Basic Kalman filter, heavily commented, for beginners to Kalman filtering.
371 Downloads
Updated 12 Oct 2005
No LicenseWhen 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.
john lewis (view profile)
Angel Fernandez (view profile)
IMHO this kalmanf(s) is wrong.
It should be as posted below. That gives good results.
function s = kalmanf(s)
%step 1: Compute Kalman gain factor:
K = s.P*s.H'*inv(s.H*s.P*s.H'+s.R);
%step 2: Correction based on observation:
s.x = s.x + K'*(s.z-s.H*s.x);
%step3: update error
s.P = s.P - K*s.H*s.P;
return
Meysam Tavakoli (view profile)
I have started to work on application of Kalman filter to estimate parameters. My question is a little strange:
we have a simple system with 2 states (x, y) and 2 rates (K1, K2).
our equations are:
dx/dt = - K1*x + K2*y
dy/dt = K1*x - K2*y
Z(x)=a*x
Z(y)=b*y
and I am looking for the parameters (a, b, K1, K2)
also we have the actual data points for the Z(x) and Z(y)
How do I can solve this problem with Kalman filter?
Hao Li (view profile)
thank you for sharing
HEC (view profile)
hello,
I put a vector of observations with noises and I got an error message :
Undefined function or variable 'z'.
Error in kalmanf (line 150)
if ~isfield(s,'x'); s.x=nan*z; end
can someone help me please
Chengcheng Zhou (view profile)
Thanks a lot!
Lyudmil Vladimirov (view profile)
Perparim, this is a common mistake of trying to define an M-function inside an M-script. Have a look at the explanation here:
http://uk.mathworks.com/matlabcentral/answers/18401-please-help-error-function-definitions-are-not-permitted-in-this-context
What I am guessing you tried to do is simply un-comment the example code and run the file. Instead, copy/cut and paste the code within the brackets in a new script and try running that instead. Hope this helps!
Perparim Fetahi (view profile)
Hello, I am getting the following error, can anyone tell me what is the issue?
Error: File: kalmanf.m Line: 147 Column: 1
Function definitions are not permitted in this context.
Evan Lucas (view profile)
Nguyen Manh Tuong (view profile)
Please! Give me a example of kalmanf function.
sami omar (view profile)
hey guys,
Im new to matlab, Im trying to implement Kalman filter with sin wave is that possible?
Auralius Manurung (view profile)
Line 173, file kalmanf.m
s.P = s.A * s.P * s.A' + s.Q;
this is wrong, it should be:
s.P = s.A * s.P * s.A' + s.B * s.Q * s.B';
the example is also misleading, see cooment by Yi Cao (25 Jan 2008) since be should not be = 0 but B should be = 1.
Xiang CAo (view profile)
Yiman (view profile)
thank you,I like it
kushwinder singh (view profile)
its very helpful
venugopal kulkarni (view profile)
Carlos M. Velez S. (view profile)
A good complement of linear Kalman filter in Simulink: http://www.mathworks.com/matlabcentral/fileexchange/46407-linear-kalman-filter-in-simulink
Koranit (view profile)
Koranit (view profile)
Angel Lopez (view profile)
very useful!! Thanks a lot.
anthony (view profile)
how do i view the document
Aaron Schurger (view profile)
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?
liliaceae (view profile)
nice documentation and easy to understand.
liliaceae (view profile)
Aliakbar Alamdari (view profile)
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).
jakub (view profile)
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.
jakub (view profile)
My case:
>> clear s
>> s.x = 12;
>> s.A = 1;
>> s.Q = 2^2;
>> s.H = 1;
>> s.R = 2^2;
>> s.B = 0;
>> s.u = 0;
>> s.x = nan;
>> s.P = nan;
>> s.z = [1 2 3 4 5 6 7 8 9 22 3 4 5 6 7 8 88];
>> kalmanf(s);
>> figure
>> hold on
>> grid on
>> hz=plot(s.z,'r.')
>> hk=plot(s,'b-')
Error using plot
Conversion to double from struct is not possible.
Where is the problem ?
Thank u
zhang blue (view profile)
Tim (view profile)
Tim (view profile)
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.
NAGA VBN (view profile)
Actually iam getting the error s not defined what can i do for this and this example gives v.gud idea.
Markus Schmidt (view profile)
thank you Shamir Alavi.
Shamir Alavi (view profile)
[rectification to the post above]: sry, 's' is not the measurement data. your data goes into 's.z' here.
