Robust Fractional Nonlinear State Estimation Against Random Incomplete Measurements and Unknown Noise Statistics

Focusing on the challenge of the measurement of random packet loss and unknown or inaccurate noise characteristics in lossy networks for engineering practice, this article investigates the state estimation problem for increasingly widely used nonlinear fractional-order stochastic systems. To tackle this issue, a modified uncertainty measurement equation with random packet loss is provided. Within the central difference Kalman filter (CDKF) framework, the matrix diagonalization technique is first adopted and it is combined with the Stirling interpolation formulation to ensure the adequate stability and wide practicality of the proposed algorithms. A robust fractional CDKF (RFCDKF) is presented to address the challenge of measurement loss. Integrating the scenarios of lossy networks and unknown noise characteristics, a recursive algorithm, namely, RFCDKF with unknown noise characteristics (RFCDKF-UN) is proposed based on the maximum likelihood criterion. This filter allows parallel estimation of state and noise parameters, where an adaptive sliding window is introduced to reduce redundancy. Last, use is made of a lithium-ion battery system and a nonlinear system to verify the effectiveness, practicality, and superiority of the proposed algorithms.