## Working out the Methodology for Predicting the Course of the Onboard Clock Using a Software Simulator

Transactions of IAA RAS, issue 69, 47–56 (2024)

**DOI**: 10.32876/ApplAstron.69.47-56

**Keywords**:
forecasting, navigation satellite, onboard clock, scales, Allan variation, model parameters, harmonic, discrepancy, random process

### Abstract

Currently, the construction of the onboard time scales forecast values relative to the central synchronizer (CS) scale is carried out on the basis of mathematical models in the form of the simplest polynomials of the first and the second degree. At the same time, in the case of the operational mode of the GLONASS spacecraft orbits calculation, linear models are accepted, the parameters of which are redefined with a 6-hour periodicity of feeding ephemeris information into the onboard computer. With urgent and a posteriori modes, the scales deviation forecasts from a day to two weeks are required. In this case, in order to maintain the ephemeris-temporal information (ETI) accuracy there is a need for a more complex prediction model that includes a quadratic term and other regular components. While developing such models, difficulties arise with estimating the values of the systematic and random components of the given scales discrepancy. In this paper an analytical three-component model for predicting the deviation of the onboard scale (OS) is proposed. The first two components define the linear and quadratic deviation part. The third one takes into account all the regularities of a periodic and quasi-periodic nature. It is represented by a polyharmonic series of 15 to 20 harmonics. The model parameters are estimated using the least squares method (LSM) individually for each navigation satellite (NS) according to the data of time-frequency corrections (TFC) at intervals from 1 to 5 months of the previous history. To estimate the magnitude of the random component of the onboard clock instability, it is proposed to use a software random number generator, which sets the desired width of the noise track. As a result of the numerical experiments to test the development of the proposed three-component model of the GLONASS and GPS OS NS divergence relative to the CS scale, it has been shown that the errors in the prediction of the GNSS OS deviation in most cases are commensurate with the approximation errors based on the data which underlie the model parameters. In particular, when testing the GLONASS OS NS divergence model (R02), the average UPC of the forecast for an interval of 30 days was about 1 ns, and for daily forecasts of the order of 0.5 ns with 100% results sampling.

### Citation

`V. M. Tissen, A. Y. Balakhnenko, V. D. Rachkov. Working out the Methodology for Predicting the Course of the Onboard Clock Using a Software Simulator // Transactions of IAA RAS. — 2024. — Issue 69. — P. 47–56.`

```
@article{tissen2024,
abstract = {Currently, the construction of the onboard time scales forecast values relative to the central synchronizer (CS) scale is carried out on the basis of mathematical models in the form of the simplest polynomials of the first and the second degree. At the same time, in the case of the operational mode of the GLONASS spacecraft orbits calculation, linear models are accepted, the parameters of which are redefined with a 6-hour periodicity of feeding ephemeris information into the onboard computer. With urgent and a posteriori modes, the scales deviation forecasts from a day to two weeks are required. In this case, in order to maintain the ephemeris-temporal information (ETI) accuracy there is a need for a more complex prediction model that includes a quadratic term and other regular components. While developing such models, difficulties arise with estimating the values of the systematic and random components of the given scales discrepancy.
In this paper an analytical three-component model for predicting the deviation of the onboard scale (OS) is proposed. The first two components define the linear and quadratic deviation part. The third one takes into account all the regularities of a periodic and quasi-periodic nature. It is represented by a polyharmonic series of 15 to 20 harmonics. The model parameters are estimated using the least squares method (LSM) individually for each navigation satellite (NS) according to the data of time-frequency corrections (TFC) at intervals from 1 to 5 months of the previous history. To estimate the magnitude of the random component of the onboard clock instability, it is proposed to use a software random number generator, which sets the desired width of the noise track.
As a result of the numerical experiments to test the development of the proposed three-component model of the GLONASS and GPS OS NS divergence relative to the CS scale, it has been shown that the errors in the prediction of the GNSS OS deviation in most cases are commensurate with the approximation errors based on the data which underlie the model parameters. In particular, when testing the GLONASS OS NS divergence model (R02), the average UPC of the forecast for an interval of 30 days was about 1 ns, and for daily forecasts of the order of 0.5 ns with 100% results sampling.},
author = {V.~M. Tissen and A.~Y. Balakhnenko and V.~D. Rachkov},
doi = {10.32876/ApplAstron.69.47-56},
issue = {69},
journal = {Transactions of IAA RAS},
keyword = {forecasting, navigation satellite, onboard clock, scales, Allan variation, model parameters, harmonic, discrepancy, random process},
pages = {47--56},
title = {Working out the Methodology for Predicting the Course of the Onboard Clock Using a Software Simulator},
url = {http://iaaras.ru/en/library/paper/2187/},
year = {2024}
}
```

```
TY - JOUR
TI - Working out the Methodology for Predicting the Course of the Onboard Clock Using a Software Simulator
AU - Tissen, V. M.
AU - Balakhnenko, A. Y.
AU - Rachkov, V. D.
PY - 2024
T2 - Transactions of IAA RAS
IS - 69
SP - 47
AB - Currently, the construction of the onboard time scales forecast
values relative to the central synchronizer (CS) scale is carried out
on the basis of mathematical models in the form of the simplest
polynomials of the first and the second degree. At the same time, in
the case of the operational mode of the GLONASS spacecraft orbits
calculation, linear models are accepted, the parameters of which are
redefined with a 6-hour periodicity of feeding ephemeris information
into the onboard computer. With urgent and a posteriori modes, the
scales deviation forecasts from a day to two weeks are required. In
this case, in order to maintain the ephemeris-temporal information
(ETI) accuracy there is a need for a more complex prediction model
that includes a quadratic term and other regular components. While
developing such models, difficulties arise with estimating the values
of the systematic and random components of the given scales
discrepancy. In this paper an analytical three-component model for
predicting the deviation of the onboard scale (OS) is proposed. The
first two components define the linear and quadratic deviation part.
The third one takes into account all the regularities of a periodic
and quasi-periodic nature. It is represented by a polyharmonic series
of 15 to 20 harmonics. The model parameters are estimated using the
least squares method (LSM) individually for each navigation satellite
(NS) according to the data of time-frequency corrections (TFC) at
intervals from 1 to 5 months of the previous history. To estimate the
magnitude of the random component of the onboard clock instability,
it is proposed to use a software random number generator, which sets
the desired width of the noise track. As a result of the numerical
experiments to test the development of the proposed three-component
model of the GLONASS and GPS OS NS divergence relative to the CS
scale, it has been shown that the errors in the prediction of the
GNSS OS deviation in most cases are commensurate with the
approximation errors based on the data which underlie the model
parameters. In particular, when testing the GLONASS OS NS divergence
model (R02), the average UPC of the forecast for an interval of 30
days was about 1 ns, and for daily forecasts of the order of 0.5 ns
with 100% results sampling.
DO - 10.32876/ApplAstron.69.47-56
UR - http://iaaras.ru/en/library/paper/2187/
ER -
```