# Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Pre-Processing

#### 2.1. GNSS Height Residuals

#### 2.2. Environmental Surface Loadings

#### 2.3. Meteorological Data

#### 2.4. Reduction of GNSS Residuals by Environmental Loadings

## 3. Methodology

#### 3.1. Temporal Convolutional Network

- (1)
- the network can take an input sequence of any length and return the same length as output by using a 1D fully convolutional architecture, and
- (2)

#### 3.2. Implementation Details

_{MOD}. These are subtracted from the corresponding GNSS residuals from the test dataset, which results in the reduced GNSS time series GNSS

_{RED}.

## 4. Results and Discussion

#### 4.1. TCN Modeling and GNSS Reduction and Comparison to Physical Loading Model Reduction

#### 4.2. TCN Modeling Based on GNSS Residuals Reduced by Loading Models

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Distribution of selected GNSS stations over Europe. The size of the circles indicates the available time series length in years.

**Figure 2.**Environmental surface loadings at station MAR3. For visualization purposes, HYDL is shifted by +30 mm, NTOL by −15 mm, and the SUM (HYDL + NTAL + NTOL) by −30 mm.

**Figure 3.**Time series of the meteorological parameters at the example station MAR3. TG = Temperature, RR = Precipitation, PP = Sea level pressure, HU = Humidity, QQ = Radiation.

**Figure 4.**(

**Left**) GNSS and meteorological station locations. (

**Right**) GNSS station locations, colored by the distance to the corresponding meteorological station.

**Figure 5.**Workflow of GNSS data processing. The main input and output datasets are colored in green, processing steps are marked in orange, and the intermediate products are in colored in red.

**Figure 7.**RMS reduction of GNSS height residuals after subtracting the sum of all environmental surface loadings.

**Figure 8.**Example of a dilated causal convolution, with a filter size $k=3$ and dilation factors $d=1,2,4$.

**Figure 10.**Flowchart of TCN training pipeline. The main input and output datasets are colored in green, processing steps are marked in orange, and the intermediate products are in colored in red and blue.

**Figure 11.**Example of TCN-modeled residuals at the example station MAR3. In blue are the GNSS residuals, and in orange are the TCN-modeled time series.

**Figure 12.**RMS reduction of GNSS height residuals after subtracting a TCN-modeled signal with meteorological parameters as input features.

**Figure 13.**Difference in RMS reductions between the reduction rates of GNSS residuals when using the physical models from GFZ and a TCN-modeled signal from meteorological parameters.

**Figure 14.**Example of resulting modeled residuals at the example station MAR3. In blue are the by environmental loadings reduced residuals, and in orange are the TCN-modeled time series.

**Figure 15.**GNSS residuals at the different reduction stages. In blue are the original GNSS residuals, in orange are the time series after subtracting the environmental loading displacements, and the green residuals result after subtracting the TCN-modeled time series.

**Figure 16.**RMS reduction of reduced GNSS height residuals after subtracting a TCN-modeled signal with meteorological parameters as input features.

**Figure 17.**Total RMS reduction of GNSS height residuals after subtracting environmental surface loadings and the TCN-modeled signal.

Parameter | Value(s) |
---|---|

batch size B | 2 |

number of features F | 8 |

sequence length (epochs) T | 7 |

filter size k | 8 |

dilations d | 1, 2, 4, 8, 16, 32, 64, 128, 256 |

number of filters | 24 |

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**MDPI and ACS Style**

Ruttner, P.; Hohensinn, R.; D’Aronco, S.; Wegner, J.D.; Soja, B.
Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach. *Remote Sens.* **2022**, *14*, 17.
https://doi.org/10.3390/rs14010017

**AMA Style**

Ruttner P, Hohensinn R, D’Aronco S, Wegner JD, Soja B.
Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach. *Remote Sensing*. 2022; 14(1):17.
https://doi.org/10.3390/rs14010017

**Chicago/Turabian Style**

Ruttner, Pia, Roland Hohensinn, Stefano D’Aronco, Jan Dirk Wegner, and Benedikt Soja.
2022. "Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach" *Remote Sensing* 14, no. 1: 17.
https://doi.org/10.3390/rs14010017