Changsheng Cai

Modeling and assessment of combined GPS/GLONASS precise point positioning

A combination of GPS and GLONASS observations can offer improved reliability, availability and accuracy for precise point positioning (PPP). We present and analyze a combined GPS/GLONASS PPP model, including both functional and stochastic components. Numerical comparison and analysis are conducted with respect to PPP based on only GPS or GLONASS observations to demonstrate the benefits of the combined GPS/GLONASS PPP. The observation residuals are analyzed for more appropriate stochastic modeling for observations from different navigation systems. An analysis is also made using different precise orbit and clock products. The performance of the combined GPS/GLONASS PPP is assessed using both static and kinematic data. The results indicate that the convergence time can be significantly reduced with the addition of GLONASS data. The positioning accuracy, however, is not significantly improved by adding GLONASS data if there is a sufficient number of GPS satellites with good geometry.

Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity

We develop a new approach for cycle slip detection and repair under high ionospheric activity using undifferenced dual-frequency GPS carrier phase observations. A forward and backward moving window averaging (FBMWA) algorithm and a second-order, time-difference phase ionospheric residual (STPIR) algorithm are integrated to jointly detect and repair cycle slips. The FBMWA algorithm is proposed to detect cycle slips from the widelane ambiguity of Melbourne–Wübbena linear combination observable. The FBMWA algorithm has the advantage of reducing the noise level of widelane ambiguities, even if the GPS data are observed under rapid ionospheric variations. Thus, the detection of slips of one cycle becomes possible. The STPIR algorithm can better remove the trend component of ionospheric variations compared to the normally used first-order, time-difference phase ionospheric residual method. The combination of STPIR and FBMWA algorithms can uniquely determine the cycle slips at both GPS L1 and L2 frequencies. The proposed approach has been tested using data collected under different levels of ionospheric activities with simulated cycle slips. The results indicate that this approach is effective even under active ionospheric conditions.

A Combined GPS/GLONASS Navigation Algorithm for use with Limited Satellite Visibility

Navigation users will significantly benefit from the combined use of GPS and GLONASS due to the improved reliability, availability and accuracy especially in an environment with limited satellite visibility, such as in urban or mountainous areas. But in such situations the visible satellite number is often still insufficient to obtain a position solution even if both GPS and GLONASS measurements are used. This is partly because at least five visible satellites are required to determine a position due to an offset between the timescales of GPS and GLONASS to be solved. In this paper, an algorithm has been proposed to obtain a position solution with only four visible GPS/GLONASS satellites. In addition to the data from IGS stations, an experiment was also conducted to assess the proposed algorithm. The results indicate that using the proposed algorithm with only four GPS/GLONASS satellites a position solution could be obtained at the cost of a slight accuracy loss.

A comparative analysis of measurement noise and multipath for four constellations: GPS, BeiDou, GLONASS and Galileo

With the rapid development of BeiDou system (BDS) and steady progress of Galileo system, the current GNSS (Global Navigation Satellite System) constellations consist of GPS, GLONASS, BeiDou and Galileo. The real signals from the four constellations have been available, which allows us to analyse and compare their measurement noises and multipath effects. In this study, a zero-baseline test is conducted using two ‘Trimble NetR9’ receivers to assess and compare the noises and multipath of measurements on multiple frequencies from the four satellite systems. The zero-baseline double difference approach is utilised to analyse the receiver noises. The code multipath combination and triple-frequency carrier phase combination approaches are exploited to analyse a comprehensive effect of the multipath and noises on the code and carrier phase measurements, respectively. Based on the analysis of the zero-baseline dataset, the results indicate that the code measurement noise levels range from 5 to 25 cm while the carrier phase noise levels vary within 0.9–1.5 mm for different frequencies and constellations. The code multipath and noise (CMN) level for GLONASS is the largest with a root mean square (RMS) value of 39 cm on both G1 and G2 frequencies whereas the Galileo code measurements exhibit a smallest level on the E5 frequency with a RMS value of only 10 cm. The RMS of the carrier phase multipath and noises (PMN) ranges from 1.3 to 2.6 mm for BeiDou and Galileo satellites. By contrast, the triple-frequency carrier phase combinations from the GPS Block IIF satellites demonstrate a much larger RMS value of 5.6 mm owing to an effect of inter-frequency clock biases.

