Global Positioning System Clock Research Articles

Phase‐Path Measurements in Space Using Receivers With GPS Clocks

A number of new perspectives on wave processes in space may be obtained using a pair of phase-coherent receivers in close proximity to measure the direction of arrival and other parameters of plasma waves. Waves of either spontaneous or artificial origin are of interest. The particular objective of sensing direction is seen as one of several ways to use a measurement of the total phase difference between signals arriving at two receiver sites with a known baseline. The limitations of phase-path measurement using two conventional radio receivers with Global Positioning System (GPS) clocks are investigated. The inherent precision of GPS time means that GPS-based clocks can support useful phase-difference measurements up to at least High Frequency (3-30 MHz). For instance, when receiver separations of hundreds or thousands of meters are permitted, interferometer modes can be envisaged for synchronous detection of natural electromagnetic waves like auroral kilometric radiation or of artificial waves from ground transmitters. The double-heterodyne receiver concept is found to be more accurate than the direct waveform capture type. A rotating double payload comprising two receivers linked by a nonconducting tether, a bolas configuration, is one way to achieve a stable two-receiver direction finder in the ionosphere.

Frequency Calibration System Design Based on FPGA

With the deepening of human exploration of the entire physical world, the precision of time synchronization is more and more accurate in some special domains. This paper presents using the precise GPS(Global Positioning System) clock function, time synchronization system with high-precision FPGA technology and the method of the direct DDS (Direct Digital Synthesizer) achieving the frequency correction. Frequency calibration system is based on FPGA design of GPS precision timing, frequency calibration, short on time and in-depth analysis on performance of frequency standards. Through the combination of hardware and software, the system function is achieved by using of large-scale programmable logic devices. In terms of the realization of high precision to build satellite timing frequency calibration system, the frequency precision can reach ns level.

GPS Orbit and Clock Error Distributions

Integrity is one of the most important requirements for civilian aviation. One method of achieving the required integrity for supplemental Global Positioning System (GPS) navigation is the use of Receiver Autonomous Integrity Monitoring (RAIM), and for primary means of navigation, Receiver Autonomous Integrity Monitoring and Exclusion (RAIME). The RAIM(E) algorithm parameters depend on the assumed probability of a satellite fault condition (anomaly) and on the fault-free standard deviation of a normal distribution that over-bounds the actual user range error distribution. In this paper, GPS clock and orbit errors are calculated based on the broadcast ephemeredes and truth data obtained from online sources for the three year period starting in June 2005. Anomalous satellite behavior is identified and removed from the data set. The remaining fault-free data are analyzed statistically. A table of anomalies, cumulative distributions, and normal distribution standard deviation overbounds are provided by satellite Block Type.

GOCE orbit predictions for SLR tracking

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).

Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.

GPS clock correction estimation for near real-time orbit determination applications

Precise orbit determination for low Earth orbiting (LEO) satellites using the global positioning system (GPS) is usually done in a post-processing mode introducing GPS satellite orbits and clock corrections. Depending on the mission objectives, the latency and required accuracy of precise LEO orbit information can vary significantly. Near real-time (NRT) orbits for certain geodetic missions (e.g. atmospheric sounding or altimetry) may require accuracy down to 10 cm (radial) or 0.1 mm s − 1 (along-track) and with a latency of less than 2–3 hours after the GPS measurements have been taken on the satellite. In order to fulfill such a demand in NRT, it is crucial that GPS orbit and clock products are available within the desired time frame and with adequate accuracy. In response to the demanding NRT processing for future geodetic satellite missions (i.e. ESA's Sentinel series), the Astronomical Institute of the University of Bern (AIUB) and Deutsches Zentrum für Luft- und Raumfahrt (DLR) have made an effort in finding an alternative approach to obtain high-rate NRT GPS orbit and clock solutions by way of GPS clock corrections estimation. A realistic NRT orbit determination (OD) scenario has been simulated in this joint-study assuming a radial orbit accuracy of 10 cm and of 3 hours latency for the orbit product. A summary of all currently available NRT GPS orbit and clock products and a description of the generation of NRT GPS clock corrections are given in detail in this paper. The estimated GPS clock corrections are validated with a kinematic precise point positioning (PPP) for static ground stations. For direct evaluation of this innovative approach on the LEO orbits, the resultant merged high-rate NRT GPS product was tested using GPS data from the GRACE (Gravity Recover And Climate Experiment) mission. The results from the NRT simulation show promising aspect of such a concept to achieve unprecedented LEO orbit accuracy in NRT.

