An Introduction to the Kalman Filter by

Abstract

In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to ad- vances in digital computing, the Kalman filter has been the subject of extensive re- search and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient com- putational (recursive) solution of the least-squares method. The filter is very pow- erful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is un- known. The purpose of this paper is to provide a practical introduction to the discrete Kal- man filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extend- ed Kalman filter, and a relatively simple (tangible) example with real numbers & results.