Implementation of Kalman Filter Program for Trajectory Filtering and Estimation

In this document, we will comprehensively discuss how to implement a Kalman filter program for trajectory filtering and estimation. We will explore the fundamental concepts and principles of Kalman filtering, accompanied by practical implementation examples. The discussion will include key algorithmic components such as the prediction step (using state transition matrices) and update step (incorporating measurement data). Additionally, we will demonstrate how to calculate estimation errors through covariance matrices and generate simulation curves to visualize filter performance. By implementing error analysis metrics like Mean Squared Error (MSE), readers will gain deeper insights into Kalman filter performance characteristics. Through this documentation, you will understand the significance of Kalman filtering in trajectory estimation and learn practical programming techniques for its implementation. Key functions such as state prediction, measurement update, and covariance propagation will be explained with code-oriented approaches. Let's begin!