An Optimization Method of Ambiguity Function Based on Multi-Antenna Constrained and Application in Vehicle Attitude Determination.

The global navigation satellite system (GNSS)-based multi-antenna attitude determination method has the advantages of a simple algorithm and no error accumulation with time in long endurance operation. However, it is sometimes difficult to simultaneous obtain the fixed solutions of all antennas in vehicle attitude determination. If float or incorrect fixed solutions are used, precision and reliability of attitude cannot be guaranteed. Given this fact, a baseline-constrained ambiguity function method (BCAFM) based on a self-built four GNSS antennas hardware platform is proposed. The coordinates obtained by BCAFM can replace the unreliable real-time kinematic (RTK) float or incorrect fixed solutions, so as to assist the direct method for attitude determination. In the proposed BCAFM, the baseline constraint is applied to improve search efficiency (searching time), and the ambiguity function value (AFV) formula is optimized to enhance the discrimination of true peak. The correctness of the proposed method is verified by vehicle attitude determination results and baseline length difference. Experimental results demonstrate that the function values of error peaks are reduced, and the only true peak can be identified accurately. The valid epoch proportion increases by 14.95% after true peak coordinates are used to replace the GNSS-RTK float or incorrect fixed solutions. The precision of the three attitude angles is 0.54°, 1.46°, and 1.15°, respectively. Meanwhile, the RMS of baseline length difference is 3.8 mm.

A Calibration-Free Method Based on Grey Relational Analysis for Heterogeneous Smartphones in Fingerprint-Based Indoor Positioning.

The fingerprint method has been widely adopted in Wi-Fi indoor positioning because of its advantage in non-line-of-sight channels between access points (APs) and mobile users. However, the received signal strength (RSS) during the fingerprint positioning process generally varies due to the dissimilar hardware configurations of heterogeneous smartphones. This difference may degrade the accuracy of fingerprint matching between fingerprint and test data. Thus, this paper puts forward a fingerprint method based on grey relational analysis (GRA) to approach the challenge of heterogeneous smartphones and to improve positioning accuracy. Initially, the grey relational coefficient (GRC) between the RSS comparability sequence of each reference point (RP) and the RSS reference sequence of the test point (TP) is calculated. Subsequently, the grey relational degree (GRD) between each RP and TP is determined on the basis of GRC, and the K most relational RPs are selected in accordance with the value of GRD. Finally, the user location is determined by weighting the K most relational RPs that correspond to the coordinates. The main advantage of this GRA method is that it does not require device calibration when handling heterogeneous smartphone problems. We further carry out extensive experiments using heterogeneous Android smartphones in an office environment to verify the positioning performance of the proposed method. Experimental results indicate that the proposed method outperforms the existing ones no matter whether heterogeneous smartphones are used.

A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography.

Water vapor is an important driving factor in the related weather processes in the troposphere, and its temporal-spatial distribution and change are crucial to the formation of cloud and rainfall. Global Navigation Satellite System (GNSS) water vapor tomography, which can reconstruct the water vapor distribution using GNSS observation data, plays an increasingly important role in GNSS meteorology. In this paper, a method to improve the distribution of observations in GNSS water vapor tomography is proposed to overcome the problem of the relatively concentrated distribution of observations, enable satellite signal rays to penetrate more tomographic voxels, and improve the issue of overabundance of zero elements in a tomographic matrix. Numerical results indicate that the accuracy of the water vapor tomography is improved by the proposed method when the slant water vapor calculated by GAMIT is used as a reference. Comparative results of precipitable water vapor (PWV) and water vapor density (WVD) profiles from radiosonde station data indicate that the proposed method is superior to the conventional method in terms of the mean absolute error (MAE), standard deviations (STD), and root-mean-square error (RMS). Further discussion shows that the ill-condition of tomographic equation and the richness of data in the tomographic model need to be discussed separately.

A Self-Organizing Spatial Clustering Approach to Support Large-Scale Network RTK Systems.

The network real-time kinematic (RTK) technique can provide centimeter-level real time positioning solutions and play a key role in geo-spatial infrastructure. With ever-increasing popularity, network RTK systems will face issues in the support of large numbers of concurrent users. In the past, high-precision positioning services were oriented towards professionals and only supported a few concurrent users. Currently, precise positioning provides a spatial foundation for artificial intelligence (AI), and countless smart devices (autonomous cars, unmanned aerial-vehicles (UAVs), robotic equipment, etc.) require precise positioning services. Therefore, the development of approaches to support large-scale network RTK systems is urgent. In this study, we proposed a self-organizing spatial clustering (SOSC) approach which automatically clusters online users to reduce the computational load on the network RTK system server side. The experimental results indicate that both the SOSC algorithm and the grid algorithm can reduce the computational load efficiently, while the SOSC algorithm gives a more elastic and adaptive clustering solution with different datasets. The SOSC algorithm determines the cluster number and the mean distance to cluster center (MDTCC) according to the data set, while the grid approaches are all predefined. The side-effects of clustering algorithms on the user side are analyzed with real global navigation satellite system (GNSS) data sets. The experimental results indicate that 10 km can be safely used as the cluster radius threshold for the SOSC algorithm without significantly reducing the positioning precision and reliability on the user side.

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization.

