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1
Yang, Songfeng, Qiyuan Zhang, Xi Zhang, and Donglie Liu. "Impact of GPS/BDS Satellite Attitude Quaternions on Precise Point Positioning with Ambiguity Resolution." Remote Sensing 13, no. 15 (August 2, 2021): 3035. http://dx.doi.org/10.3390/rs13153035.
Повний текст джерелаАнотація:
Precise point positioning with ambiguity resolution (PPP-AR) based on multiple global navigation satellite system (multi-GNSS) constellations is an important high-precision positioning tool. However, some unmodeled satellite and receiver biases (such as errors in satellite attitude) make it difficult to fix carrier-phase ambiguities. In order to fix ambiguities of eclipsing satellites, accurate integer clock and satellite attitude products (i.e., attitude quaternion) have been provided by the International GNSS Service (IGS). Nevertheless, the quality of these products and their positioning performance in multi-GNSS PPP-AR have not been investigated yet. Using the PRIDE PPP-AR II software associated with the corresponding rapid satellite orbit, integer clock and attitude quaternion products of Wuhan University (WUM), we carried out GPS/BDS PPP-AR using 30 days of data in an eclipsing season of 2020. We found that about 75% of GPS, 60% of BDS-2 and 57% of BDS-3 narrow-lane ambiguity residuals after integer clock corrections fall within ±0.1 cycles in the case of using nominal attitudes. However, when using attitude quaternions, these percentages will rise to 80% for GPS, 70% for BDS-2 and 60% for BDS-3. GPS/BDS daily kinematic PPP-AR after integer clock and nominal attitude corrections can usually achieve a positioning precision of about 10, 10 and 30 mm for the east, north and up components, respectively. In contrast, the counterparts are 8, 8 and 20 mm when using attitude quaternions. Compared with the case of using attitude quaternions only at the network end for the integer clock estimation, using attitude quaternions only at the user end shows a pronounced improvement of 15% in the east component and less than 10% in the north and up components. Therefore, we suggest PPP users apply integer clock and satellite attitude quaternion products to realize more efficient ambiguity fixing, especially in satellite eclipsing seasons.
2
Povalyaev, A. A., A. A. Baburin, and A. A. Podkorytov. "The Use of the Lattice Packing Theory for Precise Point Positioning with Ionosphere-Free Measurements in CDMA GNSS." Rocket-space device engineering and information systems 8, no. 2 (2021): 51–61. http://dx.doi.org/10.30894/issn2409-0239.2021.8.2.51.61.
Повний текст джерелаАнотація:
The paper considers the use of the lattice packing theory for Integer Precise Point Positioning (Integer PPP) with the errors usually not exceeding 1–3 cm based on GNSS signals with code division multiple access (CDMA). Positioning is carried out by processing ionosphere-free linear combinations of code and phase measurements with ambiguity resolution employing satellite corrections. The main issue of PPP algorithms is overcoming the rank deficiency problem of the linear equation system obtained by linearization of nonlinear mathematical models of measurements. Nowadays Float PPP is quite well developed, where rank deficiency is tackled by combining systematic biases in measurement models with integer carrier phase ambiguities. As a result, the number of unknowns is reduced to the rank of design matrix, which allows unambiguous estimation of precise user coordinates and values of new variables generated by the performed combinations. However, under such conditions the information about integer nature of carrier phase ambiguities is lost, and this leads to a significant increase in convergence time to obtain user coordinates estimates with the errors of 1–3 cm. It is possible to involve the information on the integer nature of phase ambiguities into processing by applying ambiguity resolution algorithms. Though, as a result of the conducted combinations, the integer nature is destroyed, which makes it impossible to apply these algorithms. In Integer PPP rank deficiency is overcome by projecting the state space of the initial linear equation system onto a so-called S-space, whose dimension is equal to the rank of this system. The orientation of the S-space and the direction of projecting are chosen so that the variables of the initial system corresponding to user coordinates are not changed during the projecting and the projections of integer variables remain integer. This makes it possible to estimate precise user coordinates involving information on the integer nature of phase ambiguities. In the literature on Integer PPP based on CDMA GNSS signals processing the description of the S-space orientation with the desired properties is given, but there is no description of the method to determine this orientation. This paper based on the notions of the lattice packing theory considers an algorithm for determining the S-space with the desired properties. It is shown that there exists an infinite set of such S-spaces connected by unimodular transformations, and a technique is proposed to enable selection from this set the S-space, which requires minimal computational cost. The use of the lattice packing theory to the Integer PPP network solution with CDMA GNSS signals will be considered in the following publication of the authors.
3
Li, Xingxing, and Xiaohong Zhang. "Improving the Estimation of Uncalibrated Fractional Phase Offsets for PPP Ambiguity Resolution." Journal of Navigation 65, no. 3 (March 23, 2012): 513–29. http://dx.doi.org/10.1017/s0373463312000112.
Повний текст джерелаАнотація:
Integer ambiguity resolution in Precise Point Positioning (PPP) can shorten convergence time and improve accuracy significantly. Uncalibrated Fractional Offsets (UFOs) originating in the satellites destroy the integer nature of carrier phase ambiguities observed at a single station. Several methods have been developed to estimate UFO information from a reference network for PPP ambiguity resolution. In this paper, we present a new approach for estimating Zero-Differenced (ZD) UFOs via float ZD ambiguities from a reference network. In this new approach, UFOs for receivers and satellites are estimated in an integrated adjustment with integer ambiguities being resolved sequentially, so that UFOs of higher quality can be achieved. The float ZD ambiguities used in the estimation can be from network or PPP solutions. Using those from PPP solutions enables the time-consuming clock estimations and the UFO estimations to be carried out separately, so that UFOs can be estimated more reliably from a much denser network. In this paper, a data processing procedure, from the estimation of UFOs through to PPP ambiguity fixing, is designed and proposed. The approach is validated with several data sets in various scenarios. The results show that satellite UFOs can be estimated precisely and reliably by using the observations from a reference network, in which the station spacing could be up to thousands of kilometres. With 30 minutes of observations, a PPP solution with fixed integer ambiguities is achievable and the positioning accuracy can be improved significantly when compared with its float solution.
4
Huang, Wei, Pascale Defraigne, Giovanna Signorile, and Ilaria Sesia. "Improved Multi-GNSS PPP Software for Upgrading the DEMETRA Project Time Monitoring Service." Sensors 19, no. 20 (October 11, 2019): 4389. http://dx.doi.org/10.3390/s19204389.
Повний текст джерелаАнотація:
The H2020 DEMETRA project provides short latency clock monitoring services to the time users using the Atomium precise point positioning (PPP) software developed by the Royal Observatory of Belgium. In this paper, three recent updates of the current Atomium software are introduced: adding Galileo signals in the PPP computation; the option to constrain the receiver clock; PPP with integer ambiguity resolution. The advantages of these updates are demonstrated: Combining the Galileo and global positioning system (GPS) signals for PPP time transfer will further improve the frequency stability inside the computation batch; PPP with receiver clock constraint is not only used to reduce the short-term noise of the clock measurements but can also be used for some specific applications to a keep continuous clock solution in the computation batch or retrieve correct clock measurements from extremely noisy environments; the integer PPP allows a continuous clock solution, and improves the mid-term and long-term stability of the frequency transfer compared to the current PPP frequency transfer techniques.
5
Li, Xu, Flechtner, Förste, Lu, and He. "Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica." Remote Sensing 11, no. 8 (April 25, 2019): 992. http://dx.doi.org/10.3390/rs11080992.
