Optimal Information Fusion Descriptor Fractional Order Kalman Filter

The fractional order Kalman filtering theory is an extension and extension of traditional integer order Kalman filters, which can solve the state estimation problem of fractional order systems. At present, the descriptor fractional order systems have been widely applied in many fields, such as circuit and sensor fault diagnosis. However, there is currently little research on the filtering problem of descriptor fractional order systems. This paper will focus on a fractional order descriptor system with canonical form. Firstly, the non singular linear transformation method is applied to transform the descriptor fractional order system into two normal fractional order subsystems. Then, based on projective theory, a fractional order Kalman state filter with correlated noise subsystems is derived. For multi-sensor descriptor fractional order systems, the globally optimal weighted measurement fusion algorithm is applied to derive the optimal information fusion fractional order Kalman filter. Simulation results verify the effectiveness and feasibility of the proposed algorithm.