Performance evaluation of single-frequency point positioning with GPS, GLONASS, BeiDou and Galileo

The single point positioning (SPP) mode has been widely used in many fields such as vehicle navigation, Geographic Information System and land surveying. For a long period, the SPP technology mainly relies on GPS system. With the recent revitalisation of the GLONASS constellation and two newly emerging constellations of BeiDou and Galileo, it is now feasible to investigate the performance of quad-constellation integrated SPP (QISPP) with GPS, GLONASS, BeiDou and Galileo measurements. As a satellite-based positioning technology, the QISPP is expected to improve the accuracy and availability of positioning solutions due to the increased number of visible satellites and the improved satellite sky distribution. In this study, a QISPP model is presented to simultaneously process observations from all four Global Navigation Satellite System (GNSS) constellations. Datasets collected at 47 globally distributed Multi-GNSS Experiment (MGEX) stations on two consecutive days and a kinematic experimental dataset are employed to fully assess the QISPP performance in terms of positioning accuracy and availability. Given that most navigation users are using single-frequency receivers, only the observations on a single frequency are utilised. The results indicate that the QISPP improves the positioning accuracy by an average of 16, 13 and 12% using the MGEX datasets, and 43, 31 and 51% using the kinematic experimental dataset over the GPS-only case in the east, north and up components, respectively. The availability of the QISPP solutions remains 100% even for a mask elevation angle of 40°, whereas it is only 37% for the GPS-only case. All these results are achieved using geodetic-type receivers and they are possibly optimistic for users who use navigation-type receivers.

Combined GPS/GLONASS precise point positioning with fixed GPS ambiguities.

Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF.

Galileo signal and positioning performance analysis based on four IOV satellites

With the availability of Galileo signals from four in-orbit validation (IOV) satellites, positioning with Galileo-only observations has become possible, which allows us to assess its positioning performance. The performance of the Galileo system is evaluated in respect of carrier-to-noise density ratio (C/N 0 ), pseudorange multipath (including noise), Galileo broadcast satellite orbit and satellite clock errors, and single point positioning (SPP) accuracy in Galileo-only mode as well as in GPS/Galileo combined mode. The precision of the broadcast ephemeris data is assessed using the precise satellite orbit and clock products from the Institute of Astronomical and Physical Geodesy of the Technische Universitat Munchen (IAPG/TUM) as references. The GPS-Galileo time offset (GGTO) is estimated using datasets from different types of GNSS receivers and the results indicate that a systematic bias exists between different receiver types. Positioning solutions indicate that Galileo-only SPP can achieve a three-dimensional position accuracy of about six metres. The integration of Galileo and GPS data can improve the positioning accuracies by about 10% in the vertical components compared with GPS-only solutions.

GNSS Vertical Coordinate Time Series Analysis Using Single-Channel Independent Component Analysis Method

Daily vertical coordinate time series of Global Navigation Satellite System (GNSS) stations usually contains tectonic and non-tectonic deformation signals, residual atmospheric delay signals, measurement noise, etc. In geophysical studies, it is very important to separate various geophysical signals from the GNSS time series to truthfully reflect the effect of mass loadings on crustal deformation. Based on the independence of mass loadings, we combine the Ensemble Empirical Mode Decomposition (EEMD) with the Phase Space Reconstruction-based Independent Component Analysis (PSR-ICA) method to analyze the vertical time series of GNSS reference stations. In the simulation experiment, the seasonal non-tectonic signal is simulated by the sum of the correction of atmospheric mass loading and soil moisture mass loading. The simulated seasonal non-tectonic signal can be separated into two independent signals using the PSR-ICA method, which strongly correlated with atmospheric mass loading and soil moisture mass loading, respectively. Likewise, in the analysis of the vertical time series of GNSS reference stations of Crustal Movement Observation Network of China (CMONOC), similar results have been obtained using the combined EEMD and PSR-ICA method. All these results indicate that the EEMD and PSR-ICA method can effectively separate the independent atmospheric and soil moisture mass loading signals and illustrate the significant cause of the seasonal variation of GNSS vertical time series in the mainland of China.

An enhanced multi-GNSS navigation algorithm by utilising a priori inter-system biases

The integration of multi-constellation Global Navigation Satellite System (GNSS) measurements can effectively improve the accuracy and reliability of navigation and positioning solutions, while the Inter-System Bias (ISB) is a key issue for compatibility. The ISB is traditionally estimated as an unknown parameter along with three-dimensional position coordinates and a receiver clock offset with respect to Global Positioning System (GPS) time. ISB estimation of this sort will sacrifice a satellite observation for each integrated GNSS system. These sacrificed observations could be vital in situations of limited satellite visibility. In this study, an enhanced multi-GNSS navigation algorithm is developed to avoid sacrificing observations under poor visibility conditions. The main idea of this algorithm is to employ a moving average filter to smooth the ISBs estimated at previous epochs. The filtered value is utilised as a priori information at the current epoch. Experimental tests were conducted to evaluate the enhanced algorithm under open and blocked sky conditions. The results show that the enhanced algorithm effectively improves the accuracy and availability of navigation solutions under the blocked sky condition, with performance being comparable to traditional ISB estimation algorithms in open sky conditions. The improvement rates of the three-dimensional position accuracy and availability reach up to 63% and 21% in the blocked sky environment. Even in the case of only four different GNSS satellites, a position solution can still be obtained using the enhanced algorithm.

Modified algorithm of combined GPS/GLONASS precise point positioning for applications in open-pit mines

A modified algorithm of combined GPS/GLONASS precise point positioning (GG-PPP) was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS (STDGG) and zenith tropospheric delay (ZTD) values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.