Rapid integer ambiguity resolution in GPS precise point positioning

GPS precise point positioning (PPP) has been used in many scientific and commercial applications due to its high computational efficiency, no need for any synchronous measurements from a nearby reference receiver and homogeneous positioning quality on a global scale. However, these merits are devalued significantly by unresolved ambiguities and slow convergences of PPP. Therefore, this thesis aims at improving PPP’s performance by resolving ambiguities for a single receiver and accelerating the convergences to ambiguity-fixed solutions in order to achieve a centimeter-level positioning accuracy with only a few seconds of measurements. In recent years, ambiguity resolution for PPP has been developed by separating fractional cycle biases (FCBs) from single-receiver ambiguity estimates. One method is to estimate FCBs by averaging the fractional parts of single-difference ambiguity estimates between satellites, and the other is to assimilate FCBs into clocks by fixing undifferenced ambiguities to integers in advance. The first method suffers from a large number of redundant satellite-pair FCBs and unnecessary 15-minute narrow-lane FCBs. Therefore, this thesis suggests undifferenced FCBs and one narrow-lane FCB per satellite-pair pass over a regional area in order to reduce the size of FCB products and achieve comparable positioning quality with that of the original method. Typical tests show that ambiguity resolution dramatically reduces the RMS of differences between hourly and daily position estimates from 3.8, 1.5 and 2.8 cm in ambiguity-float solutions to 0.5, 0.5 and 1.4 cm in ambiguity-fixed solutions for the East, North and Up components, respectively. Likewise, the RMS for real-time position estimates are reduced drastically from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm. Of particular note, this improvement can be achieved even at remote receivers which are over a few thousand kilometers from the reference receivers that are used to estimate FCBs. Furthermore, this thesis improves the accuracy of narrow-lane FCB estimates with integer constraints from double-difference ambiguities. In a one-year global network analysis, the RMS of differences for the East component between the daily and IGS weekly estimates is reduced from 2.6 mm in the solutions based on original FCBs to 2.2 mm in the solutions based on improved FCBs. Although small, this improvement is significant and critical to some geophysical studies, such as tectonic motions, sea level rise, and post-glacial rebound. More importantly, for the first time, this thesis provides a theoretical proof for the equivalence between the ambiguity-fixed position estimates derived from the aforementioned two methods. This equivalence is then empirically verified by the overall minimal discrepancies of the positioning qualities between the two methods. However, these discrepancies manifest a distribution of geographical pattern, i.e. the largest discrepancies correspond to sparse networks of reference receivers. This comparison can provide valuable reference for the GPS community to choose an appropriate method for their PPP ambiguity resolution. As the foremost contribution, an innovative method is originally developed in this thesis in order to effectively re-converge to ambiguity-fixed solutions with only a few seconds of measurements. Specifically, ionospheric delays at all ambiguity-fixed epochs are estimated and then predicted precisely to succeeding epochs in the case of re-convergences. The predicted ionospheric delays are first used to correct wide-lane measurements in order to rapidly resolve wide-lane ambiguities. The resulting ionosphere-corrected and ambiguity-fixed wide-lane measurements are then used to tightly constrain narrow-lane measurements and thus speed up narrow-lane ambiguity resolution significantly. As a result, the practicability of real-time PPP is greatly improved by eliminating the unrealistic requirement of a continuous open sky view in most PPP applications. Typical tests illustrate that over 90% of re-convergences can be achieved within five epochs of 1-Hz measurements, rather than the conventional 20 minutes, even if the latency for the predicted ionospheric delays is up to 180 s. Moreover, for a van-borne receiver moving in a GPS-adverse environment where satellite number decreases significantly and cycle slips occur frequently, only when the above rapid re-convergence technique is applied can the rate of ambiguity-fixed epochs dramatically rise from 7.7% to 93.6% of all epochs. Finally, a precise positioning service for the next-generation global RTK, characterized by both global coverage and regional augmentation, is originally proposed in this thesis based on real-time PPP enhanced by rapid (re-)convergences to ambiguity-fixed solutions. It is illustrated that a globally distributed network of 38 stations can ensure that the ambiguity-fixed epochs account for over 95% of all epochs

Comparing non‐tidal ocean loading around the southern North Sea with subdaily GPS/GLONASS data

