Global Positioning System Carrier Phase Research Articles

Multipath mitigation for GPS/Galileo/BDS-3 precise point positioning with overlap-frequency signals

The multipath effect is a major Global Navigation Satellite System (GNSS) error source due to its environment-dependent characteristic, which complicates its mitigation process for the high-rate determination of displacements. For instance, Sidereal Filtering (SF) and Multipath Hemispherical Map (MHM) require the observations spanning at least one full cycle of satellite orbit repeat period (e.g., ten days for Galileo navigation satellite system (Galileo) to reproduce the satellite geometry against ground stations. As a consequence, the practicability of SF and MHM is limited due to potential station-surrounding changes over a long period. In this study, we used the overlap-frequency signals on Global Positioning System (GPS) L1/L5, Galileo E1/E5a, and BeiDou-3 Navigation Satellite System (BDS-3) B1C/B2a to construct an interoperable MHM (i.e., MHM_GEC) across constellations to mitigate multipath more efficiently. We thus used 31 days of 1-Hz GPS/Galileo/BDS-3 data at 21 stations in Europe to compare this overlap-frequency MHM with those GNSS-specific MHMs (i.e., MHM_G for GPS, MHM_E for Galileo, and MHM_C for BDS-3), as well as SF. It is confirmed that the multipath effects on overlap-frequency signals are of a high spatial consistency across all GNSS. The mean reduction rate of applying MHM_GEC to GPS, Galileo, and BDS-3 carrier-phase residuals is 25%, 31%, and 28.5%, respectively, which are up to 25 percentage points higher than those of MHM_G, MHM_E, and MHM _C. Furthermore, the MHM_GEC constructed using 5 to 6 days of data can improve the positioning precision by 40%, outperforming the MHM_E, MHM_C, and SF using 10 days of data. Therefore, the interoperable MHM_GEC is more efficient in mitigating multipath effects for high-precision GNSS positioning.

Assessment of Swarm Kinematic Orbit Determination Using Two Different Double-Difference Methods

The Swarm mission aims to study the principle and change regularities of the Earth’s magnetic field. Precise orbit determination is essential to the successful implementation of the mission and relevant scientific research. This article focuses on using two different double-difference methods to improve the accuracy of Swarm kinematic orbit determination. The accuracy of the kinematic orbit determination relies entirely on the space-borne observation data, independent of any dynamic parameters. The article analyzes the data quality of the Swarm space-borne global positioning system (GPS) receiver and presents a detailed introduction to the data pre-processing algorithms. The double-difference observation gathering and the applied orbit determination strategy using two different double-difference methods are discussed. The results of the kinematic orbits under different solar cycle conditions are presented, along with an evaluation based on analysis of GPS carrier phase residuals, subtracting from the post-processed orbits, and assessment with satellite laser ranging (SLR) measurements. The results show that the accuracy of the kinematic orbit determination is at the centimeter level for the three Swarm satellites’ orbit solutions. The daily root mean square (RMS) values of the three satellites’ phase residuals remain at around the 6 mm level. The RMS values of the position residuals between the kinematic orbits and the reduced dynamic orbits released by the European Space Agency (ESA) are at about the 2–3 cm level. The external evaluation with SLR measurements shows a good agreement with the ESA level, with the RMS values of the SLR residuals for kinematic orbits around 2 cm.