Повний текст джерелаАнотація:
Conventional relative kinematic positioning is difficult to be applied in the polar region of Earth since there is a very sparse distribution of reference stations, while precise point positioning (PPP), using data of a stand-alone receiver, is recognized as a promising tool for obtaining reliable and accurate trajectories of moving platforms. However, PPP and its integer ambiguity fixing performance could be much degraded by satellite orbits and clocks of poor quality, such as those of the geostationary Earth orbit (GEO) satellites of the BeiDou navigation satellite system (BDS), because temporal variation of orbit errors cannot be fully absorbed by ambiguities. To overcome such problems, a network-based processing, referred to as precise orbit positioning (POP), in which the satellite clock offsets are estimated with fixed precise orbits, is implemented in this study. The POP approach is validated in comparison with PPP in terms of integer ambiguity fixing and trajectory accuracy. In a simulation test, multi-GNSS (global navigation satellite system) observations over 14 days from 136 globally distributed MGEX (the multi-GNSS Experiment) receivers are used and four of them on the coast of Antarctica are processed in kinematic mode as moving stations. The results show that POP can improve the ambiguity fixing of all system combinations and significant improvement is found in the solution with BDS, since its large orbit errors are reduced in an integrated adjustment with satellite clock offsets. The four-system GPS+GLONASS+Galileo+BDS (GREC) fixed solution enables the highest 3D position accuracy of about 3.0 cm compared to 4.3 cm of the GPS-only solution. Through a real flight experiment over Antarctica, it is also confirmed that POP ambiguity fixing performs better and thus can considerably speed up (re-)convergence and reduce most of the fluctuations in PPP solutions, since the continuous tracking time is short compared to that in other regions.
6
Zhang, Baocheng, Yunbin Yuan, and Yanju Chai. "QIF-based GPS Long-baseline Ambiguity Resolution with the Aid of Atmospheric Delays Determined by PPP." Journal of Navigation 69, no. 6 (May 27, 2016): 1278–92. http://dx.doi.org/10.1017/s037346331600028x.
Повний текст джерелаАнотація:
The Global Positioning System (GPS) long-baseline set up has been widely employed to generate high-accuracy positioning, timing and atmospheric information. Bernese GPS software adopts two appropriate strategies for long-baseline Integer Ambiguity Resolution (IAR): Quasi Ionosphere-Free (QIF) and Wide-lane/Narrow-lane (WN). With the goal of reasonably shortening the time required for long-baseline IAR, we propose the Precise Point Positioning (PPP) method for estimating, on a per receiver basis, the Zenith Tropospheric Delays (ZTDs) and the Slant Ionospheric Delays (SIDs) from zero-differenced, uncombined GPS observables. We then reformulate these PPP-derived ZTDs and SIDs into two types of atmospheric constraints with proper uncertainties that could be readily assimilated into the process of IAR with the QIF. Our numerical tests based on five independent long-baselines (>1,000 kilometres) suggest that the empirical precision of PPP-derived ZTDs (SIDs) is always better than 2 (10) centimetres. The modified QIF would be able to correctly resolve at least 98% and 88% of the wide- and narrow-lane ambiguities for all the long-baselines relying on the very simple integer rounding method. However, under the same condition, the WN can only get the correct integers of 76·6% wide-lane ambiguities and 55·2% narrow-lane ones.
7
Ma, Hongyang, Sandra Verhagen, Dimitrios Psychas, João Francisco Galera Monico, and Haroldo Antonio Marques. "Flight-Test Evaluation of Integer Ambiguity Resolution Enabled PPP." Journal of Surveying Engineering 147, no. 3 (August 2021): 04021013. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000367.
Повний текст джерела
8
Shi, Junbo, and Yang Gao. "A comparison of three PPP integer ambiguity resolution methods." GPS Solutions 18, no. 4 (October 31, 2013): 519–28. http://dx.doi.org/10.1007/s10291-013-0348-2.
Повний текст джерела
9
Alcay, Salih, Omer Faruk Atiz, and Sermet Ogutcu. "Comparison of RT-PPP and RT-PPP-AR Methods." Academic Perspective Procedia 3, no. 1 (October 25, 2020): 308–15. http://dx.doi.org/10.33793/acperpro.03.01.61.
Повний текст джерелаАнотація:
The Precise Point Positioning (PPP) is an absolute positioning method which emerged as an alternative to the relative positioning method. This method is widely used in many applications in recent years. In this method the static and kinematic positioning can be performed with high accuracy by using single GNSS receiver. In the last few years, the PPP method has started to be used in real time (RT-PPP) thanks to the real-time precise products (satellite orbit and clock data) produced by different organizations like IGS, BKG, CNES, ESA, EUREF, GFZ etc. The high interest in RT-PPP has accelerated the development of this method and many software have been developed. Recently, some of the software have ability to apply integer ambiguity resolution (AR). For this purpose, in this study the positioning performance of RT-PPP method was tested using two options of PPP-WIZARD software (RT-PPP, RT-PPP-AR). Three IGS stations were chosen in different geographical regions. The real-time coordinates of the stations belong to the observation period of about 4 hours were derived simultaneously with the RT-PPP and RT-PPP-AR options in 1 second epoch interval. The results obtained are given in a comparative approach.
10
Jokinen, Altti, Shaojun Feng, Wolfgang Schuster, Washington Ochieng, Chris Hide, Terry Moore, and Chris Hill. "GLONASS Aided GPS Ambiguity Fixed Precise Point Positioning." Journal of Navigation 66, no. 3 (March 25, 2013): 399–416. http://dx.doi.org/10.1017/s0373463313000052.
Повний текст джерелаАнотація:
The Precise Point Positioning (PPP) concept enables centimetre-level positioning accuracy by employing one Global Navigation Satellite System (GNSS) receiver. The main advantage of PPP over conventional Real Time Kinematic (cRTK) methods is that a local reference network infrastructure is not required. Only a global reference network with approximately 50 stations is needed because reference GNSS data is required for generating precise error correction products for PPP. However, the current implementation of PPP is not suitable for some applications due to the long time period (i.e. convergence time of up to 60 minutes) required to obtain an accurate position solution. This paper presents a new method to reduce the time required for initial integer ambiguity resolution and to improve position accuracy. It is based on combining GPS and GLONASS measurements to calculate the float ambiguity positioning solution initially, followed by the resolution of GPS integer ambiguities.The results show that using the GPS/GLONASS float solution can, on average, reduce the time to initial GPS ambiguity resolution by approximately 5% compared to using the GPS float solution alone. In addition, average vertical and horizontal positioning errors at the initial ambiguity resolution epoch can be reduced by approximately 17% and 4%, respectively.
11
Zhao, Lewen, Jan Douša, and Pavel Václavovic. "Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity." ISPRS International Journal of Geo-Information 10, no. 8 (July 30, 2021): 516. http://dx.doi.org/10.3390/ijgi10080516.
Повний текст джерелаАнотація:
The Precise Point Positioning (PPP) with fast integer ambiguity resolution (PPP-RTK) is feasible only if the solution is augmented with precise ionospheric parameters. The vertical ionospheric delays together with the receiver hardware biases, are estimated simultaneously based on the uncombined PPP model. The performance of the ionospheric delays was evaluated and applied in the PPP-RTK demonstration during the low solar activity period. The processing was supported by precise products provided by Deutsches GeoForschungsZentrum Potsdam (GFZ) and also by real-time products provided by the National Centre for Space Studies (CNES). Since GFZ provides only precise orbits and clocks, other products needed for ambiguity resolution, such as phase biases, were estimated at the Geodetic Observatory Pecny (GOP). When ambiguity parameters were resolved as integer values in the GPS-only solution, the initial convergence period was reduced from 30 and 20 min to 24 and 13 min when using CNES and GFZ/GOP products, respectively. The accuracy of ionospheric delays derived from the ambiguity fixed PPP, and the CODE global ionosphere map were then assessed. Comparison of ambiguity fixed ionospheric delay obtained at two collocated stations indicated the accuracy of 0.15 TECU for different scenarios with more than 60% improvement compared to the ambiguity float PPP. However, a daily periodic variation can be observed from the multi-day short-baseline ionospheric residuals. The accuracy of the interpolated ionospheric delay from global maps revealed a dependency on the location of the stations, ranging from 1 to 3 TECU. Precise ionospheric delays derived from the EUREF permanent network with an inter-station distance larger than 73 km were selected for ionospheric modeling at the user location. Results indicated that the PPP ambiguity resolution could be achieved within three minutes. After enlarging the inter-station distance to 209 km, ambiguity resolution could also be achieved within several minutes.