Markus Schmidt (view profile)
got an error with
>> s = [1 2 3 4 5 6 7 8 9 22 3 4 5 6 7 8 88];
>> kalmanf(s);
Undefined function or variable 'z'.
Error in kalmanf (line 150)
if ~isfield(s,'x'); s.x=nan*z; end
Can someone explain me why pls?
weijie (view profile)
you are awesome
vamshi (view profile)
Carolina Brum Medeiros (view profile)
helpful and clear comments
Roja e (view profile)
Thanks..but an error occurred while running this demo.
Input argument "s" is undefined
help me please
chao (view profile)
Ruban Sugumar (view profile)
Nice Explanation..
Really Helpful..
greg (view profile)
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.
prokash paul (view profile)
nice doc
lotfi (view profile)
good !
Edgar lobachevskiy (view profile)
excellent!! Thank you!!
Liu Kefeng (view profile)
thank you very much!
HARI KRISHNAN (view profile)
Ms. Mat (view profile)
What is the difference between this and kalman implementation in Control System toolbox ?
Raven (view profile)
Karthik MSwamy (view profile)
SUDHAKAR AKKI (view profile)
Henry Zhu (view profile)
Dear Michael Kleder,thank you !
osman Özkaraca (view profile)
good
zheng (view profile)
love you so much, your sample is more helpful than those books wrote by some professional guys. easy, straightforward. especially for beginners.
Joan (view profile)
Enver (view profile)
Thanks a lot because of your great explanation.
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
Daniel Armyr (view profile)
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.
Richard (view profile)
awesome! makes so much more sense now. thanks.
Steve G (view profile)
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.
Baboon LikesBananas (view profile)
Big Andy (view profile)
joybing (view profile)
thank you for sharing!
Erdal Bizkevelci (view profile)
Venche (view profile)
sehr gut!
John D (view profile)
[continued from poste above]
As expected my matrices were wrong!
Thanks for the example!
John D (view profile)
[continued from poste above]
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.
John D (view profile)
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.
? (view profile)
Thanks very much.
Steven (view profile)
Examples Learn By (view profile)
Thank you for your hard work
http://learnbyexamples.org/category/matlab
chen (view profile)
thank your
vu (view profile)
good
Toto (view profile)
Great job !
Gervasio (view profile)
Very Helpful, although i would like to see an example with a control vector u.
RAJA MOHD ZAIDI RAJA IBRAHIM (view profile)
hi,
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.
naini naveen (view profile)
very good
Shivaram (view profile)
Excellent KF implementation I have ever seen!
benouis mohamed (view profile)
thanks
Michael Jordan (view profile)
Prasetyo Utomo (view profile)
Thanks very much
Thanks
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).
Thanks for sharing. :)
Very Useful Indeed
This was extremely useful for a beginner like me. A great post!
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.
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
great
ok
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.
I can understand Kalman filter from this document, I bet anyone can.
very good
Be careful. Also we are looking at your downloads records.
i want a kalman filter
how con I find calculation of dry gas filter
for natural gas ? please
this is very good
I want this refference
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.
It is a very user friendly, recommended
Very easy to use, recommended.
very good
Good demo.
You probably should separete the example, to another m file, named like RunMeDemoKalman.
For the really beginners.
a good demo for me!
very good tools
thank you very much
discrete kalman filter
It will be better if you separate the comment from the m.file and try to add them as "help" in a pdf format.
Same Error !!!
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
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
I need Kalman Filter program.
good
Thank You! Great introduction to the Kalman filter, even if you don't use Matlab.
you have to set up matlab first and run with workspace
try to replace inv(A)*B by A\B to speed up, although it's not significant when the matrix size is small
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
The best source I've found to start working with Kalman Filters. Do you have anything for the nonlinear version?
Useful Comments in Code.
its great.
Very Useful for understanding Kalman Filter
Very well presented summary that makes more sense than that provide within the Matlab help function.
VERY GOOD
Well,it's good for first time.No at all
Simple, pretty, excellent :-))) Thanks a lot!!
ok
Its nice, no doubt.
excellent apporach
but i m unable to run this prog
plz help me
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.
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.
Would you like to give me sample 's' value?
I still don't understand it perfectly.
Very fun. Very neat.
very good, I like the idea
very good
Thanks Daniel
Aalborg university
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!
You are a great tutor !
I really appreciate it .
Thank you very much.
Very helpful. Thanks!!
Excellent!! Thank You.
Compact, well documented, very good initialization and use of structures.
great!