Understanding Kalman Filter - A Practical Approach with Sinusoidal Signal Implementation

This article discusses the comprehensive understanding of Kalman filtering. We will delve deeper into the principles and applications of Kalman filter, which is a mathematical model-based filtering method used for estimating system states. The algorithm finds widespread applications across various fields including aerospace engineering, robotics, economics, and biomedical engineering. The core concept of Kalman filtering involves establishing mathematical relationships between system states and observed measurements. Through continuous updating of the relationship between states and observations, it achieves more accurate state estimations. From an implementation perspective, the Kalman filter operates through two main phases: prediction and update. The prediction phase uses system dynamics to project the state forward, while the update phase incorporates new measurements to refine the estimate. Understanding Kalman filtering principles and applications is crucial for better comprehension of system modeling and state estimation methods. We can conduct Kalman filtering experiments using a simple sinusoidal signal, which allows us to observe how the filter tracks time-varying states. In code implementation, this typically involves defining state transition matrices, measurement matrices, process noise, and observation noise covariance matrices. Through practical implementation, we can better understand Kalman filter's effectiveness and limitations in real-world applications, such as its performance in handling non-linear systems or its sensitivity to noise characteristics.