12
Shi, J., and Y. Gao. "Improvement of PPP-inferred tropospheric estimates by integer ambiguity resolution." Advances in Space Research 50, no. 10 (November 2012): 1374–82. http://dx.doi.org/10.1016/j.asr.2012.06.036.
Повний текст джерела
13
Gratton, Paul, Simon Banville, Gérard Lachapelle, and Kyle O’Keefe. "Kinematic Zenith Tropospheric Delay Estimation with GNSS PPP in Mountainous Areas." Sensors 21, no. 17 (August 25, 2021): 5709. http://dx.doi.org/10.3390/s21175709.
Повний текст джерелаАнотація:
The use of global navigation satellite systems (GNSS) precise point positioning (PPP) to estimate zenith tropospheric delay (ZTD) profiles in kinematic vehicular mode in mountainous areas is investigated. Car-mounted multi-constellation GNSS receivers are employed. The Natural Resources Canada Canadian Spatial Reference System PPP (CSRS-PPP) online service that currently processes dual-frequency global positioning system (GPS) and Global’naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) measurements and is now capable of GPS integer ambiguity resolution is used. An offline version that can process the above and Galileo measurements simultaneously, including Galileo integer ambiguity resolution is also tested to evaluate the advantage of three constellations. A multi-day static data set observed under open sky is first tested to determine performance under ideal conditions. Two long road profile tests conducted in kinematic mode are then analyzed to assess the capability of the approach. The challenges of ZTD kinematic profiling are numerous, namely shorter data sets, signal shading due to topography and forests of conifers along roads, and frequent losses of phase lock requiring numerous but not always successful integer ambiguity re-initialization. ZTD profiles are therefore often only available with float ambiguities, reducing system observability. Occasional total interruption of measurement availability results in profile discontinuities. CSRS-PPP outputs separately the zenith hydrostatic or dry delay (ZHD) and water vapour content or zenith wet delay (ZWD). The two delays are analyzed separately, with emphasis on the more unpredictable and highly variable ZWD, especially in mountainous areas. The estimated delays are compared with the Vienna Mapping Function 1 (VMF1), which proves to be highly effective to model the large-scale profile variations in the Canadian Rockies, the main contribution of GNSS PPP being the estimation of higher frequency ZWD components. Of the many conclusions drawn from the field experiments, it is estimated that kinematic profiles are generally determined with accuracy of 10 to 20 mm, depending on the signal harshness of the environment.
14
Wang, Zhiyu, Zishen Li, Ningbo Wang, Mainul Hoque, Liang Wang, Ran Li, Yang Zhang, and Hong Yuan. "Real-Time Precise Orbit Determination for LEO between Kinematic and Reduced-Dynamic with Ambiguity Resolution." Aerospace 9, no. 1 (January 4, 2022): 25. http://dx.doi.org/10.3390/aerospace9010025.
Повний текст джерелаАнотація:
The real-time integer-ambiguity resolution of the carrier-phase observation is one of the most effective approaches to enhance the accuracy of real-time precise point positioning (PPP), kinematic precise orbit determination (KPOD), and reduced-dynamic precise orbit determination (RPOD) for low earth orbit (LEO) satellites. In this study, the integer phase clock (IPC) and wide-lane satellite bias (WSB) products from CNES (Centre National d’Etudes Spatiales) are used to fix ambiguity in real time. Meanwhile, the three models of real-time PPP, KPOD, and RPOD are applied to validate the contribution of ambiguity resolution. Experimental results show that (1) the average positioning accuracy of IGS stations for ambiguity-fixed solutions is improved from about 7.14 to 5.91 cm, with an improvement of around 17% compared to the real-time float PPP solutions, with enhancement in the east-west direction particularly significant, with an improvement of about 29%; (2) the average accuracy of the estimated LEO orbit with ambiguity-fixed solutions in the real-time KPOD and RPOD mode is improved by about 16% and 10%, respectively, with respect to the corresponding mode with the ambiguity-float solutions; (3) the performance of real-time LEO RPOD is better than that of the corresponding KPOD, regardless of fixed- or float-ambiguity solutions. Moreover, the average ambiguity-fixed ratio can reach more than 90% in real-time PPP, KPOD, and RPOD.
15
Psychas, Dimitrios, Peter J. G. Teunissen, and Sandra Verhagen. "A Multi-Frequency Galileo PPP-RTK Convergence Analysis with an Emphasis on the Role of Frequency Spacing." Remote Sensing 13, no. 16 (August 5, 2021): 3077. http://dx.doi.org/10.3390/rs13163077.
Повний текст джерелаАнотація:
The single-receiver integer ambiguity resolution-enabled variant of precise point positioning (PPP), namely PPP-RTK, has proven to be crucial in reducing the long convergence time of PPP solutions through the recovery of the integerness of the user-ambiguities. The proliferation of global navigation satellite systems (GNSS) supports various improvements in this regard through the availability of more satellites and frequencies. The increased availability of the Galileo E6 signal from GNSS receivers paves the way for speeding up integer ambiguity resolution, as more frequencies provide for a stronger model. In this contribution, the Galileo-based PPP-RTK ambiguity resolution and positioning convergence capabilities are studied and numerically demonstrated as a function of the number and spacing of frequencies, aiming to shed light on which frequencies should be used to obtain optimal performance. Through a formal analysis, we provide insight into the pivotal role of frequency separation in ambiguity resolution. Using real Galileo data on up to five frequencies and our estimated PPP-RTK corrections, representative kinematic user convergence results with partial ambiguity resolution are presented and discussed. Compared to the achieved performance of dual-frequency fixed solutions, it is found that the contribution of multi-frequency observations is significant and largely driven by frequency separation. When using all five available frequencies, it is shown that the kinematic user can achieve a sub-decimeter level convergence in 15.0 min (90% percentile). In our analysis, we also show to what extent the provision of the estimable satellite code biases as standard PPP-RTK corrections accelerates convergence. Finally, we numerically demonstrate that, when integrated with GPS, the kinematic user solution achieves convergence in 3.0 and 5.0 min on average and at 90%, respectively, in the presence of ionospheric delays, thereby indicating the single-receiver user’s fast-convergence capabilities.
16
Katsigianni, Georgia, Sylvain Loyer, and Felix Perosanz. "PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS." Remote Sensing 11, no. 21 (October 24, 2019): 2477. http://dx.doi.org/10.3390/rs11212477.
Повний текст джерелаАнотація:
Precise point positioning (PPP) has been used for decades not only for general positioning needs but also for geodetic and other scientific applications. The CNES-CLS Analysis Centre (AC) of the International GNSS Service (IGS) is performing PPP with phase ambiguity resolution (PPP-AR) using the zero-difference ambiguity fixing approach also known as “Integer PPP” (IPPP). In this paper we examine the postprocessed kinematic PPP and PPP-AR using Galileo-only, GPS-only and Multi-GNSS (GPS + Galileo) constellations. The interest is to examine the accuracy for each GNSS system individually but also of their combination to measure the current benefits of using Galileo within a Multi-GNSS PPP and PPP-AR. Results show that Galileo-only positioning is nearly at the same level as GPS-only; around 2–4 mm horizontal and aound 10 mm vertical repeatability (example station of BRUX). In addition, the use of Galileo system—even uncompleted—improves the performance of the positioning when combined with GPS giving mm level repeatability (improvement of around 30% in East, North and Up components). Repeatabilities observed for Multi-GNSS (GPS + GAL) PPP-AR, taking into account the global network statistics, are a little larger, with 8 mm in horizontal and 17 mm in vertical directions. This result shows that including Galileo ameliorates the best positioning accuracy achieved until today with GPS PPP-AR.
