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.

The real-time precise point positioning (RT PPP) technique has attracted increasing attention due to its high-accuracy and real-time performance. However, a considerable initialization time, normally a few hours, is required in order to achieve the proper convergence of the real-valued ambiguities and other estimate parameters. The RT PPP convergence time may be reduced by combining quad-constellation global navigation satellite system (GNSS), or by using RT ionospheric products to constrain the ionosphere delay. But to improve the performance of convergence and achieve the best positioning solutions in the whole data processing, proper and precise variances of the observations and ionospheric constraints are important, since they involve the processing of measurements of different types and with different accuracy. To address this issue, a weighting approach is proposed by a combination of the weight factors searching algorithm and a moving-window average filter. In this approach, the variances of ionospheric constraints are adjusted dynamically according to the principle that the sum of the quadratic forms of weighted residuals is the minimum, and the filter is applied to combine all epoch-by-epoch weight factors within a time window. To evaluate the proposed approach, datasets from 31 Multi-GNSS Experiment (MGEX) stations during the period of DOY (day of year) 023-054 in 2018 are analyzed with different positioning modes and different data processing methods. Experimental results show that the new weighting approach can significantly improve the convergence performance, and that the maximum improvement rate reaches 35.9% in comparison to the traditional method of priori variance in the static dual-frequency positioning mode. In terms of the RMS (Root Mean Square) statistics of positioning errors calculated by the new method after filter convergence, the same accuracy level as that of RT PPP without constraints can be achieved.

When satellites enter into the noon maneuver or the shadow crossing regimes, the actual attitudes will depart from their nominal values. If improper attitude models are used, the induced-errors due to the wind-up effect and satellite antenna PCO (Phase Center Offset) will deteriorate the positioning accuracy. Because different generations of satellites adopt different attitude control models, the influences on the positioning performances deserve further study. Consequently, the impact of three eclipsing strategies on the single-system and multi-GNSS (Global Navigation Satellite System) Precise Point Positioning (PPP) are analyzed. According to the results of the eclipsing monitor, 65 globally distributed MGEX (Multi-GNSS EXperiment) stations for 31-day period in July 2017 are selected to perform G/R/E/C/GR/GREC PPP in both static and kinematic modes. The results show that the influences of non-nominal attitudes are related to the magnitude of the PCO values, maximum yaw angle differences, the duration of maneuver, the value of the sun angle and the satellite geometric strength. For single-system, using modeled attitudes rather than the nominal ones will greatly improve the positioning accuracy of GLONASS-only and BDS-only PPP while slightly contributions to the GPS-only and GALILEO-only PPP. Deleting the eclipsing satellites may sometimes induce a longer convergence time and a worse solution due to the poor satellite geometry, especially for GLONASS kinematic PPP when stations are located in the low latitude and BDS kinematic PPP. When multi-GNSS data are available, especially four navigation systems, the accuracy improvements of using the modeled attitudes or deleting eclipsing satellites are non-significant.

Spatial public goods games model collective dilemmas where individual payoffs depend on population-level strategy configurations. Most existing studies rely on evolutionary update rules or value-based reinforcement learning methods. These approaches struggle to represent payoff coupling and non-stationarity in large interacting populations. This work introduces Multi-Agent Proximal Policy Optimization (MAPPO) into spatial public goods games for the first time. In these games, individual returns are intrinsically coupled through overlapping group interactions. Proximal Policy Optimization (PPO) treats agents as independent learners and ignores this coupling during value estimation. MAPPO addresses this limitation through a centralized critic that evaluates joint strategy configurations. To study neighborhood-level cooperation signals under this framework, we propose MAPPO with Local Cooperation Reward, termed MAPPO-LCR. The local cooperation reward aligns policy updates with surrounding cooperative density without altering the original game structure. MAPPO-LCR preserves decentralized execution while enabling population-level value estimation during training. Extensive simulations demonstrate stable cooperation emergence and reliable convergence across enhancement factors. Statistical analyses further confirm the learning advantage of MAPPO over PPO in spatial public goods games.