Copernicus Sentinel–1 POD reprocessing campaign

Copernicus Sentinel–1 is a C-Band Synthetic Aperture Radar (SAR) satellite mission within the European Copernicus Programme. The two satellites Sentinel-1A and -1B were launched in April 2014 and 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the determination of orbital and auxiliary products required by the Payload Data Ground Segment (PDGS). Precise orbits are determined based on the dual-frequency GPS (Global Positioning System) data delivered by dedicated geodetic-grade GPS receivers on-board the satellites. Several updates in the operational orbit determination were done during the years including an update of the GPS antenna reference point coordinates. The switch to GPS carrier phase ambiguity-fixing was a major improvement. A reprocessing of the entire mission span of both satellites became necessary to provide a consistent orbit time series for the mission based on state-of-the-art models and processing settings. Due to the lack of independent observation techniques, the Sentinel-1 orbit quality has been assessed by analysing processing metrics, orbit overlaps and orbit comparisons. For this purpose, members of the Copernicus POD Quality Working Group (QWG) provided reprocessed Sentinel-1 orbit time series based on their software packages and their orbit determination settings. A weighted average of all five delivered solutions - a combined orbit - serves as reference for the comparisons. The quality and reliability of this reference orbit depends among others on the number of available orbit solutions and whether a manoeuvre has been performed during the processed day or not. The mean orbit consistency between all orbit solutions is below 1 cm in 3D RMS for the entire mission time interval for both satellites. Only few days show inferior quality due to data gaps or orbit manoeuvres. Following this sophisticated validation process, the reprocessed Sentinel-1 orbits from the Copernicus POD Service have been made available to the user community.

Continuous Tracking of GPS Signals with Data Wipe-Off Method

The decentralized pre-filter based vector tracking loop (VTL) configuration with data wipe-off (DWO) method of the Global Positioning System (GPS) receiver is proposed for performance enhancement. It is a challenging task to continuously track the satellites’ signals in weak signal environment for the GPS receiver. VTL is a very attractive technique as it can provide tracking capability in signal-challenged environments. In the VTL, each channel will not form a loop independently. On the contrary, the signals in the channels of VTL are shared with each other; the navigation processor in turn predicts the code phases. Thus, the receiver can successfully track signals even the signal strength from individual satellite is weak. The tracking loop based on the pre-filter provides more flexible adjustment to specific environments to reduce noise interference. Therefore, even if the signals from some satellites are very weak the receiver can track them from the navigation results based on the other satellites. The navigation data, which contains information necessary to perform navigation computations, are binary phase-shift keying (BPSK) modulated onto the GPS carrier phase with the bit duration of 20 ms (i.e., 50 bits per second) for the GPS L1 C/A signals. The coherent integration interval can be extended for improved tracking performance in signal-challenged environment. However, tracking accuracy is decreased by possible data bit sign reversal. The DWO algorithm can be employed to remove the data bit in I and Q correlation values so as to avoid energy loss due to bit transitions when the integration interval of the correlator is extended over 20 ms under the low carrier-to-noise ratio (C/No) environments. The proposed method has an advantage to provide continuous tracking of signals and obtain improved navigation performance. Performance evaluation of the tracking capability as well as positioning accuracy will be presented.

Data Wipe-Off Technique for Tracking Weak GPS Signals

In this paper, the data wipe-off (DWO) algorithm is incorporated into the vector tracking loop of the Global Positioning System (GPS) receiver for improving signal tracking performance. The navigation data, which contains information that is necessary to perform navigation computations, are binary phase-shift keying (BPSK) modulated onto the GPS carrier phase with the bit duration of 20 ms (i.e., 50 bits per second). To continuously track the satellite’s signal in weak signal environment, the DWO algorithm on the basis of pre-detection method is adopted to detect data bit sign reversal every 20 ms. Tracking accuracy of a weak GPS signal is decreased by possible data bit sign reversal every 20 ms to the predetection integration time (PIT) or integration interval. To achieve better tracking performance in weak signal environment, the coherent integration interval can be extended. However, increase of the integration interval lead to decrease of the tracking accuracy by possible data bit sign reversal every 20 ms to the integration interval. When the integration interval of the correlator is extended over 20 ms in low C/No levels, the navigation DWO algorithm can be employed to avoid energy loss due to bit transitions. The method presented in this paper has an advantage to continuously estimate the navigation data bit and achieve improved tracking performance. Evaluation of the tracking performance based on the various integration intervals for the vector tracking loop of a GPS receiver will be presented.

