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An Intuitive Introduction to Kalman Filter

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An Intuitive Introduction to Kalman Filter


Alex Blekhman (view profile)


23 Dec 2006 (Updated )

A simplified tutorial example to the usage of Kalman Filter

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The purpose of this tutorial is to illustrate the usage of Kalman Filter by a simple example.

The problem: Predict the position and velocity of a moving train 2 seconds ahead, having noisy measurements of its positions along the previous 10 seconds (10 samples a second).

Ground truth: The train is initially located at the point x = 0 and moves along the X axis with constant velocity V = 10m/sec, so the motion equation of the train is X = X0 + V*t. Easy to see that the position of the train after 12 seconds will be x = 120m, and this is what we will try to find.

Approach: We measure (sample) the position of the train every dt = 0.1 seconds. But, because of imperfect apparature, weather etc., our measurements are noisy, so the instantaneous velocity, derived from 2 consecutive position measurements (remember, we measure only position) is innacurate. We will use Kalman filter as we need an accurate and smooth estimate for the velocity in order to predict train's position in the future.

We assume that the measurement noise is normally distributed, with mean 0 and standard deviation SIGMA


This file inspired Learning The Kalman Filter In Simulink V2.1 and Active Contours Implementation & Test Platform Gui.

MATLAB release MATLAB 7.1.0 (R14SP3)
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Comments and Ratings (15)
03 Jan 2016 Hadas

Hadas (view profile)

very nice and simple

21 Nov 2012 Alexander

Perfect tutorial

07 Oct 2011 Alex

Alex (view profile)

This was SUPER helpful. Thanks!

23 Feb 2011 Justin Fernandes

thank you. Very helpful.

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12 Feb 2009 Alex Feinman

Clear demonstration of basic capabilities of the Kalman filter.

18 Jun 2008 dan lon


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14 Dec 2007 OnlyD Log

Helpful indeed!

03 Dec 2007 David Adam

Excellent intro tu KFiltering!

13 Oct 2007 ihsan ul haq

good tutorial for Kalman Filter.

05 Oct 2007 s k

26 Sep 2007 nuri agab


21 Mar 2007 Daniel Porta

Dimitri u always say that close all and clear all is a bad habit... explain which one is a good one then!

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09 Feb 2007 Alireza Key

it's good but i think u could add more comment and more explain ... but it's useful for every who want have quick start in Kalman Filter...
tanks alex

25 Jan 2007 Dimitri Shvorob

And anyway, what does it add to Michael Kleder's submission? (Nothing).

25 Jan 2007 Dimitri Shvorob

Correction: this is not a 'tutorial', but 'one commented program'. Of course, it can still be helpful. Note on programming: 'close all,
clear all' is bad form.

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