Nonlinear filtering algorithms have significant implications in the optimal estimation of navigation states and in improving the accuracy, reliability, and robustness of navigation systems. This manuscript surveys the developments of the nonlinear filtering algorithms (extended Kalman filtering (EKF), unscented Kalman filtering (UKF), Cubature Kalman filtering (CKF), particle filtering (PF), neural network filtering (NNF)) and adaptive/robust KF in integrated navigation systems. The principle, application, and existing problems of these nonlinear filtering algorithms are mainly studied, and the comparative analysis and prospect are carried out.

Biomimetic vision is a promising method for efficient navigation and perception, showing great potential in modern navigation systems. Optical flow information, which comes from changes in an image on an organism’s retina as it moves relative to objects, is crucial in this process. Similarly, the star sensor is a critical component to obtain the optical flow for attitude measurement using sequences of star images. Accurate information on angular velocity obtained from star sensors could guarantee the proper functioning of spacecraft in complex environments. In this study, an optimized Kalman filtering method based on the optical flow of star images for spacecraft angular velocity estimation is proposed. The optimized Kalman filtering method introduces an adaptive factor to enhance the adaptability under dynamic conditions and improve the accuracy of angular velocity estimation. This method only requires optical flow from two consecutive star images. In simulation experiments, the proposed method has been compared with the classic Kalman filtering method. The results demonstrate the high precision and robust performance of the proposed method.

Accurate attitude estimation is critical for the navigation systems of ballistic missiles. The SINS/CNS is commonly utilized in missiles. When noise parameters are unknown or changing over time, a single Kalman filter cannot meet the accuracy requirements. Hence, this paper explores an improved multi-model adaptive estimation (IMMAE) algorithm incorporating weight parameters to improve the accuracy. The optimized estimation is obtained through a weighted sum of sub-filters with different weight parameters. Additionally, the IMMAE algorithm effectively monitors noise and exhibits rapid adaptability of weight parameters under varying conditions. The simulation results demonstrate superior performance and enhanced adaptability of IMMAE algorithm compared to traditional Kalman filter and MMAE algorithms.