Observing subdaily surface deformations is important to the interpretation of rapidly developing transient events. However, it is not known whether GNSS (Global Navigation Satellite System) is able to identify millimeter‐level transient displacements over various subdaily timescales. We studied non‐tidal ocean loading (NTOL) using 18 GNSS stations along the southern North Sea for November–December 2013, and compared 3‐hourly GPS/GLONASS displacements with NTOL predictions. It was found that they overall agreed well with a mean correlation coefficient of 0.6 and their vertical differences had an RMS of 5.7 mm, but a 10‐mm subsidence prediction for December 5th could only be marginally detected. Hence the spatial coherence among the loading signatures at the 18 stations was harnessed to improve subdaily GNSS, and then the predicted displacements of 5–10‐mm over the subdaily timescales could be discriminated successfully. We envision that adding Galileo/BeiDou signals to GPS/GLONASS can further improve the resolution of subdaily GNSS, which can also enhance the spatial coherence of transient signals captured by regional GNSS stations

Quasi-4-dimension ionospheric modeling and its application in PPP

The version of record of this article, first published in Satellite Navigation, is available online at Publisher’s website: http://dx.doi.org/10.1186/s43020-022-00085-zIonospheric delay modeling is not only important for GNSS based space weather study and monitoring, but also an efficient tool to overcome the long convergence time of PPP. In this study, a novel model, denoted as Q4DIM (Quasi-4-dimension ionospheric modeling) is proposed for wide-area high precision ionospheric delay correction. In Q4DIM, the LOS (line of sight) ionospheric delay from a GNSS station network is divided into different clusters according to not only latitude and longitude, but also elevation and azimuth. Both GIM (global ionosphere map) and SID (slant ionospheric delay) that traditionally used for wide-area and regional ionospheric delay modeling, respectively, can be regarded as special case of Q4DIM by defining proper grids in latitude, longitude, elevation and azimuth. Thus, Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision. Then four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EPN stations. The results suggested that Q4DIM is compatible with the widely acknowledged GIM products. Moreover, it is proved that by inducting the elevation and azimuth angle dependent residuals, the precision of the 2-dimensional GIM-like model, i.e., Q4DIM-2D, is improved from around 1.5 TECU to better than 0.5 TECU. In addition, by treating Q4DIM as a 4-dimensional matrix in latitude, longitude, elevation and azimuth, its sparsity is less than 5%, thus guarantees its feasibility in a bandwidth-sensitive applications, e.g., satellite-based PPP-RTK service. Finally, the advantage of Q4DIM in single frequency PPP over the 2-dimensional models is demonstrated with one month’s data from 30 EPN stations.Peer ReviewedPostprint (published version

Roadmap on signal processing for next generation measurement systems

Signal processing is a fundamental component of almost any sensor-enabled system, with a wide range of applications across different scientific disciplines. Time series data, images, and video sequences comprise representative forms of signals that can be enhanced and analysed for information extraction and quantification. The recent advances in artificial intelligence and machine learning are shifting the research attention towards intelligent, data-driven, signal processing. This roadmap presents a critical overview of the state-of-the-art methods and applications aiming to highlight future challenges and research opportunities towards next generation measurement systems. It covers a broad spectrum of topics ranging from basic to industrial research, organized in concise thematic sections that reflect the trends and the impacts of current and future developments per research field. Furthermore, it offers guidance to researchers and funding agencies in identifying new prospects.AerodynamicsMicrowave Sensing, Signals & System

