Learning the Kalman Filter in Simulink

A Simulink model to learn the Kalman filter and Gassian processes.

Description

The zip file contains a Simulink model, which describes a Gassian process and the Kalman filter. A m-script is provided to show how to use this model from the command window. Two examples taken from the File Exchange are included in the m-file to explain how the Kalman filter works.

The package provides a way for beginners to learn the Kalman filter by just editting the model parameters without the need to know the details of calculation. By looking into masked subsystems, you will also be albe to learn how it can be implemented in Simulink.

The model is developed in R14SP1 (MATLAB 7.0.1, Simulink 6.1). If you require it to work with previous version, please let me know.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Learning the Kalman Filter, An Intuitive Introduction to Kalman Filter
This submission has inspired the following:
Learning the Kalman-Bucy Filter in Simulink, Learning the Kalman Filter: A Feedback Perspective

• Required Products: Simulink
• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Published M Files: Learning the Kalman Filter in Simulink Examples

Other Files

kalman simulink/runkalmanfilter.m,
kalman simulink/html/runkalmanfilter_01.png,
kalman simulink/html/runkalmanfilter_02.png,
kalman simulink/html/runkalmanfilter_03.png,
kalman simulink/html/runkalmanfilter_eq13019.png,
kalman simulink/html/runkalmanfilter_eq39812.png,
kalman simulink/kalmanfilter.mdl,
kalman simulink/html/runkalmanfilter_eq47464.png,
kalman simulink/html/runkalmanfilter_eq488660.png,
kalman simulink/html/runkalmanfilter_eq62371.png,
kalman simulink/html/runkalmanfilter_eq42551.png

[Scheffe held]

i dont like it. more confusing than helping.
why sample time 1?

[Yi Cao]

I am sorry you do not like the model. But, I do not understand what you refer to about sample time 1. The first example does not have sample time. The second example has the sample time 0.1 second. This is because the original problem is a continuous time problem. To use the discrete time version Kalman filter, we have to discretize the system, hence need a sample time. A continuous time Simulink model of Kalman filter (Kalman-Bucy filter) has been developed and submitted to the File Exchange. You may wish to try that one to see if you like it.

[Gabrie Tejeda]

Excelent, very usefull.
Thanks

[YH Zhang]

Great, but some pictures are missing in The HTML folder
such as,feedbackKF.png,KalmanLTI.png.

[Yi Cao]

Dear YH Zhang,

Thanks for pointing out these missing files although this is regarding to another submission: Learning the Kalman Filter: A Feedback Perspective. http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=18628&objectType=FILE

These files have been added now.

[Todor Tchangov]

Dear Yi Cao,
Knowing your good level, it’s well simplified and definitely a base to get started.

It is properly presented (for the first time in US History) as Bucy and others...
and Rudolf Kalman... who then ...moved in US... and…
Please, read the history, Colleagues:
Who was the American Engineer who made this working... and rectified the Mathematicians Problems ? That way this is the American Invention.

About the Continuous Linear Process:
I think that I have problems, but the major one is with the Process model.
 
The "A-matrix Process Dynamics- Integration" of X – output of the process, presents the Result of x-dot (or k+1). And this point is “Actuated by U input. How the “u” is presented to all different states (MISO) is presented by B matrix.

After that the Matrix C will present what is measurable and what is Observable.
And then according to “how the “A dynamics” filters the Noise Spectrum presented in point "x-dot" and + + + + will make Kalman Filter to decide “what is true signal and how to restore it”.

Now understanding only “how a (negative) feedback works” and modifies the “Transfer behavior” from Point a to point b… Check out that you made a Positive feedback from X = X+1 (???) to + summing point…!?!?!?! This model has a positive feedback…which in 1985 we had fast “overloading” and had to cold restart our 4 Mb Hard Disk Drive PCs.

But I like your work and I love you guys:
Because it is hard and…
We are big Family.

Sincerely yours,
Todor Tchangov
Sonic Works
[e-mail]
[e-mail]
cell: 210 906 5110

[Imtiaz Hussain]

Thanks a lot........... very useful

[V. Poor]