An operational algorithm for satellite attitude determination from GPS carrier phase

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Combination of swarm, Jason-3, and GNSS observations to construct a new modeling of global ionospheric maps

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

Radiosonde is extensively used for understanding meteorological parameters in the vertical direction. Four typhoon events, including three landfalls (MERANTI, NEPARTAK, and MEGI) and one non-landfall (MALAKAS), were chosen in analysing the precipitable water vapour (PWV) characteristics in this study. The spatial distribution of the three radiosonde stations in Zhejiang province does not meet the requirement in analysing changes in PWV during typhoon event. Global position system (GPS) observations are an alternative method for deriving the PWV. This enables improvements in the temporal–spatial resolution of PWV computed by the radiosonde measurements. The National Centers for Environmental Prediction (NCEP) re-analysed data were employed for interpolating temperature and atmosphere pressure at the GPS antennas height. The PWV computed from GPS observations and NCEP re-analysed data were then compared with the true PWV. The maximum difference of radiosonde and GPS PWV was not more than 30 mm at Taiz station. The Root-Mean-Square (RMS) of PWV differences between radiosonde and GPS was not more than 5 mm in January, February, March, November, and December. It was slightly greater than 5 mm in April. High RMS in May, June, July, August, September, and October implies that differences in GPS and radiosonde PWVs are evident in these months. Correlation coefficients of GPS and radiosonde PWVs were more than 0.9, indicating that the changes in GPS and radiosonde PWVs are similar. Radiosonde calculated PWVs were used for GPS PWV calibration for understanding the PWV changes during the period of a typhoon event. The results from three landfall typhoons show that the average PWV over Zhejiang province is increasing and approaching China mainland. In contrast, MALAKAS did not make landfall and shows a decreasing PWV trend, although it was heading to China mainland. Generally, the PWV change can be used to predict whether the typhoon will make landfall in these cases. PWV spatial distribution of MERANTI shows that PWV peaks change along the typhoon epicenter over Zhejiang province.

The authors present the analysis of effects on global positioning system (GPS) observables using the functional modelling and simulation package of a digital baseband processor for the GPS receiver. Three issues are addressed: first, the static observable errors as functions of multipath parameters are derived mathematically in the absence of input noise; secondly, the dynamic code and carrier tracking errors as functions of time due to multipath in the presence of input noise are investigated; and finally the deterioration in the accuracy of the GPS observables due to antenna residual phase and antenna centre movement is studied with different receiver design parameters. It is shown that the functional modelling and simulation package provide an alternative approach to GPS system accuracy research where theoretical analysis and hardware methods are very difficult, inaccurate or prohibitively expensive.

Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up urban environment further degrade the quality of the GPS measurements. Due to the low-quality receivers used and the challenging urban environment, the success rate of the single epoch ambiguity resolution for dynamic attitude determination is usually quite low. In this paper, a micro-electro-mechanical system (MEMS)—inertial navigation system (INS)-aided ambiguity resolution method is proposed to improve the GPS attitude determination performance, which is particularly suitable for land vehicle attitude determination. First, the INS calculated baseline vector is augmented with the GPS carrier phase and code measurements. This improves the ambiguity dilution of precision (ADOP), resulting in better quality of the unconstrained float solution. Second, the undesirable float solutions caused by large measurement errors are further filtered and replaced using the INS-aided ambiguity function method (AFM). The fixed solutions are then obtained by the constrained least squares ambiguity decorrelation (CLAMBDA) algorithm. Finally, the GPS/MEMS-INS integration is realized by the use of a Kalman filter. Theoretical analysis of the ADOP is given and experimental results demonstrate that our proposed method can significantly improve the quality of the float ambiguity solution, leading to high success rate and better accuracy of attitude determination.