Determination of global positioning system (GPS) receiver clock errors: impact on positioning accuracy

Enhancing the positioning precision is the primary pursuit of global positioning system (GPS) users. To achieve this goal, most studies have focused on the relationship between GPS receiver clock errors and GPS positioning precision. This study utilizes undifferentiated phase data to calculate GPS clock errors and to compare with the frequency of cesium clock directly, to verify estimated clock errors by the method used in this paper. The frequency stability calculated from this paper (the indirect method) and measured from the National Standard Time and Frequency Laboratory (NSTFL) of Taiwan (the direct method) match to 1.5 × 10−12 (the value from this study was smaller than that from NSTFL), suggesting that the proposed technique has reached a certain level of quality. The built-in quartz clocks in the GPS receivers yield relative frequency offsets that are 3–4 orders higher than those of rubidium clocks. The frequency stability of the quartz clocks is on average two orders worse than that of the rubidium clock. Using the rubidium clock instead of the quartz clock, the horizontal and vertical positioning accuracies were improved by 26–78% (0.6–3.6 mm) and 20–34% (1.3–3.0 mm), respectively, for a short baseline. These improvements are 7–25% (0.3–1.7 mm) and 11% (1.7 mm) for a long baseline. Our experiments show that the frequency stability of the clock, rather than relative frequency offset, is the governing factor of positioning accuracy.

On Real-Time High Precision Velocity Determination for Standalone GPS Users

The NAVSTAR Global Positioning System (GPS) is a satellite-based radionavigation system designed for positioning, velocity determination and timing. The relative movement between a GPS receiver and a GPS satellite causes the received signal frequency to differ from the transmitted frequency due to the Doppler effect. This frequency difference, an observable in GPS measurements, is referred to as the Doppler shift. However, the Doppler shift is biased by the inherent errors in the signal propagation. Since velocities of GPS satellites are known, the velocity of a user can be determined through observing four or more satellites, similar to GPS positioning.When the GPS selective availability (SA) was activated, errors imposed on the ephemeris and satellite clocks significantly affected the accuracy of both GPS positioning and velocity determination. The removal of SA has enabled a significant improvement on the accuracy of both GPS satellite orbits and clocks. As a result, velocity accuracy at sub-centimetre per second level is achievable for standalone GPS users if all the errors associated with the Doppler observables are corrected for properly.This paper overviews the developments in precise velocity determination and investigates all error sources associated with the Doppler measurement. The properties of errors in the Doppler shift are analysed and the methods to eliminate or mitigate these errors are discussed. The relativistic errors such as the orbit eccentricity and the Sagnac effect are derived and formulated in easy forms for correction. Algorithms for modelling the atmosphere delay rates are also presented. It is concluded that real-time velocities in millimetres per second level are achievable if the error correction schemes provided are used.

Multi-scale Kalman filters algorithm for GPS common-view observation data based on correlation structure of discrete wavelet coefficients

Global positioning system (GPS) common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients. Suppose that the GPS commonview observation data has the 1/f fractal characteristic, the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data. When 0<H<1, the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process. Thus, the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients. Furthermore, the discrete clock difference can be estimated. The single-channel and multi-channel common-view observation data were processed respectively. Comparisons were made between the results obtained and the Circular T data. Simulation results show that the algorithm discussed in this paper is both feasible and effective.

Enhancements to GPS operations and clock evaluations using a "total" Hadamard deviation

We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in global positioning system (GPS) operations. The Hadamard-total deviation described in this paper provides a significant improvement in confidence indicated by an increase of 1.3 to 3.4 times the one degree of freedom of the plain Hadamard deviation at the longest averaging time. The new Hadamard-total deviation is slightly negatively biased with respect to the usual Hadamard deviation, and tau values are restricted to less than or equal to T/3, to be consistent with the usual Hadamard's definition. We give a method of automatically removing bias by a power-law detection scheme. We review the relationship between Kalman filter parameters and the Hadamard and Allan variances, illustrate the operational problems associated with estimating these parameters, and discuss how the Hadamard-total variance can improve management of present and future GPS satellite clocks.

