M_split Estimation Approach to Modeling Vertical Terrain Displacement from TLS Data Disturbed by Outliers

Round 1

Reviewer 1 Report

This work evaluates the applicability of Msplit estimation approach to estimate terrain movements from Terrestrial Laser Scanning (TLS) data. Two typical variants (namely, SMS and AMS estimation) have been compared with respect to the existing methods (such as Least-squares, Huber and Tukey) in epoch-by-epoch and batch processing cases.

 

In general, this is a well-written work, presenting the methodology involved in a rather systematic way, designing the experimental schemes so reasonable that the conclusions and findings made are quite convincing. Moreover, the English writing is very professional, which makes this work an enjoyable reading.

 

Major concerns

 

1. The presentation of Msplit is given based on the linear (functional) model. Can it be possible that one applies the Msplit to the non-linear model?

2. The weight matrix considered in this work is assumed to be diagonal or equally weighted. How about the case that the weight matrix is fully-populated? That is, the observations are subject to correlation. 

3. The outliers simulated are quite small in size and uniformly distributed. Is this the case in the real world TLS data?

4. Should the number of epochs increase from two to multiple, say, tens of epochs, do the experimental findings in this work still hold?

5. Although the experiments based simulated data are convincing, it would be more advisable to conduct the experiments using real data for validating purpose.

Author Response

Thank you very much for your review and valuable comments and questions. Here are our responses to your major concerns:

1. Usually, M_split estimation applies to linear functional models in conventional form. Probably nonlinear models can also be used. Lately, M_split estimation has been developed to Total M_split estimation, which applies an errors-in-variables model (EIV) (see, Wiśniewski 2022, Journal of Geodesy, DOI: 10.1007/s00190-022-01668-z).
2. We applied the diagonal weight matrix because of the observations used. However, applying a full-populated weight matrix in both variants of M_split estimation is possible. The solutions are presented in some reference papers.
3. We assume such outliers since outliers of higher magnitude can be easily removed from the point cloud. Usually, it is a bigger problem to flag outliers of lower magnitude or to decrease their influence on the estimation results. Outliers of such a magnitude can result from measuring not the terrain surface but, e.g., grass, falling leaves, and shrubs.
4. Theoretically, M_split(q) estimation might concern q versions of parameter vector (q split functional models), where q < n (n – number of observations). However, from the practical point of view, one usually applies two, three, or four split functional models.
5. Here, we focus on the method's sensitivity to outliers when TLS data are applied in deformation analysis. Thus, it was necessary to know the real surface and its deformation. The applications of M_split estimation to determine terrain profiles or geodetic network deformation using real data can be found in other papers.

We have placed some of our responses in the revised paper version to make it clearer.

Reviewer 2 Report

General remark:

The simulated measurement example is very simplified in relation to the real measurement conditions. In the example, the points are distributed along one profile and there are relatively few of them. The form of the displacement function is also predetermined. In reality, the measurement points are spatially distributed and the form of the displacement approximating function is completely unknown. For this reason, the manuscript can only be viewed as an approximate consideration on simplified models.

Detailed comments:

The method of calculating the accuracy of the terrain displacements described in lines 230-238 is completely arbitrary and no arguments have been given for its adoption.

 

 

 

 

Author Response

Thank you very much for your review and remarks.

RMSDs are often used to describe estimation accuracy from Monte Carlo simulations. We applied the formula of RMSD by choosing 51 points (every single meter) for which we computed height differences between estimated and simulated surfaces. One can select more such points; however, the results would be comparable.

We have placed such a remark in the revised version of the paper to make it clearer.

Reviewer 3 Report

Very interesting article. Here follows some minor suggestions:

Outliers are associated with gross errors during measurement. Then, the DSM consists of (i) terrain; (ii) objects above terrain (vegetation, buildings, etc); and (iii) outliers (gross errors). Extracting the DTM relies on two separate processes: outlier removal followed by terrain filtering.  

Just a single test with simulated data (one terrain profile)...

Author Response

Thank you very much for your review and remarks.

One can take the approach given by the reviewer that outliers are only measurements disturbed by gross errors. However, here we assume a different approach where outlying observations are those that do not describe the surface under study. The simulated outliers are of lower magnitude; hence in some sense, we assume that the point clouds are cleared from outliers of higher magnitude.