Derivation of Recursive Least Squares Method from Scratch - Introduction to Kalman Filter

#kalmanfilter #estimation #controlengineering #controltheory #mechatronics #adaptivecontrol #adaptivefiltering #adaptivefilter #roboticsengineering #roboticslab #robotics #electricalengineering #controlengineering #pidcontrol #roboticseducation
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In this video tutorial and in the accompanying web tutorial, we explain how to derive a recursive least squares method from scratch. The recursive least squares method is a very important method since it serves as the basis of adaptive control, adaptive estimation, Kalman filter, and machine learning algorithms. In this video, we start with the measurement equation, and by formulating the cost function that sums the variances of the estimation error, and by solving this cost function we obtain the recursive least squares gain matrix. We also derive an expression for the propagation of the estimation error covariance matrix.

[aleksandarhaber]

It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts in this way:
- You Can also press the Thanks YouTube Dollar button

[gj]

Hello, I'm a college student majoring in aerospace engineering in Korea. This video helped me a lot in learning recursive least squares in probability and random variables classes. Thank you so much for the perfect explanation!!

[kakunmaor]

The best explanation I've ever seen on the subject

[andresariaslondono]

Excellent video. Very well explained !!!! I followed your code and replicated in Matlab, It works great !! I had to be aware of the dimensions of the matrices and vectors. For example: the kalman matrix in this case is a column vector of three elements. The covariance matrix is a diagonal matrix whose dimensions corresponds to nxn where n is the number of variables to estimate (correct me if I am wrong); and last but not the least the Ck depends on the nature of the system. Thank you very much

[aleksandarhaber]

The webpage accompanying this video is given here:

[mehdifrotan]

Thanks for the great work that you are doing!!!

[maxwellsdaemon]

At 26:56, the derivative formulas in (36), (37) and (38), X should be K (or K should be X).
Anyway, I've always wanted to understand the Kalman filter, thanks for making this video.

[ERICX-od]

Very excellent videos and posts, I learned kalman filter with your tutorial, thanks so much for your great contribution. By the way, I noticed a small mistake in the equation numbering in the post. In the sentences 'By substituting (49) in (20), ' and 'We substitute (47) in (49)' the equation number should be 33 instead of 49.

[lamaabdullah]

Thank you for your effort this is what I'm looking for!

[michaelbaudin]

Thank you for the explanations. Don't you think that "Iterative least squares" would be a better name?

[jackhughman]

Hello, Thank you very much for the wonderful explanation. I just couldn't understand how the derivation [Eq. no. 42] answer has the term 2*KkPk-1(Ck)^t unlike the formula gives X*B^t + X*B. Similar for Eq no. 43.If you could explain it would be very helpful. Thank you.

[ly]

excellent video！btw could you please list the references you used for making this video?Could you please suggest any textbooks on this topic(RLS，RLS with forgetting factor)?