EFFECT OF SPATIAL CORRELATION ON THE PERFORMANCES OF MODERNIZED GPS AND GALILEO IN RELATIVE POSITIONING

In the context of processing GNSS (Global Navigation Satellite System) data, it is known that the estimation of the ionospheric delays decreases the strength of the observation model and makes significant the time required to fix the ambiguities namely in case of long baselines. However, considering the double-differenced (DD) ionospheric delays as stochastic quantities, the redundancy in this case increases and leads to the reduction of time of fixing the ambiguities. The approach developed in the present paper makes two considerations: 1) the DD ionospheric delays are assumed as stochastic quantities and, 2) the spatial correlation of errors is accounted for based on a simple model of correlation. A simulation is made and aims to study the effect of these two mentioned considerations on the performances of the three multifrequency GNSSs; modernized GPS, Galileo and BDS which are not yet in full capability. For each GNSS, dual-frequency combinations of frequencies as well as triple-frequency combination are investigated in the simulation. The performances studied include: the time to fix the ambiguities with high success rate and the precision of coordinates in static relative positioning with varying baseline length. A method is developed to derive what we call the spatial correlation model which approximately gives the covariance between the individual errors belonging to two stations. Furthermore, the stochastic models that follow from accounting and neglecting the spatial correlation are developed. The LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) method is implemented for ambiguity decorrelation. The results show that the time to fix the ambiguities caused by accounting the spatial correlation is less than the time of fix without the spatial correlation. Also, a slight superiority of Galileo in terms of performances is seen compared to the other GNSS. For all the dualfrequency combinations investigated, when processing a baseline length of 500 km with accounted spatial correlation, the time needed to successfully fix the ambiguities lies between 5 and 9 min, whereas it becomes only between 2.5 and 3 min for all the triple-frequency combinations, this is with a sampling time of 5 s. In addition, for all different combinations, the coordinates precision is less than 8 mm even for 500 km. We think that these high performances result from: 1) the precise codes of future GNSS signals, 2) the high redundancy in the observations equation and, 3) taking into account the spatial correlation in the definition of the stochastic model.

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First Preliminary Fast Static Ambiguity Resolution Results of Medium-Baseline with Triple-Frequency Beidou Wavebands

Journal of Navigation ◽

10.1017/s0373463314000332 ◽

2014 ◽

Vol 67 (6) ◽

pp. 1109-1119 ◽

Cited By ~ 6

Author(s):

Shengyue Ji ◽

Xiaolong Wang ◽

Ying Xu ◽

Zhenjie Wang ◽

Wu Chen ◽

...

Keyword(s):

Frequency Band ◽

Ambiguity Resolution ◽

Past Research ◽

Satellite System ◽

Tropospheric Delay ◽

Dual Frequency ◽

Long Distance ◽

Triple Frequency ◽

Global Navigation Satellite ◽

Better Than

Fast high precision relative Global Navigation Satellite System (GNSS) positioning is very important to various applications and ambiguity resolution is a key requirement. It has been a continuing challenge to determine and fix GNSS carrier-phase ambiguity, especially for medium- and long-distance baselines. In past research, with dual-frequency band Global Positioning System (GPS), it is almost impossible for fast ambiguity resolution of medium- and long-distance baselines mainly due to the ionospheric and tropospheric effects. With the launch of the BeiDou system, triple-frequency band GNSS observations are available for the first time. This research aims to test the ambiguity resolution performance with BeiDou triple-frequency band observations. In this research, two mathematical models are compared: zenith tropospheric delay as an unknown parameter versus corrected tropospheric delay. The ambiguity resolution performance is investigated in detail with BeiDou observations. Different distance baselines are tested: 45 km, 70 km and 100 km and the performances are investigated with different elevation cut-off angles. Also the performance with BeiDou alone and combined BeiDou and GPS are compared. Experimental results clearly show that with practical observations of triple-frequency bands, ambiguity of medium- or long-distance baselines can be fixed. The results also show that: the performance of ambiguity resolution with an elevation cutoff angle of 20° is much better than that of 15°; The performance with tropospheric effect corrected is slightly better than that with tropospheric effect as an estimated parameter; Dual-frequency band GPS observations will benefit ambiguity resolution of integrated BeiDou and GPS.

