This paper proposes a modified unscented Kalman filter (UKF) with both adaptivity and robustness. In the proposed filter, the adaptivity is achieved by estimating the time-varying measurement noise covariance based on variational Bayesian (VB) approximation. The robustness is achieved by modifying the filter update based on Huber's M-estimation and Gaussian-Newton iterated method. In Gaussian assumptions, the proposed filter has a comparable filtering accuracy with the original UKF and better filtering consistency. When the measurement noise covariance is time-varying and there are outliers in the measurements, the proposed filter can outperform UKF and other adaptive or robust filters (such as VB-based UKF and Huber-based UKF) in terms of both filter accuracy and consistency. The efficacy of the proposed filter is demonstrated through the numerical simulation test and integrated navigation shipborne test.

In this study, both adaptive and robust one is proposed, considering that the properties of a classic unscented Kalman filter (UKF) can be degraded severely by the outliers measured in the contamination distribution and the effects of time-varying noise. An adaptive and robust UKF approach on Gaussian process regression- assisted Variational Bayesian is proposed. The Variable Bayesian (VB) method is used to statistically approximate the time-varying noise due to the strong nonlinearity and inaccuracy of the system model. At the same time, Gaussian Process Regression (GPR) has the advantage of machine learning. The observation information trained by the GPR model performs real-time prediction of the sliding window. Based on the above two points, the output source of the measurement information is estimated to realize the robustness of the filter measurement update. When the noise is uncertain and there are outliers in the measurement information, simulation and SINS/GPS integrated navigation of actual tests were performed, respectively. The test outcomes indicate that the algorithm has better nonlinear estimation performance than the traditional method, the effectiveness of the filtering algorithm proposed is verified.

The current research on integrated navigation is mainly focused on filtering or integrated navigation equipment. Studies systematically comparing and analyzing how to choose appropriate integrated filtering methods under different circumstances are lacking. This paper focuses on integrated navigation filters that are used by different filters and attitude parameters for inertial integrated navigation. We researched integrated navigation filters, established algorithms, and examined the relative merits for practical integrated navigation. Some suggestions for the use of filtering algorithms are provided. We completed simulations and car-mounted experiments for low-cost strapdown inertial navigation system (SINS) to assess the performance of the integrated navigation filtering algorithms.

This paper explores a modified inertial-integrated navigation approach for the strapdown inertial navigation system and Global Positioning System (SINS/GPS). Since every realization of state error must be expressed with respect to the same coordinate basis, how to express the navigation parameter errors is important, especially for inertial measurement unit (IMU) errors. To this respect, the IMU errors including gyro drift and accelerometer bias expressed in common frame are more reasonable than the unframed one. This paper derives the IMU errors defined with respect to the common frame, thereby extending to propose a common frame based unscented quaternion estimator for the inertial-integrated navigation. The simulation test and car-mounted experiments for a low-cost SINS are shown to assess the performance of the new filter compared with that of the traditional filter.

In this paper, the quaternion of ${b}$ -frame based nonlinear error model is proposed for the INS. According to the definition of the attitude error, the quaternion of ${b}$ -frame based nonlinear error model has been derived by additive and multiplicative relationship. Then, a discussion and analysis is made to compare the proposed model in additive and multiplicative relationship with the quaternion of ${n}$ -frame based nonlinear error model. In addition, an analysis and comparsion of ${b}$ -frame and ${n}$ -frame based nonlinear error model is made to have a theoretical justification to describe why ${b}$ -frame is superior to ${n}$ -frame based nonlinear error model. Finally, field tests are carried out to access the performance of the quaternion of ${b}$ -frame and ${n}$ -frame based nonlinear error model in the additive and multiplicative relationship for the INS.