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Petit, Gérard, Amale Kanj, Sylvain Loyer, Jérôme Delporte, Flavien Mercier, and Félix Perosanz. "1 × 10−16frequency transfer by GPS PPP with integer ambiguity resolution." Metrologia 52, no. 2 (March 24, 2015): 301–9. http://dx.doi.org/10.1088/0026-1394/52/2/301.
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Innac, Anna, Antonio Angrisano, Salvatore Gaglione, Mario Vultaggio, and Nicola Crocetto. "Performance Comparison among Multi-GNSS Single Frequency Precise Point Positioning Techniques." Kartografija i geoinformacije 18, no. 32 (December 15, 2019): 80–99. http://dx.doi.org/10.32909/kg.18.32.6.
Повний текст джерелаАнотація:
Precise Point Positioning (PPP) is a technique able to compute high accuracy positioning anywhere using a single GNSS receiver and without the need for corrections from reference stations. A wide range of possible PPP algorithms, using different correction models and processing strategies, exist for both post-processing and real-time applications. PPP relies on accurate satellite and clock data, with the use of precise carrier-phase measurements. Single Frequency-PPP (SF-PPP) is currently under investigation by the scientific community, owing to its cheap implementation with respect to classical differential positioning and multi-frequency un-differenced techniques. Unfortunately, the carrier-phase observable is ambiguous by an a priori unknown integer number of cycles, called ambiguity, which is difficult to resolve with SF receivers. The aim of this paper was to study the opportunity provided by the use of a multi-GNSS constellation applied to two widespread SF-PPP models, based on different carrier-phase and code observable combinations. The algorithms were tested using static data collection carried out in an open-sky scenario. The results show decimeter level accuracy on the horizontal and vertical components of the position.
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Zhang, Baocheng, Peter J. G. Teunissen, and Dennis Odijk. "A Novel Un-differenced PPP-RTK Concept." Journal of Navigation 64, S1 (October 14, 2011): S180—S191. http://dx.doi.org/10.1017/s0373463311000361.
Повний текст джерелаАнотація:
In this contribution, a novel un-differenced (UD) (PPP-RTK) concept, i.e. a synthesis of Precise Point Positioning and Network-based Real-Time Kinematic concept, is introduced. In the first step of our PPP-RTK approach, the UD GNSS observations from a regional reference network are processed based upon re-parameterised observation equations, corrections for satellite clocks, phase biases and (interpolated) atmospheric delays are calculated and provided to users. In the second step, these network-based corrections are used at the user site to restore the integer nature of his UD phase ambiguities, which makes rapid and high accuracy user positioning possible. The proposed PPP-RTK approach was tested using two GPS CORS networks with inter-station distances ranging from 60 to 100 km. The first test network is the northern China CORS network and the second is the Australian Perth CORS network. In the test of the first network, a dual-frequency PPP-RTK user receiver was used, while in the test of the second network, a low-cost, single-frequency PPP-RTK user receiver was used. The performance of fast ambiguity resolution and the high accuracy positioning of the PPP-RTK results are demonstrated.
20
Shi, Junbo, and Yang Gao. "A Troposphere Constraint Method To Improve PPP Ambiguity-Resolved Height Solution." Journal of Navigation 67, no. 2 (October 8, 2013): 249–62. http://dx.doi.org/10.1017/s0373463313000647.
Повний текст джерелаАнотація:
Integer ambiguity resolution is able to improve positioning accuracy and reduce convergence time in Precise Point Positioning (PPP). Although significantly improved horizontal positioning accuracy has been demonstrated, the height solution improvement is found to be less significant, and improving this requires further investigation. In this paper, a troposphere constraint method using precise troposphere corrections is proposed to improve the PPP ambiguity-resolved height solution. This is different from the conventional approach that typically applies meteorological data to calculate the a priori troposphere delay and estimates the residual troposphere delay. The effects of the troposphere delay on PPP ambiguity-resolved height solutions are first studied. Numerical analysis is conducted to ambiguity-resolved positioning results based on the decoupled clock model and hourly Global Positioning System (GPS) observations from a Canadian PPP-inferred troposphere precipitable water vapour system. The results show that by using the proposed method the PPP ambiguity-resolved height accuracy can be further improved to 3·86 cm compared to 5·32 cm using the conventional approach.
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Yang, Liu, Jingxiang Gao, Zengke Li, Fangchao Li, Chao Chen, and Yifan Wang. "New Satellite Selection Approach for GPS/BDS/GLONASS Kinematic Precise Point Positioning." Applied Sciences 9, no. 24 (December 4, 2019): 5280. http://dx.doi.org/10.3390/app9245280.
Повний текст джерелаАнотація:
With the development of global satellite navigation systems, kinematic Precise Point Positioning (PPP) is facing the increasing computational load of instantaneous (single-epoch) processing due to more and more visible satellites. At this time, the satellite selection algorithm that can effectively reduce the computational complexity causes us to consider its application in GPS/BDS/GLONASS kinematic PPP. Considering the characteristics of different systems and satellite selection algorithms, we proposed a new satellite selection approach (NSS model) which includes three different satellite selection algorithms (maximum volume algorithm, fast-rotating partition satellite selection algorithm, and elevation partition satellite selection algorithm). Additionally, the inheritance of ambiguity was also proposed to solve the situation of constantly re-estimated integer ambiguity when the satellite selection algorithm is used in PPP. The results show that the NSS model had a centimeter-level positioning accuracy when the original PPP and optimal dilution of precision (DOP) algorithm solution were compared in kinematic PPP based on the data at five multi-GNSS Experiment (MGEX) stations. It can also reduce a huge amount of computation at the same time. Thus, the application of the NSS model is an effective method to reduce the computational complexity and guarantee the final positioning accuracy in GPS/BDS/GLONASS kinematic PPP.
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Bisnath, S., and P. Collins. "Recent Developments in Precise Point Positioning." GEOMATICA 66, no. 2 (June 2012): 103–11. http://dx.doi.org/10.5623/cig2012-023.
Повний текст джерелаАнотація:
In standard Precise Point Positioning (PPP), the carrier phase ambiguities are estimated as real-valued constants, so that the carrier-phases can provide similar information as the pseudoranges. As a consequence, it can take tens of minutes to several hours for the ambiguities to converge to suitably precise values. Recently, new processing methods have been identified that permit the ambiguities to be estimated more appropriately as integer-valued constants, as they are in relative Real-Time Kinematic (RTK) positioning. Under these conditions, standard ambiguity resolution techniques can be applied to strengthen the PPP solution. The result can be a greatly reduced solution convergence and re-convergence period, representing a significant step toward improving the performance of PPP with respect to that of RTK processing. This paper describes the underlying principles of the method, why the enhancements work, and presents some results.
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Li, Haojun, Jingxin Xiao, Shoujian Zhang, Jin Zhou, and Jiexian Wang. "Introduction of the Double-Differenced Ambiguity Resolution into Precise Point Positioning." Remote Sensing 10, no. 11 (November 9, 2018): 1779. http://dx.doi.org/10.3390/rs10111779.
Повний текст джерелаАнотація:
According to the advantages of the precise point positioning (PPP) and the double-differenced (DD) model based algorithm, a new method for the integration of DD integer ambiguity resolution into PPP is presented. This method uses the undifferenced ambiguity estimated with PPP computation and the DD ambiguity generated from the DD model based algorithm to realize the PPP ambiguity fixing. In the presented method, the selection of the undifferenced ambiguity bases on the ratio test of the DD ambiguity and the ratio values based weight is used in PPP processing. This ensures the quality of the used undifferenced ambiguity. To validate the presented method, two experiments are implemented using the ten days (11 to 20 August 2014) data from local and regional reference stations and the moved two receivers. The results of the presented strategy show that improvements are achieved in all three coordinate components. The 1-h, 2-h, and 4-h PPP results indicate that the mean relative improvements were about 19%, 18%, and 15% for north, east, and up components. These results also show that prominent improvements of 29%, 31%, and 25% for north, east, and up components were obtained when the ratio values based weight was used. The application of the presented method in the displacement monitoring was implemented with the experiment and it showed that the PPP estimation computed with the presented strategy benefits local or regional displacement monitoring and improves the detecting ability for displacement.
