Nonstationary analysis by bpes (backward prediction error space)

Abstract

AbstractThis paper describes a method of non‐stationary analysis based on the geometrical orthogonal projection with least‐squares estimation for a linear model. In the past, local stationary analysis and adaptive methods which successively estimate the parameters have been used for this purpose. However, in application to the nonstationarity case as in biomedical signals these methods have the disadvantage that it is difficult to see the physical significance of the parameters. In consideration of this, the present paper defines the backward prediction error space (BPES) consisting of the backward prediction error vector in each dimension and proposes to handle the nonstationarity by expanding the property into the orthogonal states in each dimension. The backward prediction error vectors constitute an orthogonal system in the least‐squares estimation and the reflection coefficient is the parameter directly related to this system. The orthogonality can be interpreted in direct relation to the independence of physical functions. As a measure of the nonstationarity, the angle between the vectors is adopted in the BPES. When the parameters which were optimum in the stationary interval are applied to an arbitrary interval, the angle is an exact expression of the discrepancy due to the nonstationarity. By an example of analysis of biomedical signals it is verified that the angle is useful in evaluation of the nonstationarity, especially of that arising from the change of orders. Thus, it is anticipated that the deterministic nonstationary analysis by BPES will provide new information about biological systems.