## Zenith Wet Delay Approximation by Random Walk

Transactions of IAA RAS, issue 54, 44–51 (2020)

**DOI**: 10.32876/ApplAstron.54.44-51

**Keywords**:
tropospheric zenith wet delay, water vapor radiometer, very long baseline interferometry, stochastic approximation

### Abstract

One of the important problem of data processing of space geodesy is the accounting of some rapidly meant parameters, including fluctuations of zenith wet delay (ZWD). Accounting for the given parameter is especially important in analyzing VLBI and GNSS data. The standard method of processing these parameters is the approximation by some stochastic process, most often by a random walk. The purpose of this work is to calculate the random walk parameter for models with a trend and without a trend based on the results of water vapor radiometer (WVR) observations in 2019 for the stations “Svetloe”, “Zelenchukskaya” and “Badary”, as well as an analysis of the model quality. To estimate the random walk parameter, the methods of Kalman and collocation were used for the models without a trend and with a trend, respectively. To speed up the calculation of estimates in the case of the model with a trend, an algorithm for the rapid solution of a linear system with matrix of a special appearance. This algorithm is a modification of the well-known tridiagonal matrix algorithm. Finally, a comparison of the predicted ZWD value with the value obtained by the WVR was used to check the quality of the assessment. The paper presents the calculation of the maximum likelihood estimate for the parameter of the normal random walk of the ZWD stochastic part for random walk models with and without a trend. The obtained algorithms were applied to WVR observations at the “Svetloe”, “Zelenchukskaya”, and “Badary” stations. The compliance of the data and the model was verified using Shapiro–Wilk test, and visually. It is shown that the normal random walk is a rather rough approximation and describes adequate the data only in cases where the ZWD value is small. In addition, it was established that random walk with a linear trend in short intervals gives a more accurate approximation than the model without a trend.

### Citation

`А. A. Kudelkin. Zenith Wet Delay Approximation by Random Walk // Transactions of IAA RAS. — 2020. — Issue 54. — P. 44–51.`

```
TY - JOUR
TI - Zenith Wet Delay Approximation by Random Walk
AU - Kudelkin, А. A.
PY - 2020
T2 - Transactions of IAA RAS
IS - 54
SP - 44
AB - One of the important problem of data processing of space geodesy is
the accounting of some rapidly meant parameters, including
fluctuations of zenith wet delay (ZWD). Accounting for the given
parameter is especially important in analyzing VLBI and GNSS data.
The standard method of processing these parameters is the
approximation by some stochastic process, most often by a random
walk. The purpose of this work is to calculate the random walk
parameter for models with a trend and without a trend based on the
results of water vapor radiometer (WVR) observations in 2019 for the
stations “Svetloe”, “Zelenchukskaya” and “Badary”, as well as an
analysis of the model quality. To estimate the random walk parameter,
the methods of Kalman and collocation were used for the models
without a trend and with a trend, respectively. To speed up the
calculation of estimates in the case of the model with a trend, an
algorithm for the rapid solution of a linear system with matrix of a
special appearance. This algorithm is a modification of the well-
known tridiagonal matrix algorithm. Finally, a comparison of the
predicted ZWD value with the value obtained by the WVR was used to
check the quality of the assessment. The paper presents the
calculation of the maximum likelihood estimate for the parameter of
the normal random walk of the ZWD stochastic part for random walk
models with and without a trend. The obtained algorithms were applied
to WVR observations at the “Svetloe”, “Zelenchukskaya”, and “Badary”
stations. The compliance of the data and the model was verified using
Shapiro–Wilk test, and visually. It is shown that the normal random
walk is a rather rough approximation and describes adequate the data
only in cases where the ZWD value is small. In addition, it was
established that random walk with a linear trend in short intervals
gives a more accurate approximation than the model without a trend.
DO - 10.32876/ApplAstron.54.44-51
UR - http://iaaras.ru/en/library/paper/2062/
ER -
```