A Causality Optimal Method for System Identification

Abstract

An optimal method is proposed for system identification. This method is based on the principle of causality and includes an algorithm of the learning identification method.
In this method, a generalized weighting function model with a pseudo-predictive portion (PPP) is used. This PPP is a weighting function with negative delays and the main portion (MP) is an ordinary weighting function with positive delays. The PPP accuracy can be exactly calculated through the law of causality, and it has been shown that the PPP accuracy is quite useful to estimate the MP accuracy.
Ordinarily it is impossible to estimate the optimal error-correcting coefficient α_j^op at the time j. However, this estimated MP accuracy has made it possible to calculate an estimate α_j of α_j^op at the time j. This optimal error-correcting coefficient may settle the trade-off problem between the shortening of the transient state and the improvement of the limit-accuracy. Therefore, this novel method, which will be referred to as a causality optimal method, will perform a practically optimal approximation by using α_j at each step of the iteration.
In addition, this algorithm is simple enough for use in a real time identification.
Some characteristics of the algorithm have been investigated by theoretical analysis as well as by numerical simulations with a digital computer.