Precise Point Positioning Using Triple GNSS Constellations in Various Modes

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.

Precise Point Positioning Using Triple GNSS Constellations in Various Modes

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.

Improved GNSS-Based Bistatic SAR Using Multi-Satellites Fusion: Analysis and Experimental Demonstration

The Global Navigation Satellite System (GNSS)-based Bistatic Synthetic Aperture Radar (SAR) is getting more and more attention in remote sensing for its all-weather and real-time global observation capability. Its low range resolution results from the narrow signal bandwidth limits in its development. The configuration difference caused by the illumination angle and movement direction of the different satellites makes it possible to improve resolution by multi-satellite fusion. However, this also introduces new problems with the resolution-enhancing efficiency and increased computation brought about by the fusion. In this paper, we aim at effectively improving the resolution of the multi-satellite fusion system. To this purpose, firstly, the Point Spread Function (PSF) of the multi-satellite fusion system is analyzed, and focusing on the relationship between the fusion resolution and the geometric configuration and the number of satellites. Numerical simulation results show that, compared with multi-satellite fusion, dual-satellite fusion is a combination with higher resolution enhancement efficiency. Secondly, a method for dual-satellite fusion imaging based on optimized satellite selection is proposed. With the greedy algorithm, the selection is divided into two steps: in the first step, according to geometry configuration, the single-satellite with the optimal 2-D resolution is selected as the reference satellite; in the second step, the angles between the azimuthal vector of the reference satellite and the azimuthal vector of the other satellites were calculated by the traversal method, the satellite corresponding to the intersection angle which is closest to 90° is selected as the auxiliary satellite. The fused image was obtained by non-coherent addition of the images generated by the reference satellite and the auxiliary satellite, respectively. Finally, the GPS L1 real orbit multi-target simulation and experimental validation were conducted, respectively. The simulation results show that the 2-D resolution of the images produced by our proposed method is globally optimal 15 times and suboptimal 8 times out of 24 data sets. The experimental results show that the 2-D resolution of our proposed method is optimal in the scene, and the area of the resolution unit is reduced by 70.1% compared to the single-satellite’s images. In the experiment, there are three navigation satellites for imaging, the time taken to the proposed method was 66.6% that of the traversal method. Simulations and experiments fully demonstrate the feasibility of the method.

An Enhanced Method for Detecting and Repairing the Cycle Slips of Dual-Frequency Onboard GPS Receivers of LEO Satellites

Cycle slip detection and repair play important roles in the processing of data from dual-frequency GPS receivers onboard low-Earth orbit (LEO) satellites. To detect and repair cycle slips more comprehensively, an enhanced error method (EEM) is proposed. EEM combines single-frequency and narrow-lane carrier phase observations to construct special observations and observation equation groups. These special observations differ across time and satellite (ATS). ATS observations are constructed by three steps. The first step is differencing single-frequency and narrow-lane observations through a time difference (TD). The second step is to select a satellite as a reference satellite and other satellites as nonreference satellites. The third step is to difference the single-frequency TD observations from the reference satellite and the narrow-lane TD observations from the nonreference satellites by a satellite difference. If cycle slips occur at the reference satellite, the correction values for these ATS observations can be significantly enlarged. To process all satellites, the EEM selects each satellite as a reference satellite and builds the corresponding equation group. The EEM solves these observation equation groups according to the weighted least-squares adjustment (LSA) criterion and obtains the correction values; these correction values are then used to construct the χ 2 values corresponding to different equation groups, and the EEM subsequently carries out a chi-square distribution test for these χ 2 . The satellite corresponding to the maximum χ 2 will be marked. Then, the EEM iteratively processes the other satellites. Cycle slips can be estimated by rounding the float solutions of changes in the ambiguities of cycle slip satellites to the nearest integer. The simulation test results show that the EEM can be used to detect special cycle slip pairs such as (1, 1) and (9, 7). The EEM needs only observation data in two adjacent epochs and is still applicable to observation epochs with continuous cycle slips.

