Author: Zen and the Art of Computer Programming
1 Introduction
In the late 1970s, Kalman first proposed the concept of "prediction of nonlinear systems" in his doctoral dissertation. Since engineers had not yet gained the popularity of computers at that time, the previous prediction models could only simply use linear equations fit. In the late 1990s, Kalman developed a Kalman filter with Dave Greenteper and showed how to use this algorithm for prediction and control. By the early 2010s, Kalman filtering had become a widely used technique for processing data from physical systems, economic indicators, financial markets, and more.
In this blog post, I will do a more in-depth analysis and elaboration on Kalman filtering from the following three perspectives: first, what it is and why it is important; second, how it works, including the defects of traditional filters and advantages; third, build a machine learning model based on Kalman filtering and apply it in practical business.
2. Related concepts
2.1 Traditional filter
Traditional filters (such as moving average filter, moving average filter, minimum mean square error filter) refer to simple methods of estimating the current input signal from some historical input signal. Its idea is to continuously update the current state over a period of time, so that the estimate of the new input is constantly moving closer to the true value. Traditional filters have two main defects. First, they often use a certain window length, which causes the filtering effect to be affected by noise. Second, they cannot solve the problem of response delay.
2.2 Kalman filter
Kalman filter is a type of recursive prediction/observation filter. It was proposed by Kalman and Gauss in the 1960s, and it is the earliest set of algorithms for nonlinear system prediction. Its basic idea is to combine the input signal and noise of the system according to the law of motion of the system,