The Extended H_∞ Particle Filter for Attitude Estimation Applied to Remote Sensing Satellite CBERS-4

Round 1

Reviewer 1 Report

The paper « The extended H∞ particle filter for attitude estimation applied to remote sensing satellite CBERS-4» is devoted to performance study of the attitude estimation algorithm. Unfortunately, the quality of the paper is low. It should be significantly revised before the publication.

First of all, the process equation (3) and measurement equation (5) are not the nonlinear functions of the state vector x, as initially assumed in (1). In the text equation (3) is linear function, equation (5) is not a function of x at all. So, the initial assumption on nonlinearity is not correct.

The paper considers angular velocity sensor, though there is no measurement equation for this sensor in (5). It is not clear how does the gyro bias can be estimated in this case? At least, there should be connection between the angular velocity vector and the gyro bias in (3): ω = ω_meas – ε. In this case there should not be zeros in the upper right block in the matrix in (3).

The state vector (2) contains all the components of the attitude quaternion. In this case it the integration and correction stages the quaternion norm could be not equal to 1. How do the authors solve this problem? More comments on this is required.

The measurement model of the Sun sensor requires more explanation on the specific values of the angles – arguments in the cosine function: cos(60), cos(150), 24. It seems that the specific installation angles are used in the model. What is the field of view of this sensor? Is it possible that the sensor will be in the satellite shadow or there are a set of sensors?

The paper does not provide important algorithms parameters (matrices Q, R, S, P0, values of the measurement noise and so on) and initial conditions of the simulations. It is not correct to refer to other authors paper [19] to search for the conditions. The authors compare the performance of two algorithms, though there are no comments that the algorithm parameters are the same. Moreover, it would be better to compare simulation results of algorithms with equal number of particles.

The authors compare the estimation results converting the quaternion into the angles, though more accurate would be to compute the rotation angle using the scalar part of the error quaternion.

It is not clear how does the 3 sigma values were computed for the figure 2.

In conclusion section the authors should avoid emotional adjective such as “very effective”, “great alternative”, “adequate accuracy” and so on.

The English of the paper should be improved. There are many mistakes in the text and not correct sentences.

Some statements are not clear, they sound not scientifically and should be corrected:

-        Line 111. “… it is assumed that nature is our adversary…”

-        Line 177. “The weight matrices are projects…”

-        Line 209. “This configuration can provides global coverage using your cameras…”

-        Line 249. “ … the gyros bias estimation error with your results…”

The English of the paper should be improved. There are many mistakes in the text and not correct sentences.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments

The paper studied the extended H∞ particle filter for attitude estimation applied to remote sensing satellite CBERS-4. It seems a hot topic, as many research papers have been published in this area. Below, I have provided my comments, which are as follows:

* It is not clear to me what the difference is between your study and the published study.

* What is the main contribution of your previous study (DOI: 10.1016/j.actaastro.2021.07.049) to the current study? I need clarification on it.

* There are many grammatical issues in the paper.

* When you talk about published studies, you should provide references. See the second paragraph in your paper that you claimed, ". Analyzing the feasibility together,…

* The introduction and literature review needs to be comprehensively expanded, which confuses the author to follow you on what you plan to do with your paper.

* The literature review did not cover all studies close to your research area, which is a weakness of your study. Please summarize it in a table by adding more recent and relevant papers.

* I need clarification on why the author just provided the analytical results.

* There are a lot of equations with little explanation. This puts the entire burden on ‎the ‎reader ‎to figure out what is going on. It would be much more helpful if you would add ‎more ‎relevant ‎explanations for each equation. Further, all symbols should be defined in all ‎equations, not some symbols in ‎several equations. Please explain clearly all symbols in the ‎formulas. ‎ Also, please define different indices throughout the formulation.

The abstract and conclusion must be revised by including rationale, solid reasoning, solutions, etc.

In this round of revision, I will go for a significant revision to see how the author responds to my comments.

 

 

Minor

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Please see the comments in the uploaded file.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

In this paper, an H∞ particle filter method is proposed to estimate the attitude of the spacecraft in orbit. It is pointed out that the method is an extension of the classical H∞ linear filter to the non-linear system, and has higher accuracy than the particle filter under the same computational burden. The work of this paper is relatively complete, but some problems are not explained clearly as follows.

1. Is it necessary to adopt nonlinear models? The scene of attitude estimation in this paper is the attitude estimation and control of an orbiting spacecraft, which uses the observation data from the Digital Sun Sensor (DSS). Firstly, remote sensing satellites need to maintain a stable attitude, so their attitude changes slowly. Secondly, DSS can achieve higher detection frequency for control purposes. For this reason, a linear model may be sufficient for attitude estimation. Considering the high efficiency of EKF, the necessity of H∞ particle filter should be clarified in this paper.

2. How does the method solve the problem? H∞ filter is common in cybernetics, but considering that it is the main method of this work, it is necessary to combine the specific problems proposed in this paper (non-linearity, measurement error, etc.), and introduce the principle of this method to solve the related problems. At the same time, the adjustable parameters, γ etc., need to be introduced in more detail.

3. The simulation results presented in Figure 2 require a more detailed explanation. In the process of PF, the estimation error does not decrease with the filter process, and eventually converges around a value outside 3σ , as if converging on a wrong solution. However, in the process of EH∞PF , the estimation error has kept a relatively stable change.

4. Do the results meet the actual application requirements? The research background of this paper is a specific working satellite, so it is suggested to clarify the requirements of the satellite for attitude estimation accuracy and calculation timeliness in an appropriate place, so that readers can understand whether the simulation results meet the above requirements well.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

My comments are properly addressed. I have no further comments. 

Minor

Reviewer 3 Report

The comments have been considered.

Minor editing of English language required

Reviewer 4 Report

My comments were reasonably responded to and revised. I have no further comment.