Minimum error entropy high-order extend Kalman filter with fiducial points

High-order extend Kalman filtering (HEKF) is an excellent tool for addressing state estimation challenges in highly nonlinear systems under Gaussian noise conditions. However, HEKF may yield estimates with significant biases when the considered system is subjected to non-Gaussian disturbances. In response to this challenge, based on the minimum error entropy with fiducial points (MEEF), a novel HEKF (MEEFHEKF) is developed, and it exhibits robustness against intricate non-Gaussian noises. First, the nonlinear system is transformed into an augmented linear model through high-order Taylor approximation techniques. Subsequently, the development of the MEEFHEKF ensues through the resolution of an optimization problem grounded in the MEEF within the context of an augmented linear model. The MEEFHEKF, as put forward, operates as an online algorithm adopting a recursive structure, wherein the iterative equation is utilized to update the posterior estimates. Moreover, a sufficient condition is presented to confirm the existence and uniqueness of the fixed point in the iteration equation, guaranteeing the convergence of the introduced MEEFHEKF. Furthermore, an analysis of its computational complexity is also conducted to illustrate the computational burden. Finally, simulations substantiate the elevated precision in filtering and formidable robustness exhibited by the proposed algorithms when confronted with non-Gaussian disturbances.