Learning the Extended Kalman Filter

An implementation of Extended Kalman Filter for nonlinear state estimation.

Description

This is a tutorial on nonlinear extended Kalman filter (EKF). It uses the standard EKF fomulation to achieve nonlinear state estimation. Inside, it uses the complex step Jacobian to linearize the nonlinear dynamic system. The linearized matrices are then used in the Kalman filter calculation.

The complex step differentiation seems improving the EKF performance particularly in accuracy such that the optimization and NN training through the EKF are better than through the UKF (unscented Kalman filter, http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=18217&objectType=FILE). Other complex step differentiation tools include the CSD Hessian available at http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=18177&objectType=FILE.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Learning the Kalman Filter
This submission has inspired the following:
Unconstrained Optimization using the Extended Kalman Filter, Neural Network training using the Extended Kalman Filter, Learning the Unscented Kalman Filter

• MATLAB release: MATLAB 7.4 (R2007a)

[sayed mohammad mousavi gazafrudi]

 

[edwin de Vries]

??? Error: File: ekf.m Line: 19 Column: 10
Expression or statement is incomplete or incorrect.

??? Maximum recursion limit of 500 reached. Use set(0,'RecursionLimit',N)
to change the limit. Be aware that exceeding your available stack space can
crash MATLAB and/or your computer.

Error in ==> ekf>create@(x)[x(2);x(3);0.05*x(1)*(x(2)+x(3))] at 25
 f=@(x)[x(2);x(3);0.05*x(1)*(x(2)+x(3))]; % nonlinear state equations

[Yi Cao]

Dear Edwin,

As I expected, this error is due to your way to run the example because the error message shows that the error occures at line 19, which is a commented line to begin the example.

To correctly run the example, you can follow the following steps:

1. select the example lines correctly
2. press control-t to uncomment the selection
3. right-click to run the selection
4. click un-do to recover the file. (DO NOT click the save button.)

For you and other users' convenient, I updated the file with block-comment lines for the example. Now, you just need to select and right-click to run the example without change the file. The update will appear a few hours later.

Hope this help.

[Taher DERBEL]

 

[Reza Baghaei]

 

[meng jun]

very well.

[feng yu]

 

[hu aijun]

 

[Dmitry Sh]

Nicely made, and very intuitive if one has an idea how a linear Kalman Filter works. However I found that numerically solving the Jacobian is not always the best form of linerisation, especially for simpler cases when an analytic Jacobian can be computed by hand.
In my experiments (with simple non-linear models) an analytic Jacobian usually gave a significant improvement of fit when compared to its numeric counterpart. Maybe you could add an option on how it should be solved

[Neric Lau]

Very helpful for learning Kalman Filter Implementation.

[Saroj Pandey]

it is very good and helpful in my project.

[Tim Davis]

Excellent! Nice use of CHOL instead of INV (as can be seen in two other Kalman-filter codes on the File Exchange). Nice to see good numerics at work.

I see that "K=P12*inv(...)" is commented out; that's perfect. It gives the math behind what the CHOL and backslashes are doing.

[Lihong Wang]

Nice code. But if there is load disturbance on the state, why the estimate from the EKF almost ignores the load disturbance?

[maureen clerc]

Beware: function ekf changes the value of the measurement covariance matrix R. It shouldn't be the case. Otherwise the code is nice and efficient.

[Zhongjie Chen]

Hi, I still get the error

??? Maximum recursion limit of 500 reached. Use set(0,'RecursionLimit',N)
to change the limit. Be aware that exceeding your available stack space
can
crash MATLAB and/or your computer.

Error in ==> ekf>create@(x)[x(2);x(3);0.05*x(1)*(x(2)+x(3))]

after following your instructions. How do I correctly run the code?

[Yi Cao]

This error occurs because you run the example incorrectly so that ekf calls itself more than 500 times. To run the example, you need copy contents between "%{" and "%}" then past it on matlab command window to execute the example.

It also could be because your MATLAB version is too old to support block comments. If that is the case, you can comment out all line by adding "%" at the begining of each line between "%{" and "%}" to solve the problem.

[V. Poor]

 

[Dapat Chawah]

This code is working good for N<=150
but when N exceeds this limit, a nonsense happens
Is there any improvement to the code considering this error?

[Dapat Chawah]

Sorry, this comment is meant to be in the unscented kalman filter file discussion

[Rohit Hippalgaonkar]

Hi I am looking for an example where the EKF is applied to a continuous-time non-linear system with non-zero inputs (say measurements are taken at regular time samples through a non-linear (even linear would do) measurement process. I have looked around for this kind of example in the standard texts but haven't found any. Also a good source showing the implementation of the EKF wherein we linearize about a single operating point (as against linearizing about the predicted state every time) would be really helpful! Thanks in advance! Rohit

[Yi Cao]

For continuous-time EKF, please look at http://www.mathworks.com/matlabcentral/fileexchange/18485

[Chao]

 

[tim Heights]

if in EKF i have to add state noise compensation, any good example or guidance here. how can i add to the example given by Yi Cao.
secondly, any one who could also recommend some book about it.