Absolute frequency measurement of an Yb optical clock at the 10−16 level using International Atomic Time

We report on the absolute frequency measurement of the 6s2 1S0–6s6p 3P0 transition in 171Yb with a fractional uncertainty of 7.3 × 10–16. A global positioning system carrier phase frequency transfer was established between National Institute of Metrology of China and East China Normal University, which linked the optical frequency of the ECNU Yb1 clock to the second in the International System of Units (SI) through international atomic time. Frequency measurements were carried out in 15 separate days with a total time over 3.8 × 105 s. The absolute frequency was determined to be 518 295 836 590 863.30(38) Hz. Our result is in good agreement with the recommended value in neutral Yb as a secondary representation of the SI second endorsed by the International Committee for Weights and Measures.

Stochastic noise modelling of kinematic orbit positions in the Celestial Mechanics Approach

Abstract. Gravity field models may be derived from kinematic orbit positions of Low Earth Orbiting satellites equipped with onboard GPS (Global Positioning System) receivers. An accurate description of the stochastic behaviour of the kinematic positions plays a key role to calculate high quality gravity field solutions. In the Celestial Mechanics Approach (CMA) kinematic positions are used as pseudo-observations to estimate orbit parameters and gravity field coefficients simultaneously. So far, a simplified stochastic model based on epoch-wise covariance information, which may be efficiently derived in the kinematic point positioning process, has been applied. We extend this model by using the fully populated covariance matrix, covering correlations over 50 min. As white noise is generally assumed for the original GPS carrier phase observations, this purely formal variance propagation cannot describe the full noise characteristics introduced by the original observations. Therefore, we sophisticate our model by deriving empirical covariances from the residuals of an orbit fit of the kinematic positions. We process GRACE (Gravity Recovery And Climate Experiment) GPS data of April 2007 to derive gravity field solutions up to degree and order 70. Two different orbit parametrisations, a purely dynamic orbit and a reduced-dynamic orbit with constrained piecewise constant accelerations, are adopted. The resulting gravity fields are solved on a monthly basis using daily orbital arcs. Extending the stochastic model from utilising epoch-wise covariance information to an empirical model, leads to a – expressed in terms of formal errors – more realistic gravity field solution.

Estimating satellite and receiver differential code bias using a relative Global Positioning System network

Abstract. Precise total electron content (TEC) is required to produce accurate spatial and temporal resolution of global ionosphere maps (GIMs). Receivers and satellite differential code biases (DCBs) are one of the main error sources in estimating precise TEC from Global Positioning System (GPS) data. Recently, researchers have been interested in developing models and algorithms to compute DCBs of receivers and satellites close to those computed from the Ionosphere Associated Analysis Centers (IAACs). Here we introduce a MATLAB code called Multi Station DCB Estimation (MSDCBE) to calculate satellite and receiver DCBs from GPS data. MSDCBE based on a spherical harmonic function and a geometry-free combination of GPS carrier-phase, pseudo-range code observations, and weighted least squares was applied to solve observation equations and to improve estimation of DCB values. There are many factors affecting the estimated values of DCBs. The first one is the observation weighting function which depends on the satellite elevation angle. The second factor is concerned with estimating DCBs using a single GPS station using the Zero Difference DCB Estimation (ZDDCBE) code or using the GPS network used by the MSDCBE code. The third factor is the number of GPS receivers in the network. Results from MSDCBE were evaluated and compared with data from IAACs and other codes like M_DCB and ZDDCBE. The results of weighted (MSDCBE) least squares show an improvement for estimated DCBs, where mean differences from the Center for Orbit Determination in Europe (CODE) (University of Bern, Switzerland) are less than 0.746 ns. DCBs estimated from the GPS network show better agreement with IAAC than DCBs estimated from precise point positioning (PPP), where the mean differences are less than 0.1477 and 1.1866 ns, respectively. The mean differences of computed DCBs improved by increasing the number of GPS stations in the network.

Discovery of new code interference phenomenon in GPS observables

The Global Positioning System (GPS) provides satellite-based navigation signals, which are employed in many fields, including agriculture, transportation, aviation, and military/personal navigation. In an effort to minimize interference among GPS satellites and to enable GPS receivers to discern satellite identity, each satellite is assigned a specific pseudorandom noise (PRN) sequence that is used to modulate the phase of the corresponding signal. The codes that modulate the current GPS landscape are constructed in such a way that cross-correlation among codes is kept to a bounded minimum, which should significantly limit harmful signal interference. In this study, the efficacy of the current PRN-based modulation system is called into question as GPS signal amplitude and carrier phase data over the past decade show frequent interference between satellite signals.