Rapid integer ambiguity resolution in GPS precise point positioning

GPS precise point positioning (PPP) has been used in many scientific and commercial applications due to its high computational efficiency, no need for any synchronous measurements from a nearby reference receiver and homogeneous positioning quality on a global scale. However, these merits are devalued significantly by unresolved ambiguities and slow convergences of PPP. Therefore, this thesis aims at improving PPP’s performance by resolving ambiguities for a single receiver and accelerating the convergences to ambiguity-fixed solutions in order to achieve a centimeter-level positioning accuracy with only a few seconds of measurements. In recent years, ambiguity resolution for PPP has been developed by separating fractional cycle biases (FCBs) from single-receiver ambiguity estimates. One method is to estimate FCBs by averaging the fractional parts of single-difference ambiguity estimates between satellites, and the other is to assimilate FCBs into clocks by fixing undifferenced ambiguities to integers in advance. The first method suffers from a large number of redundant satellite-pair FCBs and unnecessary 15-minute narrow-lane FCBs. Therefore, this thesis suggests undifferenced FCBs and one narrow-lane FCB per satellite-pair pass over a regional area in order to reduce the size of FCB products and achieve comparable positioning quality with that of the original method. Typical tests show that ambiguity resolution dramatically reduces the RMS of differences between hourly and daily position estimates from 3.8, 1.5 and 2.8 cm in ambiguity-float solutions to 0.5, 0.5 and 1.4 cm in ambiguity-fixed solutions for the East, North and Up components, respectively. Likewise, the RMS for real-time position estimates are reduced drastically from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm. Of particular note, this improvement can be achieved even at remote receivers which are over a few thousand kilometers from the reference receivers that are used to estimate FCBs. Furthermore, this thesis improves the accuracy of narrow-lane FCB estimates with integer constraints from double-difference ambiguities. In a one-year global network analysis, the RMS of differences for the East component between the daily and IGS weekly estimates is reduced from 2.6 mm in the solutions based on original FCBs to 2.2 mm in the solutions based on improved FCBs. Although small, this improvement is significant and critical to some geophysical studies, such as tectonic motions, sea level rise, and post-glacial rebound. More importantly, for the first time, this thesis provides a theoretical proof for the equivalence between the ambiguity-fixed position estimates derived from the aforementioned two methods. This equivalence is then empirically verified by the overall minimal discrepancies of the positioning qualities between the two methods. However, these discrepancies manifest a distribution of geographical pattern, i.e. the largest discrepancies correspond to sparse networks of reference receivers. This comparison can provide valuable reference for the GPS community to choose an appropriate method for their PPP ambiguity resolution. As the foremost contribution, an innovative method is originally developed in this thesis in order to effectively re-converge to ambiguity-fixed solutions with only a few seconds of measurements. Specifically, ionospheric delays at all ambiguity-fixed epochs are estimated and then predicted precisely to succeeding epochs in the case of re-convergences. The predicted ionospheric delays are first used to correct wide-lane measurements in order to rapidly resolve wide-lane ambiguities. The resulting ionosphere-corrected and ambiguity-fixed wide-lane measurements are then used to tightly constrain narrow-lane measurements and thus speed up narrow-lane ambiguity resolution significantly. As a result, the practicability of real-time PPP is greatly improved by eliminating the unrealistic requirement of a continuous open sky view in most PPP applications. Typical tests illustrate that over 90% of re-convergences can be achieved within five epochs of 1-Hz measurements, rather than the conventional 20 minutes, even if the latency for the predicted ionospheric delays is up to 180 s. Moreover, for a van-borne receiver moving in a GPS-adverse environment where satellite number decreases significantly and cycle slips occur frequently, only when the above rapid re-convergence technique is applied can the rate of ambiguity-fixed epochs dramatically rise from 7.7% to 93.6% of all epochs. Finally, a precise positioning service for the next-generation global RTK, characterized by both global coverage and regional augmentation, is originally proposed in this thesis based on real-time PPP enhanced by rapid (re-)convergences to ambiguity-fixed solutions. It is illustrated that a globally distributed network of 38 stations can ensure that the ambiguity-fixed epochs account for over 95% of all epochs.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Editorial for Multi-Constellation Global Navigation Satellite Systems: Methods and Applications

This is a great era of significant changes and innovations in the field of geodesy and navigation with the emerging multi-constellation Global Navigation Satellite Systems (GNSS) [...

On the feasibility of resolving Android GNSS carrier-phase ambiguities

High-precision navigation using low-cost handsets has profound potential for mass-market applications, which has been being boosted by the release of raw GNSS data from Google Android smart devices. However, integer ambiguity fixing for centimeter-level GNSS positioning is prevented by the unaligned chipset initial phase biases (IPBs) found within Android carrier-phase data. In this study, we thus investigate the temporal behaviors of those chipset IPBs using zero baselines where smart devices are linked to external survey-grade antennas, and find that the IPBs are generally stable over time as the mean standard deviation of single-epoch IPB estimates derived from continuous carrier-phase data is as low as 0.04 cycles for all satellites. Unfortunately, these chipset IPBs differ randomly among satellites and change unpredictably if carrier-phase signals are re-tracked, discouragingly suggesting that the chipset IPBs cannot be pre-calibrated or even calibrated on the fly. We therefore have to presumably correct for them in a post-processing manner with the goal of inspecting the potential of Android GNSS ambiguity resolution if hopefully the IPBs can be gone. For a vehicle-borne Nexus 9 tablet with respect to a survey-grade receiver located 100-2000 m away, we achieve the first ambiguity-fixed solution within 321 s and finally 51.6% of all epochs are resolved; the ambiguity-fixed epochs can achieve a positioning accuracy of 1.4, 2.2 and 3.6 cm for the east, north and up components, respectively, showing an improvement of 30%-80% compared to the ambiguity-float solutions. While all smart devices above are connected to external survey-grade antennas, we find that a Xiaomi 8 smartphone can be coupled effectively with a miniaturized portable patch antenna, and then achieve commensurate carrier-phase tracking and ambiguity-fixing performance to those of a commercial μ-blox receiver with its dedicated patch antenna. This is encouraging since a compact and inexpensive patch antenna paired with smart devices can promote the democratization of high-precision GNSS

