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Real-time satellite orbit and clock corrections obtained from the broadcast ephemerides can be improved using IGS real-time service (RTS) products. Recent research showed that applying such corrections for broadcast ephem erides can significantly improve the RMS of the estimated coordinates. However, unintentional streaming interruption may happen for many reasons such as software or hardware failure. Streaming interruption, if happened, will cause sudden degradation of the obtained solution if only the broadcast ephemerides are used. A better solution can be obtained in real-time if the predicted part of the ultra-rapid products is used. In this paper, Harmonic analysis technique is used to predict the IGS RTS corrections using historical broadcasted data. It is shown that using the predicted clock corrections improves the RMS of the estimated coordinates by about 72%, 58%, and 72% in latitude, longitude, and height directions, respectively and reduces the 2D and 3D errors by about 80% compared with the predicted part of the IGS ultra-rapid clock corrections.

Since 1994, the “International GNSS Service” (IGS) produces precise ephemerides, which includes satellite coordinates and clock corrections at equidistant epochs, typically 15 minutes. Precise ephemerides can be obtained from the IGS website (https://igscb.jpl.nasa.gov/). Precise ephemerides accuracies vary depending on availability. For example, the ultra-rapid precise ephemerides are available in real-time through the predicted part, the rapid precise ephemerides are available with latency about 17 - 41 Hours, and the final precise ephemerides is available with delay about 12 - 18 days [^{st}, 2013.

RTS utilizes the main infrastructure of the IGS, including global network stations (see

IGS01/IGC01 is a single-epoch combined solution in which no filters are applied, and each epoch is independent of the other. IGS01 product refers to “Antenna Phase Center” (APC), while the IGC01 refers to satellite “Center of Mass” (CoM). IGS02, on the other hand, is a combined solution using Kalman filter. The orbit in this case is one of the IGU solutions, which refers to satellite APC. Both IGS01/IGC01 and IGS02 include corrections to the GPS system only. However, IGS03 includes GLONASS corrections in addition to GPS corrections.

RTS corrections are expressed within the “International Terrestrial Reference Frame 2008” (ITRF08). To broadcast the RTS corrections, users have to register through the IGS RTS web page (http://igs.org/rts) and download the NTRIP client application from e.g., BKG analysis center web page (http://igs.bkg.bund.de/ntrip/download). The real-time orbital corrections are expressed in the orbital coordinate system (radial, along-track, and cross-track). So, to apply the RTS orbital corrections, it should be computed at the current epoch using the rate of change of each component and then transformed to “Earth Centered Earth Fixed” (ECEF) components. RTS clock corrections, on the other hand, are streamed as polynomial coefficients and can be computed at the current epoch from the corresponding values at the issue of data time (IOD). The standard deviation of the IGS RTS clock corrections is ten times better than the IGU clock corrections. Moreover, the PPP solution using the IGS RTS products can improve the RMS of the estimated coordinates by about 50% [

Real-time streaming of the RTS corrections is the key to maintain the above- mentioned accuracies. However, unintentional streaming interruption may happen for many reasons such as software or hardware failure. Streaming interruption, if happened, will cause sudden degradation of the obtained solution if only the broadcast ephemerides is used. A better solution can be obtained in real-time if the IGU orbit and clock corrections are used. In this paper, a method to predict the IGS RTS corrections using historical broadcasted data is introduced. It is shown that the solution obtained using the predicted RTS clock corrections is better than that obtained from the IGU products.

In practice, it is usually common to use trigonometric polynomials to represent data sets that experience periodic nature as a type of harmonic analysis. Any periodic signal can be presented by a trigonometric series as follows [

where

Several techniques can be used to estimate the constant term

The trigonometric method is used to fit four hours of the IGS RTS clock corrections collected in several sessions during GPSW 1842, then the coefficients are used to predict two hours of such corrections for all satellites. If the IGS RTS clock corrections are considered as targets, the error in the IGU clock corrections can be computed after removing the common offset and trend. Fitting and prediction errors of the predicted clock corrections (PRD) are computed during the period of study for all satellites.