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Predicting the Success Rate of Long-baseline GPS+Galileo (Partial) Ambiguity Resolution

Journal of Navigation ◽

10.1017/s037346331400006x ◽

2014 ◽

Vol 67 (3) ◽

pp. 385-401 ◽

Cited By ~ 22

Author(s):

Dennis Odijk ◽

Balwinder S. Arora ◽

Peter J.G. Teunissen

Keyword(s):

Ambiguity Resolution ◽

Satellite System ◽

Observation Time ◽

Baseline Length ◽

Success Rates ◽

Dual Frequency ◽

Variance Matrix ◽

Partial Ambiguity Resolution ◽

Long Baseline ◽

Triple Frequency

This contribution covers precise (cm-level) relative Global Navigation Satellite System (GNSS) positioning for which the baseline length can reach up to a few hundred km. Carrier-phase ambiguity resolution is required to obtain this high positioning accuracy within manageable observation time spans. However, for such long baselines, the differential ionospheric delays hamper fast ambiguity resolution as based on current dual-frequency Global Positioning System (GPS). It is expected that the modernization of GPS towards a triple-frequency system, as well as the development of Galileo towards a full constellation will be beneficial in speeding up long-baseline ambiguity resolution. In this article we will predict ambiguity resolution success rates for GPS+Galileo for a 250 km baseline based on the ambiguity variance matrix, where the Galileo constellation is simulated by means of Yuma almanac data. From our studies it can be concluded that ambiguity resolution will likely become faster (less than ten minutes) in the case of GPS+Galileo when based on triple-frequency data of both systems, however much shorter times to fix the ambiguities (one-two minutes) can be expected when only a subset of ambiguities is fixed instead of the complete vector (partial ambiguity resolution).

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Triple-Frequency GPS Un-Differenced and Uncombined PPP Ambiguity Resolution Using Observable-Specific Satellite Signal Biases

Remote Sensing ◽

10.3390/rs12142310 ◽

2020 ◽

Vol 12 (14) ◽

pp. 2310 ◽

Cited By ~ 1

Author(s):

Gen Liu ◽

Fei Guo ◽

Jian Wang ◽

Mingyi Du ◽

Lizhong Qu

Keyword(s):

Ambiguity Resolution ◽

Bias Correction ◽

Correction Method ◽

Satellite System ◽

Space Vehicles ◽

Observation Data ◽

Dual Frequency ◽

Triple Frequency ◽

Original Observation ◽

Global Navigation Satellite

The new generations of global navigation satellite system (GNSS) space vehicles can transmit three or more frequency signals. Multi-frequency observations bring a significant improvement to precise point positioning ambiguity resolution (PPP AR). However, the multi-frequency satellite code and phase biases need to be properly handled before conducting PPP AR. The traditional satellite bias correction methods, for example, the commonly used differential code biases (DCB), are limited to the dual-frequency ionosphere-free (IF) case and become more and more difficult to extend to multi-GNSS and multi-frequency cases. In this contribution, we propose the observable-specific signal bias (OSB) correction method for un-differenced and uncombined (UDUC) PPP AR. The OSB correction method, which includes observable-specific satellite code and phase bias correction, can directly apply kinds of OSBs to GNSS original observation data, thus, it is more appropriate for multi-GNSS and multi-frequency cases. In order to verify the performance of multi-frequency UDUC-PPP AR based on the OSB correction method, triple-frequency GPS observation data provided by 142 Multi-GNSS Experiment (MGEX) stations were used to estimate observable-specific satellite phase biases at the PPP service end and some of them were also used to conduct AR at the PPP user end. The experiment results showed: the averaged time-to-first-fix (TTFF) of triple-frequency GPS kinematic UDUC-PPP AR with observable-specific satellite code bias (SCB) corrections could reach about 22 min with about 29% improvement, compared with that without observable-specific SCB corrections; TTFF of triple-frequency static UDUC-PPP AR with observable-specific phase-specific time-variant inter-frequency clock bias (IFCB) corrections took about 15.6 min with about 64.3% improvement, compared with that without observable-specific IFCB corrections.

