Research

22 pages, 8602 KiB

Open AccessArticle

Wide-Area Grid-Based Slant Ionospheric Delay Corrections for Precise Point Positioning

by Simon Banville, Elyes Hassen, Micah Walker and Jason Bond

Remote Sens. 2022, 14(5), 1073; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14051073 - 22 Feb 2022

Cited by 5 | Viewed by 2442

Introducing ionospheric information into a precise point positioning (PPP) solution enables faster ambiguity resolution and significantly improves positioning accuracy. To compute such corrections over wide areas, sparse networks with potentially irregular station distributions are often used. This aspect brings a new level of [...] Read more.

Introducing ionospheric information into a precise point positioning (PPP) solution enables faster ambiguity resolution and significantly improves positioning accuracy. To compute such corrections over wide areas, sparse networks with potentially irregular station distributions are often used. This aspect brings a new level of complexity as ionospheric corrections should be weighted appropriately in the PPP filter. This paper presents a possible implementation of grid-based wide-area slant ionospheric delay corrections, with a focus on the reported uncertainties. A balance is obtained between obtaining corrections with formal errors small enough to enable fast convergence, while large enough to overbound most errors. Based on least-squares collocation, the method uses satellite-specific variograms based on the 99th percentile values in each distance bin. Tested in southern Canada over a 53-week period in 2020, ionospheric grids allowed dual-frequency receivers to obtain around 5 cm accuracy in each horizontal component within 5 min of static data collection. For single-frequency solutions using data from geodetic receivers, positioning errors were reduced by over 60% for both static and kinematic processing. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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17 pages, 2393 KiB

Open AccessArticle

Performance Analysis of Zero-Difference GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 Point Positioning Using CNES Uncombined Bias Products

by Lei Zhao, Paul Blunt and Lei Yang

Remote Sens. 2022, 14(3), 650; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14030650 - 29 Jan 2022

Cited by 8 | Viewed by 2889

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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18 pages, 4244 KiB

Open AccessArticle

LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

by Pengyu Hou, Jiuping Zha, Teng Liu and Baocheng Zhang

Remote Sens. 2022, 14(2), 258; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14020258 - 06 Jan 2022

Cited by 3 | Viewed by 1803

Abstract

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is [...] Read more.

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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17 pages, 9309 KiB

Open AccessArticle

A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

by Tzu-Pang Tseng

Remote Sens. 2021, 13(22), 4681; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13224681 - 19 Nov 2021

Cited by 4 | Viewed by 2122

Abstract

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit [...] Read more.

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit mainly serves as a reference datum not only for its ranging measurement but also for the so-called precise point positioning (PPP) technique. Compared to a complex procedure of orbit determination with real tracking data, the so-called orbit fitting technique simply uses satellite positions from GNSS ephemeris as pseudo-observations to estimate the initial state vector and SRP parameters. The accuracy of the reference orbit is mainly dominated by the SRP, which is usually handled by either ECOM1 or ECOM2. However, the reference orbit derived by ECOM1 produces periodic variations on orbit differences with respect to International GNSS Service (IGS) final orbit for GPS IIR satellites. Such periodic variations are removed from a reference orbit formed using the ECOM2 model, which, however, yields large cross-track orbit errors for the IIR and IIF satellites. Such large errors are attributed to the fact that the ECOM2 intrinsically lacks 1 cycle per revolution (CPR) terms, which stabilize the estimations of the even-order CPR terms in the satellite-Sun direction when the orbit fitting is used. In comparison, a reference orbit constructed with the ECOMC model is free of both the periodic variations from the ECOM1 and the large cross-track orbit errors from the ECOM2. The above improvements from the ECOMC are associated with (1) the even CPR terms removing the periodic variations and (2) the 1 CPR terms compensating for the force mismodeling at

∆ u

= 90° and 270°, where the

∆ u

is the argument of the latitude of the satellite with respect to the Sun. The parameter correlation analysis also presents that the direct SRP estimation is sensitive to the 1 and 2 CPR terms in the ECOMC case. In addition, the root-mean-square (RMS) of orbit difference with respect to IGS orbit is improved by ~40%, ~10%, and ~50% in the radial, along-track, and cross-track directions, respectively, when the SRP model is changed from the ECOM2 to the ECOMC. The orbit accuracy is assessed through orbit overlaps at day boundaries. The accuracy improvements of the ECOMC-derived orbit over the ECOM2-derived orbit in the radial, along-track, and cross-track directions are 13.2%, 14.8%, and 42.6% for the IIF satellites and 7.4%, 7.7%, and 35.0% for the IIR satellites. The impact of the reference orbit using the three models on the PPP is assessed. The positioning accuracy derived from the ECOMC is better than that derived from the ECOM1 and ECOM2 by approximately 13% and 20%, respectively. This work may serve as a reference for forming the GNSS reference orbit using the orbit fitting technique with the ECOMC SRP model. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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19 pages, 4615 KiB

Open AccessArticle

Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model

by Nacer Naciri and Sunil Bisnath

Remote Sens. 2021, 13(18), 3768; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13183768 - 20 Sep 2021

Cited by 6 | Viewed by 2012

Abstract

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in [...] Read more.