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Wang, Siyao, Rui Tu, Bofeng Li, Rui Zhang, Lihong Fan, Junqiang Han, and Xiaochun Lu. "Tight Integration Kinematic PPP-AR Using GPS/Galileo/QZSS Overlapping Frequency Signals and Its Performance in High-Shade Environments." Remote Sensing 15, no. 2 (January 13, 2023): 485. http://dx.doi.org/10.3390/rs15020485.
Повний текст джерелаАнотація:
Several global navigation satellite systems (GNSS) broadcast overlapping frequencies to enhance interoperability, allowing tight integration with only one reference satellite for every system with the same frequency. The key to realizing tight integration is estimating and utilizing differential intersystem biases, which allows the integer characteristic of the differenced ambiguity of two satellites from different systems to be retrieved. In this study, a detailed algorithm flow of a tight integration kinematic uncalibrated phase delay (UPD)-based PPP ambiguity resolution (PPP-AR) method, which includes multiple parts, is introduced. Subsequently, PPP-AR numerical experiments were conducted in a high-shade observation environment to determine the performance. In comparison with traditional methods, our results indicate that the average success fix rate improves from 83% to 100% after using the tight integration method in an environment where only three satellites are observed for each system. Moreover, for fewer than nine satellites, the tight integration method can still consistently maintain a fixed state. However, for comparison, the traditional loose integration method could no longer be implemented.
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Zhao, Lei, Paul Blunt, and Lei Yang. "Performance Analysis of Zero-Difference GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 Point Positioning Using CNES Uncombined Bias Products." Remote Sensing 14, no. 3 (January 29, 2022): 650. http://dx.doi.org/10.3390/rs14030650.
Повний текст джерелаАнотація:
The modernization of Global Navigation Satellite System (GNSS) including the transmission of signals on multiple frequencies has greatly promoted the development of the popular PPP (Precise Point Positioning) technique. A key issue of multi-frequency PPP is the handling of the observable-specific signal biases in order to allow for carrier-phase ambiguity resolution (AR). As a result, PPP modeling at a user side in the multi-frequency case varies depending on the definition of the applied phase bias products. In this study, we investigate the positioning performance of GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 undifferenced ionosphere-float model in the conventional PPP mode and the single-epoch mode using the uncombined code and phase bias products generated at the French CNES (Centre National D’Etudes Spatiales). A series of widelane ambiguities are configured in our multi-frequency PPP functional model instead of forming the classical Melbourne–Wübbena (MW) combination. The best integer equivariant (BIE) estimator is used for the ambiguity resolution in a conventional cascading scheme according to the wavelength of the combined ambiguities for each constellation. Real data collected at IGS stations with a 30-s sampling interval is applied to evaluate the above models. For the conventional kinematic PPP configuration, a significant accuracy improvement of 63% on the east component of the fixed solution is obtained with respect to the ambiguity-float solution. The PPP convergence is accelerated by 17% after the AR. Regarding the single-epoch positioning, an accuracy of 32 and 31 cm for north and east components can be achieved, respectively, (68th percentile) with the instantaneous widelane-ambiguity resolution, which is improved by 13% and 16% compared to multi-frequency code-based or float solution.
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Ma, Hongyang, Qile Zhao, Sandra Verhagen, Dimitrios Psychas, and Xianglin Liu. "Assessing the Performance of Multi-GNSS PPP-RTK in the Local Area." Remote Sensing 12, no. 20 (October 13, 2020): 3343. http://dx.doi.org/10.3390/rs12203343.
Повний текст джерелаАнотація:
The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS parameter estimation to meet user needs. This contribution focuses on integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) in the use of the observations from four global navigation systems, i.e., GPS (Global Positioning System), Galileo (European Global Navigation Satellite System), BDS (Chinese BeiDou Navigation Satellite System), and GLONASS (Global’naya Navigatsionnaya Sputnikova Sistema). An undifferenced and uncombined PPP-RTK model is implemented for which the satellite clock and phase bias corrections are computed from the data processing of a group of stations in a network and then provided to users to help them achieve integer ambiguity resolution on a single receiver by calibrating the satellite phase biases. The dataset is recorded in a local area of the GNSS network of the Netherlands, in which 12 stations are regarded as the reference to generate the corresponding corrections and 21 as the users to assess the performance of the multi-GNSS PPP-RTK in both kinematic and static positioning mode. The results show that the root-mean-square (RMS) errors of the ambiguity float solutions can achieve the same accuracy level of the ambiguity fixed solutions after convergence. The combined GNSS cases, on the contrary, reduce the horizontal RMS of GPS alone with 2 cm level to GPS + Galileo/GPS + Galileo + BDS/GPS + Galileo + BDS + GLONASS with 1 cm level. The convergence time benefits from both multi-GNSS and fixing ambiguities, and the performances of the ambiguity fixed solution are comparable to those of the multi-GNSS ambiguity float solutions. For instance, the convergence time of GPS alone ambiguity fixed solutions to achieve 10 cm three-dimensional (3D) positioning accuracy is 39.5 min, while it is 37 min for GPS + Galileo ambiguity float solutions; moreover, with the same criterion, the convergence time of GE ambiguity fixed solutions is 19 min, which is better than GPS + Galileo + BDS + GLONASS ambiguity float solutions with 28.5 min. The experiments indicate that GPS alone occasionally suffers from a wrong fixing problem; however, this problem does not exist in the combined systems. Finally, integer ambiguity resolution is still necessary for multi-GNSS in the case of fast achieving very-high-accuracy positioning, e.g., sub-centimeter level.
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Liu, Yanyan, Yidong Lou, Shirong Ye, Rui Zhang, Weiwei Song, Xing Zhang, and Qingquan Li. "Assessment of PPP integer ambiguity resolution using GPS, GLONASS and BeiDou (IGSO, MEO) constellations." GPS Solutions 21, no. 4 (June 5, 2017): 1647–59. http://dx.doi.org/10.1007/s10291-017-0641-6.
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Song, Chuanfeng, Hongyang Ma, Huizhong Zhu, Bo Wu, and Nan Shen. "External Tropospheric Corrections by Using Kriging Interpolation for Improving PPP-RTK Positioning Solutions." Remote Sensing 14, no. 15 (August 4, 2022): 3747. http://dx.doi.org/10.3390/rs14153747.
Повний текст джерелаАнотація:
With the availability of satellite carrier-phase delay corrections provided by a reference network or the International GNSS Service (IGS), the integer ambiguity resolution for a single receiver can be successfully achieved, which is the so-called PPP-RTK concept. Although PPP-RTK can significantly shorten the convergence time, it is still worthwhile to further investigate fast and high-precision GNSS parameter estimation to improve efficiency and productivity. In order to fully exploit the potential of GNSS for positioning applications, we herein introduce external troposphere corrections as constrained pseudo observables to the undifferenced and uncombined PPP-RTK model. Since the uncertainties of the corrections are considered in the data processing, the PPP-RTK model with the weighted tropospheric corrections is referred to as the tropospheric-weighted model. Kriging interpolation is applied to generate the tropospheric corrections, as well as the corresponding variances. The quality of the tropospheric-weighted model is assessed by the positioning Root Mean Square (RMS) errors and the convergence time to reach a 10 cm accuracy. The 90% 3D convergence time of the kinematic positioning mode of the tropospheric-weighted model is 43.5 min with the ambiguity-float solution and 21.5 min with the ambiguity-fixed solution, which are shortened by 4.5 min and 5.5 min as compared to those of the standard PPP-RTK model, respectively. As for the static positioning mode, the 90% 3D convergence time of the tropospheric-weighted model for the ambiguity-float and -fixed solutions is 25.5 min and 15 min, while the 3D convergence time is 31.5 min and 18.5 min for the standard PPP-RTK model, respectively. The results also show that the tropospheric-weighted model can still work well in a 5 cm convergence threshold.
