Maximum Likelihood Estimation of Stochastic Fractional Singular Models

Abstract

Using the non-causal nature of a fractional-order singular (FOS) model, this paper deals with the modification of an estimation algorithm developed by Nosrati and Shafiee, and demonstrates how the derived estimation procedure can be adjusted by additional information related to the future dynamics. The procedure adopts the maximum likelihood (ML) method leading to a 3-block fractional singular Kalman filter (FSKF). In addition to some conditions on existence and uniqueness of solutions for discrete-time linear stochastic FOS models, the estimability analyses are given and an optimal filter is presented. Finally, the performance of the derived filter is verified and validated via numerical simulation on a three machine infinite bus system.

Keywords

• Filtering and estimation
• maximum likelihood approach
• fractional-order singular model
• non-causality
• machine infinite bus system