## The Algorithm of Adaptive Measurements Sampling for Satellite Navigation Equipment on High-orbit Spacecraft

Transactions of IAA RAS, issue 59, 14–18 (2021)

**DOI**: 10.32876/ApplAstron.59.14-18

**Keywords**:
satellite navigation, high-orbit spacecraft, bad conditioning

### Abstract

Since 2017 Kometa Corporation, JSC has been developing satellite navigation equipment for high-orbit spacecrafts. Algorithms of position and velocity evaluation for such equipment must operate in discontinuous navigational field when a number of visible navigational satellites is small, and relative location of spacecraft and navigational satellites changes slowly. These circumstances often lead to ill-conditioned problems of measurements processing. Position and velocity evaluation process in the algorithms for the above mentioned satellite navigation equipment consists of four stages: getting an initial approximation vector, collecting of smoothed measurements, getting a normal place, and normal places processing. At the stage of getting a normal place smoothed measurements are processed with the Least Squares Method. This stage is often associated with computational problems. The algorithm of adaptive measurements sampling is used to avoid bad conditioning in the algorithm of getting a normal place. In this algorithm conditioning is estimated every time when new smoothed measurements are obtained. One should start the algorithm of getting a normal place only if smoothed measurements processing is a well-conditioned problem. Specific methods for solving ill-conditioned problems often require a lot of auxiliary calculations and analysis of their results. It is not necessary for the algorithm of adaptive measurements sampling. This algorithm allows selecting duration of smoothed measurements collection automatically. According to simulation results the algorithm of adaptive measurements sampling ensures that the algorithm of getting a normal place will converge in approximately 98 percent cases. At the same time this algorithm provides required accuracy of position and velocity estimation.

### Citation

`G. V. Skorynina, A. V. Doronkin. The Algorithm of Adaptive Measurements Sampling for Satellite Navigation Equipment on High-orbit Spacecraft // Transactions of IAA RAS. — 2021. — Issue 59. — P. 14–18.`

```
@article{skorynina2021,
abstract = {Since 2017 Kometa Corporation, JSC has been developing satellite navigation equipment for high-orbit spacecrafts. Algorithms of position and velocity evaluation for such equipment must operate in discontinuous navigational field when a number of visible navigational satellites is small, and relative location of spacecraft and navigational satellites changes slowly. These circumstances often lead to ill-conditioned problems of measurements processing.
Position and velocity evaluation process in the algorithms for the above mentioned satellite navigation equipment consists of four stages: getting an initial approximation vector, collecting of smoothed measurements, getting a normal place, and normal places processing. At the stage of getting a normal place smoothed measurements are processed with the Least Squares Method. This stage is often associated with computational problems. The algorithm of adaptive measurements sampling is used to avoid bad conditioning in the algorithm of getting a normal place. In this algorithm conditioning is estimated every time when new smoothed measurements are obtained. One should start the algorithm of getting a normal place only if smoothed measurements processing is a well-conditioned problem.
Specific methods for solving ill-conditioned problems often require a lot of auxiliary calculations and analysis of their results. It is not necessary for the algorithm of adaptive measurements sampling. This algorithm allows selecting duration of smoothed measurements collection automatically. According to simulation results the algorithm of adaptive measurements sampling ensures that the algorithm of getting a normal place will converge in approximately 98 percent cases. At the same time this algorithm provides required accuracy of position and velocity estimation.},
author = {G.~V. Skorynina and A.~V. Doronkin},
doi = {10.32876/ApplAstron.59.14-18},
issue = {59},
journal = {Transactions of IAA RAS},
keyword = {satellite navigation, high-orbit spacecraft, bad conditioning},
pages = {14--18},
title = {The Algorithm of Adaptive Measurements Sampling for Satellite Navigation Equipment on High-orbit Spacecraft},
url = {http://iaaras.ru/en/library/paper/2101/},
year = {2021}
}
```

```
TY - JOUR
TI - The Algorithm of Adaptive Measurements Sampling for Satellite Navigation Equipment on High-orbit Spacecraft
AU - Skorynina, G. V.
AU - Doronkin, A. V.
PY - 2021
T2 - Transactions of IAA RAS
IS - 59
SP - 14
AB - Since 2017 Kometa Corporation, JSC has been developing satellite
navigation equipment for high-orbit spacecrafts. Algorithms of
position and velocity evaluation for such equipment must operate in
discontinuous navigational field when a number of visible
navigational satellites is small, and relative location of spacecraft
and navigational satellites changes slowly. These circumstances often
lead to ill-conditioned problems of measurements processing.
Position and velocity evaluation process in the algorithms for the
above mentioned satellite navigation equipment consists of four
stages: getting an initial approximation vector, collecting of
smoothed measurements, getting a normal place, and normal places
processing. At the stage of getting a normal place smoothed
measurements are processed with the Least Squares Method. This stage
is often associated with computational problems. The algorithm of
adaptive measurements sampling is used to avoid bad conditioning in
the algorithm of getting a normal place. In this algorithm
conditioning is estimated every time when new smoothed measurements
are obtained. One should start the algorithm of getting a normal
place only if smoothed measurements processing is a well-conditioned
problem. Specific methods for solving ill-conditioned problems
often require a lot of auxiliary calculations and analysis of their
results. It is not necessary for the algorithm of adaptive
measurements sampling. This algorithm allows selecting duration of
smoothed measurements collection automatically. According to
simulation results the algorithm of adaptive measurements sampling
ensures that the algorithm of getting a normal place will converge in
approximately 98 percent cases. At the same time this algorithm
provides required accuracy of position and velocity estimation.
DO - 10.32876/ApplAstron.59.14-18
UR - http://iaaras.ru/en/library/paper/2101/
ER -
```