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Keshin, Maxim, Yuki Sato, Kenji Nakakuki, and Rui Hirokawa. "A Novel Clock Parameterization and Its Implications for Precise Point Positioning and Ionosphere Estimation." Sensors 22, no. 9 (April 19, 2022): 3117. http://dx.doi.org/10.3390/s22093117.
Повний текст джерелаАнотація:
By convention, IGS precise clock products are computed using the ionosphere-free linear combination. Due to the broad use of IGS products, this convention is exploited in PPP-RTK models not using such a linear combination. So, in different carrier phase combinations, the code hardware biases are contained in different combinations, thus making the problem of separating biases from integer ambiguities more complicated. In this paper, we proposed a novel clock parameterization which allows facilitating this problem. Based on the proposed parameterization, we derived a dual-frequency PPP-RTK model for the undifferenced measurements and assessed this model for the static positioning case in terms of positioning accuracy, convergence, and ambiguity resolution performance. The results showed that a cm-level accuracy level is achievable with the derived models with nearly instant convergence and almost 100% successfully resolved ambiguities. We demonstrated the use of this parameterization for slant ionosphere estimation. We derived the analog of the equation linking the wide-lane, geometry-free, and ionosphere-free biases from the Fast-PPP system and used it to retrieve slant ionosphere information. Our TEC estimates showed some evidence of capability to reach an agreement of 1–2 TECU and the standard deviation of 3–4 TECU with GIM TEC values.
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Elsobeiey, M. "Receiver Widelane Analysis and Its Effect on Precise Point Positioning." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-2 (November 11, 2014): 133–36. http://dx.doi.org/10.5194/isprsarchives-xl-2-133-2014.
Повний текст джерелаАнотація:
Typically, differential carrier-phase-based methods have been used in positioning applications that require high accuracy. The main advantage of differential methods is solving the carrier-phase ambiguities and obtain millimetre-level accuracy carrier-phase measurements. Recent studies showed that it is possible to fix the un-differenced carrier-phase ambiguities into integers which is well-known as un-differenced carrier-phase ambiguity resolution. Unfortunately, the IGS neglects satellite hardware delay during satellite clock corrections estimation process. In case of differential methods, however, this will not affect the user as all common errors between the reference and rover receivers will be cancelled out by. Point positioning, on the other hand, will be affected by neglecting satellite hardware delays as those hardware delays will be lumped into the carrier-phase ambiguities destroying its integer nature. To solve this problem, satellite clock corrections must be estimated based on clock correction for each observable bases. The user, on the other hand, can form the ionosphere-free linear combination and divide and fix its two components, namely widelane and narrowlane. If both ambiguities are successfully fixed, few millimetres level of accuracy measurements are then obtained. In this paper, one month (December, 2013) of GPS data is used to study the receiver widelane bias, its behaviour over time, and receiver dependency are provided. It is shown that the receiver widelane bias is receiver dependent, stable over time for high-grade geodetic receivers. These results are expected to have a great impact on precise point positioning (PPP) conversion time and PPP carrierphase ambiguity resolution.
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LAURICHESSE, DENIS, FLAVIEN MERCIER, JEAN-PAUL BERTHIAS, PATRICK BROCA, and LUCA CERRI. "Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination." Navigation 56, no. 2 (June 2009): 135–49. http://dx.doi.org/10.1002/j.2161-4296.2009.tb01750.x.
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Kim, Euiho, Jaeyoung Song, Yujin Shin, Saekyul Kim, Pyo-Woong Son, Sulgee Park, and Sanghyun Park. "Fault-Free Protection Level Equation for CLAS PPP-RTK and Experimental Evaluations." Sensors 22, no. 9 (May 7, 2022): 3570. http://dx.doi.org/10.3390/s22093570.
Повний текст джерелаАнотація:
Centimeter level augmentation system (CLAS) of the quasi-zenith satellite system (QZSS) is the first precise point positioning-real time kinematic (PPP-RTK) augmentation system of the global navigation satellite system (GNSS), which is currently providing services for Japan. CLAS broadcasts the state-space representation of correction messages along with integrity messages regarding satellite faults and the quality index of each correction. In other GNSS augmentation systems, such as the space-based augmentation system (SBAS) of GNSS, the quality indices of correction messages are used to generate fault-free protection levels that represent a position bound containing a true user position with a probability of missed detections. Although the protection level equations are well defined for the SBAS, a protection level equation for the CLAS PPP-RTK service has not been rigorously discussed in the literature. This paper proposes a fault-free protection level equation for the PPP-RTK methods that considers the probability of correct integer ambiguity fixes in the GNSS carrier phase measurements as well as the CLAS correction quality messages. The computed protection levels with position errors were experimentally compared by processing the GNSS measurements from the GNSS Earth Observation Network (GEONET) stations in Japan and the L6 messages from the CLAS broadcast using the virtual reference station-real time kinematic (VRS-RTK) techniques. Our results, based on the GEONET dataset spanning 7 days, showed that the computed protection levels using the proposed equations were larger than the position errors for all epochs. In the dataset, the RMS errors of the CLAS VRS-RTK position were 4.6 and 14 cm in the horizontal and vertical directions, respectively, whereas the horizontal protection levels ranged from 25 cm to 2.3 m and the vertical protection levels ranged from 50 cm to 5.2 m based on fault-free integrity risk of 10−7.
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Psychas, Dimitrios, and Sandra Verhagen. "Real-Time PPP-RTK Performance Analysis Using Ionospheric Corrections from Multi-Scale Network Configurations." Sensors 20, no. 11 (May 26, 2020): 3012. http://dx.doi.org/10.3390/s20113012.
Повний текст джерелаАнотація:
The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.
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Yang, Yang, Xiaokui Yue, and Jianping Yuan. "GPS Based Reduced-Dynamic Orbit Determination for Low Earth Orbiters with Ambiguity Fixing." International Journal of Aerospace Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/723414.
Повний текст джерелаАнотація:
With the ever-increasing number of satellites in Low Earth Orbit (LEO) for scientific missions, the precise determination of the position and velocity of the satellite is a necessity. GPS (Global Positioning System) based reduced-dynamic orbit determination (RPOD) method is commonly used in the post processing with high precision. This paper presents a sequential RPOD strategy for LEO satellite in the framework of Extended Kalman Filter (EKF). Precise Point Positioning (PPP) technique is used to process the GPS observations, with carrier phase ambiguity resolution using Integer Phase Clocks (IPCs) products. A set of GRACE (Gravity Recovery And Climate Experiment) mission data is used to test and validate the RPOD performance. Results indicate that orbit determination accuracy could be improved by 15% in terms of 3D RMS error in comparison with traditional RPOD method with float ambiguity solutions.
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Pecheritsa, D. S., S. Y. Burtsev, and A. A. Frolov. "Method for determining the fractional part of the carrier frequency cycle of the simulator GNSS signals." Izmeritel`naya Tekhnika, no. 11 (2020): 42–48. http://dx.doi.org/10.32446/0368-1025it.2020-11-42-48.
Повний текст джерелаАнотація:
The article presents the calibration problem of a navigation signals simulator while ensuring the measurements uniformity of coordinate and time measuring instruments. The method of determining the carrier frequency cycle fractional part in the simulator RF circuit output and standart deviation estimate of the pseudorange generation error by the simulator on the carrier phase with using of an oscilloscope is presented. The method essence is to determine the phase difference between two signals: the simulator absolute calibration with a single RF output – the phase difference between the navigation signal generated by the simulator and the reference harmonic signal; the simulator relative calibration with two or more RF outputs – the phase difference between the navigation signals generated by the simulator from different RF outputs. The applying of the simulator absolute calibration by the carrier frequency phase to solve the receiver calibration problem by the carrier frequency phase is shown, which will significantly simplify the implementation of the promising Integer-PPP technology. Presented the use of the simulator relative calibration to determine the accuracy characteristics of angular receiver in its development and testing.
