A Multi-Frame GLMB Smoothing Based on the Image-Observation Sensor for Tracking Multiple Weak Targets Using Belief Propagation

Round 1

Reviewer 1 Report

1.     The definition of C(x) in line 187 is still not expound.

 

2.     There is not any false alarm or interference in simulation setup.

Only the information of the targets is expounded in simulation setup. But there is not any false alarm or interference, which should have been existed in the detection results.

Maybe you can provide a dot plot which including false alarms, interference and target points, and explain how your algorithm handles them.

Author Response

Dear reviewer:

  The all authors wish to thank the reviewer for your carefully reading this paper and providing the valuable and important suggestions on improving the quality of this paper. Here, we make some point-by-point revisions according to the reviewer’s suggestions. The revised results have been marked in blue color.

Author Response File: Author Response.pdf

Reviewer 2 Report

The comments of the manuscript No. remotesensing-1950918 is given as follows:

 

This paper generalizes the multi-frame GLMB model to the image pixeled track-before-detect observation model, thereby making it suitable for tracking weak targets. Furthermore, the belief propagation algorithm is used to approximately calculate the marginal densities from high-dimensional joint probability density. The MF-GLMB-TBD smoother based on belief propagation enables the multi-target posterior recursion for tracking multiple targets in low-SNR scenario. The simulation results demonstrate that the MF-GLMB-TBD smoother is superior than single-frame in tracking accuracy albeit with higher computational load. Moreover, the performance of the MF-GLMB-TBD smoother based on belief propagation can outperform that of Gibbs sampling version. This paper addresses the very challenging problem of tracking weak targets in the presence of clutter, misdetection and data association uncertainty. Meanwhile, the authors have proved the convergence of the proposed belief propagation. The also presented numerical studies to validate the proposed algorithms. Overall, this is an excellent paper. It addressed a challenging problem with novel numerical solution with sound mathematical justification. The paper is well organized, and very well written. It is a pleasure to read. Hence, I believe that the manuscript deserves publication. I only have some minor comments which I hope the authors can revise the manuscript to improve the standing of their work.

 

1. The belief propagation algorithm provides alternative way to calculate the approximate marginal probability density by passing messages among the neighboring nodes in factor graph. It is suggested that author should discuss the sufficient condition of the belief-propagation convergence.

 

2. The performance of the BP-version is better than that of the Gibbs sampling-version. It is suggested that author should discuss the relationship between the belief propagation-version and Gibbs sampling-version.

 

3. As indicated in introduction part of the original manuscript, the belief propagation is effective method for approximating joint association probability densities by the product of its marginals. The authors have presented a recursive Bayesian method of GLMB-TBD in reference [1] using Kullback-Leibler Divergence (KLD). Please discuss the relationship between the KLD-based version and BP-based version.

 

4. The readability of this manuscript needs further improvement because there are a few typos or grammar mistakes in the manuscript. The authors must proofread the whole paper for improving English writing in order to get accepted.

 

 This article presents BP-based implementation of the MF-GLMB-TBD smoothing for tracking multiple weak targets. Overall, it is suggested to be accepted with minor revisions for this manuscript.

 

Reference

 

 

[1] Chenghu Cao, Yongbo Zhao, Xiaojiao Pang, Zhiling Suo, Sheng Chen. An efficient implementation of multiple weak targets tracking filter with labeled random finite sets for marine radar. Digital Signal Processing, 101(102710), 2020.

Author Response

Dear reviewer:

  The all authors wish to thank the reviewer for your carefully reading this paper and providing the valuable and important suggestions on improving the quality of this paper. Here, we make some point-by-point revisions according to the reviewer’s suggestions. The revised contents are marked in red color.

Author Response File: Author Response.pdf

Reviewer 3 Report

The multi frame (MF) - generalized labeled multi-Bernoulli (GLMB) model that incorporates the track-before-detect (TBD) scheme of point targets using an image sensor model is presented in this manuscript. Also, the belief propagation algorithm is adapted to approximately calculating the marginal association probabilities of the multi-target posterior density. The manuscript is well written. The theme and idea of the manuscript are contemporary, and deserve the reader's attention.

The paper describes in detail the proposed algorithm with many variables and parameters. Some of the variables are not mentioned with the same labels below, as they were labeled at the beginning of the paper, so the reader may be confused.

The authors deal with the problem of non-linear measurements, which are widely represented in the literature. Unfortunately, this group of algorithms suffers from the problem of non data association, i.e. inability to associate new measurements with corresponding existing targets.

The problems that arose in the domain of false track discrimination (FTD), using the first non-linear filters, such as the Particle filter (PF), probability hypothesis density (PHD) filter, multi Bernoulli etc., were not generally solved, so the authors continued research in the direction that is common today, without analyzing the underlying problems that they wearing.

Additionally, the authors have made an extra effort to prove the convergence of the proposed algorithm, and that effort is commendable.

 

Suggestions for improvement the manuscript:

 

-          change the term "pixeled-image" in the title with an adequate announcement,

-          renumber all equations, so that each mathematical expression in the manuscript gets its own number (for example echo intensity h_A),

-          double-check all variables, subscripts and subscripts so that each variable listed appears in the appropriate equation (for example ‘h’ ),

-          equation 55 is incomprehensible, complete the equation.

Author Response

Dear reviewer:

  The all authors wish to thank the reviewer for your carefully reading this paper and providing the valuable and important suggestions on improving the quality of this paper. Here, we make some point-by-point revisions according to the reviewer’s suggestions. The revised contents are marked in purple color.

Author Response File: Author Response.pdf