Sequential Joint State Estimation and Track Extraction Algorithm Based on Improved Backward Smoothing

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Algorithm Presentation: The paper describes a "sequential joint state estimation and track extraction algorithm" based on backward smoothing and label iterative processing. However, it's essential to clearly and explicitly lay out the steps of this algorithm. Using pseudocode or a flowchart could greatly enhance the clarity of the algorithmic process.
2. Clarification on Terminology: Terms like "backward smoothing," "label random finite set," "LMB filtering," and "label iterative processing" are frequently mentioned. While they may be familiar to domain experts, the paper could benefit from brief explanations or references to ensure clarity for a broader audience.
3. Comparison Metrics: The paper claims that the proposed algorithm improves tracking performance when compared to other latest research algorithms. It's crucial to detail the specific metrics (e.g., accuracy, precision, recall, processing time) used for this comparison. Additionally, details on how these metrics were computed would provide clarity.
4. Simulation and Measured Data Details: When discussing the verification using simulation data and measured data, the paper should provide more information about the nature of this data. Was the simulation data synthetically generated? If so, based on what model? Where was the measured data sourced from? Clarifying these aspects can help the reader gauge the reliability of the test results.
5. Computational Efficiency: The proposed algorithm's computational complexity and run-time performance, especially when compared to existing methods, need to be addressed. Multi-target tracking can be computationally intensive, and if the algorithm is to be used in real-time applications, its efficiency becomes crucial.
6. Results and Discussion: While the paper suggests that the proposed algorithm can eliminate outliers and improve targets' cardinality and state estimation, it would be beneficial to present a detailed results section. This section should contain graphs, tables, or other visual aids, followed by a discussion section to interpret these results in the context of the problem and the proposed solution.
7. Scalability and Limitations: The paper should address how the proposed algorithm scales with an increase in the number of targets and the complexity of the environment. Additionally, an open discussion on the algorithm's limitations would provide a more balanced perspective.

In conclusion, the research topic is promising, and the efforts made in this work are commendable. However, providing more granularity in terms of algorithmic details, results presentation, and comprehensive discussions will make the paper more robust and clear for the intended audience.

Comments on the Quality of English Language

Moderate editing of English language required.

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper before. In response to your comments, I spent nearly 10 days significantly revising our paper and made revisions to the outcomes you mentioned one by one. In addition to this reply text (Please refer to the attachment for details), there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations《Manuscript With Revision Note》. In《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, red represents supplementary content, and yellow represents modified content. I hope it will be convenient for you to review our paper in this way. Below are further detailed explanations and answers to your questions.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regard,

Mr. JiuChao

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper deals with the problem of joint estimation and tracking via label iterative processing by combining LMB filtering and backward smoothing. The topic is interesting, and the comments are listed for further improvement:

1. A framework to illustrate the overall processing procedures is suggested.

2. It is suggested to add the corresponding analysis on the computational complexity of the paper.

3. The format is poor. Please re-organize and uniform the whole paper.

4. Some necessary papers, such as the GLRT-based detection methods for FDA-MIMO radar are suggested to be considered.

5.  The language should be improved and the paper should be carefully proofread to avoid any typos.

For example:

'to sequentially eliminate'-- to eliminate xxxx sequentially'

'(LMB )'--'(LMB)'

'Regarding the issue of'---'Regarding to the issue of'

'These strategies are lack of lose'  not correct with 'lack of' and 'lose'

.....

Comments on the Quality of English Language

needs to be improved

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper before. In response to your comments, I spent nearly 10 days significantly revising our paper and made revisions to the outcomes you mentioned one by one. In addition to this reply text (Please refer to the attachment for details), there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations《Manuscript With Revision Note》. In《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, red represents supplementary content, and yellow represents modified content. I hope it will be convenient for you to review our paper in this way. Below are further detailed explanations and answers to your questions.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regard,

Mr. JiuChao

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. There is a discrepancy between the size of the equation and the accompanying text.

 

2. In Eq.(9), 1_{\theta}(z) is puzzling and seems to have a different meaning than what is expressed on page 3.

 

3. It is suggested that the authors add the concept of backward smoothing in the first paragraph of section 2.3.

 

4. The title of section 2.3 is backward smoothing, which needs further clarification, for example, the interpretation of the physical meaning of Eq.22 needs to be supplemented.

In addition, in the figure above, the assumption that the PDF distribution at the previous time is in LMB form leads to the conclusion that the predicted PDF at the next time is also in LMB form. There is nothing wrong with this section.  

 

Assuming t=k-1, the author holds that the inference "the prediction PDF of the current moment is in LMB form assuming that the PDF of the previous moment is also in LMB form" is valid, please explain.

 

5. The numerical experiment must be performed many times, otherwise, the results will not be trusted.

 

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Further improvement is needed in English grammar. 

