Smartphones, being one of the most ubiquitous sensors in daily life, have the capability to receive Global Navigation Satellite System (GNSS) signals, thereby enabling them to provide location-based services (LBSs) for mass-market users. Spatial information is one of the vital components in intelligent transportation and internet of things applications, and transportation-related applications like lane-level navigation are among the most frequently used smartphone LBSs. Considering the high noise level of smartphone GNSS measurements in such applications, there is a risk of selecting a reference satellite with measurement outliers in relative positioning technology, which would therefore decrease positioning accuracy and reliability. To address this issue, this paper proposes a resilient reference satellite configuration in smartphone relative positioning, where two reference satellites are selected per frequency for each constellation, accompanied by an automatic switching strategy between single and dual-reference satellite configurations. The proposed method extends the observation equations with a second reference satellite, and is validated with 18 datasets collected in driving environments, and both theoretical analysis and positioning results demonstrate that the dual-reference satellite configuration outperforms conventional single-reference satellite strategies except in extremely harsh environments. When applying the resilient switch, the percentage of horizontal positioning errors within 4 meters is largely improved. Moreover, the 68th percentile horizontal positioning errors are reduced by ~3 decimeters compared to single reference satellite method, and the percentages of positioning errors within 1.0 and 1.5 meters are improved by 8% and 9%, respectively, indicating a higher capability and great potential of providing lane-level navigation with the proposed resilient reference satellite configuration.

The accuracy of ionospheric delay modeling for user stations is intimately tied to the precise characterization of the ionospheric information in the domain of Global Navigation Satellite Systems (GNSSs). Current methods for model identification often face difficulties due to the scarcity of data from limited and sparsely located ground reference stations, and the irregular ionospheric characteristics during active periods. This is particularly true in active low latitudes, where disturbances, including GNSS signal scintillation and influence outcomes. This article introduces a universal framework, termed the global and local consistency methodology (GLCM), dedicated to extracting ionospheric spatial information by aligning estimated characteristics across global and subset spatial information. The proposed model adheres to a specifically designed objective to generate the appropriate form of functions and, based on them, to derive the ionospheric information for given areas. We carried out the simulation test to intuitively demonstrate the capabilities to improve the accuracy of the model in a direct and noninterference way. In addition, the model has been verified based on real-world data at low latitudes from a network of ground GNSS stations from all visible Global Position System (GPS) and GALILEO (GAL) satellites. The model achieves a reduction in the root-mean-square error (RMSE) of differential slant total electron content (dSTEC) by approximately 18% and 15% compared with the multiquadratic model and the Kriging model, respectively, during periods of high ionospheric activity. The proposed model has demonstrated effectiveness in ionospheric modeling and is actively being adapted for a wide range of GNSS applications and beyond.

Ionospheric structure is important for estimating ionospheric delay for user stations in Global Navigation Satellite System (GNSS). However, most existing parameter estimation methods suffer from challenges due to data inaccuracy and unavailability of limited and sparse scattered data at ground reference stations. The high variability of active low latitude or disturbed ionosphere leads to GNSS signal scintillation. It is critical to capture ionospheric random structure and estimate ionospheric parameter using data of disperse receivers to improve accuracy. This paper proposes a unifying method named Ionosphere Kernel Estimation Algorithm (IKEA) to retrieve the information of ionospheric spatial structure. The proposed model utilities the semi-parametric representation theorem to incorporate prior information and constraints. The multiple kernel technique is adopted firstly to include physical correlations. Additionally, a learning approach is deployed to determine model parameters. The IKEA model has been verified based on simulated and experimental data at active low latitudes from a network of ground GNSS reference stations from all visible GPS and GALILEO satellites. The IKEA model reduces approximately 19.5% and 24.2% of differential Slant Total Electron Content (dSTEC) in the root mean square error with respect to Inverse Distance Weighting (IDW) and the Kriging model during high ionospheric activities. The IKEA architecture has been demonstrated effective to make robust ionospheric estimation, which may be further extended for various GNSS applications and beyond.

We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. It is known for its inherent hardness of approximation. We focus on the well known minimum degree greedy algorithm for this problem. This algorithm iteratively chooses a minimum degree vertex in the graph, adds it to the solution and removes its neighbors, until the remaining graph is empty. The approximation ratios of this algorithm have been very widely studied, where it is augmented with an advice that tells the greedy which minimum degree vertex to choose if it is not unique. Our main contribution is a new mathematical theory for the design of such greedy algorithms with efficiently computable advice and for the analysis of their approximation ratios. With this new theory we obtain the ultimate approximation ratio of 5/4 for greedy on graphs with maximum degree 3, which completely solves the open problem from the paper by Halldórsson and Yoshihara (1995). Our algorithm is the fastest currently known algorithm with this approximation ratio on such graphs. We also obtain a simple and short proof of the (D+2)/3-approximation ratio of any greedy on graphs with maximum degree D, the result proved previously by Halldórsson and Radhakrishnan (1994). We almost match this ratio by showing a lower bound of (D+1)/3 on the ratio of any greedy algorithm that can use any advice. We apply our new algorithm to the minimum vertex cover problem on graphs with maximum degree 3 to obtain a substantially faster 6/5-approximation algorithm than the one currently known. We complement our positive, upper bound results with negative, lower bound results which prove that the problem of designing good advice for greedy is computationally hard and even hard to approximate on various classes of graphs. These results significantly improve on such previously known hardness results. Moreover, these results suggest that obtaining the upper bound results on the design and analysis of greedy advice is non-trivial.