Inertial Navigation System (INS) is often combined with Global Navigation Satellite System (GNSS) to increase the positioning accuracy and continuity. In complex urban environments, GNSS/INS integrated systems suffer not only from dynamical model errors but also GNSS observation gross errors. However, it is hard to distinguish dynamical model errors from observation gross errors because the observation residuals are affected by both of them in a loosely-coupled integrated navigation system. In this research, an optimal Radial Basis Function (RBF) neural network-enhanced adaptive robust Kalman filter (KF) method is proposed to isolate and mitigate the influence of the two types of errors. In the proposed method, firstly a test statistic based on Mahalanobis distance is treated as judging index to achieve fault detection. Then, an optimal RBF neural network strategy is trained on-line by the optimality principle. The network’s output will bring benefits in recognizing the above two kinds of filtering fault and the system is able to choose a robust or adaptive Kalman filtering method autonomously. A field vehicle test in urban areas with a low-cost GNSS/INS integrated system indicates that two types of errors simulated in complex urban areas have been detected, distinguished and eliminated with the proposed scheme, success rate reached up to 92%. In particular, we also find that the novel neural network strategy can improve the overall position accuracy during GNSS signal short-term outages.

Due to its low-cost, sub-meter-precision, and large number of possible users, precise point positioning with single-frequency receivers (SF-PPP) has attracted a great deal of interest in recent years. One crucial issue in SF-PPP is the handling of ionospheric delays, which cannot be eliminated by combining observations on different frequencies. For validation and evaluation purposes, four SF-PPP models, which are ionospheric-corrected, -free, -unconstrained, and -constrained, were realized with different ionosphere treatments in SF-PPP. To enhance real-time SF-PPP performance, the contribution of multi-Global Navigation Satellite System (GNSS) observations and (predicted) global ionosphere maps (GIMs) was investigated in this study. To demonstrate the performance of the four SF-PPP models, two sets of multi-GNSS observations, which came from 33 Multi-GNSS Experiment (MGEX) ground static and one airborne kinematic observation data, were utilized to perform SF-PPP in simulated kinematic and real kinematic mode, respectively. The results indicated that the ionospheric-corrected and -constrained SF-PPP models performed better than the ionospheric-free and -unconstrained SF-PPP models in positioning convergence, while the ionospheric-unconstrained SF-PPP model showed advantages over the other three SF-PPP models in positioning accuracy after convergence. The positioning accuracy derived from Global Positioning System (GPS)  +  GLONASS  +  BeiDou Navigation Satellite System  +  Galileo ionospheric-constrained (IC)SF-PPP solutions is 9.1, 7.2, and 17.0 cm in the east, north, and the up components, respectively, which is somewhat worse than that of the ionospheric-unconstrained (IU)SF-PPP solutions (7.3, 6.1, and 15.2 cm) due to the low accuracy of GIMs. Compared to the IUSF-PPP solutions, the positioning accuracy during the convergence period (e.g. 1 h) derived from ICSF-PPP solutions is improved by 85.3% from 116.3 to 17.1 cm in the east, by 71.6% from 67.6 to 19.2 cm in the north, and by 72.6% from 194.7 to 53.4 cm in the up, respectively. Overall, the ionospheric-constrained SF-PPP demonstrated good performance in both positioning convergence and accuracy. Enhanced by employing multi-GNSS observations and external ionospheric products (i.e. GIMs), the ionospheric-constrained SF-PPP can achieve the positioning accuracy of about 0.7–1.0 dm in the horizontal component and 0.15–0.25 dm in the vertical component after a certain convergence time, i.e. 1 h in this study.

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