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Experimental Evaluation of Cooperative Relative Positioning for Intelligent Transportation System

International Journal of Navigation and Observation ◽

10.1155/2014/314371 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12

Author(s):

Suhua Tang ◽

Nao Kawanishi ◽

Rei Furukawa ◽

Nobuaki Kubo

Keyword(s):

Spatial Correlation ◽

Urban Areas ◽

Intelligent Transportation System ◽

Signal Strength ◽

Intelligent Transportation ◽

Satellite System ◽

Relative Positioning ◽

Safe Driving ◽

Global Navigation Satellite ◽

Multipath Errors

Support system for safe driving heavily depends on global navigation satellite system. Pseudoranges between satellites and vehicles are measured to compute vehicles’ positions and their relative positions. In urban areas, however, multipath errors (MPEs) in pseudoranges, caused by obstruction and reflection of roadside buildings, greatly degrade the precision of relative positions. On the other hand, simply removing all reflected signals might lead to a shortage of satellites in fixing positions. In our previous work, we suggested solving this dilemma by cooperative relative positioning (CoRelPos) which exploits spatial correlation of MPEs. In this paper, we collected the trace data of pseudoranges by driving cars in urban areas, analyzed the properties of MPEs (specifically, their dependency on signal strength, elevation angles of satellites, and receivers’ speeds), and highlighted their spatial correlation. On this basis, the CoRelPos scheme is refined by considering the dynamics of MPEs. Evaluation results under practical vehicular scenarios confirm that properties of MPEs can be exploited to improve the precision of relative positions.

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Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

Satellite Navigation ◽

10.1186/s43020-021-00039-x ◽

2021 ◽

Vol 2 (1) ◽

Author(s):

Jin Wang ◽

Qin Zhang ◽

Guanwen Huang

Keyword(s):

Estimation Method ◽

Satellite Orbit ◽

Satellite System ◽

Assessment System ◽

Navigation Satellite ◽

Dual Frequency ◽

Fractional Cycle Bias ◽

The Stability ◽

High Consistency ◽

Global Navigation Satellite

AbstractThe Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

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Improving DGNSS Performance through the Use of Network RTK Corrections

Remote Sensing ◽

10.3390/rs13091621 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1621

Author(s):

Duojie Weng ◽

Shengyue Ji ◽

Yangwei Lu ◽

Wu Chen ◽

Zhihua Li

Keyword(s):

Carrier Phase ◽

Local Area ◽

Satellite System ◽

High Accuracy ◽

Single Frequency ◽

Baseline Length ◽

Low Latitude ◽

Phase Measurements ◽

Network Rtk ◽

Global Navigation Satellite

The differential global navigation satellite system (DGNSS) is an enhancement system that is widely used to improve the accuracy of single-frequency receivers. However, distance-dependent errors are not considered in conventional DGNSS, and DGNSS accuracy decreases when baseline length increases. In network real-time kinematic (RTK) positioning, distance-dependent errors are accurately modelled to enable ambiguity resolution on the user side, and standard Radio Technical Commission for Maritime Services (RTCM) formats have also been developed to describe the spatial characteristics of distance-dependent errors. However, the network RTK service was mainly developed for carrier-phase measurements on professional user receivers. The purpose of this study was to modify the local-area DGNSS through the use of network RTK corrections. Distance-dependent errors can be reduced, and accuracy for a longer baseline length can be improved. The results in the low-latitude areas showed that the accuracy of the modified DGNSS could be improved by more than 50% for a 17.9 km baseline during solar active years. The method in this paper extends the use of available network RTK corrections with high accuracy to normal local-area DGNSS applications.

