Distributionally Robust Kalman Filtering for INS/GPS Tightly Coupled Integration With Model Uncertainty and Measurement Outlier

The Kalman filter (KF) has been widely used in inertial navigation system (INS)/global positioning system (GPS) tightly coupled integration system. However, KFs are prone to divergence when the INS/GPS tightly coupled integration suffers from model uncertainties, measurement outliers caused by sensor errors, or changes in the hostile environment. Existing studies can hardly address all of these conditions. In this article, to ensure accurate and robust positioning performance for the INS/GPS tightly coupled integration under uncertainties and outliers, an improved distributionally robust KF (DRKF) based on Wasserstein and moment-based ambiguity sets is proposed. To this end, the state least favorable conditional prior distribution is obtained using the Wasserstein metric, and the moment-based ambiguity set is adopted to describe the distribution of the measurement noise. Furthermore, we use a novel saturation mechanism to suppress outliers, and this ensures robust-bounded-error state estimation in the presence of outliers. Experimental results demonstrate that the proposed algorithm can effectively deal with the model uncertainties and measurement outliers for the INS/GPS, with higher estimation accuracy and stronger robustness as compared to most relevant methods.