## 5 Conclusions  
In this paper, a statistical approach to data processing for dam monitoring based on the use of GNSS techniques has been described and detailed. In particular, the description of the approach focused on the treatment of the processed GNSS daily solutions composing the three-dimensional displacement time series of four points monitoring a dam body.  
First, a filtering procedure for reducing the observation noise was applied. This task was performed by applying the collocation approach after estimating and removing a deterministic component from the observations. For the deterministic modeling, a \(t\)-test was implemented to choose the polynomial order and avoid over-parametrization. Cubic polynomials resulted in being, in almost all cases, the optimal choice for removing the trend component from the observed time series. On these preliminary residual data, Fourier analyses were carried out to also determine the presence of significant periodic components. They are detected by looking for spikes in the ASD and then removed to obtain a sort of second-order residual data to be further filtered. Such residual data revealed still having an S/N ranging between 30 and 50%, as it came out from the analysis of the corresponding covariance functions. Therefore, exploiting the signal correlation, a final stochastic filtering by the collocation approach was implemented on the residual data. By restoring the previously removed deterministic trend and periodic components, the resulting filtered time series were obtained and were ready for interpretation. Submillimeter RMS was obtained from the comparisons between the original and the filtered GNSS time series, showing the high accuracy of the implemented low-cost GNSS system in the case study.  
The filtered time series interpretation was performed by means of correlation analyses with typical HTT models. They revealed that temperature was more correlated with displacements in the XZ crest vertical plane, while the reservoir water level was more related to displacements in the Y downstream direction, and this is particularly true for points located on the dam crest. These results led to estimate a linear autoregressive model including both temperature and reservoir filling with a maximum delay of 1 day. The resulting model was able to explain most of the 3D logged displacements, especially for the central point on the dam crest. From such an approach, an empirical indication of the \"unexpected\" displacements deserving more attention, and maybe alerting a surveillance team can be achieved. Although environmental temperature cannot be controlled, the reservoir water level can be tuned in the case of necessity by predicting reliable, expected displacements. On the other hand, unexpected displacements that can be observed could be signs of mechanical inefficiencies or, in general, criticalities of the structure.  
Conceptualization, all authors; methodology, M.R., L.R. and C.I.D.G.; software, M.R., L.R. and S.C.; validation, L.R. and C.I.D.G.; formal analysis, M.R. and L.R.; experiment implementation, M.R. and R.B.; data curation, S.C.; writing--original draft preparation, L.R. and C.I.D.G.; writing--review and editing, all authors; supervision, M.R. and R.B. All authors have read and agreed to the published version of the manuscript. This research was funded by a third party, which is not specified due to privacy reasons. Not applicable. Not applicable. Not applicable. Data Availability Statement: Restrictions apply to the availability of these data. Data were obtained from a third party and are not publicly available due to privacy reasons. The authors declare no conflict of interest.