Design of a new algorithm to improve the convergence of extended Kalman filter based on incremental predictive model for inertial navigation system alignment and its stability analysis

In this paper, a new predictive filter for alignment of the inertial navigation system with a nonlinear model is presented, and its stability is analyzed. The stability is analyzed according to the Lyapunov method. The Lyapunov function is selected as a quadratic cost function. This method provides sufficient conditions for the stability of the estimated state against measurement uncertainty and noise. The proposed method is used to improve the initial alignment accuracy of the inertial navigation system with a large misalignment azimuth angle. The measurement model of this system is nonlinear and has a modeling error. In this method, the model error is estimated and compensated in the filter algorithm; therefore, the error of the state estimation is reduced in the updating step. By performing various simulations of this method on the real data of microelectromechanical (MEMS) sensor and comparing it with EKF and UKF, it is observed that the proposed method has higher accuracy and convergence speed than EKF and UKF. The new filter proves to have asymptotic stability.