A New Approach to Earth’s Gravity Field Modeling Using GPS-Derived Kinematic Orbits and Baselines

Earth’s gravity field recovery from GPS observations collected by low earth orbiting (LEO) satellites is a well-established technique, and kinematic orbits are commonly used for that purpose. Nowadays, more and more satellites are flying in close formations. The GPS-derived kinematic baselines between them can reach millimeter precision, which is more precise than the centimeter-level kinematic orbits. Thus, it has long been expected that the more precise kinematic baselines can deliver better gravity field solutions. However, this expectation has not been met yet in practice. In this study, we propose a new approach to gravity field modeling, in which kinematic orbits of the reference satellite and baseline vectors between the reference satellite and its accompanying satellite are jointly inverted. To validate the added value, data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are used. We derive kinematic orbits and inter-satellite baselines of the twin GRACE satellites from the GPS data collected in the year of 2010. Then two sets of monthly gravity field solutions up to degree and order 60 are produced. One is derived from kinematic orbits of the twin GRACE satellites (‘orbit approach’). The other is derived from kinematic orbits of GRACE A and baseline vectors between GRACE A and B (‘baseline approach’). Analysis of observation postfit residuals shows that noise in the kinematic baselines is notably lower than the kinematic orbits by 50, 47 and 43% for the along-track, cross-track and radial components, respectively. Regarding the gravity field solutions, analysis in the spectral domain shows that noise of the gravity field solutions beyond degree 10 can be significantly reduced when the baseline approach is applied, with cumulative errors up to degree 60 being reduced by 34%, when compared to the orbit approach. In the spatial domain, the recovered mass changes with the baseline approach are more consistent with those inferred from the K-Band Ranging based solutions. Our results demonstrate that the proposed baseline approach is able to provide better gravity field solutions than the orbit approach. The findings may facilitate, among others, bridging the gap between GRACE and GRACE Follow-On satellite mission.

Accounting for the differential inter-system bias (DISB) of code observation in GPS+BDS positioning

If the associated differential inter-system biases (DISBs) are priori known, only one common reference satellite is sufficient, which is called the inter-system model. The inter-system model can help to maximize the redundancy of the positioning model, and thus can improve the positioning performance, especially in harsh environment. However, in practice use not all receivers can be calibrated with DISBs in advance. In this paper, taking combined GPS and BDS pseudorange positioning as the example, we compare three positioning models and their positioning performance. One is traditional intra-system model, and the other two belongs to the inter-system models, i. e. the model with calibration of DISB and the model with real-time estimation of DISB parameter. Positioning performance using the three models is evaluated with simulated obstructed environments. It will be shown that besides the model with calibration of DISB, the model with real-time estimation of DISB parameter can also effectively improve positioning accuracy and reliability compared with the traditional intra-system model, especially for the severely obstructed environment with only a few satellites observed. When no more than 7 satellites visible, the positioning accuracies in each directions can be improved by no less than 15 %. The proposed model can be used alternatively when no priori DISB calibration is available.

The Stratospheric Water and Ozone Satellite Homogenized (SWOOSH) database: a long-term database for climate studies

In this paper, we describe the construction of the Stratospheric Water and Ozone Satellite Homogenized (SWOOSH) database, which includes vertically resolved ozone and water vapor data from a subset of the limb profiling satellite instruments operating since the 1980s. The primary SWOOSH products are zonal-mean monthly-mean time series of water vapor and ozone mixing ratio on pressure levels (12 levels per decade from 316 to 1 hPa). The SWOOSH pressure level products are provided on several independent zonal-mean grids (2.5, 5, and 10°), and additional products include two coarse 3-D griddings (30° long × 10° lat, 20° × 5°) as well as a zonal-mean isentropic product. SWOOSH includes both individual satellite source data as well as a merged data product. A key aspect of the merged product is that the source records are homogenized to account for inter-satellite biases and to minimize artificial jumps in the record. We describe the SWOOSH homogenization process, which involves adjusting the satellite data records to a “reference” satellite using coincident observations during time periods of instrument overlap. The reference satellite is chosen based on the best agreement with independent balloon-based sounding measurements, with the goal of producing a long-term data record that is both homogeneous (i.e., with minimal artificial jumps in time) and accurate (i.e., unbiased). This paper details the choice of reference measurements, homogenization, and gridding process involved in the construction of the combined SWOOSH product and also presents the ancillary information stored in SWOOSH that can be used in future studies of water vapor and ozone variability. Furthermore, a discussion of uncertainties in the combined SWOOSH record is presented, and examples of the SWOOSH record are provided to illustrate its use for studies of ozone and water vapor variability on interannual to decadal timescales. The version 2.5 SWOOSH data are publicly available at doi:10.7289/V5TD9VBX.