Single Baseline Solution Research Articles

BDS/GPS Multi-Baseline Relative Positioning for Deformation Monitoring

The single-baseline solution (SBS) model has been widely adopted by the existing global navigation satellite system (GNSS) deformation monitoring systems due to its theoretical simplicity and ease of implementation. However, the SBS model neglects the mathematical correlation between baselines, and the accuracy and reliability can be degraded for baselines with long length, large height difference or frequent satellite signal occlusion. When monitoring large-area ground settlement or long-spanned linear objects such as bridges and railroads, multiple reference stations are frequently utilized, which can be exploited to improve the monitoring performance. Therefore, this paper evaluates the multi-baseline solution (MBS) model, and constrained-MBS (CMBS) model that has a prior constraint of the spatial-correlated tropospheric delay. The reliability and validity of the MBS model are verified using GPS/BDS datasets from ground settlement deformation monitoring with a baseline length of about 20 km and a height difference of about 200 m. Numerical results show that, compared with the SBS model, the MBS model can reduce the positioning standard deviation (STD) and root-mean-squared (RMS) errors by up to (47.4/51.3/66.2%) and (56.9/60.4/58.4%) in the north/east/up components, respectively. Moreover, the combined GPS/BDS positioning performance for the MBS model outperforms the GPS-only and BDS-only positioning models, with an average accuracy improvement of about 13.8 and 25.8%, with the highest accuracy improvement of about 41.6 and 43.8%, respectively. With the additional tropospheric delay constraint, the CMBS model improves the monitoring precision in the up direction by about 45.0%.

Phase Centre Corrections of GNSS Antennas and Their Consistency with ATX Catalogues

Changes of the antenna models on permanent global navigation satellite system (GNSS) stations can lead to jumps and discontinuities in the coordinate time series. In this paper, the results of research on the adequacy of the antenna phase centre corrections (PCC) variations are presented by analysing its component—the antennas’ phase centre offset (PCO). For this purpose, height differences were determined using different and independent methods: EUREF Permanent Network (EPN) combined solutions, Precise Point Positioning (PPP), and the single baseline solution. The results of GNSS processing were referenced to direct geometric levelling outputs. The research was conducted only within the global positioning system (GPS) system due to the compatibility of one of the receivers, and the experiment was based on a comparison of the height differences between four GNSS antennas located on the roof of a building: two permanent station antennas and two auxiliary points. The antennas were located at similar heights; precise height differences were determined by geometric levelling, both at the beginning and the end of the session. Post-processing was conducted with the use of the GPS system, precise ephemeris, the adopted antenna correction model, and a zero-elevation mask. For one of the antennas, a change of the antenna characteristic model from IGS08 to IGS14 leads to an 8-mm difference in height. Older antennas used in the national (or transnational) permanent network need individual PCC.

A simplified processing algorithm for multi-baseline RTK positioning in urban environments

The real-time kinematic (RTK) positioning with the multi-baseline solution (MBS) can provide high accuracy and availability for emerging applications. When the multi-systems and multi-frequencies observations for multiple stations are adopted, a heavy computational burden can arise to degrade the performance of RTK positioning. In this paper, a simplified multi-baseline solution (SMBS) algorithm based on the equivalence principle is proposed to improve the computational efficiency. Firstly, the classical equivalent observation equations (COE) are introduced and the variance–covariance (VC) matrix for SD observations is presented. Then, the simplified equivalent observation equations (SOE) can be obtained throughthe formuladerivationof transformation matrix. Secondly, the sequential Kalman filter (SKF) with multiple groups is used instead of the classical Kalman filter (CKF) to improve filtering efficiency. Finally, the performance of the proposed algorithm is comprehensively evaluated and analyzed by the static and kinematic experiments. The results demonstrate that the SMBS algorithm adopting SOE and SKF strategies can significantly accelerate the processing procedure of RTK positioning and reduce the processing time for a single epoch. The SOE strategy has an average efficiency improvement by approximately 74.7% for static, and 60.6% for the kinematic experiment, and the improvement of the SKF strategy is 49.6% and 58.0%. Moreover, the SMBS algorithm can provide a higher positioning accuracy and availability than the single-baseline solution (SBS) model. Especially for multiple reference stations, the state parameters of the rover station can be compressed to enhance the geometric strength of the positioning model, which can provide a smaller PDOP and ADOP values and improve the performance of ambiguity resolution (AR).

A new algorithm for a multi-baseline solution based on the equivalence principle

A new algorithm of a multi-baseline solution (MBS) based on the equivalence principle for precise relative positioning is proposed in this paper. The objective of the solution is to keep the observations independent when eliminating the satellite and receiver’s clock errors. The equivalent differenced observation equations are developed through the equivalent transform. Because of the high-dimension characteristics of the MBS ambiguity, a modified partial ambiguity resolution of the MBS (PAR-MBS) strategy is developed to determine an ambiguity subset. Compared with the traditional single-baseline solution (SBS), the zero and short baseline experiments are carried out to validate and evaluate the proposed algorithm. The results show that the MBS can enhance the strength of the relative positioning model and improve positioning accuracy and availability. The PAR-MBS can shorten the convergence time for the epoch to first fix by on average 41.7% with all 80 observation segments. Moreover, the difference of the positioning errors between the MBS and SBS is indistinguishable for the 45 and 60 min schemes. However, for the 30 min scheme, there is a significant performance improvement by approximately 11%, 10% and 14% in the N, E, and U components, respectively. The closure errors of the repeated baselines and triangle closed loops can also deliver similar results for the 45 and 60 min schemes; however, for the 30 min scheme, there is a remarkable performance improvement by approximately 48%, 59%, and 12%, and 54%, 65%, and 10% in the N, E, and U components, respectively.

