Broadcast Ephemeris Research Articles

Compass/BeiDou‐2 spaceborne clock performance assessment and its error detection, mitigation

The performance of a spaceborne atomic clock on a navigation satellite and the accuracy of the clock data in broadcast ephemeris are two critical factors for real‐time high‐accuracy global navigation satellite systems applications. A novel clock performance assessment method is proposed, which is indexed by the maximum clock error, clock rate, and clock drift rate, and the performance of the BeiDou‐2 satellite‐borne clock is assessed by this method compared to the GPS. To mitigate the negative effects of clock errors on pseudo‐range measurements and positioning results, an integrated clock prediction method is also presented in this paper based on polynomial modeling, wavelet denoising, and autoregressive integrated moving average modeling. An example is shown to test and verify the effectiveness of the integrated clock prediction method. Real data clock assessment results demonstrate the equivalent quality of BeiDou‐2 and GPS spaceborne clocks. The proposed clock prediction method can be used to detect and mitigate clock errors in broadcast ephemeris. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Time-differenced carrier phases technique for precise GNSS velocity estimation

Classically, a stand-alone GNSS receiver estimates its velocity by forming the approximate derivative of consecutive user positions or more often by using the Doppler observable. The first method is very inaccurate, while the second one allows estimation of the order of some cm/s. The time-differenced carrier phase (TDCP) technique, which consists in differencing successive carrier phases, enables accuracies at the mm/s level. A study on the existing TDCP velocity estimation algorithms has revealed that the use of different broadcast ephemeris sets to calculate the satellite positions and clock offsets produces a discontinuity in the TDCP measurements that affects the velocity estimation. We propose a method to overcome this limitation based on the use of the same set of ephemeris to calculate the satellite positions and clock offsets at consecutive epochs. We describe in detail the TDCP algorithm used, and the complete implementation in MATLAB is included.

BeiDou satellite-induced code pseudorange variations: diagnosis and therapy

Code pseudorange measurements of the Chinese GNSS BeiDou reveal variations which result in code---phase divergences of more than 1 m. We have analyzed these delay variations based on observation data of the International GNSS Service and its Multi-GNSS Experiment campaign. Our results confirm that these code variations are elevation-dependent when observed by receiving antennas on the earth's surface. In addition, we found significant differences between two groups of satellites and among carrier frequencies. These delay variations have only little effects on absolute BeiDou positioning using broadcast ephemerides due to the limited accuracy of the obtainable positions. But, all precise applications which use code measurements are severely affected. These applications include, e.g., certain algorithms used in Precise Point Positioning (PPP), especially PPP ambiguity fixing and single-frequency PPP based on the ionosphere-free code---carrier combination. We developed a correction model and determined correction parameters in order to accommodate these symptoms. Application examples demonstrate the successful mitigation of these code pseudorange variations.

QZSS Satellite-borne Atomic Clock Performance Evaluation

Performance of satellite-borne atomic clock is a critical factor to the availability and precision of global and regional satellite navigation systems. Nonetheless, at present, practical clock performance assessment method is in absence. A space-borne clock performance assessment method is first proposed indexed by maximum clock error, clock rate and clock drift rate, and the performance of QZSS satellite-borne clock is assessed by this method comparing with GPS. Furthermore, the system performance of QZSS is assessed in the aspect of clock data precision in broadcast ephemeris by comparing with the final precise ephemeris. The evaluation result shows that the performance of space-borne clock of QZSS is similar to GPS, and the system performance of QZSS and GPS is also equivalent to each other regarding to the precision of broadcast ephemeris.

Differential Code Bias Estimation using Multi-GNSS Observations and Global Ionosphere Maps

Measurements of Global Navigation Satellite System (GNSS) receivers are affected by systematic offsets re- lated to group and phase delays of the signal generation and processing chain. The resulting code and phase biases depend on the transmission frequency and the employed signal modulation. Within this study differential code biases (DCBs) of legacy an d modernized GNSS signals are derived from pseudodrange observations of a global multi-GNSS receiver network. Global ionosphere maps (GIMs) are employed for th e correction of ionospheric path delays. Satellite and receiver-specific contributions are separated based on the a ssumption of additive biases and a zero-mean condition for the satellite biases within a constellation. Based on 6 months of data collected within the Multi-GNSS Experiment (M GEX) of the International GNSS Service (IGS), DCBs for the publicly available signals of GPS, Galileo and BeiDou have been deter- mined. The quality of the resulting DCB estimates is as- sessed and compared against group delay parameters transmitted by the GNSS providers as part of the broad- cast ephemeris data.