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Implementation of a Dual-Frequency GLONASS and GPS L1 C/A Software Receiver

Journal of Navigation ◽

10.1017/s0373463309990476 ◽

2010 ◽

Vol 63 (2) ◽

pp. 269-287 ◽

Cited By ~ 4

Author(s):

S. Abbasian Nik ◽

M. G. Petovello

Keyword(s):

Global Navigation Satellite System ◽

Critical Role ◽

Satellite System ◽

Navigation Satellite ◽

Dual Frequency ◽

Software Receiver ◽

The Public ◽

Global Navigation ◽

Global Navigation Satellite

These days, Global Navigation Satellite System (GNSS) technology plays a critical role in positioning and navigation applications. Use of GNSS is becoming more of a need to the public. Therefore, much effort is needed to make the civilian part of the system more accurate, reliable and available, especially for the safety-of-life purposes. With the recent revitalization of Russian Global Navigation Satellite System (GLONASS), with a constellation of 20 satellites in August 2009 and the promise of 24 satellites by 2010, it is worthwhile concentrating on the GLONASS system as a method of GPS augmentation to achieve more reliable and accurate navigation solutions.

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Assessing the quality of ionospheric models through GNSS positioning error: methodology and results

GPS Solutions ◽

10.1007/s10291-019-0918-z ◽

2019 ◽

Vol 24 (1) ◽

Cited By ~ 6

Author(s):

Adrià Rovira-Garcia ◽

Deimos Ibáñez-Segura ◽

Raul Orús-Perez ◽

José Miguel Juan ◽

Jaume Sanz ◽

...

Keyword(s):

Satellite System ◽

Ionospheric Delay ◽

Single Frequency ◽

Positioning Error ◽

Dual Frequency ◽

Error Sources ◽

Ionospheric Models ◽

Evaluation Metric ◽

Global Navigation Satellite

Abstract Single-frequency users of the global navigation satellite system (GNSS) must correct for the ionospheric delay. These corrections are available from global ionospheric models (GIMs). Therefore, the accuracy of the GIM is important because the unmodeled or incorrectly part of ionospheric delay contributes to the positioning error of GNSS-based positioning. However, the positioning error of receivers located at known coordinates can be used to infer the accuracy of GIMs in a simple manner. This is why assessment of GIMs by means of the position domain is often used as an alternative to assessments in the ionospheric delay domain. The latter method requires accurate reference ionospheric values obtained from a network solution and complex geodetic modeling. However, evaluations using the positioning error method present several difficulties, as evidenced in recent works, that can lead to inconsistent results compared to the tests using the ionospheric delay domain. We analyze the reasons why such inconsistencies occur, applying both methodologies. We have computed the position of 34 permanent stations for the entire year of 2014 within the last Solar Maximum. The positioning tests have been done using code pseudoranges and carrier-phase leveled (CCL) measurements. We identify the error sources that make it difficult to distinguish the part of the positioning error that is attributable to the ionospheric correction: the measurement noise, pseudorange multipath, evaluation metric, and outliers. Once these error sources are considered, we obtain equivalent results to those found in the ionospheric delay domain assessments. Accurate GIMs can provide single-frequency navigation positioning at the decimeter level using CCL measurements and better positions than those obtained using the dual-frequency ionospheric-free combination of pseudoranges. Finally, some recommendations are provided for further studies of ionospheric models using the position domain method.

