Fractional Order Estimation Schemes for Fractional and Integer Order Systems with Constant and Variable Fractional Order Colored Noise

Abstract

The paper presents estimation schemes for discrete fractional and integer order state-space systems with fractional order colored noise. The fractional order colored noise is a generalization of the traditional colored noise (noise with dynamic dependency) for the case when the dynamics of noise is of fractional order. Proposed estimation algorithm additionally uses information about noise dynamics, which allows for obtaining better estimates of state vector. The numerical experiments of estimation integer order system with fractional noise are presented as well.