A Novel Fractional Kalman Filter Algorithm With Noisy Input

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.