Design of a robust central difference kalman filter in the presence of uncertainties and unknown measurement errors

Abstract

In this study, a novel RCDKF11Robust Central Difference Kalman Filter. is proposed for nonlinear plants. The system under consideration is a comprehensive case where the norm bounded uncertainties are supposed in both the state and output equations. Since the filtering methodology has been suggested based on the Stirling formula, it requires no derivative or Jacobian matrix computations. Furthermore, the mean value of uncertainties has been eliminated in the development of the filter structure. Different types of uncertainties are incorporated in the standard formulation of CDKF and it is demonstrated that the upper bound of covariance matrices can be derived according to them. In contrast to the similar works, the stability of the proposed filtering strategy is proved by the Lyapunov theory and the upper bound of state estimation error covariance is found for all admissible uncertainties. To demonstrate the performance of the introduced estimation algorithm, it will be evaluated on the attitude determination system of a three-axis satellite including a star camera and gyro sensor. The simulation results of the proposed filter are compared with the conventional CDKF,22Central Difference Kalman Filter. NRF,33Nonlinear Robust Filter. EKF44Extended Kalman Filter. and PF55Particle Filter. and the better efficiency of the developed method is established.