Absolute and relative orbit determination for the CHAMP/GRACE constellation

Precise orbit determination was investigated for a satellite constellation comprised of two different missions, the CHAllenging Minisatellite Payload (CHAMP) satellite and the Gravity Recovery And Climate Experiment (GRACE) twin satellites. The orbital planes of these two missions aligned closely during March to May 2005, allowing precise baseline determinations between the associated three satellites based on their onboard BlackJack Global Positioning System (GPS) receivers. The GRACE-A/B satellites fly in tandem formation with a baseline of around 220 km, whereas the baselines between CHAMP and the GRACE tandem vary from about 110 to 7500 km during 24-h orbital arcs centered around the points of closest approaches. A number of factors had to be dealt with for orbit determinations, including the cross-talk between the CHAMP GPS main navigation and occultation antennas, the different levels of non-gravitational accelerations, and the rapidly changing geometry that complicates the fixing of integer ambiguities for the GPS carrier-phase observations.Quality assessments of the orbit solutions were based on comparisons with Satellite Laser Ranging (SLR) observations, best orbit solutions had a precision of typically 1.7–2.3 cm. Consistency checks between reduced-dynamic and kinematic orbit solutions were done. For the GRACE baselines, the reduced-dynamic/kinematic baseline consistency was typically better than 1 cm, with an ambiguity fixing success rate of around 94%. The agreement with the K/Ka-Band Radar Ranging (KBR) measurements was about 0.6 mm. For the CHAMP/GRACE pairs, the reduced-dynamic/kinematic baseline consistency varied from 0.5 to 2.5 cm, where better consistency was obtained for shorter arcs.

Mitigation of ionospheric signatures in Swarm GPS gravity field estimation using weighting strategies

Abstract. Even though ESA's three-satellite low-earth orbit (LEO) mission Swarm is primarily a magnetic field mission, it can also serve as a gravity field mission. Located in a near-polar orbit with initial altitudes of 480 km for Swarm A and Swarm C and 530 km for Swarm B and equipped with geodetic-type dual frequency Global Positioning System (GPS) receivers, it is suitable for gravity field computation. Of course, the Swarm GPS-only gravity fields cannot compete with the gravity fields derived from the ultra-precise Gravity Recovery And Climate Experiment (GRACE) K-band measurements. But for various reasons like the end of the GRACE mission in October 2017, data gaps in the previous months due to battery aging, and the gap between GRACE and the recently launched GRACE Follow-On mission, Swarm gravity fields became important to maintain a continuous time series and to bridge the gap between the two dedicated gravity missions. By comparing the gravity fields derived from Swarm kinematic positions to the GRACE gravity fields, systematic errors have been observed in the Swarm results, especially around the geomagnetic equator. These errors are already visible in the kinematic positions as spikes up to a few centimeters, from where they propagate into the gravity field solutions. We investigate these systematic errors by analyzing the geometry-free linear combination of the GPS carrier-phase observations and its time derivatives using a combination of a Gaussian filter and a Savitzky–Golay filter and the Rate of Total Electron Content (TEC) Index (ROTI). Based on this, we present different weighting schemes and investigate their impact on the gravity field solutions in order to assess the success of different mitigation strategies. We will show that a combination of a derivative-based weighting approach with a ROTI-based weighting approach is capable of reducing the geoid rms from 21.6 to 12.0 mm for a heavily affected month and that almost 10 % more kinematic positions can be preserved compared to a derivative-based screening.