From

It is clear also from

Error Parameter | Minimum (cm) | Maximum (cm) | STD (cm) |
---|---|---|---|

Fitting | −11.08 | 10.57 | 2.1 |

Prediction | −14.84 | 14.24 | 5.33 |

IGU | −19.34 | 18.51 | 7.61 |

After prediction of RTS satellite clock corrections, two options are available to perform PPP in real-time. The first option is to use the predicted clock corrections (PRD) along with the IGU orbit. The second option is to use the IGU orbit and clock corrections. Beside the previously statistical analysis, positioning performance can be used as a measure for the quality of both PRD and IGU products. The mathematical model of the first-order ionosphere-free linear combination of pseudorange and carrier phase can be given as follows [

where, _{d} is the slant tropospheric delay,

To test the predicted clock corrections, GPS data from several IGS stations is processed in kinematic mode (

ionosphere-free code and carrier phase. The IGU orbit is used to account for satellite orbit and APC corrections are applied. Satellite clock corrections are accounted for using the PRD or the IGU clock corrections. The “Global Pressure and Temperature 2” (GPT2) model is used to account for dry tropospheric delay [

As can be seen in

Our results showed that the average RMSs of the estimated coordinates are 0.09 m, 0.19 m, and 0.19 m in latitude, longitude, and height directions, respectively can be obtained when using our predicted satellite clock corrections. Using the IGU clock corrections, on the other hand, can produce RMSs of 0.34 m, 0.47 m, and 0.70 m in latitude, longitude, and height directions, respectively. These results mean an average improvement of about 72%, 58%, and 72% in latitude, longitude, and height directions, respectively. Moreover, Figures 5-7 show that

Prediction Time | PRD Positioning Error (m) | IGU Positioning Error (m) | ||||
---|---|---|---|---|---|---|

Latitude | Longitude | Ellipsoidal Height | Latitude | Longitude | Ellipsoidal Height | |

05 Minutes | 0.002 | −0.009 | −0.033 | 0.320 | 0.125 | −0.184 |

10 Minutes | 0.024 | 0.011 | 0.085 | 0.166 | −0.415 | −0.452 |

15 Minutes | 0.069 | −0.044 | 0.071 | 0.429 | −0.500 | 0.100 |

20 Minutes | 0.094 | 0.143 | 0.009 | 0.389 | −0.170 | 0.505 |

25 Minutes | 0.097 | 0.043 | 0.053 | 0.352 | −0.273 | 0.124 |

30 Minutes | 0.108 | 0.038 | 0.063 | 0.284 | −0.245 | 0.176 |

RMSs of the estimated coordinates, using our predicted clocks, is stable regardless the prediction period (5 to 30 minutes) which is not the case when using the IGU clock corrections. Such improvement is attributed to the quality of PRD clock corrections compared with the IGU clock corrections (see

In this paper, the IGS RTS clock corrections are predicted with harmonic analysis technique using historical broadcasted data. We found that the RMSs of the predicted clock corrections are stable over a prediction time of two hours. It is shown that using the predicted clock corrections improves the RMS of the estimated coordinates by about 72%, 58%, and 72% in latitude, longitude, and height directions, respectively compared with the solution of the IGU clock corrections. Moreover, the 2D and 3D error is reduced by about 80% compared with the IGU clock corrections. Such improvement is mainly attributed to the quality of the predicted clock corrections as it is predicted from RTS clock corrections, which are ten times better than the predicted ultra-rapid clock corrections.

Elsobeiey, M.E. (2017) Efficient Harmonic Analysis Technique for Prediction of IGS Real-Time Satellite Clock Corrections. Positioning, 8, 37-45. https://doi.org/10.4236/pos.2017.83003