When I first studied Kalman filtering, I saw many advanced signal processing submissions here at the MATLAB Central File exchange, but I didn't see a heavily commented, basic Kalman filter present to allow someone new to Kalman filters to learn about creating them. So, a year later, I've written a very simple, heavily commented discrete filter.

Excellent resource for those of us who are new to Kalman filtering. Thank you! What if the state of my system is given by a vector rather than a scalar? Can Kalman filtering work in n dimensions? If I want to train the filter on one set of data and then apply it to another, how would I do that? What if my observations are a sum of two or more signals, plus noise? How do I "tell" the Kalman filter which of the signals I want it to estimate?

Very nice implementation. But there is a minor mistake in the Kalman filter block. In propagation equation, 1/Z must be placed in somewhere else. We have P(k+1) = A.P(k).A' + Q. after this part we have to put 1/z to get P(k).

In other words, how to draw their values, provided they are stored in my data.mat?
Will the "plot" are the same and I have to use a loop "for"?
Ask directly about the code sample, it's here I deal with a couple of hours.

I am new to k. filtering, and I don't understand the following: the covariance matrix P appears to be only a function of the following inputs: A (defined by the system), P (itself), Q (known p.noise cov.), and H (typically identity), and also the Kalman gain K. K itself is a function only of P, H, and R (known m.noise cov.).

None of these are re-defined during iteration except P. How then is the estimate of the covariance matrix P tied to observations z? The result of this appears to be that the Kalman gain explodes by the third or fourth iteration, making the output mirror the noisy input. This seems to be what Enver Bahar is noticing too, I think.

Nicely documented.
As a practicing engineer I would never use the implementation shown. This is the standard covariance form of the Kalman filter. In operation the statement
s.P = s.P - K*s.H*s.P;
causes significant issues. s.P needs to always be positive definite but with rounding this will tend to violate this assmption making the Kalman filter 'blow up' over time or with poorly conditioned data.

The alternative is to process in the square root domain where the P matrix is expressed as a P=Psr'*Psr. Therefore the resuting matrix must always be positive definite and does not have this issue. An added advantage is the precision is doubled processing in this domain and can be similar to the input data resolution rather than 2x the number of bits to provide comparable precision.

For more information see
'Linear estimation' Kailath, Sayed, Hassibi or
'adaptive filter thoery' Haykin

IMHO one should always to filtering in the SR domain. There are also advantages of processing with separated real/imag data rather then complex if the underling data is complex.

But, I have a simple question, why results don't change when we give very high measurement noise?
You gave standart deviation as 2 in your example, but when I make it for example 1000, it estimates perfectly. Doesn't supposed to change?

Can anyone explain this to me?
Thanks a lot
-Enver

Good commenting, byt unfortunately, the code is wrong in several places. It absolutely does not handle vector inputs and some inputs that are defined as optional will cause the program to crash if they are not provided. From a file that is top ranked on the file exchange, I expected alot more.

Very clean example of KF, but not general enough to deal with state vectoc. For example, s.x = inv(s.H)*s.z; and s.P = inv(s.H)*s.R*inv(s.H') would not work if number of state and number of measurement are not the same.

I have solved the problem by modifying the line to;

>> s.x = s.x + K' * (s.z-s.H*s.x); %added transpose of K

This was required as my observance vector (z) was a 2X1 matrix(and so is K and hence they couldn't be multiplied). Although the calculation now works I am still wondering why it doesnt work with the original code.

I get an error during the correction step.
>> s.x = s.x + K*(s.z-s.H*s.x);

Error using==>mtimes
Inner matrix dimensions must agree

The error makes sense given the size of my matrices but I don't see how they could be wrong. Is this code expected to not work for a system with two observer inputs (position and speed)?

Thanks for the help!
ps: let me know if you need more info - tried to keep it short.

is there anyone got the right solution in learning Kalman Filter.
Could you email file.m to me, rmzaidi8@gmail.com
I've run the file given but have alot error.
Please help me.
Thank.