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Feng, Shaojun, Washington Ochieng, Jaron Samson, Michel Tossaint, Manuel Hernandez-Pajares, J. Miguel Juan, Jaume Sanz, Àngela Aragón-Àngel, Pere Ramos-Bosch, and Marti Jofre. "Integrity Monitoring for Carrier Phase Ambiguities." Journal of Navigation 65, no. 1 (November 25, 2011): 41–58. http://dx.doi.org/10.1017/s037346331100052x.
Повний текст джерелаАнотація:
The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.
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Liu, Fei, and Yang Gao. "Triple-Frequency GPS Precise Point Positioning Ambiguity Resolution Using Dual-Frequency Based IGS Precise Clock Products." International Journal of Aerospace Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/7854323.
Повний текст джерелаАнотація:
With the availability of the third civil signal in the Global Positioning System, triple-frequency Precise Point Positioning ambiguity resolution methods have drawn increasing attention due to significantly reduced convergence time. However, the corresponding triple-frequency based precise clock products are not widely available and adopted by applications. Currently, most precise products are generated based on ionosphere-free combination of dual-frequency L1/L2 signals, which however are not consistent with the triple-frequency ionosphere-free carrier-phase measurements, resulting in inaccurate positioning and unstable float ambiguities. In this study, a GPS triple-frequency PPP ambiguity resolution method is developed using the widely used dual-frequency based clock products. In this method, the interfrequency clock biases between the triple-frequency and dual-frequency ionosphere-free carrier-phase measurements are first estimated and then applied to triple-frequency ionosphere-free carrier-phase measurements to obtain stable float ambiguities. After this, the wide-lane L2/L5 and wide-lane L1/L2 integer property of ambiguities are recovered by estimating the satellite fractional cycle biases. A test using a sparse network is conducted to verify the effectiveness of the method. The results show that the ambiguity resolution can be achieved in minutes even tens of seconds and the positioning accuracy is in decimeter level.
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Nosek, Jakub, and Pavel Václavovic. "Earthquake Magnitude Estimation using Precise Point Positioning." IOP Conference Series: Earth and Environmental Science 906, no. 1 (November 1, 2021): 012107. http://dx.doi.org/10.1088/1755-1315/906/1/012107.
Повний текст джерелаАнотація:
Abstract An accurate estimation of an earthquake magnitude plays an important role in targeting emergency services towards affected areas. Along with the traditional methods using seismometers, site displacements caused by an earthquake can be monitored by the Global Navigation Satellite Systems (GNSS). GNSS can be used either in real-time for early warning systems or in offline mode for precise monitoring of ground motion. The Precise Point Positioning (PPP) offers an optimal method for such purposes, because data from only one receiver are considered and thus not affected by other potentially not stable stations. Precise external products and empirical models have to be applied, and the initial convergence can be reduced or eliminated by the backward smoothing strategy or integer ambiguity resolution. The product for the magnitude estimation is a peak ground displacement (PGD). PGDs observed at many GNSS stations can be utilized for a robust estimate of an earthquake magnitude. We tested the accuracy of estimated magnitude scaling when using displacement waveforms collected from six selected earthquakes between the years 2016 and 2020 with magnitudes in a range of 7.5–8.2 Moment magnitude MW. We processed GNSS 1Hz and 5Hz data from 182 stations by the PPP method implemented in the G-Nut/Geb software. The precise satellites orbits and clocks corrections were provided by the Center for Orbit Determination in Europe (CODE). PGDs derived on individual GNSS sites formed the basis for ground motion parameters estimation. We processed the GNSS observations by the combination of the Kalman filter (FLT) and the backward smoother (SMT), which significantly enhanced the kinematic solution. The estimated magnitudes of all the included earthquakes were compared to the reference values released by the U. S. Geological Survey (USGS). The moment magnitude based on SMT was improved by 20% compared to the FLT-only solution. An average difference from the comparison was 0.07 MW and 0.09 MW for SMT and FLT solutions, respectively. The corresponding standard deviations were 0.18 MW and 0.22 MW for SMT and FLT solutions, which shows a good consistency of our and the reference estimates.
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Eggleton. "Equisum Partitions of Sets of Positive Integers." Algorithms 12, no. 8 (August 11, 2019): 164. http://dx.doi.org/10.3390/a12080164.
Повний текст джерелаАнотація:
Let V be a finite set of positive integers with sum equal to a multiple of the integer b. When does V have a partition into b parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, albeit incomplete, answers for the following classes of set V, where n is a given positive integer: (1) an initial interval a∈Z+:a≤n; (2) an initial interval of primes p∈P:p≤n, where P is the set of primes; (3) a divisor set d∈Z+:d|n; (4) an aliquot set d∈Z+:d|n, d<n. Open general questions and conjectures are included for each of these classes.
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Xu, Xiaofei, Zhixi Nie, Zhenjie Wang, and Yuanfan Zhang. "A Modified TurboEdit Cycle-Slip Detection and Correction Method for Dual-Frequency Smartphone GNSS Observation." Sensors 20, no. 20 (October 10, 2020): 5756. http://dx.doi.org/10.3390/s20205756.
Повний текст джерелаАнотація:
Recently, some smartphone manufacturers have subsequently released dual-frequency GNSS smartphones. With dual-frequency observations, the positioning performance is expected to be significantly improved. Cycle-slip detection and correction play an important role in high-precision GNSS positioning, such as precise point positioning (PPP) and real-time kinematic (RTK) positioning. The TurboEdit method utilizes Melbourne–Wübbena (MW) and phase ionospheric residual (PIR) combinations to detect cycle-slips, and it is widely used in the data processing applications for geodetic GNSS receivers. The smartphone pseudorange observations are proved to be much noisier than those collected with geodetic GNSS receivers. Due to the poor pseudorange observation, the MW combination would be difficult to detect small cycle-slips. In addition, some specific cycle-slip combinations, where the ratio of cycle-slip values at different carrier frequencies is close to the frequency ratio, are also difficult to be detected by PIR combination. As a consequence, the traditional TurboEdit method may fail to detect specific small cycle-slip combinations. In this contribution, we develop a modified TurboEdit cycle-slip detection and correction method for dual-frequency smartphone GNSS observations. At first, MW and PIR combinations are adopted to detect cycle-slips by comparing these two combinations with moving-window average values. Then, the epoch-differenced wide-lane combinations are used to estimate the changes of smartphone position and clock bias, and the cycle-slip is identified by checking the largest normalized residual whether it exceeds a predefined threshold value. The process of estimation and cycle-slip identification is implemented in an iterative way until there is no over-limit residual or there is no redundant measurement. At last, the cycle-slip values at each frequency are estimated with the epoch-differenced wide-lane and ionosphere-free combinations, and the least-square ambiguity decorrelation adjustment (LAMBDA) method is adopted to further obtain an integer solution. The proposed method has been verified with 1 Hz dual-frequency smartphone GNSS data. The results show that the modified TurboEdit method can effectively detect and correct even for specific small cycle-slip combinations, e.g., (4, 3), which is difficult to be detected with the traditional TurboEdit method.
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Liu, Wei, and Yong-Gao Chen. "On the exponents modulo 3 in the standard factorisation of n!" Bulletin of the Australian Mathematical Society 73, no. 3 (June 2006): 329–34. http://dx.doi.org/10.1017/s000497270003536x.
Повний текст джерелаАнотація:
Let p be a prime and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n) | n and pep(n)+1 ∤ n. As a corollary of our main result we derive an asymptotic formula for the counting function with regard to the condition ep(n!) ≡ ɛ (mod 3), where ɛ ∈ Z3. In 2001, Sander proved the result with modulus 2.
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Nyamugure, Philimon, Elias Munapo, ‘Maseka Lesaoana, and Santosh Kumar. "A Heuristic for a Mixed Integer Program using the Characteristic Equation Approach." International Journal of Mathematical, Engineering and Management Sciences 2, no. 1 (March 1, 2017): 1–16. http://dx.doi.org/10.33889/ijmems.2017.2.1-001.
