# Grey Box system identification using LMS algorithm

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Ayushya Pare il 20 Ott 2022
Risposto: Vatsal il 17 Ott 2023
Hello Everyone,
The transfer function and the input output data of the system are known. The transfer function is given by G(s) = K/((J*s+b)(L*s+R)+K^2). How are the parameters of the transfer function determined using the LMS algorithm? Should the number of weights of the LMS algorithm always be same as the number of parameters of the transfer function? Any help on this is highly appreciated.
Best regards,
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### Risposte (1)

Vatsal il 17 Ott 2023
Hi,
I understand that you want to know how to determine the parameter of transfer function using the Least Mean Square (LMS) algorithm. To determine the parameters of the transfer function using the LMS algorithm, you can follow the steps below:
1. Calculate the error signal by finding the difference between the desired output and the actual output of the system.
2. Obtain the input signal from the input-output data of the system and initialize the parameter vector with initial values.
3. Update the parameter vector using the LMS algorithm.
4. Repeat the above steps until convergence or until enough iterations have passed.
In the LMS algorithm, the number of weights does not necessarily have to be the same as the number of parameters in the transfer function. The number of weights represents the complexity or order of the adaptive filter, which can be chosen based on the desired accuracy and computational complexity.
For a more comprehensive understanding of the LMS algorithm to determine transfer function parameters, you can refer to the MathWorks documentation links below:
I hope this helps!
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