Alpha-Beta Kalman Filter: A Classic Implementation of Constant-Gain Kalman Filtering

This article presents a typical case study of constant-gain Kalman filtering, providing a detailed explanation of its working principles and application scenarios. We begin by exploring the fundamental concepts and advantages of Kalman filters to establish a solid foundation for understanding constant-gain implementations. The mathematical model and computational formulas are then introduced with practical code implementation considerations, including key functions for state prediction and measurement updates. Specifically, we discuss the implementation of prediction steps using state transition matrices and the update mechanism incorporating measurement residuals with constant gains. Finally, we examine practical limitations and potential enhancements for constant-gain Kalman filters, addressing computational efficiency trade-offs and adaptive filtering alternatives to help readers understand both current limitations and future development directions in this technology.