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Kinematic PPP Using Mixed GPS/Glonass Single-Frequency Observations

Artificial Satellites ◽

10.2478/arsa-2019-0008 ◽

2019 ◽

Vol 54 (3) ◽

pp. 97-112

Author(s):

Mostafa Hamed ◽

Ashraf Abdallah ◽

Ashraf Farah

Keyword(s):

Low Cost ◽

Satellite System ◽

Single Frequency ◽

Future Research ◽

Frequency Data ◽

Dual Frequency ◽

Trajectory Data ◽

Average Improvement ◽

Kinematic Ppp ◽

Global Navigation Satellite

Abstract Nowadays, Precise Point Positioning (PPP) is a very popular technique for Global Navigation Satellite System (GNSS) positioning. The advantage of PPP is its low cost as well as no distance limitation when compared with the differential technique. Single-frequency receivers have the advantage of cost effectiveness when compared with the expensive dual-frequency receivers, but the ionosphere error makes a difficulty to be completely mitigated. This research aims to assess the effect of using observations from both GPS and GLONASS constellations in comparison with GPS only for kinematic purposes using single-frequency observations. Six days of the year 2018 with single-frequency data for the Ethiopian IGS station named “ADIS” were processed epoch by epoch for 24 hours once with GPS-only observations and another with GPS/GLONASS observations. In addition to “ADIS” station, a kinematic track in the New Aswan City, Aswan, Egypt, has been observed using Leica GS15, geodetic type, dual-frequency, GPS/GLONASS GNSS receiver and single-frequency data have been processed. Net_Diff software was used for processing all the data. The results have been compared with a reference solution. Adding GLONASS satellites significantly improved the satellite number and Position Dilution Of Precision (PDOP) value and accordingly improved the accuracy of positioning. In the case of “ADIS” data, the 3D Root Mean Square Error (RMSE) ranged between 0.273 and 0.816 m for GPS only and improved to a range from 0.256 to 0.550 m for GPS/GLONASS for the 6 processed days. An average improvement ratio of 24%, 29%, 30%, and 29% in the east, north, height, and 3D position components, respectively, was achieved. For the kinematic trajectory, the 3D position RMSE improved from 0.733 m for GPS only to 0.638 m for GPS/GLONASS. The improvement ratios were 7%, 5%, 28%, and 13% in the east, north, height, and 3D position components, respectively, for the kinematic trajectory data. This opens the way to add observations from the other two constellations (Galileo and BeiDou) for more accuracy in future research.

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A Joint Dual-Frequency GNSS/SINS Deep-Coupled Navigation System for Polar Navigation

Applied Sciences ◽

10.3390/app8112322 ◽

2018 ◽

Vol 8 (11) ◽

pp. 2322 ◽

Cited By ~ 2

Author(s):

Lin Zhao ◽

Mouyan Wu ◽

Jicheng Ding ◽

Yingyao Kang

Keyword(s):

Navigation System ◽

Density Ratio ◽

Satellite System ◽

The Arctic ◽

Observation Data ◽

Dual Frequency ◽

Vector Tracking ◽

Time Observation ◽

Global Navigation Satellite ◽

Navigation Accuracy

The strategic position of the polar area and its rich natural resources are becoming increasingly important, while the northeast and northwest passages through the Arctic are receiving much attention as glaciers continue to melt. The global navigation satellite system (GNSS) can provide real-time observation data for the polar areas, but may suffer low elevation problems of satellites, signals with poor carrier-power-to-noise-density ratio (C/N0), ionospheric scintillations, and dynamic requirements. In order to improve the navigation performance in polar areas, a deep-coupled navigation system with dual-frequency GNSS and a grid strapdown inertial navigation system (SINS) is proposed in the paper. The coverage and visibility of the GNSS constellation in polar areas are briefly reviewed firstly. Then, the joint dual-frequency vector tracking architecture of GNSS is designed with the aid of grid SINS information, which can optimize the tracking band, sharing tracking information to aid weak signal channels with strong signal channels and meet the dynamic requirement to improve the accuracy and robustness of the system. Besides this, the ionosphere-free combination of global positioning system (GPS) L1 C/A and L2 signals is used in the proposed system to further reduce ionospheric influence. Finally, the performance of the system is tested using a hardware simulator and semiphysical experiments. Experimental results indicate that the proposed system can obtain a better navigation accuracy and robust performance in polar areas.

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