What is the cost function in the optimization problem of the pem and greyest functions for multiple outputs?

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Dieter Verbeke 2013-5-5

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Hi,

I am using the greyest and pem command of the System Identification Toolbox and I am wondering what the cost function in the optimization problem is for multiple outputs.

In general it is 1/2(e^TM^-1e) with M a symmetric weighing matrix. I assume the weighing matrix is in these cases, the identity matrix. Is that correct?

Thank you

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Answer 1

Rajiv Singh 2013-5-6

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The weighting matrix by default is inverse of noise variance which is simultaneously estimated along with the model parameters. If you set the OutputWeight estimation option (see greyestOptions) to eye(ny), where ny is number of outputs, the weighting becomes fixed to Identity matrix.