Investigation of GPS positioning accuracy during the seasonal variation

This study investigated long-term land subsidence derived from borehole extensometer and Global Positioning System (GPS) observations from Addicks, a suburb located in West Houston, Texas. The Addicks borehole extensometer was built in 1974 by the USGS. Two GPS stations were installed at this site in 1993 and 1996, respectively. One GPS antenna (ADKS) is mounted on the inner pipe of the extensometer borehole, which is firmly anchored 549 m below the land surface. Another GPS antenna (PA05) is mounted on a permanent antenna pole anchored 6 m below the land surface. The horizontal distance between these two GPS antennas is 50 m. Continuous GPS data collected from the deeply anchored GPS antenna indicate that the bottom of the borehole has been stable over the past 20 years (1993–2012). Hence the compaction derived from the borehole extensometer data represents the total subsidence at this site, which should be approximately equivalent to the vertical displacement (subsidence) recorded by the shallowly anchored GPS antenna (PA05). In this study, the vertical displacement time series recorded by the shallowly anchored GPS antenna are regarded as the true values to assess the accuracy of the subsidence time series recorded by the extensometer. The authors' analysis indicates that the difference between the cumulative subsidence measured by the extensometer and the GPS antenna (PA05) is less than 5 mm for a 17-year span (1996–2012). The RMS of the residuals of the monthly subsidence time series derived from the extensometer and GPS antenna (PA05) data over 13 years (2000–2012) is 2 mm.

Dual-frequency global navigation satellite systems (GNSS) observations provide most of the input data for development of global ionosphere map (GIM) of vertical total electron content (VTEC). The international GNSS service (IGS) develops different ionosphere products. The IGS tracking network stations are not homogeneously distributed around the world. The large gaps of this network in Middle East, e.g., Iran plateau, reduce the accuracy of the IGS GIMs over this region. Empirical ionosphere models, such as international reference ionosphere (IRI), also provide coarse forecasts of the VTEC values. This paper presents a new regional VTEC model based on the IRI 2007 and global positioning system (GPS) observations from Iranian Permanent GPS Network. The model consists of a given reference part from IRI model and an unknown correction term. Compactly supported base functions are more appropriate than spherical harmonics in regional ionosphere modeling. Therefore, an unknown correction term was expanded in terms of B-spline functions. The obtained results are validated through comparison with the observed VTEC derived from GPS observations.

Phase artifacts in interferometric synthetic aperture radar (InSAR) images frequently degrade the interpretability of the phase and correlation signatures of terrain. Often, these distortions are attributed to spatially variable ionospheric propagation delays at two different SAR acquisition times. We present here L-band InSAR data from Iceland, California, and Hawaii. The California and Hawaii interferograms show no significant ionospheric artifacts, while the Iceland interferogram shows a maximum misregistration of three pixels in the azimuth direction, which leads to severe phase decorrelation artifacts in the InSAR image. We relate the misregistration of complex pixels seen in the interferograms to the gradient of the ionospheric total electron content (TEC) observed by global positioning system (GPS) data and confirm that indeed the phase artifacts in the Iceland interferogram are due to dispersive ionospheric propagation rather than other decorrelation factors such as neutral atmospheric delays. We develop a method to measure the spatial TEC variation at synthetic aperture length scales using dual-frequency GPS carrier phase data. We solve for the GPS data ambiguities using a low-resolution ionosphere reference derived from either available ionospheric observations or the GPS carrier phase data themselves. GPS observations show directly the level of ionospheric variability, and the spatial TEC gradient as observed by GPS predicts the misregistration of complex pixels in interferograms in all three areas. This confirmation of the cause of the image artifacts suggests that they can be routinely corrected from the InSAR data alone, provided that the sensor measures the change in TEC along the radar swath.

A real-time integrated navigation system with 2-cm position accuracy was developed using commercial off-the shelf (COTS) equipment including inertial sensors and differential Global Positioning System (GPS) receivers, and was demonstrated for transportation applications with an emphasis on lane departure detection. A 900-MHz radiofrequency communications link transmits GPS base station range and carrier phase measurements to a GPS receiver on the vehicle. The GPS receiver calculates the vehicle position relative to the surveyed base location. The loosely coupled eight-state extended Kalman filter with 10-Hz navigation aids provides smoothed position information between 2-Hz GPS updates and provides graceful degradation in the presence of GPS blockages or communication dropouts. Currently, the navigation aids include anti-lock braking system wheel turns, electronic compass heading and pitch, and map vertical height. Data acquisition and Kalman filtering systems were developed to handle real-time processing and recording of all instrument data for further post-test system evaluation to determine the optimum configuration. An accurate rapid survey and map representation approach for measuring lane boundaries was validated using a vehicle, demonstrating inherit repeatability by the GPS positioning system. Real-time lane departure monitoring was developed. A video camera was installed to assist in accurate surveying and real-time system validation. This GPS-based positioning system is suitable for highway speeds during all weather conditions. It can be extended to other collision avoidance, drowsy driver awareness, advanced curve or intersection warnings, SOS, tracking, automated control, fast precision road mapping, and traffic management applications.

