On weighting of data matrix in subspace identification

The MOESP types of the subspace algorithms which are originally proposed by Verhaegen are considered at the point of view from the weighting of the data matrices. We have proposed an interpretation of these types of subspace algorithms by using the Schur complement (SC) of the data product moment and derive a unified framework for the subspace-based identification. This paper shows the proposed unified approach for the subspace identification will be reviewed at the point of view from the results of the Subspace-based identification using instrumental variables (SIV) approach by Gustafsson. Furthermore, we consider the introduction of exponential forgetting factor which windows the data matrices to apply the algorithms to the slowly time-varying system. The data matrix is windowed to reduce the influence of old data, which the forgetting factor or the sliding window can be used. Here it will show that the window weighting can also be reformed as the weighting of the data product moment and the proposed unified framework still kept consequently.