Nice comments. Awful numerics. Why would you consider multiplying by the inverse? That's horribly inaccurate and slow. Replace

x = inv(H)*z
P = inv(H)*R*inv(H')

with, at least

x = H\z
P = (H\R)/H'

likewise

K = P * H' * inv (lots of stuff)

should be

K = P * H' / (lots of stuff)

further more, if H is not changing, it should be factorized just once and the factors kept (LU or CHOL).

13 Jul 2008

Vipin Gupta

Thanks for sharing. :)

03 Jul 2008

Imtiaz Hussain

Very Useful Indeed

19 Jun 2008

Sid Saraiya

This was extremely useful for a beginner like me. A great post!

03 Jun 2008

Behnam Molaee Ardekani

Good for those who want to see what the Kalman Filter is for the first time.
It works and there is a simple example in the m file.

27 Apr 2008

Sahil Ganguly

I keep getting this error,can someone explain what i'm doing wrong?

kalmanf ??? Input argument "s" is undefined. Error in ==> kalmanf at 150 if ~isfield(s,'x'); s.x=nan*z; end

22 Apr 2008

bekir pasaoglu

great

03 Mar 2008

mohamed pumma

ok

25 Jan 2008

Yi Cao

This is a very popular file in the File Exchange. The function itself is excelent. However, I just noticed that the example provide with the file is not correct. Somehow, it is misleading to beginers.

In line 131, the process is defined as:
true(end+1) = randn*2 + 12;
i.e. the state is a constant plus a noise. If so, the process in the standard state space form should be:
x(k+1) = 0 * x(k) + 12 + w(k)
i.e. s.A = 0; s.B = 1; s.u = 12;
However, in the file it is wrongly defined as:
s.A = 1; s.B = 0; s.u = 0;
The difference is that the process noise is not dynamically cumulated in the former definition but does in the later.

04 Jan 2008

marc luc

31 Dec 2007

James Hokanson

27 Dec 2007

Arsalan Khan

I can understand Kalman filter from this document, I bet anyone can.

28 Nov 2007

Randy Coleman

27 Nov 2007

wang yi

very good

06 Nov 2007

P. McNamara

Be careful. Also we are looking at your downloads records.

19 Oct 2007

djeunang brigitte

i want a kalman filter

05 Oct 2007

Utkarsh Gaur

04 Oct 2007

Duong Minh Au

11 Jul 2007

hamid reza ghazizadeh

how con I find calculation of dry gas filter
for natural gas ? please

14 Jun 2007

X. King

10 Jun 2007

sk imtiaj

this is very good

07 Jun 2007

Bouchemmella abdelhalim

I want this refference

29 May 2007

mehmet ali arabaci

Actually, I am not a beginner at Kalman filter issue. But, i think this is a very useful tool and i wish i got this m-file when i first started to work with Kalman. Because, it is very important for the beginners to have the simplest form of the problem and to see its solution with a simulation program.

23 May 2007

SOURAV DAS

It is a very user friendly, recommended

15 May 2007

Edward Taylor

Very easy to use, recommended.

09 May 2007

zhu Yi Yong zhuyiyong

very good

29 Apr 2007

Rodrigo Badínez

Good demo.
You probably should separete the example, to another m file, named like RunMeDemoKalman.
For the really beginners.

26 Apr 2007

lai zuomei

a good demo for me!

25 Apr 2007

xu zheng

very good tools
thank you very much

29 Mar 2007

Rajesh Krishnan

28 Mar 2007

fatemeh shoormij

discrete kalman filter

13 Mar 2007

v ram

13 Mar 2007

Way Jch

08 Jan 2007

u v

11 Dec 2006

karim kiko

It will be better if you separate the comment from the m.file and try to add them as "help" in a pdf format.

30 Nov 2006

ravindar reddy

14 Nov 2006

Tansel Yucelen

Same Error !!!