Broadcast Ephemeris Accuracy Analysis for GPS Based on Precise Ephemeris

The accuracy of broadcast ephemeris is an important index of a satellite navigation system. The theory and method of precise ephemeris assessing broadcast ephemeris are introduced. The accuracy of GPS satellite broadcast ephemeris is assessed with the precise ones provided by IGS. The orbital coordinates of GPS broadcast ephemeris from 18th to 24th October 2013 are calculated. The analysis shows that during this time the GPS satellite broadcast ephemeris is reliable, accurate and safe as the whole, meanwhile the broadcast ephemeris accuracy is about 1 meter, better than nominal accuracy of 5 meters.

An analysis of intersystem biases for multi-GNSS positioning

The capability of commercial receivers to track multiple GNSSs poses the problem of mutual alignments of reference frames and time scales. System biases should possibly be computed in advance and made known to the user, so that the only unknowns for code point positioning are the receiver coordinates and the receiver clock offset relative to a unique time scale. We have examined data from the five GNSS constellations GPS, GLONASS, Galileo, QZSS and BeiDou for 4 days in 2013, nine European stations and four different GNSS receivers, with the goals to (a) evaluate the quality of the broadcast ephemeris relative to the precise orbits and clocks, when available (GPS, GLONASS, Galileo, QZSS), (b) estimate systematic offsets of the time scales kept by each GNSS relative to GPS and (c) investigate possible receiver-dependent system biases. We report an agreement at the meter level between coordinates of satellites computed with broadcast ephemeris and precise orbits. Differences between broadcast and precise clocks are up to ± few nanoseconds (1 ns = 10?9 s) for GPS (IGS products). For GLONASS, the difference of the broadcast clock to the Russian (IAC) SP3 values is also smaller than ±10 ns, but rises to about 200 ns when the broadcast clock is compared to the combined IGL product of IGS. For QZSS, the difference broadcast to SP3 products of the JAXA are also confined to ±10 ns. For Galileo, for which data are broadcast in a test mode, we report different values depending on the F-NAV or I-NAV satellite clock model: Using the SP3 products of Technical University of Munich (TUM), we report discrepancies between broadcast and SP3 of some tens of nanoseconds. System Time Biases lump together satellite-dependent Differential Code Biases, receiver-dependent Inter System Biases and offsets of a given GNSS time scale to a reference (we assume GPS) time scale. The System Time Bias is typically of the order of 360---380 ns for GLONASS, quite consistently with broadcast or precise (IAC) ephemeris. For Galileo, the biases are more variable and depend on the use of broadcast or precise data. For QZSS, we evaluate a QZSS to GPS System Time Bias very nearly constant in time. Its value differs of about 20 ns depending on the SP3 data source (TUM or JAXA). For BeiDou, we find Time System Biases of the order of 10---100 ns depending on day and receiver type. Receiver-dependent Time System Biases relative to GPS are quite evident in several different stations and are reasonably consistent across receiver type. We conclude by emphasizing the need for a monitoring activity of such inter-GNSS biases, both GNSS dependent and receiver dependent, and that appropriate means are devised for making them available to the final user.

A Galileo IOV assessment: measurement and position domain

The European GNSS, Galileo, is currently in its in-orbit validation (IOV) phase where four satellites are finally available for computing the user position. In this phase, the analysis of the measurements and position velocity and time (PVT) obtained from the IOV satellites can provide insight into the potentialities of the Galileo system. A methodology is suggested for the analysis of the Galileo IOV pseudorange and pseudorange rates collected from the E1 and E5 frequencies. Several days of data were collected and processed to determine figures of merit such as root mean square and maximum errors of the Galileo observables. From the analysis, it emerges that Galileo is able to achieve better accuracy than GPS. A thorough analysis of the PVT performance is also carried out using broadcast ephemerides. Galileo and GPS PVTs are compared under similar geometry conditions showing the potential of the Galileo system.