Study of time link calibration based on GPS carrier phase observation

The time link calibration of Global Positioning System (GPS) based on carrier phase observation has been performed in the past few years. However, the calibration accuracy is expected to be improved. In this paper, an approach of time link calibration for reducing the uncertainty is proposed. The mechanism and procedure for time link calibration based on GPS are investigated in depth firstly. And then GPS data processing method and strategies in calibration are discussed, where the precise time transfer solution (PTTSol) software is also developed. The experiment of zero baseline time link is employed, of which the standard deviation (STD) value of clock difference reaches 0.03 ns. The root mean square (RMS) value of clock difference in long distance time link is 0.11 ns which compared with the international GPS service (IGS) value. At last, one calibration campaign was organized at the national time service center (NTSC) from modified Julian day (MJD) 57598 to MJD 57616. With a travel receiver forming three common clock difference (CCD) modes, the estimated uncertainty of the calibration value was 0.13 ns, which neglected uncertainty of 1 pulse per second (1 PPS) signal relative to the local time reference point.

Rapid initialization method in real-time deformation monitoring of bridges with triple-frequency BDS and GPS measurements

Rapid initialization with ambiguity fixed resolution plays a key role in real-time Global Navigation Satellite Systems (GNSS) displacement monitoring of bridges. In this study, we propose a rapid initialization method with triple-frequency (TF) BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) observations. The key step of this method is to form extra-wide-lane (EWL) ambiguity with TF BDS and GPS carrier-phase to reduce the ambiguity search space. In order to improve the speed of ambiguity resolution (AR) further, the strategies of fixing ambiguities in groups sequentially from long wavelength to the short and partial AR (PAR) with elevation and signal-to-noise ratio (SNR) criterions were proposed. Based on the real monitoring data on the Baishazhou Yangtze River Bridge, the AR efficiency was tested. The results illustrate that over 90% EWL ambiguities can be fixed by only single-epoch with TF BDS + GPS. After EWL ambiguity is fixed, the wide-lane (WL) ambiguity success rate could improve from 20% with dual-frequency (DF) BDS + GPS data to 70% with TF BDS + GPS data, 50–80% and 80–90% for the three stations respectively. Since the area of ambiguity search space is reduced by TF observations, the ambiguity search time decrased significantly compared with the DF BDS + GPS. In the Time-to-first-fix (TTFF) test, over 85% of epochs can complete the initialization process by only one epoch with one hour of 10 Hz TF BDS + GPS data. However, DF BDS + GPS has only 25%. As for the initialization time longer than two epochs, the counts of TTFFs of TF BDS + GPS are significantly less than that of DF BDS + GPS. Meanwhile, the integrated BDS and GPS can further enhance the geometry of satellites, which will be better for the precision improvement than the increase of signal frequencies.

Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR

Ground-based GNSS-R (global navigation satellite system reflectometry) can provide the absolute vertical distance from a GNSS antenna to the reflective surface of the ocean in a common height reference frame, given that vertical crustal motion at a GNSS station can be determined using direct GNSS signals. This technique offers the advantage of enabling ground-based sea level measurements to be more accurately determined compared with traditional tide gauges. Sea level changes can be retrieved from multipath effects on GNSS, which is caused by interference of the GNSS L-band microwave signals (directly from satellites) with reflections from the environment that occur before reaching the antenna. Most of the GNSS observation types, such as pseudo-range, carrier-phase and signal-to-noise ratio (SNR), suffer from this multipath effect. In this paper, sea level altimetry determinations are presented for the first time based on geometry-free linear combinations of the carrier phase at low elevation angles from a fixed global positioning system (GPS) station. The precision of the altimetry solutions are similar to those derived from GNSS SNR data. There are different types of observation and reflector height retrieval methods used in the data processing, and to analyze the performance of the different methods, five sea level determination strategies are adopted. The solutions from the five strategies are compared with tide gauge measurements near the GPS station, and the results show that sea level changes determined from GPS SNR and carrier phase combinations for the five strategies show good agreement (correlation coefficient of 0.97–0.98 and root-mean-square error values of <0.2 m).

