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.

Fractional Extended and Unscented Kalman Filtering for State of Charge Estimation of Lithium-Ion Batteries

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Unscented Kalman filter for continuous‐time nonlinear fractional‐order systems with process and measurement noises

“…Because of the memory property of fractional-order operators, fractional-order systems can better reveal the dynamic characteristics of many physical systems, compared with the integer-order systems [9]. For fractional-order control systems, it is extremely important to study whether the system is stable, observable, and controllable [10,11].…”

Fractional order chaotic cryptography in colored noise environment by using fractional order interpolatory cubature Kalman filter

“…When dealing with the state estimation algorithms design, the colored noise is often considered as the main design problem. For this purpose, several different methods have been presented to solve the presence of colored noise in fractional order systems, such as the state augmentation approach (Gao, 2017; Sierociuk and Ziubinski, 2014) and the measurement differencing method (Asad et al, 2015). In Sierociuk and Ziubinski (2014), the colored noised is assumed to be present only in the state vector of a linear fractional order system, which have been estimated by using the colored noise state augmentation approach with the system states.…”