Incremental Parameter Estimation under Rank-Deficient Measurement Conditions

Round 1

Reviewer 1 Report

This paper proposes a novel procedure for parameter estimation within the extent-based framework. This procedure combines structural observability labeling, matrix factorization, and graph-based system partitioning. Simulations are carried out to illustrate the approach. 

This paper is very well written, and contains interesting and important results. I would recommend it for publication with minor modifications. 

On page 6, Line 100, please clarify if G is full-row or full-column rank.

Please explain in a revision why inputs and measurements are not included in the graph.

Author Response

We have adjusted for the minor comments, in particular we have:

Added an indication the matrix G on line 100 is full column rank

Explained that the information flow graph can be augmented with measured variables and known input signals yet also indicate that this does not affect the resulting subsystem partitioning and is therefore omitted for clarity.

Reviewer 2 Report

The paper presents a extensive study about parameters estimations problems. The article is well written and brings value to the field. Therefore I would recommend the manuscript publication after minor revisions following the bellow commentaries.

The introduction miss a short review about the previous developments in the parameters estimation field. Furthermore, the presented approach is somehow similar to the estimability analysis, however I did not find any reference about the subject. The authors should comment this point. Several works in the literature address those issues such as: Quaiser et al 2009, Yao et al. 2003, Weijie et al 2010, Nogueira and Pontes 2017. Thus, I recommend the authors address these points in the manuscript with a short review about the topic in order to give the readers a better overview about the advances in parameters estimation.

The study cases present small number of parameters, I wonder if the methodology is still and feasible to be applied (in terms of computational effort)  in a case where is found several parameters. The authors should introduce some commentaries about this issue.

Several formatting problems are found through the text.

Author Response

We have adjusted our work as follows:

The reviewer claims to "miss a short review about the previous developments in the parameters estimation field.", particularly focused on parameter estimability, which is known better as parameter identifiability. However, in the first paragraph, we clearly state that parameter identifiability is not the focus of our work. Still, our work produce the tangential result that at least some structurally unidentifiable parameters can be identified through the system partitioning step. To put this in context, we have modified the first paragraph of the section 5.3, where identifiability analysis is discussed to some length.

We have added comments on the scalability of our method in the second paragraph of the discussion

The reviewer claims "Several formatting problems are found through the text." but we could not find any. Please note that we have used the available LaTeX templates for submission to Processes.