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.