Learning the Kalman Filter: A Feedback Perspective

A feedback view of Kalman filter to gain more useful insights.

Description

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.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Learning the Kalman Filter in Simulink v2.1

• Required Products: Simulink
• MATLAB release: MATLAB 7.5 (R2007b)

[manoj agrawal]

 

[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!

[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)

[Yi Cao]

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

[chita samir]

N/A

[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.

[V. Poor]

 

[justice wei]

GOOD EXAMPLE

[zhou jianshan]

Thank you for your sharing, thanks very much!