Training prescription and monitoring of team-sport athletes rely on accurate quantification of player movement. Our aim was to determine the sensitivity, reliability and construct validity of measures derived from a wearable device incorporating Global Positioning System (GPS) and accelerometer technology to quantify the peak periods of rugby competition. Match movement data were collected from 30 elite and 30 sub-elite rugby union players across respective competitive seasons. Accelerometer and GPS measures were analysed using a rolling average to identify peak movement for epochs ranging from 5 to 600 seconds. General linear mixed modelling was used to quantify the effects of playing position and match-half on the peak movement and variabilities within and between players represented reliability of each measure. Mean positional differences and match-half changes were assessed via standardisation and magnitude-based decisions. Sensitivity of measures was quantified via evaluation of ("signal") and typical error of measurement ("noise"). GPS and accelerometer measures had poor sensitivity for quantifying peak movement across all epochs and both levels of rugby union competition (noise 4× to 5× the signal). All measures displayed correspondingly low reliability across most epochs and both levels of competition (ICC<0.50). Construct validity was evident in mean differences between playing positions and match halves that were consistent with expected activity profiles in rugby union. However, it was clear from the pattern of differences across epoch durations and levels of competition that GPS and accelerometer measures provided different information about player movement. The poor sensitivity and low reliability of GPS and accelerometer measures of peak movement imply that rugby union players need to be monitored across many matches to obtain adequate precision for assessing individuals. Although all measures displayed construct validity, accelerometers provided meaningful information additional to that of GPS. We recommend using accelerometers alongside GPS to monitor and prescribe match respresentative training.

Seismo‐ionospheric anomalies have been reported, while its disturbance modes, patterns, and mechanism are very complex for different kinds of earthquakes. The earthquake with Mw = 7.2 occurred off the coast of Northern California with strike‐slip faulting on 15 June 2005, which may provide a new insight on ionospheric disturbance waves and patterns from dense Global Positioning System (GPS) observations. In this paper, the detailed seismic ionospheric disturbance modes and characteristics are investigated from dense GPS observations following the 2005 Northern California offshore earthquake. Around 10 min after the earthquake, significant ionospheric disturbances are observed by GPS total electron content (TEC). Furthermore, two‐mode ionospheric disturbances are clearly found with two speeds, 1.51 and 2.31 km/s. The slow‐propagating mode has an amplitude of 0.02–0.04 total electron content unit (TECU), while the fast‐propagating mode has an amplitude of 0.1–0.2 TECU. The frequency spectrogram of the slow mode is around 3.7 mHz, while typical frequency of the fast mode is about 5.3 mHz. The fast‐propagating mode is close to the speed of the seismic Rayleigh wave, which is the up propagating secondary acoustic wave triggered by the Rayleigh wave. The slow mode ionospheric disturbance is propagating horizontally as the acoustic wave at the ionospheric level, which is caused by the fault rupture in focal regions.

This paper presents the current design status and some preliminary calibration/performance analyses of the prototype of a multi-sensor personal navigator currently under development at The Ohio State University. The main purpose of this research project is to develop a theoretical foundation and algorithms which integrate the Global Positioning System (GPS), Micro-electro-mechanical inertial measurement unit (MEMS IMU), barometer and compass to provide seamless position information to support navigation and tracking of ground military and rescue personnel. The system is designed with an open-ended architecture, which would be able to incorporate additional navigation and imaging sensor data, extending the system's operations to the indoor environments. The current target accuracy of the system is at 3–5 m CEP (circular error probable). In the current prototype implementation, the following sensors are integrated in the tightly coupled Extended Kalman Filter (EKF): GPS carrier phase and pseudorange data, Crossbow MEMS IMU400C, PTB220A barometer, and KVH Azimuth 1000 digital compass. This paper focuses on the design architecture of the integrated system and the preliminary performance analysis, with a special emphasis on the navigation during the loss of GPS signal. A brief description of the individual sensors and their calibration is presented, together with the navigation performance of the system of sensors.

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.