Linear algebra with Pyomo
Pyomo is mainly a package for optimization. i.e. specifying data -> building problem -> sending to the solver -> wait for solver's results -> retrieving solution. Even if it can handle matrix-like data, it cannot manipulate it with matrix operations. This should be done using a good external library, before you send your data to Pyomo. Once you have all your matrixes ready to be used as data in your optimization model, then you can use Pyomo for optimization. 
That being said, you should look into finding a library that fits your needs to build your data, since your data values must be static, once you provide it as an input to your model. 
Also, keep in mind that Pyomo, like any optimization tools, is deterministic. It is not meant to do data analysis or data description, but to provide a way to find one optimal solution of a mathematical problem. In your case, Pyomo is not meant to do the Kalman filter problem, but to give you the solution of minimizing the mean square error.
I'm trying put my optimization problem into Pyomo, but it is strongly dependent upon standard linear algebra operations - qr, inverse, transpose, product. Actually, this is Kalman filter problem; recursive linear algebra for long time series. I failed to find pyomo functions to implement it like I could in tensor flow. Is it possible?
Connected questions:

Am I right that numpy target function is practically not usable in pyomo? 
Is there a better free optimization solution for the purpose? (scipy cannot approach efficiency of Matlab by far, tensor flow is extremely slow for particular problem, though I do not see why, algorithmic differentiation in Matlab was reasonably fast though not fast enough)

Many thanks,
Vladimir