Stochastic Subspace Realization

A tool to identify a state space model from stochastic signals

Description

This code provides a tool to identify a state space model from stochastic signals using a subspace approach.

The code is implemented in two steps using a nested function. The first step returns a vector of subspace singular values, from which a user can determine an appropriate order for the state space to be identified. Then by calling the nested function using the returned function handle the matrices of the state space model are obtained.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Multivariable Subspace Identification: MOESP

• MATLAB release: MATLAB 7.6 (R2008a)

[V. Poor]

 

[M H]

Dear Mr Cao,
I am dealing with 20 channels of 50 Hz acceleration data to perform system identification and extraction of modal parameters. I found your code very helpful!
A short question:
- during the for-loop (line 51 to 54 in the code) You fill the future- and past-Block-Hankel matrix (Yf,Yp) with shifted blocks of the time series.

for k=1:d
    Yp((d-k)*ny+1:(d-k+1)*ny,:)=sy(:,k:k+N-1);
    Yf((k-1)*ny+1:k*ny,:)=sy(:,d+k:d+k+N-1);
end

I was wondering if the order within the past-matrix "Yp" is changed due to the LQ-decomposition?
Here, Yp is filled from bottom to top, "max past" is at the bottom "min past" is at the top. As far as I understand some papers "max past" is at the top and "min past" is at the bottom, so that there is only one time shift between the bottom of Yp and the top of Yf when performing Yh=[Yp;Yf]?

Yp could be filled analogue to Yf?:
Yp((k-1)*n_y+1 : k*n_y, :) = sy(:, k : k+N-1);

the results seem to be pretty equal...

Best regards,
Moritz Häckell