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in a few minutes to seconds can be achieved thanks to the additional frequencies that are being broadcast by the modernized GNSS constellations. Due to discrepancies in the number of signals broadcast by each satellite/constellation, it is necessary to have a model that can process a mix of signals, depending on availability, and perform ambiguity resolution (AR), a technique that proved necessary for rapid convergence. This manuscript does so by expanding the uncombined Decoupled Clock Model to process and fix ambiguities on up to three frequencies depending on availability for GPS, Galileo, and BeiDou. GLONASS is included as well, without carrier-phase ambiguity fixing. Results show the possibility of consistent quasi-instantaneous global precise positioning through an assessment of the algorithm on a network of global stations, as the 67th percentile solution converges below 10 cm horizontal error within 2 min, compared to 8 min with a triple-frequency solution, showing the importance of having a flexible PPP-AR model frequency-wise. In terms of individual datasets, 14% of datasets converge instantaneously when mixing dual- and triple-frequency measurements, compared to just 0.1% in that of dual-frequency mode without ambiguity resolution. Two kinematic car datasets were also processed, and it was shown that instantaneous centimetre-level positioning with a moving receiver is possible. These results are promising as they only rely on ultra-rapid global satellite products, allowing for instantaneous real-time precise positioning without the need for any local infrastructure or prior knowledge of the receiver’s environment. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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21 pages, 5106 KiB

Open AccessArticle

A Multi-Frequency Galileo PPP-RTK Convergence Analysis with an Emphasis on the Role of Frequency Spacing

by Dimitrios Psychas, Peter J. G. Teunissen and Sandra Verhagen

Remote Sens. 2021, 13(16), 3077; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13163077 - 05 Aug 2021

Cited by 24 | Viewed by 3136

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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16 pages, 20205 KiB

Open AccessArticle

Impact of GPS/BDS Satellite Attitude Quaternions on Precise Point Positioning with Ambiguity Resolution

by Songfeng Yang, Qiyuan Zhang, Xi Zhang and Donglie Liu

Remote Sens. 2021, 13(15), 3035; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13153035 - 02 Aug 2021

Cited by 1 | Viewed by 2283

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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18 pages, 7471 KiB

Open AccessArticle

Ocean Real-Time Precise Point Positioning with the BeiDou Short-Message Service

by Kaifei He, Duojie Weng, Shengyue Ji, Zhenjie Wang, Wu Chen and Yangwei Lu

Remote Sens. 2020, 12(24), 4167; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12244167 - 19 Dec 2020

Cited by 11 | Viewed by 3031

Abstract

Real-time precise point positioning (RTPPP) is a popular positioning method that uses a real-time service (RTS) product to mitigate various Global Navigation Satellite Systems (GNSS) errors. However, communication links are not available in the ocean. The use of a communication satellite for data [...] Read more.

Real-time precise point positioning (RTPPP) is a popular positioning method that uses a real-time service (RTS) product to mitigate various Global Navigation Satellite Systems (GNSS) errors. However, communication links are not available in the ocean. The use of a communication satellite for data transmission is so expensive that normal users could not afford it. The BeiDou short-message service provides an efficient option for data transmission at sea, with an annual fee of approximately 160 USD. To perform RTPPP using BeiDou short messages, the following two challenges should be appropriately addressed: the maximum size of each BeiDou message is 78 bytes, and the communication frequency is limited to once a minute. We simplify the content of RTS data to minimize the required bandwidth. Moreover, the orbit and clock corrections are predicted based on minute-interval RTS orbital and clock corrections. An experiment was conducted to test the performance of the proposed method. The numerical results show that the three-dimensional positioning precision can reach approximately 0.4 m with combined GPS + GLONASS and approximately 0.2 m with combined GPS + GLONASS + Galileo + BeiDou. Full article

(This article belongs to the Special Issue GNSS Precise Point Positioning: Towards Global Instantaneous cm-Level Accuracy)

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