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper before. In response to your comments, I spent nearly 10 days significantly revising our paper and made revisions to the outcomes you mentioned one by one. In addition to this reply text (Please refer to the attachment for details), there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations《Manuscript With Revision Note》. In《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, red represents supplementary content, and yellow represents modified content. I hope it will be convenient for you to review our paper in this way. Below are further detailed explanations and answers to your questions.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regard,

Mr. JiuChao

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript introduces a sequential joint state estimation and track extraction algorithm. But the experimental verification of the algorithm is not convincing, and there are some problems in the expression of the text. Therefore, the reviewer suggests a new submission after the following issues are resolved:

1. The quality of picture 1 is not good, please provide better quality pictures.

2. Please check the format of the manuscript carefully. For example, the format of the first line of step1 in page7 needs to be adjusted; in page10, the size of digital fonts in Experiment Analysis is different.

3. In the verification of measured data, there only has the trajectory diagram. Why is there no trace of the actual detection process? In this case, what is the difference from the previous simulation data?

4. How to overcome the object being blocked and continue to track as the same target?

5. What is the result of tracking more than 3 targets with similar trajectories?

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper before. In response to your comments, I spent nearly 10 days significantly revising our paper and made revisions to the outcomes you mentioned one by one. In addition to this reply text (Please refer to the attachment for details), there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations《Manuscript With Revision Note》. In《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, red represents supplementary content, and yellow represents modified content. I hope it will be convenient for you to review our paper in this way. Below are further detailed explanations and answers to your questions.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regard,

Mr. JiuChao

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised can be accepted now. However, I suggest the authors to include a nomenclature table comprising of all the symbols and notations towards the end of introduction section. I have nothing to add further.

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper. In response to your comments, we made revisions to the comments you mentioned and further improved the quality of the article. In addition to this reply text, there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations 《Manuscript With Revision Note》. In 《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, green represents supplementary content, and yellow represents modified content. we hope it will be convenient for you to review our article in this way. Below are further detailed explanations and answers to your questions.

Q1: The revised can be accepted now. However, I suggest the authors to include a nomenclature table comprising of all the symbols and notations towards the end of introduction section. I have nothing to add further.

A1: First of all, thank you for your meticulous review and valuable comment. According to your suggestion, we have developed a nomenclature table to explain all symbols and notations in the article, and placed it at the end of the introduction section. In addition, we have also adjusted the symbols used in the article to avoid confusion. Thank you again for your valuable suggestion.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regards，

Mr. JiuChao.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The author stated that the numerical experimental results in the article were obtained by counting 100 MCs. Therefore, it is necessary to clarify the reasons for the distortion points in various algorithms in Fig. 15 (especially the distortion reasons of the OL-delta-GLMB algorithm at 14s, 18s, and 19s), and the multiple MC results seem to be not smooth.

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper. In response to your comments, we made revisions to the comments you mentioned and further improved the quality of the article. In addition to this reply text, there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations 《Manuscript With Revision Note》. In 《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, green represents supplementary content, and yellow represents modified content. we hope it will be convenient for you to review our article in this way. Below are further detailed explanations and answers to your questions.

Q1: The author stated that the numerical experimental results in the article were obtained by counting 100 MCs. Therefore, it is necessary to clarify the reasons for the distortion points in various algorithms in Fig. 15 (especially the distortion reasons of the OL-delta-GLMB algorithm at 14s, 18s, and 19s), and the multiple MC results seem to be not smooth.

A1: First of all, thank you for your meticulous review and valuable comment. Before explaining and clarifying your comment, allow us to elaborate and understand that. In this comment, you have a problem with Fig. 15, but Fig. 15 does not exist in the article. Therefore, based on the content of the article and your description of the problem, we personally understand that there is a problem with Fig. 10 in the article. Next, we provide the following explanations and clarifications for the questions you mentioned.

For the four smoothers (FB-LMB, OL-δ-GLMB, BI-LMB, IBR-LMB) compared in the article, we mainly explain the reasons for the distortion points in Figure 10 from three aspects: outlier removal, short-lived track removal, and track continuity processing. First, we explain these three aspects one by one: outlier removal is to remove outliers using backward smoothing under the control of backward smoothing step length; short-lived track removal is also to process short-lived tracks using backward smoothing processing combined with track start determination; track continuity processing is to use backward smoothing to reasonably recover track fractures. Among the four smoothers, except for the smoother proposed in the article, the other three methods only have partial capabilities.