[tim]

i wrote a very simple compound pendulum code, and some how this ekf algorithm does not work for that. only change that i had to do to that example file was change the states to 2 and rest
f=@(x)[x(2);-(g/l)*sin(x(1))];
this should give me sinusoidal waveform but it does not.
can you point out to me what could be wrong.

[maheswaran Rathinasamy]

 

[iasri icar]

hi yi, would like to know if its appropriate to use EKF for forecasting of agricultural yields like fish ,rice etc. i am planning to use EXPAR with EKF for the problem stated above and would you kindly be able to give some of your ideas regarding the same.thankyou, with regards bishal.

[Aeimit Lakdawala]

Is it possible to do constrained nonlinear optimization with EKF?

[Yi Cao]

Aeimit

Yes, it is possible. For example, see

http://www.mathworks.com/matlabcentral/fileexchange/18286

Yi

[Joao Henriques]

 

[Matthew Coleman]

Congratulations. This is the first EKF library I manged to get working at all.

The example takes measurements go in the s matrix, not the x. Now that is fixed everything is good.

It is a long time since I did Kalman or Matlab. You clever guys underestimate how dumb you need to make your comments to get us newbies started.

[Matthew Coleman]

 

[Daniel]

Hi, how should I modify the m-file if I want to change the measurement- and process noise to:
w ~ N(u,Q)
v ~ N(e,R)

[Christy]

.hii..
when i run this program..the following error is displayed in the command window:
"??? Input argument "fstate" is undefined.

Error in ==> ekf at 51
[x1,A]=jaccsd(fstate,x); %nonlinear update and linearization at current state"

please rectify my problem asap...
Also suggest to me how to implement this code for multi sensor data fusion wherein the input is in the form of signals from n different sensors..as in how do I express my input here in terms of f and h.

[Big Andy]

 

[Krzysztof]

hi Yi
could you suggest an examplar definition of the function "f" together with initial state "s" for some real life example of a system? this would help me and other inexperienced guys to better understand this example. thank you very much in advance.

[Maria Perdomo]

Hi, Is it possible to use your code for parameter identfication?

[Yi Cao]

Maria,

Yes, it is possible. Please look at the submission:

http://www.mathworks.com/matlabcentral/fileexchange/18289

[George Lim]

Hi! This is a nice code for EKF. I have a question though: In your example if we assume that the value 0.05 is unknown parameter and we want simultaneous state and parameter estimation can we augment the state as with the parameter as:
n=4; %number of state
q=0.1; %std of process
r=0.1; %std of measurement
Q=q^2*eye(n); % covariance of process
% or Q=diag[Q 0]; % if no process noise is included in the parameter
R=r^2; % covariance of measurement
f=@(x)[x(2);x(3);x(4)*x(1)*(x(2)+x(3));x(4)]; % nonlinear state equations
h=@(x)x(1); % measurement equation
s=[0;0;1;0.1]; % initial state
x=s+q*randn(4,1); %initial state % initial state with noise
P = eye(n); % initial state covraiance
N=20; % total dynamic steps
xV = zeros(n,N); %estmate % allocate memory
sV = zeros(n,N); %actual
zV = zeros(1,N);
for k=1:N
  z = h(s) + r*randn; % measurments
  sV(:,k)= s; % save actual state
  zV(k) = z; % save measurment
  [x, P] = ekf(f,x,P,h,z,Q,R); % ekf
  xV(:,k) = x; % save estimate
  s = f(s) + q*randn(3,1); % update process
end;

[moises]

Hi!

Is there possible to use the code in a case where I have different rates of prediction and correction steps. (e.g., could I have 10 predictions before make one correction...). Is it easy to do this in the current version of the code?

[wawan]

thanks you

[Elke]

Hi;
I get the error message "??? Undefined function or method 'ekf' for input arguments of type 'function_handle'"

[Prithwiraj]

I downloaded the file and ran it on R2006b. Got the following error. Could someone tell me what I am doing wrong? I guess I have to uncomment a few things and run in some sequence, but unable to figure out what

??? Input argument "fstate" is undefined.

Error in ==> ekf at 51
[x1,A]=jaccsd(fstate,x); onlinear update and linearization at current state

[Simon Omekanda]

 

[Simon Omekanda]

Can you go over the steps to properly run this function please?! I am still getting error that have been mentioned above in some comments, mainly:
??? Maximum recursion limit of 500 reached. Use set(0,'RecursionLimit',N)
to change the limit. Be aware that exceeding your available stack space can
crash MATLAB and/or your computer.

Error in ==> ekf>create@(x)[x(2);x(3);0.05*x(1)*(x(2)+x(3))]

Thanks:)

[dab483]

run the code as below in command window:

n=3
:
:
end

has an error:
??? Undefined function or method 'ekf' for input arguments of type
'function_handle'.
 how to run these codes?

[Olaf Gerritse]