The impact of GPS receiver modifications and ionospheric activity on Swarm baseline determination

The European Space Agency (ESA) Swarm mission is a satellite constellation launched on 22 November 2013 aiming at observing the Earth geomagnetic field and its temporal variations. The three identical satellites are equipped with high-precision dual-frequency Global Positioning System (GPS) receivers, which make the constellation an ideal test bed for baseline determination. From October 2014 to August 2016, a number of GPS receiver modifications and a new GPS Receiver Independent Exchange Format (RINEX) converter were implemented. Moreover, the on-board GPS receiver performance has been influenced by the ionospheric scintillations.The impact of these factors is assessed for baseline determination of the pendulum formation flying Swarm-A and -C satellites. In total 30 months of data - from 15 July 2014 to the end of 2016 - is analyzed. The assessment includes analysis of observation residuals, success rate of GPS carrier phase ambiguity fixing, a consistency check between the so-called kinematic and reduced-dynamic baseline solution, and validations of orbits by comparing with Satellite Laser Ranging (SLR) observations. External baseline solutions from The German Space Operations Center (GSOC) and Astronomisches Institut - Universität Bern (AIUB) are also included in the comparison.Results indicate that the GPS receiver modifications and RINEX converter changes are effective to improve the baseline determination. This research eventually shows a consistency level of 9.3/4.9/3.0 mm between kinematic and reduced-dynamic baselines in the radial/along-track/cross-track directions. On average 98.3% of the epochs have kinematic solutions. Consistency between TU Delft and external reduced-dynamic baseline solutions is at a level of 1 mm level in all directions.

Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations

The Sentinel-3 mission takes routine measurements of sea surface heights and depends crucially on accurate and precise knowledge of the spacecraft. Orbit determination with a targeted uncertainty of less than 2 cm in radial direction is supported through an onboard Global Positioning System (GPS) receiver, a Doppler Orbitography and Radiopositioning Integrated by Satellite instrument, and a complementary laser retroreflector for satellite laser ranging. Within this study, the potential of ambiguity fixing for GPS-only precise orbit determination (POD) of the Sentinel-3 spacecraft is assessed. A refined strategy for carrier phase generation out of low-level measurements is employed to cope with half-cycle ambiguities in the tracking of the Sentinel-3 GPS receiver that have so far inhibited ambiguity-fixed POD solutions. Rather than explicitly fixing double-difference phase ambiguities with respect to a network of terrestrial reference stations, a single-receiver ambiguity resolution concept is employed that builds on dedicated GPS orbit, clock, and wide-lane bias products provided by the CNES/CLS (Centre National d’Etudes Spatiales/Collecte Localisation Satellites) analysis center of the International GNSS Service. Compared to float ambiguity solutions, a notably improved precision can be inferred from laser ranging residuals. These decrease from roughly 9 mm down to 5 mm standard deviation for high-grade stations on average over low and high elevations. Furthermore, the ambiguity-fixed orbits offer a substantially improved cross-track accuracy and help to identify lateral offsets in the GPS antenna or center-of-mass (CoM) location. With respect to altimetry, the improved orbit precision also benefits the global consistency of sea surface measurements. However, modeling of the absolute height continues to rely on proper dynamical models for the spacecraft motion as well as ground calibrations for the relative position of the altimeter reference point and the CoM.

Methods for acquiring data on terrain geomorphology, course geometry and kinematics of competitors' runs in alpine skiing: a historical review.

This paper aims at the description and comparison of methods of topographic analysis of racing courses at all disciplines of alpine skiing sports for the purposes of obtaining: terrain geomorphology (snowless and with snow), course geometry, and competitors' runs. The review presents specific methods and instruments according to the order of their historical appearance as follows: (1) azimuth method with the use of a compass, tape and goniometer instruments; (2) optical method with geodetic theodolite, laser and photocells; (3) triangulation method with the aid of a tape and goniometer; (4) image method with the use of video cameras; (5) differential global positioning system and carrier phase global positioning system methods. Described methods were used at homologation procedure, at training sessions, during competitions of local level and during International Ski Federation World Championships or World Cups. Some methods were used together. In order to provide detailed data on course setting and skiers' running it is recommended to analyse course geometry and kinematics data of competitors' running for all important competitions.

