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Learning the Kalman Filter: A Feedback Perspective

version (218 KB) by Yi Cao
A feedback view of Kalman filter to gain more useful insights.


Updated 19 Feb 2011

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The Kalman filter is a feedback system. A Simulink model is developed to view this more clearly. From the feedback blocks, it is clear the normal Kalman filter is a linear time-variant system. By replacing the time-varying filter gain with its steady-state values, a simple linear time-invariant version of Kalman filter is provided in Simulink as well. Examples show that all these models provide similar performance.

Cite As

Yi Cao (2020). Learning the Kalman Filter: A Feedback Perspective (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (12)


thanks very much

mohamed meridjet

thank you for this example A+


zhou jianshan

Thank you for your sharing, thanks very much!

justice wei


V. Poor

YH Zhang

HI, YICao, I'm grad to see that the typo has removed quickly.
Now I have a question about the sampling period in your example 2:predict the position and velocity of a moving train.
For some latency or some other reasons in reality, I can't keep the sample period as a constant value. for example, I measurement the position at the time: 0.1, 0.3, 0.7, 0.8....... This means that the Equation : X(k) = AX(k-1) + BU(k-1) + W(k-1). the Matrix A is not a constant(time-variance) . So, can I still use the kalman filter? or I could use some non-linear method. Thank you.

chita samir


Yi Cao

Thank you yh Zhang. The typo has been corrected now. It may take a few days to be online.

YH Zhang

Hi, YI Cao, I have found a bug in your tutorials, when I want to send the bug to your email address, but all were were be rejected.

the formula(5) Kk = Pk|k-1 * C^T * Sk^-1 ( Change A to C)

Zhang YH

This is a great tutorial about Kalman filter, since there are many articles on the "matlab file exchange" talking about kalman filter. Your tutorial had made a summary and a survey which is very important for the beginners like me. Also, you add your some news view of kalman filter. Thank you very much!

manoj agrawal

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Learning the Kalman Filter in Simulink v2.1

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