The impact of orbital errors on the estimation of satellite clock errors and PPP

Precise satellite orbit and clocks are essential for providing high accuracy real-time PPP (Precise Point Positioning) service. However, by treating the predicted orbits as fixed, the orbital errors may be partially assimilated by the estimated satellite clock and hence impact the positioning solutions. This paper presents the impact analysis of errors in radial and tangential orbital components on the estimation of satellite clocks and PPP through theoretical study and experimental evaluation. The relationship between the compensation of the orbital errors by the satellite clocks and the satellite-station geometry is discussed in details. Based on the satellite clocks estimated with regional station networks of different sizes (∼100, ∼300, ∼500 and ∼700km in radius), results indicated that the orbital errors compensated by the satellite clock estimates reduce as the size of the network increases. An interesting regional PPP mode based on the broadcast ephemeris and the corresponding estimated satellite clocks is proposed and evaluated through the numerical study. The impact of orbital errors in the broadcast ephemeris has shown to be negligible for PPP users in a regional network of a radius of ∼300km, with positioning RMS of about 1.4, 1.4 and 3.7cm for east, north and up component in the post-mission kinematic mode, comparable with 1.3, 1.3 and 3.6cm using the precise orbits and the corresponding estimated clocks. Compared with the DGPS and RTK positioning, only the estimated satellite clocks are needed to be disseminated to PPP users for this approach. It can significantly alleviate the communication burdens and therefore can be beneficial to the real time applications.

Broadcast versus precise ephemerides: a multi-GNSS perspective

A consistent analysis of signal-in-space ranging errors (SISREs) is presented for all current satellite navigation systems, considering both global average values and worst-user-location statistics. The analysis is based on 1 year of broadcast ephemeris messages of the Global Positioning System (GPS), GLONASS, Galileo, BeiDou and QZSS collected with a near-global receiver network. Position and clock values derived from the navigation data are compared against precise orbit and clock products provided by the International GNSS Service and its multi-GNSS experiment. Satellite laser ranging measurements are used for a complementary and independent assessment of the orbit-only SISRE contribution. The need for proper consideration of antenna offsets is highlighted and block-/constellation-specific radial antenna offset values for the center-of-mass correction of broadcast orbits are derived. Likewise, the need for application of differential code biases in the comparison of broadcast and precise clock products is emphasized. For GPS, the analysis of the legacy navigation message is complemented by a discussion of the CNAV message performance based on the first CNAV test campaign in June 2013. Global average SISRE values for the individual constellations amount to 0.7 ± 0.02 m (GPS), 1.5 ± 0.1 m (BeiDou), 1.6 ± 0.3 m (Galileo), 1.9 ± 0.1 m (GLONASS), and 0.6 ± 0.2 m (QZSS) over a 12-month period in 2013/2014.

Galileo Signal and Positioning Performance Analysis Based on Four IOV Satellites

With the availability of Galileo signals from four in-orbit validation (IOV) satellites, positioning with Galileo-only observations has become possible, which allows us to assess its positioning performance. The performance of the Galileo system is evaluated in respect of carrier-to-noise density ratio (C/N0), pseudorange multipath (including noise), Galileo broadcast satellite orbit and satellite clock errors, and single point positioning (SPP) accuracy in Galileo-only mode as well as in GPS/Galileo combined mode. The precision of the broadcast ephemeris data is assessed using the precise satellite orbit and clock products from the Institute of Astronomical and Physical Geodesy of the Technische Universität München (IAPG/TUM) as references. The GPS-Galileo time offset (GGTO) is estimated using datasets from different types of GNSS receivers and the results indicate that a systematic bias exists between different receiver types. Positioning solutions indicate that Galileo-only SPP can achieve a three-dimensional position accuracy of about six metres. The integration of Galileo and GPS data can improve the positioning accuracies by about 10% in the vertical components compared with GPS-only solutions.

Basic performance of BeiDou-2 navigation satellite system used in LEO satellites precise orbit determination

The visibility for low earth orbit (LEO) satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system (GPS). In addition, the spaceborne receivers’ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination (POD) results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional (3D) accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about 30cm. As for the precise relative orbit determination (PROD), the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4mm over the service area, and it is still better than 1cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit (GEO) satellites is illustrated for POD.

