I'm going to create an adaptive Model Predictive Controller (MPC). The model is a state space model. Due to noise, it's very difficult to determine the model order.
I'm using subspace identification method OKID/ERA and due to noise, I get many very large hankel singular values, which gives an answer how large the model will be. But noise pervent me to select the right model order.
If I had low noise, then I would have like 1 or 2 big hankel singular values, which gives the result of model order.
So in this case, I don't have a model to begin with and therefore I cannot use a kalman filter. Do you have any suggestion I could use to "remove" the noise from measurements?
Try "unscented Kalman filter" as it does not require any model.
"Ensemble Kalman filter" uses a probablistic model. Have a look at "ensemble kalman filtering without a model".
Moving Horizon Estimation (MHE) in general also needs a model which would not be better than Kalman filter.
As a comment, in a very highly noisy situation, Stochastic MPC might help your optimization although it does not improve your measurement.