01 Nov 2006

MORSHED MAHMUD

29 Oct 2006

Priyanka Gupta

I get the same error:

kalmanf
??? Input argument "s" is undefined.

Error in ==> kalmanf at 150
if ~isfield(s,'x'); s.x=nan*z; end

26 Oct 2006

clayonjj Harrison

i like the explanation but I cant run the file the following error pops up.HELP!!

kalmanf
??? Input argument "s" is undefined.

Error in ==> kalmanf at 150
if ~isfield(s,'x'); s.x=nan*z; end

17 Oct 2006

shao litang

I need Kalman Filter program.

27 Aug 2006

diop bara

good

15 Aug 2006

Colin O'Flynn

Thank You! Great introduction to the Kalman filter, even if you don't use Matlab.

14 Jun 2006

ti toe

you have to set up matlab first and run with workspace

26 Apr 2006

Bing Li

try to replace inv(A)*B by A\B to speed up, although it's not significant when the matrix size is small

23 Apr 2006

Teo chai

I try to run the "learning the kalman filter" in the matlab but i unable to run it.
May i know how to run the file? thks

13 Apr 2006

Indiana Jones

06 Apr 2006

Carlos Orduno

The best source I've found to start working with Kalman Filters. Do you have anything for the nonlinear version?

29 Mar 2006

Camilo Lozoya

22 Feb 2006

swami nathan

15 Feb 2006

Franz Dietrich

Useful Comments in Code.

09 Feb 2006

Eduardo Veras

20 Jan 2006

akher falcon

its great.

13 Jan 2006

Xuewu Dai

Very Useful for understanding Kalman Filter

12 Jan 2006

Carlos Roldan

07 Jan 2006

Robert Kaddu

Very well presented summary that makes more sense than that provide within the Matlab help function.

07 Jan 2006

ALEXANDRE EDUARDO

VERY GOOD

25 Dec 2005

Mehdi Sanaatiyan

Well,it's good for first time.No at all

20 Nov 2005

Rafal G.

Simple, pretty, excellent :-))) Thanks a lot!!

15 Nov 2005

nemesio CARDENAS LOPES

ok

29 Oct 2005

Zahid Ullah Khan

Its nice, no doubt.

21 Oct 2005

shobi kumar

excellent apporach
but i m unable to run this prog
plz help me

03 Aug 2005

Tsanko Tsankov

A good try to explain something. Keep up the good work! There are, however, some mistakes (at the autoinitialization step). Anyway I still don't quite understand the use of Kalman filter. The given example is good, but I'm still confused how to apply this filter to my data.

10 Jul 2005

ammar saleem

08 Jul 2005

Rentian Xiong

Nice work. It would be better if there is an example for vector state. Also it would be very cool if someone can put Kalman filter algorithm in simulink so that we can see the estimation of states dynamically. And of course, an extended kalman filter for nonlinear system would be also very useful.

30 Jun 2005

lee yk

Would you like to give me sample 's' value?
I still don't understand it perfectly.

29 Jun 2005

Tim Gebbie

Very fun. Very neat.

16 Jun 2005

Flop Flop

19 May 2005

ARLINDA SAQELLARI

very good, I like the idea

30 Mar 2005

Daniel O. Fufa

very good
Thanks Daniel
Aalborg university

23 Mar 2005

Nathir Rawashdeh

This is a very good example and shows how easy it is to apply the Kalman filter. It does, however, require some background knowledge. It would be nice to have a more complicated example with non-zero u and where H and A are not =1. Thanks Michael!

23 Mar 2005

Liu Baolong

You are a great tutor !
I really appreciate it .
Thank you very much.

25 Jan 2005

ARLINDA SAQELLARI

21 Jan 2005

Giuliano Scimone

14 Jan 2005

Simon Tippler

Very helpful. Thanks!!

11 Jan 2005

Hooman Dejnabadi

29 Nov 2004

Thomas Byrne

Excellent!! Thank You.

05 Oct 2004

Vassilios Moussas

Compact, well documented, very good initialization and use of structures.