version 1.0.0.0 (2.83 KB) by
Michael Kleder

Basic Kalman filter, heavily commented, for beginners to Kalman filtering.

90 Downloads

Updated 12 Oct 2005

No License

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.

Michael Kleder (2021). Learning the Kalman Filter (https://www.mathworks.com/matlabcentral/fileexchange/5377-learning-the-kalman-filter), MATLAB Central File Exchange. Retrieved .

Created with
R11.1

Compatible with any release

**Inspired:**
Kalman Filter Tutorial, Learning the Extended Kalman Filter, Learning the Unscented Kalman Filter, Learning the Kalman Filter in Simulink v2.1

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li junfangBharat CharukuJoe GibbsAhmad Mujahid bin Turins undefined. what to do?

Federico RodariMahdi TorabiMoussMandela ouafosamYar Zar TunRaed IbrahimThanks a lot!

Amir Allahverdi zadehAlireza RSeyed Resalatchenxi zouI can not run the file at the beginning, error shows: All functions in a script must be closed with an 'end'.

and in the function, I have problem to understand the if... else...why there is end in it?

Could anyone please help me?

john lewisAngel FernandezIMHO 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 TavakoliI 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 Lithank you for sharing

HEChello,

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 ZhouThanks a lot!

Lyudmil VladimirovPerparim, 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 FetahiHello, 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 LucasNguyen Manh TuongPlease! Give me a example of kalmanf function.

sami omarhey guys,

Im new to matlab, Im trying to implement Kalman filter with sin wave is that possible?

Auralius ManurungLine 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 CAoYimanthank you,I like it

kushwinder singhits very helpful

venugopal kulkarniCarlos M. Velez S.A good complement of linear Kalman filter in Simulink: http://www.mathworks.com/matlabcentral/fileexchange/46407-linear-kalman-filter-in-simulink

KoranitKoranitAngel Lopezvery useful!! Thanks a lot.

anthonyhow do i view the document

Aaron SchurgerExcellent 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?

liliaceaenice documentation and easy to understand.

liliaceaeAliakbar AlamdariVery 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).

jakubIn 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.

jakubMy 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 blueTimTimI 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 VBNActually iam getting the error s not defined what can i do for this and this example gives v.gud idea.

Markus Schmidtthank you Shamir Alavi.

Shamir Alavi[rectification to the post above]: sry, 's' is not the measurement data. your data goes into 's.z' here.

Markus Schmidtgot 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?

weijieyou are awesome

vamshiCarolina Brum Medeiroshelpful and clear comments

Roja eThanks..but an error occurred while running this demo.

Input argument "s" is undefined

help me please

chaoRuban SugumarNice Explanation..

Really Helpful..

gregNicely 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 paulnice doc

lotfigood !

Edgar lobachevskiyexcellent!! Thank you!!

Liu Kefengthank you very much!

HARI KRISHNANMs. MatWhat is the difference between this and kalman implementation in Control System toolbox ?

RavenKarthik MSwamySUDHAKAR REDDY AKKIHenry ZhuDear Michael Kleder,thank you !

osman Özkaracagood

zhenglove you so much, your sample is more helpful than those books wrote by some professional guys. easy, straightforward. especially for beginners.

JoanEnverThanks 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 ArmyrGood 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.

Richardawesome! makes so much more sense now. thanks.

Steve GVery 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 LikesBananasBig Andyjoybingthank you for sharing!

Erdal BizkevelciVenchesehr gut!

John D[continued from poste above]

As expected my matrices were wrong!

Thanks for the example!

John D[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 DI 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.

?Thanks very much.

StevenExamples Learn ByThank you for your hard work

http://learnbyexamples.org/category/matlab

chenthank your

vugood

TotoGreat job !

GervasioVery Helpful, although i would like to see an example with a control vector u.

RAJA MOHD ZAIDI RAJA IBRAHIMhi,

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 naveenvery good

ShivaramExcellent KF implementation I have ever seen!

benouis mohamedthanks

Michael JordanPrasetyo UtomoThanks very much

mohammad khorrami araniThanks

Tim DavisNice 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).

Vipin GuptaThanks for sharing. :)

Imtiaz HussainVery Useful Indeed

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

Behnam Molaee ArdekaniGood 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.

Sahil GangulyI 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

bekir pasaoglugreat

mohamed pummaok

Yi CaoThis 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.

marc lucJames HokansonArsalan KhanI can understand Kalman filter from this document, I bet anyone can.

Randy Colemanwang yivery good

P. McNamaraBe careful. Also we are looking at your downloads records.

djeunang brigittei want a kalman filter

Utkarsh GaurDuong Minh Auhamid reza ghazizadehhow con I find calculation of dry gas filter

for natural gas ? please

X. Kingsk imtiajthis is very good

Bouchemmella abdelhalimI want this refference

mehmet ali arabaciActually, 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.

SOURAV DASIt is a very user friendly, recommended

Edward TaylorVery easy to use, recommended.

zhu Yi Yong zhuyiyongvery good

Rodrigo BadínezGood demo.

You probably should separete the example, to another m file, named like RunMeDemoKalman.

For the really beginners.

lai zuomeia good demo for me!

xu zhengvery good tools

thank you very much

Rajesh Krishnanfatemeh shoormijdiscrete kalman filter

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

ravindar reddyTansel YucelenSame Error !!!

MORSHED MAHMUDPriyanka GuptaI get the same error:

kalmanf

??? Input argument "s" is undefined.

Error in ==> kalmanf at 150

if ~isfield(s,'x'); s.x=nan*z; end

clayonjj Harrisoni 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

shao litangI need Kalman Filter program.

diop baragood

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

ti toeyou have to set up matlab first and run with workspace

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

Teo chaiI 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

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

Camilo Lozoyaswami nathanFranz DietrichUseful Comments in Code.

Eduardo Verasakher falconits great.

Xuewu DaiVery Useful for understanding Kalman Filter

Carlos RoldanRobert KadduVery well presented summary that makes more sense than that provide within the Matlab help function.

ALEXANDRE EDUARDOVERY GOOD

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

Rafal G.Simple, pretty, excellent :-))) Thanks a lot!!

nemesio CARDENAS LOPESok

Zahid Ullah KhanIts nice, no doubt.

shobi kumarexcellent apporach

but i m unable to run this prog

plz help me

Tsanko TsankovA 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.

ammar saleemRentian XiongNice 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.

lee ykWould you like to give me sample 's' value?

I still don't understand it perfectly.

Tim GebbieVery fun. Very neat.

Flop FlopARLINDA SAQELLARIvery good, I like the idea

Daniel O. Fufavery good

Thanks Daniel

Aalborg university

Nathir RawashdehThis 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!

Liu BaolongYou are a great tutor !

I really appreciate it .

Thank you very much.

ARLINDA SAQELLARIGiuliano ScimoneSimon TipplerVery helpful. Thanks!!

Hooman DejnabadiThomas ByrneExcellent!! Thank You.

Vassilios MoussasCompact, well documented, very good initialization and use of structures.

Giap Do vangreat!