Results of the application of tropospheric corrections from different troposphere models for precise GPS rapid static positioning

In many surveying applications, determination of accurate heights is of significant interest. The delay caused by the neutral atmosphere is one of the main factors limiting the accuracy of GPS positioning and affecting mainly the height coordinate component rather than horizontal ones. Estimation of the zenith total delay is a commonly used technique for accounting for the tropospheric delay in static positioning. However, in the rapid static positioning mode the estimation of the zenith total delay may fail, since for its reliable estimation longer observing sessions are required. In this paper, several troposphere modeling techniques were applied and tested with three processing scenarios: a single baseline solution with various height differences and a multi-baseline solution. In specific, we introduced external zenith total delays obtained from Modified Hopfield troposphere model with standard atmosphere parameters, UNB3m model, COAMPS numerical weather prediction model and zenith total delays interpolated from a reference network solution. The best results were obtained when tropospheric delays derived from the reference network were applied.

Development and Assessment of a Multiple Rover Network Approach for Real-Time GNSS Networks

: In this paper multiple GNSS users are considered as a virtual network of stations that can operate autonomously and combine with the reference station network. The existing network infrastructure is densified through the shorter inter-receiver distances. A new network RTK methodology that encompasses the multiple users of network RTK services for instantaneous positioning is presented. Users are equipped with a means of two-way communication that enables the data to be transmitted to a central processing facility (CPF) on an epoch by epoch basis. Once the reference station ambiguities are resolved and the regional ionospheric corrections are estimated and filtered, the proposed Multiple Rover Network (MRN) solution is applied. The MRN solution increases the ambiguity success rates for all rovers for the designed testbed network compared to the single baseline solution (SBS) and the single rover network solution (SRN). The highest increment is observed for the rover operating outside the network.

Optimal Integration of Single-Baseline GPS Solutions in Network-Based Kinematic Positioning

Although the demand for high accuracy kinematic positioning using multiple base stations has increased over the last several years, most commercial GPS processing software still only provides single-baseline solutions. Thus, methods were investigated to improve the accuracy of kinematic positioning by using network configuration on the basis of several single-baseline solutions. As discussed in this study, the positioning accuracy and network stability are improved by applying geodetic network adjustment theories to a kinematic positioning application. Four different methods to remove the rank-deficiency (RLESS, BLIMPBE, SCLESS, and PMINOLESS) are analyzed in this study. The 3D RMS (root mean squared) error has been improved from 4.4 cm (maximum) to 2.7 cm by using network-based kinematic positioning, and BLIMPBE is preferable over other methods in terms of the minimum bias in the rover position and the reproducing property of the reference stations.

GPS Carrier‐Phase Time Transfer Using Single‐Difference Integer Ambiguity Resolution

GPS is widely used for time and frequency transfer. To estimate the clock difference between two ground stations, a single baseline solution can be performed using external products for the modelling of the geometrical effects (constellation ephemeris and station coordinates). The baseline solution relies on a single‐difference formulation, using code and phase ionosphere‐free measurements. The phase ambiguities are usually adjusted as floating parameters. Such solutions give very good results when modelling hypotheses are consistent between the external solution (e.g., GPS orbits) and the baseline solution. However, the frequency bias in the computed clock is very sensitive to discrepancies in the models, and is only observed thanks to the code measurement, with limitations due to the noise. Here, we propose to solve the integer ambiguities on single‐difference phase measurements. The advantage is the complete elimination of the clock drifts observed in floating ambiguities solutions. This formulation allows also a reliable continuous connection between overlapping clock solutions (jumps between such solutions can be completely eliminated). Several time transfer results are analyzed and compared to TWSTFT. The methodology has been extended to a network of stations using integer ambiguities on zero‐difference measurements. The corresponding results are given for a few European stations.

Static Network Code Dgps Positioning vs. Carrier Phase Single Baseline Solutions for Short Observation time and Medium-Long Distances

Static Network Code Dgps Positioning vs. Carrier Phase Single Baseline Solutions for Short Observation time and Medium-Long DistancesGPS land surveys are usually based on the results of processing GPS carrier phase data. Code or pseudorange observations due to considerations of accuracy requirements and robustness are preferred in navigation and some GIS applications. Generally, the accuracy of that positioning is in the range of about 1-2 meters or so, on average. But the main problem in code GPS positioning is to know how to estimate the real accuracy of DGPS positions. It is not such an easy process in code positioning when one reference station is used. In most commercial software, there are no values of accuracy but only positions are presented. DGPS positions without estimated errors cannot be used for surveying tasks and for most GIS applications due to the fact that every point has to be have accuracy determined. However, when we used static GPS positioning, it is well known that the accuracy is determined, both during baseline processing and next by the adjustment of a GPS network. These steps of validation with redundancy in classical static phase baseline solutions allow wide use of static or rapid static methods in the main land surveying tasks. Although these control steps are commonly used in many major surveying and engineering tasks, they are not always effective in terms of short-observation-time sessions. This paper presents a new network DGPS approach of positioning with the use of at least three reference stations. The approach concerns also valid accuracy estimation based on variance-covariance (VC) matrix in the least-squares (LS) calculations. The presented network DGPS approach has the ability of reliable accuracy estimation. Finally, network DGPS positioning is compared with static baselines solutions where five-min sessions were taken into consideration for two different rover stations. It was shown that in a short observation time of GPS positioning, code network DGPS results can give even centimetre accuracy and can be more reliable than static relative phase positioning where gross errors often happen.