Online GPS processing services: an initial study

There are a number of online Global Positioning System (GPS) processing services that provide GPS processing results to the user free of charge and with unlimited access. These services provide solutions for a user-submitted Receiver Independent Exchange Format (RINEX) file based on differential methods using reference stations or precise point positioning using precise GPS orbit and clock data. Different data sets varying in time and location were submitted to the online services and their results compared. Although the quality of results depends on many factors, in most cases the users can expect reliable online processing results for a 10-h data set made by a geodetic dual frequency receiver anywhere in the world.

Power System Harmonic Analysis Using State-Estimation Method for Japanese Field Data

The harmonic state-estimation (HSE) method appears to be effective but its applicability has yet been fully verified using actual data in power systems. Particularly in Japan, there has been no verification of the applicability of the method in actual power systems. In this paper, for Japanese field data synchronized with a Global Positioning System (GPS) clock, a practical method for power system harmonic analysis is proposed, which is based on HSE. In the proposed method, in order to improve the precision of HSE, uncertain parameters R, X, and Y of the transmission lines are determined from measured fundamental data, and bad measured harmonic data excluded systematically. It is also possible to estimate the error of each measurement instrument by using HSE. It is confirmed that by using only partial and selected measurement data synchronized with a GPS clock, the entire harmonic distribution of the actual power system has been obtained effectively. In this paper, field-test results of the HSE on an actual Japanese power system are shown. Furthermore, an example of harmonic analysis based on HSE in the actual power system is presented, which is prediction of harmonic voltage distribution after a change of the actual power system configuration.

Charge coupled device based phase resolved stroboscopic photometry of pulsars

A stroboscope designed to observe pulsars in the optical spectrum is presented. The absolute phase of the stroboscope is synchronized to better than 2.5 μs with the known radio ephemerides for a given pulsar. The absolute timing is provided by the Global Positioning System clock. With such a device resolved photometry of pulsars can be performed. We demonstrated the instrument’s capabilities with the results of a set of observations of the Crab pulsar, the brightest of the known optical pulsars, with a visual magnitude of 16.5, and a rotational frequency of ∼29 Hz.

Precise absolute GPS positioning with and without selective availability

This paper presents the method and the results of investigations to determine the position vector of a static or moving vehicle using the Global Positioning System (GPS) in the absolute (point) positioning mode with and without selective availability. Starting from the basic positioning scheme with code observation, the most accurate positioning strategy using the phase is described. The main strategy for the highest accuracy absolute positioning is to estimate GPS satellite clock errors independently, thus obviating the between-station differencing. The GPS clock errors are estimated at 30-second intervals using International GPS Service (IGS) orbits and stations. The clock error estimates are then used in an absolute positioning algorithm to determine the coordinates without any other reference site. Static and kinematic GPS data at 1-second sampling rate were processed and compared with the known values and the corresponding DGPS solutions. For the static case, an IGS station was assumed as unknown and its coordinates were estimated. For the kinematic case, the aircraft survey observations were tested. The positions were compared with the corresponding DGPS solutions for each case. Since Selective Availability (SA) is now turned off, its effect on the clock estimation as well as on the position is compared and emphasized.

GPS radio occultation with CHAMP: Atmospheric profiling utilizing the space‐based single difference technique

The GPS (Global Positioning System) radio occultation experiment onboard the German CHAMP (CHAllenging Minisatellite Payload) satellite was successfully started in February 2001. By the end of July 2001 more than 11,000 globally distributed vertical profiles of atmospheric temperature were derived. Operational data processing is based on the double difference method to correct for satellite clock errors. This technique requires a continuous data stream from a global network of GPS ground stations. Termination of the GPS Selective Availability mode on May 2, 2000 reduced the GPS clock errors by orders of magnitude, thereby rendering space‐based single differencing feasible. First results using this single difference technique without direct use of GPS ground station data are presented. The comparison of two data sets consisting of 436 occultations, one processed with space‐based single differencing, the other with classical double differencing, yields no discernible temperature bias below 30 km altitude, a standard deviation of &lt;0.6 K below 20 km and &lt;1.2 K below 30 km. The comparison of both data sets with corresponding meteorological analyses shows nearly identical results with differences in mean and standard deviation of &lt;0.15 K up to 30 km.

