Adaptive fractional‐order unscented Kalman filter with unknown noise statistics

Abstract

Summary This article deals with state estimation of complex nonlinear discrete fractional‐order systems with unknown noise statistics by means of an adaptive fractional‐order Unscented Kalman filter (AFUKF). Firstly, in order to alleviate the communication burden of fractional‐order Unscented Kalman filter, short‐term memory effect is utilized to decide an appropriate memory length. Then aiming at the problem of filtering divergence and accuracy degradation caused by unknown statistical characteristics of noise, based on the maximum a posterior (MAP) principle, a noise statistical estimator is introduced to estimate and correct the statistical characteristics of noise in real‐time. Finally, the unbiasedness of the proposed algorithm is analyzed to verify that the estimated mean and covariance of noise are unbiased. The effectiveness and accuracy of AFUKF are demonstrated via simulation experiments.

Parameter estimation of fractional‐order Hammerstein state space system based on the extended Kalman filter

“…22 There are many researches on fractional-order systems, but the fractional-order estimation method of fractional-order systems is not consummate. 23 In many identification algorithms, the fractional-order is considered as a known prior, 24 but system order may not be a known prior in practice. In the time-domain, a subspace iterative method was proposed to identify the parameters of the fractional-order system, but a nonlinear optimization problem must be solved to estimate the fractional-order.…”

“…The fractional‐order Hammerstein model is a generalization of the Hammerstein model 22 . There are many researches on fractional‐order systems, but the fractional‐order estimation method of fractional‐order systems is not consummate 23 . In many identification algorithms, the fractional‐order is considered as a known prior, 24 but system order may not be a known prior in practice.…”