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I have a multivariate linear-gaussian model and I am trying to estaimte a particular scalar set of parameters of the model.

I know how to derive the MLE in order to find the matrices A and Q (linear transfer function and covariance respectively).

I take the log of the joint distribution, find the above parameter derivatives, equal the expression to zero and solve for each of the 2 above parameters. The expression for A only depends on the data. The expression of Q depends on A and on the data. So I solve A first and then I can solve Q.

However, I have a specific application where I do not want to estimate the entire matrix A. Some scalar elements of the matrix I know a priori and some other scalar elements are the parameters to be estimated.

This is where my problems start:

1- The matrix calculus gets very hairy and I do not know how to solve this symbolically.

2- I tried to skip the step above and expanded the linear equation into a scalar expression with Matlab Symbolic toolbox since the parameters to be estimated are now scalars. I then went through Matlab differentiation and solving tools as well. It seems to work in principle.

3- On the original problem (the one I know how to solve), the expressions for A do not depend on Q. But now the Matlab solution shows that my estimated scalar Aij parameters do depend on Q and I believe it is correct. So now I have a set of parameters that all depend on each other and I am not sure what to do to solve them.

Any light on what I might need here would be appreciated.

Regards,

Carlos

BTW. this is my first post here, how do I insert latex expressions in these posts?

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# Linear Gaussian parameter estimation

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