Coastal acoustic tomography system and its field application

The coastal acoustic tomography system (CATS), composed of five moored acoustic stations, has been constructed to measure current fields. The system is developed with special considerations in mind, including the use of Global Positioning System clock signals in the synchronization of the system clock timing among the multiple acoustic stations, and the use of the differently coded Gold sequences to identify the acoustic signals corresponding to individual stations from a received signal. The CATS was successfully applied to map the structure of strongly nonlinear tidal currents in the coastal sea. In spite of the limited spatial resolution caused by inadequate sound transmission data, the two-dimensional tidal vortices features of growth, translation, and decay processes are reconstructed through an inverse analysis of the acoustic travel time obtained among the station pairs. It is evident that the CATS is a powerful tool for measuring variable current fields generated in the coastal seas.

Accurate absolute GPS positioning through satellite clock error estimation

An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them.

Estimation of Clock Stability Using GPS

The recent development of low-cost, high-precision oscillators has allowed many applications in various fields to become financially feasible. The stability of an oscillator is ultimatively what determines its usefulness for a certain application, and is therefore desirable to quantify. Current methods of evaluating stability require a direct comparison of the oscillator under test (OUT) with amore stable reference oscillator, the cost of which often offsets the initial benefit of a low-cost device. However, a relatively inexpensive Global Positioning System (GPS) receiver is capable of exploiting the highly stable GPS time scale, thus obviating the need for an expensive reference oscillator. By allowing the OUT to drive a GPS receiver, and processing the data with precise GPS orbits and clock corrections to eliminate the effects of selective availability (SA), the time series of computed clock offsets provides a measure of the oscillator's stability relative to GPS time. The use of GPS for assessing clock stability in the time domain is evaluated herein via the computation of Allan variance values. Performance of one rubidium and three ovenized crystal oscillator are investigated. Results show the method is limited to time intervals less than about two seconds or longer than about 300 seconds, where the effects of measurement noise and residual SA is less pronounced. © 2000 John Wiley & Sons, Inc.

GPS time synchronization system for K2K

The K2K (KEK E362) long-baseline neutrino oscillations experiment requires synchronization of clocks with 100 nsec accuracy at the near and far detector sites (KEK and Super-Kamiokande, respectively), which are separated by 250 km. The Global Positioning System (GPS) provides a means for satisfying this requirement at very low cost. In addition to low-resolution time data (day of year, hour, minute, second), commercial GPS receivers output a 1 pulse per sec (1PPS) signal whose leading edge is synchronized with GPS seconds rollovers to well within the required accuracy. For each beam spill trigger at KEK, and each event trigger at Super-Kamiokande, 50 MHz free-running Local Time Clock (LTC) modules at each site provide fractional-second data with 20 nsec ticks. At each site, two GPS clocks run in parallel, providing hardware backup as well as data quality checks.

A New GPS Data Processing Algorithm for the Positioning of Oceanographic Experiments

Abstract In this paper, the authors present a Global Positioning System (GPS) algorithm for medium accuracy (1-m rms) positioning of ocean buoys. The application addressed in this paper is that of the Fast Pegasus experiments that require the positioning of surface buoys used in collecting subsurface acoustic data for ocean current profiling. The current GPS system designed for the Fast Pegasus experiments requires a land-based single-frequency GPS receiver for differential GPS positioning. In contrast, the technique presented here is designed for the point positioning of a stand-alone single-frequency GPS receiver (which is in motion) and does not require the use of a land-based reference receiver. The precise point positioning algorithm developed here uses postprocessed GPS satellite ephemerides and clock corrections to compute the position of a single GPS receiver. A square root information filter/smoother uses the GPS pseudorange and carrier phase measurements to estimate the position and clock offset...