An 18-element GEO broadcast ephemeris based on non-singular elements

Compass/Beidou2 uses uniform GPS-type broadcast ephemerides for its mixed constellation, which consists of geostationary earth orbit (GEO), inclined geosynchronous orbit and medium earth orbit satellites. The ephemeris parameters adopted by Compass are singular for the small inclinations of GEOs, and some intermediate orbital planes are currently used to avoid the singularities of parameter fitting. To directly deal with GEOs, an improved 18-element broadcast ephemeris is proposed, which consists of the non-singular elements and some correction terms. First, the non-singular elements are used to enable the orbit representation of GEOs to be completely free from the singularity. Second, two additional parameters, which express the predominant characteristics of east---west drift of the subsatellite point of GEO, are added into the correction terms for improving the modeling precision. Third, the user satellite position and velocity computation model based on the designed broadcast ephemeris parameters are presented. Simulation results show that the fitting arc length of the proposed broadcast ephemeris can be reduced to as short as 2 h, and that the improvement of the fitting user range error (URE) is obtained. The typical RMS of the fitting URE obtained in a non-eclipse period is less than 1 and 5 mm for 2- and 3-h fitting arcs, respectively.

Satellite Clock Error and Orbital Solution Error Estimation for Precise Navigation Applications

Global Positioning System (GPS) is a satellite-based navigation system that provides a three-dimensional user position (x,y,z), velocity and time anywhere on or above the earth surface. The satellite-based position accuracy is affected by several factors such as satellite clock error, propagation path delays and receiver noise due to which the GPS does not meet the requirements of critical navigation applications such as missile navigation and category I/II/III aircraft landings. This paper emphasizes on modelling the satellite clock error and orbital solution (satellite position) error considering the signal emission time. The transmission time sent by each satellite in broadcast ephemerides is not accurate. This has to be corrected in order to obtain correct satellite position and in turn a precise receiver position. Signal transmission time or broadcast time from satellite antenna phase center is computed at the receiver using several parameters such as signal reception time, propagation time, pseudorange observed and satellite clock error correction parameters. This corrected time of transmission and broadcast orbital parameters are used for estimation of the orbital solution. The estimated orbital solution was validated with the precise ephemerides which are estimated by Jet Propulsion Laboratory (JPL), USA. The errors are estimated for a typical day data collected on 11th March 2011 from dual frequency GPS receiver located at Department of Electronics and Communication Engineering, Andhra University College of Engineering, Visakhapatnam (17.73°N/83.319°E).

Ionospheric delays compensation for on-the-fly integer ambiguity resolution in long baseline LEO formations

This paper deals with the real–time onboard accurate relative positioning by carrier–phase differential GPS (CDGPS) of LEO formations with baselines of hundreds of kilometres. On long baselines, high accuracy can be achieved only using dual–frequency measurements and exploiting the integer nature of double difference (DD) carrier–phase ambiguities. However, large differential ionospheric delays and broadcast ephemeris errors complicate the integer resolution task. This paper is concerned with analysing possible approaches to DD ionospheric delays compensation in such applications. The first formulation models differential ionospheric delays as a function of the vertical electron content above the receivers, whereas the second one is based on combining DD measurements for removing ionospheric delays from the observation model. The effectiveness of the developed solutions is assessed by comparing the relative positioning accuracy that can be obtained on flight data. Results show that modelling the delays is advantageous for relative positioning only in mild ionospheric conditions.

CODE coefficients based Single frequency Ionospheric Error Correction Model to improve GPS Positional Accuracy of the Low-latitude regions

