Off-line state-dependent parameter models identification using simple fixed interval smoothing

This paper shows a detailed study about the Young's algorithm for parameter estimation on ARX-SDP models and proposes some improvements. To reduce the high entropy of the unknown parameters, data reordering according to a state ascendant ordering is used on that algorithm. After the Young's temporal reordering process, the old data do not necessarily continue so. We propose to reconsider the forgetting factor, internally used in the exponential window past, as a fixed and small value. This proposal improves the estimation results, especially in the low data density regions, and improves the algorithm velocity as experimentally shown. Other interesting improvement of our proposal is characterized by the flexibility to the changes on the state-parameter dependency. This is important in a future On-Line version. Interesting features of the SDP estimation algorithm for the case of ARX-SDP models with unitary regressors and the case with correlated state-parameter are also studied. Finally a example shows our results using the INCA toolbox we developed for our proposal.