Повний текст джерелаАнотація:
While most linear programming (LP) problems can be solved in polynomial time, pure and mixed integer problems are NP-hard and there are no known polynomial time algorithms to solve these problems. A characteristic equation (CE) was developed to solve a pure integer program (PIP). This paper presents a heuristic that generates a feasible solution along with the bounds for the NP-hard mixed integer program (MIP) model by solving the LP relaxation and the PIP, using the CE.
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HALAVA, VESA, TERO HARJU, and MIKA HIRVENSALO. "UNDECIDABILITY BOUNDS FOR INTEGER MATRICES USING CLAUS INSTANCES." International Journal of Foundations of Computer Science 18, no. 05 (October 2007): 931–48. http://dx.doi.org/10.1142/s0129054107005066.
Повний текст джерелаАнотація:
There are several known undecidable problems for 3 × 3 integer matrices the proof of which use a reduction from the Post Correspondence Problem (PCP). We establish new lower bounds in the number of matrices for the mortality, zero in the left upper corner, vector reachability, matrix reachability, scalar reachability and freeness problems. Also, we give a short proof for a strengthened result due to Bell and Potapov stating that the membership problem is undecidable for finitely generated matrix semigroups R ⊆ ℤ 4×4 whether or not kI4 ∈ R for any given |k| > 1. These bounds are obtained by using the Claus instances of the PCP.
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Azimi, Parham, and Hamid Reza Charmchi. "A New Optimization via Simulation Approach for Dynamic Facility Layout Problem with Budget Constraints." Modelling and Simulation in Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/189742.
Повний текст джерелаАнотація:
A new efficient heuristic algorithm has been developed for the dynamic facility layout problem with budget constraint (DFLPB) using optimization via simulation technique. The heuristic integrates integer programming and discrete event simulation to address DFLPB. In the proposed algorithm, the nonlinear model of the DFLP has been changed to a pure integer programming (PIP) model. Then, the optimal solution of the PIP model has been used in a simulation model that has been designed in a similar manner as the DFLP for determining the probability of assigning a facility to a location. After a sufficient number of runs, the simulation model obtains near optimum solutions. Finally, to test the performance of the algorithm, several test problems have been taken from the literature and solved. The results show that the proposed algorithm is more efficient in terms of speed and accuracy than other heuristic algorithms presented in previous works.
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Kaplan, Ilya G. "Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation." Symmetry 13, no. 1 (December 24, 2020): 21. http://dx.doi.org/10.3390/sym13010021.
Повний текст джерелаАнотація:
The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.
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Contardo, Claudio. "Decremental Clustering for the Solution of p-Dispersion Problems to Proven Optimality." INFORMS Journal on Optimization 2, no. 2 (January 2020): 134–44. http://dx.doi.org/10.1287/ijoo.2019.0027.
Повний текст джерелаАнотація:
Given n points, a symmetric dissimilarity matrix D of dimensions n × n, and an integer p ? 2, the p-dispersion problem (pDP) consists of selecting a subset of exactly p points in such a way that the minimum dissimilarity between any pair of selected points is maximum. The pDP is [Formula: see text] when p is an input of the problem. We propose a decremental clustering method to reduce the problem to the solution of a series of smaller pDPs until reaching proven optimality. A k-means algorithm is used to construct and refine the clusterings along the algorithm’s execution. The proposed method can handle problems orders of magnitude larger than the limits of the state-of-the-art solver for the pDP for small values of p.
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Ber-Lin, Yu, Huang Ting-Zhu, Jie Cui, and Deng Chunhua. "Potentially eventually positive star sign patterns." Electronic Journal of Linear Algebra 31 (February 5, 2016): 541–48. http://dx.doi.org/10.13001/1081-3810.2963.
Повний текст джерелаАнотація:
An $n$-by-$n$ real matrix $A$ is eventually positive if there exists a positive integer $k_{0}$ such that $A^{k}>0$ for all $k\geq k_{0}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is potentially eventually positive (PEP) if there exists an eventually positive real matrix $A$ with the same sign pattern as $\mathcal{A}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is a minimal potentially eventually positive sign pattern (MPEP sign pattern) if $\mathcal{A}$ is PEP and no proper subpattern of $\mathcal{A}$ is PEP. Berman, Catral, Dealba, et al. [Sign patterns that allow eventual positivity, {\it ELA}, 19(2010): 108-120] established some sufficient and some necessary conditions for an $n$-by-$n$ sign pattern to allow eventual positivity and classified the potentially eventually positive sign patterns of order $n\leq 3$. However, the identification and classification of PEP signpatterns of order $n\geq 4$ remain open. In this paper, all the $n$-by-$n$ PEP star sign patterns are classified by identifying all the MPEP star sign patterns.
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Chmaj, Grzegorz, Krzysztof Walkowiak, Michał Tarnawski, and Michał Kucharzak. "Heuristic algorithms for optimization of task allocation and result distribution in peer-to-peer computing systems." International Journal of Applied Mathematics and Computer Science 22, no. 3 (September 1, 2012): 733–48. http://dx.doi.org/10.2478/v10006-012-0055-0.
Повний текст джерелаАнотація:
Abstract Recently, distributed computing system have been gaining much attention due to a growing demand for various kinds of effective computations in both industry and academia. In this paper, we focus on Peer-to-Peer (P2P) computing systems, also called public-resource computing systems or global computing systems. P2P computing systems, contrary to grids, use personal computers and other relatively simple electronic equipment (e.g., the PlayStation console) to process sophisticated computational projects. A significant example of the P2P computing idea is the BOINC (Berkeley Open Infrastructure for Network Computing) project. To improve the performance of the computing system, we propose to use the P2P approach to distribute results of computational projects, i.e., results are transmitted in the system like in P2P file sharing systems (e.g., BitTorrent). In this work, we concentrate on offline optimization of the P2P computing system including two elements: scheduling of computations and data distribution. The objective is to minimize the system OPEX cost related to data processing and data transmission. We formulate an Integer Linear Problem (ILP) to model the system and apply this formulation to obtain optimal results using the CPLEX solver. Next, we propose two heuristic algorithms that provide results very
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Liu, Wenhao, and Marc L. Melcher. "Matching Kidneys with Priority in Kidney Exchange Programs." Medical Decision Making 39, no. 4 (May 2019): 336–46. http://dx.doi.org/10.1177/0272989x19849457.
Повний текст джерелаАнотація:
Kidney exchanges were developed to match kidney failure patients with willing but incompatible donors to other donor-patient pairs. Finding a match in a large candidate pool can be modeled as an integer program. However, these exchanges accumulate participants with characteristics that increase the difficulty of finding a match and, therefore, increase patients’ waiting time. Therefore, we sought to fine-tune the formulation of the integer program by more accurately assigning priorities to patients based on their difficulty of matching. We provide a detailed formulation of prioritized kidney exchange and propose a novel prioritization algorithm. Our approach takes advantage of the global knowledge of the donor-patient compatibility within a pool of pairs and calculates an iterative, paired match power (iPMP) to represent the donor-patient pairs’ abilities to match. Monte Carlo simulation shows that an algorithm using the iPMP reduces the waiting time more than using paired match power (PMP) for the difficult-to-match pairs with hazard ratios of 1.3480 and 1.1100, respectively. Thus, the iPMP may be a more accurate assessment of the difficulty of matching a pair in a pool than PMP is, and its use may improve matching algorithms being used to match donors and recipients.
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Hall, R. R., and G. Tenenbaum. "On Behrend sequences." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (November 1992): 467–82. http://dx.doi.org/10.1017/s0305004100071140.
Повний текст джерелаАнотація:
Let denote a sequence of integers exceeding 1, and let τ(n, ) be the number of those divisors of n which belong to . We say that is a Behrend sequence ifwhere, here and in the sequel, we use the notation p.p. to indicate that a relation holds on a set of asymptotic density one.