GPS (Global Positioning System) is a satellite based navigation system which provides reliable positioning information to its users (receivers) based on the concept of Time of Arrival (TOA) of the signal at the receiver. The positional accuracy of GPS is affected by several sources such as atmosphere, multipath and satellite-receiver geometry etc., of which ionosphere is one of the major sources of error for single frequency GPS user. When GPS signal propagates through the ionosphere, due to the change in refractive index in atmospheric layers, the signal bends which causes a delay in the arrival of the signal at the receiver. This delay of the signal introduces an error in ranging measurements at the receiver which in turn leads to an error in positioning information. Hence, to improve the positional accuracy, it is necessary estimate the delay of the signal in ionosphere during its transit from satellite to receiver. As this delay is caused by the electron content of the ionosphere, it is also necessary to estimate the Total Electron Content (TEC) in the signal path. The only way of estimating the ionospheric delay for single frequency receivers is by using Klobuchar algorithm which is based on the GPS broadcast ephemeris data. But this algorithm is optimized for mid latitudes and is very poor in high and low latitude regions. Hence it is required to have a model that is suitable for low latitude regions and near-equatorial regions such as Indian subcontinent. In this paper, low latitude suitable CODE coefficients based Klobuchar algorithm is implemented and is validated. The paper aims to investigate the performance of the CODE based Klobuchar algorithm by estimating the ionospheric delay using the CODE coefficients for data due to a low-latitude receiver data i.e. IGS station (HYDE: Lat/Long: 17°24'39N/78°33'4E) located in Hyderabad, Andhra Pradesh, India. This CODE based ionospheric delay is compared with delay due to Klobuchar model using the broadcast ephemeris data of the IGS receiver (HYDE). The model performance is validated with the ionospheric delay computed using the IONO-Lab data for the IGS station (HYDE). The CODE based algorithm is implemented, compared and validated for several days data of the IGS receiver (HYDE) and in this paper, it is presented for a typical day i.e. 11 th September 2014. The work yields the conclusion that Klobuchar model is simple due to short

Real-Time Relative Positioning of Spacecraft over Long Baselines

This paper deals with the problem of real-time onboard relative positioning of low-Earth-orbit spacecraft over long baselines using the Global Positioning System. Large intersatellite separations, up to hundreds of kilometers, are of interest to multistatic and bistatic synthetic-aperture radar applications, in which highly accurate relative positioning may be required in spite of the long baseline. To compute the baseline with high accuracy, the integer nature of dual-frequency, double-difference carrier-phase ambiguities can be exploited. However, the large intersatellite separation complicates the integer-ambiguities determination task due to the presence of significant differential ionospheric delays and broadcast ephemeris errors. To overcome this problem, an original approach is proposed, combining an extended Kalman filter with an integer least-square estimator in a closed-loop scheme, capable of fast on-the-fly integer-ambiguities resolution. These integer solutions are then used to compute the relative positions with a single-epoch kinematic least-square algorithm that processes ionospheric-free combinations of debiased carrier-phase measurements. Approach performance and robustness are assessed by using the flight data of the Gravity Recovery and Climate Experiment mission. Results show that the baseline can be computed in real time with decimeter-level accuracy in different operating conditions.

Influence of Ephemeris Error on GPS Single Point Positioning Accuracy

Abstract The Global Positioning System (GPS) user makes use of the navigation message transmitted from GPS satellites to achieve its location. Because the receiver uses the satellite's location in position calculations, an ephemeris error, a difference between the expected and actual orbital position of a GPS satellite, reduces user accuracy. The influence extent is decided by the precision of broadcast ephemeris from the control station upload. Simulation analysis with the Yuma almanac show that maximum positioning error exists in the case where the ephemeris error is along the line-of-sight (LOS) direction. Meanwhile, the error is dependent on the relationship between the observer and spatial constellation at some time period.

A Satellite Ephemeris Correction Calculating Algorithm Based on the Hill Differential Equation

The Hill differential equation is used to describe the change characteristic of the ephemeris prediction error in order to calculate the satellite broadcast ephemeris error and the error change rate. After the ECEF coordinate system converses the satellite inertial coordinate system, both the satellite ephemeris correction and the correction accuracy can be calculated by the Kalman filter. When the GEO, IGSO and MEO satellites move over the China, the calculation algorithms based on the weighted least square, the velocity model of the Kalman filter and the Hill differential equation are compared in the computing performance of the ephemeris corrections by using the reference date of IGS website. The simulation results show that: the ephemeris correction solver value based on the Hill differential equation can accurately reflect the ephemeris error characteristics at the current time. And it is able to correctly reflect the perturbation impact for the satellite ephemeris error. The Hill differential equation method is more suitable at the master station for engineering application about the MEO, IGSO and GEO satellites.

The BeiDou Navigation Message

The article provides an overview of the BeiDou navigation message contents and highlights its specific communalities and differences with respect to other GNSS constellations. Making use of data collected by multi-GNSS monitoring stations of the MGEX and CONGO networks, the quality of BeiDou broadcast ephemerides is assessed through the analysis of satellite laser ranging measurements, comparison with post-processed orbit and clock products as well as positioning tests. Specific attention is given to signal-specific group delays and their proper consideration in the positioning.