Rock Santerre

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.

GPS interactive time series analysis software

Time series analysis is an important part of geodetic and geodynamic studies, especially when continuous GPS observations are used to explore areas with a low rate of deformation. In this domain, having precise and robust tools for processing and analyzing position time series is a prerequisite. To meet this requirement, a new software package called GPS Interactive Time Series Analysis was developed using the MATLAB language. Along with calculating basic statistics and quality parameters such as mean and variance, the software is capable of importing and visualizing different time series formats, determining and removing jumps and outliers, interpolating data, and producing numerical and publication quality graphical outputs. Furthermore, bivariate statistical analysis (such as correlation coefficients, curvilinear and nonlinear regression), residual analysis, and spectral analysis (such as auto-spectrum, Lomb–Scargle spectrum, evolutionary power spectrum, and wavelet power spectrum) form the main analysis features of the software.

A proposed GPS method with multi-antennae and single receiver

A method based on multi-antennae linked to a common GPS receiver is proposed. The goal of the technique is to improve height determination for baselines a few kilometres in length. The advantage of this technique resides in the elimination of relative clock parameters in the “between-antenna” single difference observations. Because single difference observations are free of clock errors more geometrical strength remains to determine the baseline components. This statement is valid as long as intercable biases can be carefully calibrated. For millimetre height determination, the intercable calibration must be done at the same level of accuracy. Under this assumption it is shown that in general the height standard deviation improves by a factor of about three compared to standard GPS data processing. With the proposed method, the effect of relative tropospheric zenith delay errors becomes a bit smaller (in absolute value), compared to standard data processing. To absorb this error, a relative tropospheric zenith delay parameter may be estimated. Even with this additional parameter in the solution the height standard deviation remains two times smaller than the results of standard processing techniques (without tropospheric zenith delay parameter), and at least five times smaller than in the results obtained from standard processing including one tropospheric zenith delay parameter.

EPC: Matlab software to estimate Euler pole parameters

The estimation of Euler pole parameters has always been an important issue in global tectonics and geodynamics studies. In addition, the increasing number of permanent GPS stations and the ease of access to their data, along with advances in computers, promise new methods and tools for the estimation and the quantitative analysis of Euler pole parameters. Therefore, we developed the Euler pole calculator software using a set of mathematical algorithms based on the model of tectonic plate motion on a spherical surface. The software is able to calculate the expected velocities for any points located on the earth’s surface given the relevant Euler pole parameters and to estimate the Euler pole parameters given the observed velocities of a set of sites located on the same tectonic plate. Mathematical algorithms and functions of the software are explained in detail.

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.

Time-Relative Positioning with a Single Civil GPS Receiver

Time-relative positioning is a recent method for processing GPS phase observations. The operational method undertaken in this paper consists of the following steps: first, recording phase observations at a station of known coordinates; second, moving the GPS receiver to an unknown station (which can be located up to a few hundred meters away, dependint on what type of transportation – e. g., walking, motorcycle – is available) while continuously observing carrier phases; and, third, recording phase observations at a second station of unknown coordinates with a single GPS receiver. To obtain the position of the unknown station relative to the first (known) station, the processing method uses combined observations taken at two different epochs and two different stations with the same receiver. For this reason, the errors that vary between two epochs must be taken into account in an appropriate way, especially errors in satellite clock corrections and ephemerides, and errors related to tropospheric and ionospheric delays. Ionospheric modeling using IONEX files (the ionospheric maps calculated by the International GPS Service) was also tested to correct L1 phase observations. This method has been used to calculate short vectors with an accuracy of a few centimeters (for a processing interval of 30 s) using a single civil GPS receiver.

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.

Modified GPS-OTF Algorithms for Bridge Monitoring: Application to the Pierre-Laporte Suspension Bridge in Quebec City

Algorithms for On-The-Fly ambiguity resolution have been modified for the deformation monitoring of a suspension bridge. Instantaneous relative positioning of a deformation network at a precision of about ±5 mm horizontally and ±10 mm vertically has been achieved using GPS LI phase observations. Particular attention has been paid to the modeling of relative tropospheric delay and to the phase center calibration between antennas of different types. Moving averages on station coordinates have also been applied to reduce multipath effects.

Improving vertical GPS precision with a GPS-over-fiber architecture and real-time relative delay calibration

A limitation of GPS positioning is that the vertical component is generally two to three times less precise than the horizontal components. In a previous work by R. Santerre of Laval University and G. Beutler of University of Bern, it was shown in simulations that it is possible to improve the GPS vertical positioning precision by using a multi-antenna GPS receiver and a precise calibration technique of the relative hardware delay between the antennas and the receiver. However, no actual implementation of the system was done to prove the concept until now. A new multi-antenna, GPS-over-fiber architecture with real-time delay monitoring, designed and implemented to improve the vertical precision is presented. The improvement in vertical precision arises from the elimination of the relative receiver clock error in single difference, between antennas, and the precision real-time calibration of the relative hardware delay. Experiments were conducted with a zero baseline and a short baseline configuration. The results show, as expected by the theory and the simulations, a two to three times improvement in the precision of the vertical component such that it reached the same level of performance as the horizontal components. These promising results will enable the use of this type of configuration in several applications where the same precision in all 3D components is essential and could not be achieved before with standard GPS positioning techniques.

Noise behavior in CGPS position time series : the eastern North America case study

Abstract We analyzed the noise characteristics of 112 continuously operating GPS stations in eastern North America using the Spectral Analysis and the Maximum Likelihood Estimation (MLE) methods. Results of both methods show that the combination ofwhite plus flicker noise is the best model for describing the stochastic part of the position time series. We explored this further using the MLE in the time domain by testing noise models of (a) powerlaw, (b)white, (c)white plus flicker, (d)white plus randomwalk, and (e) white plus flicker plus random-walk. The results show that amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of white noise model in (c–e) are almost equal across the study area, they are prevailed by the flicker and Random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model.