A Tropospheric Zenith Delay Forecasting Model Based on a Long Short-Term Memory Neural Network and Its Impact on Precise Point Positioning

Round 1

Reviewer 1 Report

The authors proposed a novel approach based on previously available GNSS data to estimate ZTD using machine learning algorithms. In the proposed method, at first, the gross errors in the ZTD values are detected and removed. Afterward, the missing data is estimated with the help of the KNN model. After that, the ZTD residual signal, which is concluded by subtracting the ZTD sequence from the periodic signal, is fed into an LSTM network. Finally, the ZTD values are predicted with the help of the LSTM network, the proposed method can improve the convergence time of PPP.

However, there are some problems should be solved before its possible acceptance. Specific suggestions are provided below.

 

Point 1: In the whole paper, you mentioned periodical model to express ZTD periodical signal, however, in Fig. 1, you show a ‘period model’, you’d better keep consistent.

Point 2: L25, ‘Over than’. Both ‘over’ and ‘than’ have the meaning of comparison, which is a bit repetitive. It is suggested that ‘than’ be removed.

Point 3: In Fig. 4 ‘periodical model’, keep consistent, the same as Fig. 1.

Point 4: Fig.7. You reported the activation function, number of LSTM layers (dropouts), hyperparameters involved, and so on. Was your LSTM neural network developed by trial-and-error? If yes, how many trials have it taken to find such a network topology/structure? It is important to highlight the way in which these network parameters were determined.

Point 5: Here, the forecast ZTD model applied the 29-days historical data to predict the data on the next day. So why the 29 days and the 1 day are selected to build the forecast model?

Point 6: The manuscript would benefit from further careful proofreading to correct for minor errors in several typos and grammatical errors.

Author Response

Dear Reviewer,

Thanks for your constructive comments on our manuscript " A Tropospheric Zenith Delay forecasting model based on Long Short-Term Memory neural network and its impact on Precise Point Positioning". We appreciate your warm and careful work earnestly, which has a significant improvement for our manuscript. We have carefully considered your suggestions and comments, and we have revised and enriched the manuscript accordingly. All revisions are highlighted in red in manuscript, and point-to-point responses to the comments are listed in rebuttal letters.

 

Many thanks and best regards.

Yours sincerely,

--Mingxian Hu

E-mail:  hu_mingx@whu.edu.cn

On behalf of all contributing authors

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

This study attempts to apply the long-short term memory (LSTM) neural network on ZTD prediction and explore its usage in PPP augmentation. It may be an interesting work; however, the manuscript is poorly prepared. The main methods and the purpose of the experiment are not explained clearly, which makes it very hard to understand the study. Also, the writing and language are poor and wrong expressions often appear. Hence, major improvement is needed before the work can be assessed.

 

Title: ‘…based on Long Short-Term Memory neural network…’ may be better

L49: to solve this problem

L90: ‘it only predicts the accuracy of140 epochs [31].’ Not understand

L103-104: grammar mistake

L108-109: not understand. What is BP-Hopfield ZTD?

L117-120: ‘Tropospheric delay can be divided into …’ not necessary

Section 2.1.1: explain your method used for outlier detection

Figure 3: why do outliers occur at the same time for those stations?

Section 2.1.2: present a statistic on the data gap

Section 2.1.2: Explain the KNN method more clearly. Not understand the description in this section.

L152: why do you use model data as a reference?  Which model is used?  period model or periodic model?

Equation (1) is incorrect for annual and semi-annual periods.

Fig 4 refers to which station? How do you obtain the results of Table 1?

L173: outer accuracy?

L180: re-set. what is the above mentioned GNSS ZTD?

L182: explain STD, MAE, RMSE, and R

L183-184: not understand

Section 2.2: improve the description of the ZTD prediction method.

Author Response

Dear Reviewer,

Thanks for your constructive comments on our manuscript " A Tropospheric Zenith Delay forecasting model based on Long Short-Term Memory neural network and its impact on Precise Point Positioning". We appreciate your warm and careful work earnestly, which has a significant improvement for our manuscript, and we have carefully considered your suggestions and comments, and we have revised and enriched the manuscript accordingly. All revisions are highlighted in red in manuscript, and point-to-point responses to the comments are listed in rebuttal letters.

 

Many thanks and best regards.

Yours sincerely,

--Mingxian Hu

E-mail:  hu_mingx@whu.edu.cn

On behalf of all contributing authors

Author Response File: Author Response.docx

Reviewer 3 Report

This manuscript proposed a method for developing tropospheric delay model using LSTM. The topic is highly relevant to precise positioning. Authors have introduced their method properly before presenting the experiment results to support their conclusions. The manuscript reads well. However, some aspects of the paper can still be improved, as listed below.

 

1) Lines 64-70: The latest work on PPP with tropospheric augmentation should be introduced (e.g., WAPTC augmenting BDS3 PPP etc.)  

2) Lines 112-120. Please elaborate the details on ZTD estimation using PPP, e.g., filtering parameters and the corresponding process noise.

3) Lines 112-120. Reasons should be given or specified for the outliers in ZTD series

4) Lines 173-184 Height differences between the VMF grid and GPS sites should be carefully handled when make comparisons.

Author Response

Dear Reviewer,

Thanks for your constructive comments on our manuscript " A Tropospheric Zenith Delay forecasting model based on Long Short-Term Memory neural network and its impact on Precise Point Positioning". We appreciate your warm and careful work earnestly, which has a significant improvement for our manuscript, and we have carefully considered your suggestions and comments, and we have revised and enriched the manuscript accordingly. All revisions are highlighted in red in manuscript, and point-to-point responses to the comments are listed in rebuttal letters.

 

Many thanks and best regards.

Yours sincerely,

--Mingxian Hu

E-mail:  hu_mingx@whu.edu.cn

On behalf of all contributing authors

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The writing can be improved further. 

Author Response

Dear Reviewer,

Thanks for your constructive comments on our manuscript " A Tropospheric Zenith Delay forecasting model based on Long Short-Term Memory neural network and its impact on Precise Point Positioning". We appreciate your warm and careful work earnestly, which has a significant improvement for our manuscript, and we have carefully considered your suggestions and comments, and we have revised using the “Track Changes” function. We sincerely hope to meet your requirements.

 

Many thanks and best regards.

Yours sincerely,

--Mingxian Hu

E-mail:  hu_mingx@whu.edu.cn

On behalf of all contributing authors