FB-LMB smoother has an ability to remove outliers using backward smoothing, but there is a problem of erroneous removal due to missed detection, and it does not have the ability to process track continuity. Therefore, combined with the multi-target simulation scenario settings given in Table 5 in the article (where the backward smoothing step length and track continuity processing length are 5, and the track start determination length is 5), it can be seen that FB-LMB smoother can effectively remove outliers, so all distorted points are free of the interference of outliers and short-lived tracks. In the processing result of FB-LMB smoother given in Figure 10, points 6, 7, 8, 9, and 10 are erroneously removed due to missed detection of target T3 at time 11-12 under the influence of the smoothing step length, while points 11 and 12 are caused by missed detection of target T3 itself. Point 13 is due to the thresholding of the first point at the beginning of the track due to its low initial survival probability. Points 16, 17, 18, 19, and 20 are also erroneously removed due to missed detection of target T3 at time 21-24 under the influence of the smoothing step length, while points 21,23 and 24 are caused by missed detection of target T3 itself. Point 30, 31, 32, 33, and 34 are also erroneously removed due to missed detection of target T1 at time 35-38 under the influence of the smoothing step length. Points 35-38 are affected by missed detection of target T3 itself and point 36 may also be affected by unstable determination due to ineffective processing of outliers. Points 37 and 38 are erroneously removed due to the algorithm's assumption of missed detection of target T1 at 41, while point 39 is erroneously removed due to the thresholding of the first point at the beginning of the track due to its low initial survival probability, and target T1 is not measured at 41, which the algorithm assumes to be a missed detection. Point 40 is erroneously removed due to the algorithm's assumption of missed detection of target T1 at 41.

BI-LMB smoother has an ability to remove outliers using backward smoothing and corrects the problem of erroneous removal caused by missed detections. However, it does not have the ability to process trajectory continuity. Therefore, compared to FB-LMB smoother, BI-LMB smoother has distortion points only at targets T1 in time 11-12, targets T3 in time 21-24 and 35-38 due to missed detections, and at points 13, 25, and 39 due to the threshold removal of the first point at the start of the trajectory due to its low survival probability.

OL-δ-GLMB smoother only has an ability to remove outliers and incomplete short-lived tracks in one-step processing, but it still has the problem of one-step error removal due to missed detection. In addition, it does not have the ability to process track continuity. Here, we first analyze the removal results of short-lived tracks J1-J6 by OL-δ-GLMB smoother: Due to the one-step smoothing of OL-δ-GLMB smoother, it cannot effectively remove short-lived tracks like other smoothers. Due to its one-step smoothing step length, its ability to remove short-lived tracks is limited. In addition, due to the threshold removal effect of the first point in the track initiation, the result is that J1 is normally removed, but point 13 in J2 is not removed, and points 18 and 19 in J3 are not removed. Point 30 in J4 and J5 is not removed and point 40 in J6 is not removed. Therefore, further analysis is conducted based on the above results. Point 10 is due to one-step error removal caused by missed detection of target T3 in time 11-12. Points 11 and 12 are due to missed detection of target T3 itself in time 11-12. In addition, it should be noted that although point 13 appears to be undistorted, it is actually retained due to the one-step smoothing of OL-δ-GLMB smoother, which leads to the removal of short-lived track J1 at point 13. However, there is an impact of threshold removal due to the low survival probability of the first point in the track initiation, which makes point 13 appear undistorted but actually has a problem. Point 18 and 19 are due to the removal of short-lived track J3 at points 18 and 19. Point 20 is due to one-step error removal caused by missed detection of target T3 in time 21-24. Points 21-24 are due to missed detection of target T3 itself in 21-24. Point 34 is due to one-step error removal caused by missed detection of target T3 in points 35-38. Points 35-38 are due to missed detection of target T1 itself in 35-38. Point 39 is due to threshold removal due to the low survival probability of the first point in the track initiation.

In addition, regarding the issue of multiple MC results that do not appear smooth, the simulation experiments conducted in this article are based on the simulation data generated from the scene setting given in Table 5. From the parameters given, it can be seen that there are multiple scenarios in the set-up, including normal targets, missed targets, outliers, and interfering targets (this is to fully test the processing capabilities of the algorithm), which results in a large variation in the cardinality of multiple targets in the simulation scenario. This can be seen from the cardinality correlation estimation results given in the article. Therefore, due to the above factors, the results produced by multiple MC processing do not appear as smooth as in the actual algorithm. Combining the above explanation of the causes of distortion, it also jointly illustrates the different processing effects and performance of the comparison smoothers. Based on your suggestions and considerations, we will add the refined causes of distortion to the paper to help readers understand. Thank you again for your valuable comments.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regards，

Mr. JiuChao.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

NO

Author Response

Dear Reviewer:

First of all, thank you very much for your meticulous review of our paper before. Thank you again for your recognition of our work. During this round of review, we made modifications and quality improvements to the article based on the comments of other reviewers. In addition to this reply text, there are also two documents included in the reply materials for you, one is a docx without modification annotations《Manuscript Without Revision Note》, and the other is a docx with modification annotations 《Manuscript With Revision Note》. In 《Manuscript With Revision Note》, we distinguished different issues using different colors. Among them, blue represents grammar modifications, green represents supplementary content, and yellow represents modified content. we hope it will be convenient for you to review our article in this way.

Finally, thank you again for your meticulous review work. If you have any further questions, please give us feedback in a timely manner, and we will make adjustments and respond as soon as possible.

Thank you very much for your valuable work on our paper again.

Kind regards，

Mr. JiuChao.

Author Response File: Author Response.pdf