Due to the great influence of multipath effect, noise, clock and error on pseudorange, the carrier phase double difference equation is widely used in high-precision indoor pseudolite positioning. The initial position is determined mostly by the known point initialization (KPI) method, and then the ambiguities can be fixed with the LAMBDA method. In this paper, a new method without using the KPI to achieve high-precision indoor pseudolite positioning is proposed. The initial coordinates can be quickly obtained to meet the accuracy requirement of the indoor LAMBDA method. The detailed processes of the method follows: Aiming at the low-cost single-frequency pseudolite system, the static differential pseudolite system (DPL) method is used to obtain the low-accuracy positioning coordinates of the rover station quickly. Then, the ambiguity function method (AFM) is used to search for the coordinates in the corresponding epoch. The real coordinates obtained by AFM can meet the initial accuracy requirement of the LAMBDA method, so that the double difference carrier phase ambiguities can be correctly fixed. Following the above steps, high-precision indoor pseudolite positioning can be realized. Several experiments, including static and dynamic tests, are conducted to verify the feasibility of the new method. According to the results of the experiments, the initial coordinates with the accuracy of decimeter level through the DPL can be obtained. For the AFM part, both a one-meter search scope and two-centimeter or four-centimeter search steps are used to ensure the precision at the centimeter level and high search efficiency. After dealing with the problem of multiple peaks caused by the ambiguity cosine function, the coordinate information of the maximum ambiguity function value (AFV) is taken as the initial value of the LAMBDA, and the ambiguities can be fixed quickly. The new method provides accuracies at the centimeter level for dynamic experiments and at the millimeter level for static ones.

Impacts of Satellite Orbit and Clock on Real-Time GPS Point and Relative Positioning.

Satellite orbit and clock corrections are always treated as known quantities in GPS positioning models. Therefore, any error in the satellite orbit and clock products will probably cause significant consequences for GPS positioning, especially for real-time applications. Currently three types of satellite products have been made available for real-time positioning, including the broadcast ephemeris, the International GNSS Service (IGS) predicted ultra-rapid product, and the real-time product. In this study, these three predicted/real-time satellite orbit and clock products are first evaluated with respect to the post-mission IGS final product, which demonstrates cm to m level orbit accuracies and sub-ns to ns level clock accuracies. Impacts of real-time satellite orbit and clock products on GPS point and relative positioning are then investigated using the P3 and GAMIT software packages, respectively. Numerical results show that the real-time satellite clock corrections affect the point positioning more significantly than the orbit corrections. On the contrary, only the real-time orbit corrections impact the relative positioning. Compared with the positioning solution using the IGS final product with the nominal orbit accuracy of ~2.5 cm, the real-time broadcast ephemeris with ~2 m orbit accuracy provided <2 cm relative positioning error for baselines no longer than 216 km. As for the baselines ranging from 574 to 2982 km, the cm-dm level positioning error was identified for the relative positioning solution using the broadcast ephemeris. The real-time product could result in <5 mm relative positioning accuracy for baselines within 2982 km, slightly better than the predicted ultra-rapid product.

A New Method for Single-Epoch Ambiguity Resolution with Indoor Pseudolite Positioning.

Ambiguity resolution (AR) is crucial for high-precision indoor pseudolite positioning. Due to the existing characteristics of the pseudolite positioning system, such as the geometry structure of the stationary pseudolite which is consistently invariant, the indoor signal is easy to interrupt and the first order linear truncation error cannot be ignored, and a new AR method based on the idea of the ambiguity function method (AFM) is proposed in this paper. The proposed method is a single-epoch and nonlinear method that is especially well-suited for indoor pseudolite positioning. Considering the very low computational efficiency of conventional AFM, we adopt an improved particle swarm optimization (IPSO) algorithm to search for the best solution in the coordinate domain, and variances of a least squares adjustment is conducted to ensure the reliability of the solving ambiguity. Several experiments, including static and kinematic tests, are conducted to verify the validity of the proposed AR method. Numerical results show that the IPSO significantly improved the computational efficiency of AFM and has a more elaborate search ability compared to the conventional grid searching method. For the indoor pseudolite system, which had an initial approximate coordinate precision better than 0.2 m, the AFM exhibited good performances in both static and kinematic tests. With the corrected ambiguity gained from our proposed method, indoor pseudolite positioning can achieve centimeter-level precision using a low-cost single-frequency software receiver.

Surface Subsidence Analysis by Multi-Temporal InSAR and GRACE: A Case Study in Beijing.

The aim of this study was to investigate the relationship between surface subsidence and groundwater changes. To investigate this relationship, we first analyzed surface subsidence. This paper presents the results of a case study of surface subsidence in Beijing from 1 August 2007 to 29 September 2010. The Multi-temporal Interferometric Synthetic Aperture Radar (multi-temporal InSAR) technique, which can simultaneously detect point-like stable reflectors (PSs) and distributed scatterers (DSs), was used to retrieve the subsidence magnitude and distribution in Beijing using 18 ENVISAT ASAR images. The multi-temporal InSAR-derived subsidence was verified by leveling at an accuracy better than 5 mm/year. Based on the verified multi-temporal InSAR results, a prominent uneven subsidence was identified in Beijing. Specifically, most of the subsidence velocities in the downtown area were within 10 mm/year, and the largest subsidence was detected in Tongzhou, with velocities exceeding 140 mm/year. Furthermore, Gravity Recovery and Climate Experiment (GRACE) data were used to derive the groundwater change series and trend. By comparison with the multi-temporal InSAR-derived subsidence results, the long-term decreasing trend between groundwater changes and surface subsidence showed a relatively high consistency, and a significant impact of groundwater changes on the surface subsidence was identified. Additionally, the spatial distribution of the subsidence funnel was partially consistent with that of groundwater depression, i.e., the former possessed a wider range than the latter. Finally, the relationship between surface subsidence and groundwater changes was determined.

The smallest spectral radius of graphs with a given clique number.

The first four smallest values of the spectral radius among all connected graphs with maximum clique size ω ≥ 2 are obtained.

On the signless laplacian spectral radius of bicyclic graphs with perfect matchings.

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.