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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High-level applications of geo-processing services generally lack accurate temporal and spatial information. BDS-3 provides high precision temporal and spatial reference for geoprocessing services, but their signal is prone to cycle slips in a severe multipath environment. Aiming at the problem of the reliable detection and repair of cycle slips in BDS-3 (B1c+B2a) dual-frequency positioning in a severe multipath environment, an AR (autoregressive) model-assisted MW+GF BDS dual-frequency combined detection method (AMG method) is proposed in this research. A sliding-window autoregressive prediction strategy is introduced to correct the pseudorange observations interfered by a multipath, then an AR+MW+GF cycle slips detection model is constructed, and a cycle slips statistical completeness test index is established to verify the effectiveness of the algorithm. Six groups of cycle slips are artificially added into the different constellations and dual-frequency point phase observations of BDS-3 (B1c and B2a) in a multipath environment to demonstrate the cycle slips’ detection performance. The experimental results show that the traditional MW+GF method fails, but the proposed AMG method still maintains accurate cycle slip detection and repair capabilities. The detection success rate and repair success rate obtained by using the new method are significantly improved by 63.4%, and the cycle slips’ false detection rate and missed detection rate are reduced by 64.5% and 42.0%, respectively, even in harsh environments.

In this paper, we propose a partial ambiguity method of global navigation satellite system (GNSS) reliable positioning based on a robust estimation model to address the problems of the low reliability and availability of GNSS positioning in urban complex environments. First, the high-precision observations selected on the basis of the signal-to-noise ratio (SNR) were used to solve ambiguities. Then, the fixed ambiguities were used as constraints to solve the ambiguities of low-quality observations. The robust estimation method was used to reduce the impact of outliers for the ambiguity solutions. The robust estimation was also used to solve the position parameters to reduce the influence of the residual errors and uncorrected ambiguities for GNSS high-accuracy positioning. Static and dynamic data were used to evaluate the proposed algorithm. These experiments show that the proposed algorithm with the robust estimation can reduce the fixed time of ambiguity initialization, compared with the conventional algorithm without the robust estimation. The positioning accuracy and solution rate are similar regardless of whether the robust estimation is used in the GNSS unblocked environment. In blocked environments, the solution rate improves to more than 99%, and the three-dimensional (3D) position accuracy improves by more than 70% when the robust estimation is used. When the observation number of simulated small gross error accounts for 40.91% of total observations, the centimeter-level positioning accuracy can still be obtained via several robust estimation models. In the urban blocked environment, the IGG (Institute of Geodesy and Geophysics) III scheme has a better performance than other robust schemes discussed in this paper with regard to the positioning performance and computational efficiency.