Computationally Efficient Carrier Integer Ambiguity Resolution in Multiepoch GPS/INS: A Common-Position-Shift Approach

Integer ambiguity resolution is a challenging technical issue that exists in real-time kinematic (RTK) global positioning system (GPS) navigation. Once the integer vector is resolved, centimeter-level positioning estimation accuracy can be achieved using the GPS carrier phase measurements. Recently, a real-time sliding window Bayesian estimation approach to RTK GPS and inertial navigation was proposed to provide reliable centimeter accurate-state estimation, via integer ambiguity resolution utilizing a prior along with all inertial measurement unit and GPS measurements within the time window. One challenge to implementing that approach in practice is the high computation cost. This paper proposes a novel implementation approach with significantly lower computational requirements and includes a thorough theoretical analysis. The implementation results show that the proposed method resolves an integer vector identical to that of the original method and achieves state estimation with centimeter global positioning accuracy.

Detection of Shifts in GPS Measurements for a Long-Span Bridge Using CUSUM Chart

Timely and correctly evaluating the quality of Global Positioning System (GPS) data is essential for reduction in the number of false alarms and missed detection of a GPS-based bridge deformation monitoring system. This paper investigates how to use the statistical process control technique, known as the cumulative sum (CUSUM) chart, for the detection of small but persistent shifts in the high-rate GPS carrier-phase measurements. First, a mathematical model for the shift detection based on the continuous hypothesis testing is established. The main features and implementation procedure of the CUSUM chart for the shift detection are then summarized, and the corresponding parameter selection method is discussed in detail. To meet the normality requirement of the CUSUM chart, a novel method that transfers the data to the Q-statistic by the estimated cumulative distribution functions is proposed according to the probability integral transform theory. This is followed by a simulation carried out to evaluate the detection performance of the CUSUM chart and exploit its advantages to the commonly used Shewhart chart for the high-rate GPS monitoring data with different shift sizes. Experimental results have showed that the CUSUM chart is sensitive to small persistent shifts compared to the Shewhart chart although it has a delay problem. The integration of CUSUM chart and Shewhart chart would be a reliable approach for the shift detection. Finally, an on-site dynamic monitoring experiment is carried out on a long-span bridge to validate the proposed approach’s effectiveness in detecting an actual deformation shift, and the experimental results proved to be very encouraging.

Toward Continuous GPS Carrier-Phase Time Transfer: Eliminating the Time Discontinuity at an Anomaly.

The wide application of Global Positioning System (GPS) carrier-phase (CP) time transfer is limited by the problem of boundary discontinuity (BD). The discontinuity has two categories. One is “day boundary discontinuity,” which has been studied extensively and can be solved by multiple methods [1–8]. The other category of discontinuity, called “anomaly boundary discontinuity (anomaly-BD),” comes from a GPS data anomaly. The anomaly can be a data gap (i.e., missing data), a GPS measurement error (i.e., bad data), or a cycle slip. Initial study of the anomaly-BD shows that we can fix the discontinuity if the anomaly lasts no more than 20 min, using the polynomial curve-fitting strategy to repair the anomaly [9]. However, sometimes, the data anomaly lasts longer than 20 min. Thus, a better curve-fitting strategy is in need. Besides, a cycle slip, as another type of data anomaly, can occur and lead to an anomaly-BD. To solve these problems, this paper proposes a new strategy, i.e., the satellite-clock-aided curve fitting strategy with the function of cycle slip detection. Basically, this new strategy applies the satellite clock correction to the GPS data. After that, we do the polynomial curve fitting for the code and phase data, as before. Our study shows that the phase-data residual is only ~3 mm for all GPS satellites. The new strategy also detects and finds the number of cycle slips by searching the minimum curve-fitting residual. Extensive examples show that this new strategy enables us to repair up to a 40-min GPS data anomaly, regardless of whether the anomaly is due to a data gap, a cycle slip, or a combination of the two. We also find that interference of the GPS signal, known as “jamming”, can possibly lead to a time-transfer error, and that this new strategy can compensate for jamming outages. Thus, the new strategy can eliminate the impact of jamming on time transfer. As a whole, we greatly improve the robustness of the GPS CP time transfer.