TY - JOUR
T1 - A Novel Fractional Kalman Filter Algorithm With Noisy Input
AU - Zhang, Xinyu
AU - Fan, Keyi
AU - Ma, Wentao
AU - Duan, Jiemin
AU - Liang, Junli
AU - Ji, Ruirui
N1 - Publisher Copyright:
© 2004-2012 IEEE.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - For a fractional order system (FOS) affected by input noise, the result of general fractional Kalman filter (GFKF) is biased. To overcome this, this brief proposes a new fractional Kalman filter (FKF) algorithm considering input noise. Firstly, it is proved that the result of the GFKF method is biased when the input vector includes the noise. Secondly, we redefine the criterion function of the error of state estimation during the derivation process of the FKF, in which a term about the input noise is added into the covariance matrix during the prior-estimation. Then an improved covariance matrix and Kalman gain are gotten, respectively. Due to the consideration of the input noise, this method can remove the error caused by the input noise. Experiment results illustrate that the algorithm of this brief has superior performance for systems with input noise compared with the GFKF method.
AB - For a fractional order system (FOS) affected by input noise, the result of general fractional Kalman filter (GFKF) is biased. To overcome this, this brief proposes a new fractional Kalman filter (FKF) algorithm considering input noise. Firstly, it is proved that the result of the GFKF method is biased when the input vector includes the noise. Secondly, we redefine the criterion function of the error of state estimation during the derivation process of the FKF, in which a term about the input noise is added into the covariance matrix during the prior-estimation. Then an improved covariance matrix and Kalman gain are gotten, respectively. Due to the consideration of the input noise, this method can remove the error caused by the input noise. Experiment results illustrate that the algorithm of this brief has superior performance for systems with input noise compared with the GFKF method.
KW - control vector with input noise
KW - Fractional Kalman filter
KW - linear discrete fractional order system
KW - state estimation
UR - http://www.scopus.com/inward/record.url?scp=85144088725&partnerID=8YFLogxK
U2 - 10.1109/TCSII.2022.3223945
DO - 10.1109/TCSII.2022.3223945
M3 - 文章
AN - SCOPUS:85144088725
SN - 1549-7747
VL - 70
SP - 1239
EP - 1243
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
IS - 3
ER -