An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors can be
found in the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Professor,

Thank you for all your valuable comments. They were very helpful.

Please see attached our responses.

Kind regards.

Author Response File: Author Response.docx

Reviewer 2 Report

This considers an application of a Kalman filter to Gaussian error. 

As such the idea is basically a good one but the presentation leaves a lot to be desired. 

1. Several places different symbols are used for the same item. For example line 188 used v_subscript_t while line 189 uses nu_sbscript_t while line 191 has delta_subscrpt_t and delta_t. There are a number of subscripts left off throughout?
2. Several items need clarification and at least a reference, such as on line 152, F_subscipt_mSigma-algebra, line 168, Rieimann measurement, line 177, Riccati transformation, etc.
3. Line 200 says Q_subscript_t is diagonal but clearly from line 198 it is not. 
4. Delta-t seems to be 1 from line 184 but not at line 191?
5. Line 329 mentions use of the Hamiltonian. Where is this? Not H of line 202 which is not an energy?
6. ' is defined at line 155 but used earlier so should be defined earlier?
7. Line 162 claims an inclusion in Q which is a set of symmetric matrices but the matrices of (17), line 161 do not look symmetric. 
8. An explanation as to why the estimation errors should be smaller than the measurement errors seems in order especially for Figure 2.
9. Overall the English is understandable but the manuscript should be checked as for example the "the" left out before "state" line 291. 
10. Overall the chain of logic could be better explained. Probably a flow chart would be of assistance. 

Author Response

Dear Professor,

Thank you for all your valuable comments. They were very helpful.

Please see attached our responses.

Kind regards.

Author Response File: Author Response.docx

Reviewer 3 Report

In this paper, the authors develop a methodology of estimating the Gaussian errors by minimizing the symmetric loss function.
They use a recursive algorithm of the Kalman Filter to estimate the Gaussian errors. Also, other mathematical methods were used to estimate the Gaussian errors, such as the semigroup of the Hamiltonian matrices and con-329 traction property.

However, there are too many parameters and symbols present in Section 2, in which I couldn't follow the calculations. Thus, I suggest the authors rewrite and check their calculations again. Otherwise, I would reject the paper, thanks!

Author Response

Dear Professor,

Thank you for all your valuable comments. They were very helpful.

Please see attached our responses.

Kind regards.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

This looks in much better form.

It is still not clear that given (17) Q [of(18)] is symmetric. Once this is proven

to be valid, or the statement dropped, then this could be published.

Author Response

The statement was dropped.