卡爾曼濾波器之簡要理論

Abstract

中文摘要

本篇報告以較簡要的方法來探討卡爾曼濾波器(Kalman Filter)的由來以及原理探討，以最小均方誤差演算法為基礎，將卡爾曼濾波器最重要的五條式子推導出來，而其中推導過程將會使用到統計信號處理之相關內容，並且使用到有關最小均方誤差之演算法，在最後以一個簡單的例子來驗證卡爾曼濾波器的成效。而卡爾曼濾波器適合用於交通工具的導航或者飛航科技、機器人的控制、軌跡最佳化等。在這篇報告中，在驗證部分使用的是MATLAB (2018b, MathWorks®, Inc., USA)，而卡爾曼濾波器則是以副程式的方式來撰寫。而在最後結果分別依照不同雜訊的影響進行卡爾曼濾波器之性能探討。

Abstract

This paper use a brief way to explore the origin of Kalman filter and develop five important algorithms based on minimum mean-square-error algorithm. Before we develop those algorithms, you need to know some basic knowledge about statistical signal processing and minimum mean-square-error algorithm. This filter is used in a vehicle’s navigation, robot control, flying technology and trajectory optimization, where a signal trajectory can be well defined. In this paper, all of computer experiments were conducted in MATLAB (2018b, MathWorks®, Inc., USA). Kalman filter was written as a subroutine. In the result, the performance of Kalman filter is discussed according to the influence of different noise.