System Identification Parameter Estimation

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Hello,
I have a multi input multi output system. I am using tfest in the system identification toolbox. My issue is that the transfer function relating input 1 to output 2 and the transfer function relating input 2 and output 1, or the off diagonal, should be the same. However when I do the system identification these are different. Because of this I am unsure which estimation is the correct one. Is the any way to bound the system identification algorithm such that it takes into account that these two transfer functions must be the same?
I am also open to other suggestions for or examples to look at.

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Urmila Rajpurohith

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