Beyond three frequencies: An extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals

GNSS is indispensable to self-driving vehicles by delivering decimeter-level or better absolute positioning solutions. Such a high precision normally requires a convergence time spanning seconds to minutes, which is however unrealistic in extremely difficult driving conditions where GNSS signals are obstructed frequently. Such convergences, no matter how short, will greatly risk and discredit autonomous driving in satisfying stringent life-safety standards. In this study, we therefore developed an extendable GNSS precise point positioning (PPP) model to exploit the advanced Galileo/BeiDou-3 more-than-three-frequency signals with the goal of achieving instant or single-epoch 10-30 cm positioning accuracy and over 99% availability for the horizontal components over wide areas. In particular, uncombined Galileo/BeiDou-3 signals on all available frequencies were injected simultaneously into PPP to perform single-epoch wide-lane ambiguity resolution (PPP-WAR) after phase bias calibrations on raw observations. Experimenting on the Galileo five-frequency data from 36 stations in Australia, we found that instant PPP-WAR was accomplished at more than 99.5% of all epochs; we achieved an instant positioning accuracy of 0.10 and 0.11 m (1) for the east and north components, respectively, using Galileo E1/E5a/E5/E5b/E6 signals from less than 10 satellites, while 0.16 and 0.23 m using BeiDou-3 B1C/B1I/B2a/B2b/B3I signals from only 5-6 satellites per epoch observed by 10 stations within China. Moreover, we carried out vehicle-borne experiments collecting multi-frequency Galileo/BeiDou-3 signals in case of overpass and tunnel adversities. With 7 Galileo/BeiDou-3 satellites per epoch on average, instant PPP-WAR reached a mean positioning accuracy of 0.23 and 0.24 m for the horizontal components, which can be further improved to 0.14 and 0.12 m when multi-epoch filtering is preferably enabled. More encouragingly, though this positioning accuracy can also be ensured with triple-frequency data, the data redundancy favored by even more frequencies can reduce the high-precision recovery time from up to 4 s to 2 s in case of total signal blockages. With the rapidly ongoing deployment of Galileo, BeiDou-3 and other GNSS constellations, we can envision an instant global positioning service characterized by around 20-cm horizontal accuracy and over 99% availability for self-driving vehicles

An Improved Hatch Filter Algorithm towards Sub-Meter Positioning Using only Android Raw GNSS Measurements without External Augmentation Corrections

In May 2016, the availability of GNSS raw measurements on smart devices was announced by Google with the release of Android 7. It means that developers can access carrier-phase and pseudorange measurements and decode navigation messages for the first time from mass-market Android-devices. In this paper, an improved Hatch filter algorithm, i.e., Three-Thresholds and Single-Difference Hatch filter (TT-SD Hatch filter), is proposed for sub-meter single point positioning with raw GNSS measurements on Android devices without any augmentation correction input, where the carrier-phase smoothed pseudorange window width adaptively varies according to the three-threshold detection for ionospheric cumulative errors, cycle slips and outliers. In the mean time, it can also eliminate the inconsistency of receiver clock bias between pseudorange and carrier-phase by inter-satellite difference. To eliminate the effects of frequent smoothing window resets, we combine TT-SD Hatch filter and Kalman filter for both time update and measurement update. The feasibility of the improved TT-SD Hatch filter method is then verified using static and kinematic experiments with a Nexus 9 Android tablet. The result of the static experiment demonstrates that the position RMS of TT-SD Hatch filter is about 0.6 and 0.8 m in the horizontal and vertical components, respectively. It is about 2 and 1.6 m less than the GNSS chipset solutions, and about 10 and 10 m less than the classical Hatch filter solution, respectively. Moreover, the TT-SD Hatch filter can accurately detect the cycle slips and outliers, and reset the smoothed window in time. It thus avoids the smoothing failure of Hatch filter when a large cycle-slip or an outlier occurs in the observations. Meanwhile, with the aid of the Kalman filter, TT-SD Hatch filter can keep continuously positioning at the sub-meter level. The result of the kinematic experiment demonstrates that the TT-SD Hatch filter solution can converge after a few minutes, and the 2D error is about 0.9 m, which is about 64%, 89%, and 92% smaller than that of the chipset solution, the traditional Hatch filter solution and standard single point solution, respectively. Finally, the TT-SD Hatch filter solution can recover a continuous driving track in this kinematic test