Maneuvering Spacecraft Orbit Determination Using Polynomial Representation

Round 1

Reviewer 1 Report

In this work, a polynomial representation-based method for maneuvering spacecraft orbit determination (OD) has been proposed. The OD performance of the proposed method is tested by applying it over different cases. Numerical simulations show that the method can well track the maneuvering spacecraft. It is found that the extended Kalman filter (EKF) using sixth-order polynomials are enough to provide valid OD solutions. Higher-order polynomials bring more accurate estimations. Furthermore,  the proposed method can also be applied into non-maneuvering cases and the noise-induced errors will not be wrongly compensated by the polynomial representation.

The manuscript is providing a special insight in the topic of orbit determination, and it is novel at all. The manuscript includes sufficient original contribution to be considered acceptable for publication. In conclusion: Some results obtained in this work are novel. Moreover, they are incremental improvements of earlier results. The level of mathematical and physical difficulty and originality of these results makes them suitable for publication. The experts in this field of astrodynamics will appreciate some technical progress exposed in this work. But I have some comments before recommend the publication of this manuscript.

• The abstract must be concise and includes only new results, for example it is not necessary to write “Orbit determination (OD) for spacecraft with unknown maneuver is a complicated challenge in space missions. Conventional OD approaches cannot robustly cope with the maneuvering OD problem as they rely on specific orbit dynamic equations”. I think you can write this sentence in the introduction section
• The introduction must be rewritten properly, it is not acceptable to writ a series of references, [1- 10],   …..[11-20]. I think that the authors have write in some details, what happened in this work.
•  Eqs, 1, 2,3: Either the authors construct these equations or  quoted the work of providing them, and the same for all mathematical relations  in the whole manuscript.
• There is a warranty to convergence of polynomials in Relations 5, It is important to explain
• The size of figures is so small that they are not visible

In general, the authors have to describe in more detail the purpose of their study and its original contents. A clear explanation, what is the new result in their work, and how it is build up upon previous work in the field.

If the authors submit a modified version according to my suggestions where they also give more details/explanations about the abovementioned criticisms, I could recommend the paper for publication in Aerospace.

              

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors propose a method for determining the orbit and the unknown perturbing acceleration using the Kalman filter. The idea is that a polynomial that approximates an unknown acceleration is represented as a solution to some system of differential equations. As a consequence, 1) we avoid the need to exponentiate time, 2) we can consider the dependent variables of the equation as part of a state that can be determined using the Kalman filter. The degree of observability is estimated by numerical modeling. The method is simulated in situations when there is and when there is no acceleration of the maneuver, this allows us to understand how the method perceives noise.

1. It seems to me that the Introduction should explain in more detail the difference between the second and third methods of determining the orbit, maybe by giving a simple example. It seems that the both approaches are based on measurements and both determine the orbit and the maneuver.
2. Though English is not native for me, it seems that language should to be worked on in this article. There are typos and incorrect use of pronouns, endings and forms of words.
3. In Figures 4 and 5, it is necessary to explain what the blue and red lines are. The legend is not immediately visible.
4. In Section 5.1, the perturbing acceleration is chosen to be trigonometric while it is approximated by polynomials. It is clear that it will not be possible to approximate the sines and cosines with a polynomial on the entire numerical axis. Do the authors mean that the disturbing acceleration is limited in time and at this time interval it is approximated by a polynomial? If the time interval is not limited, then it seems that it is not reasonable to use polynomials to approximate such functions. The authors need to clarify this in the text. I suppose to think about how the method could be generalized so that acceleration could be approximated not by polynomials, but by sines and cosines.

In general, the work is good. I recommend minor revision according to my commentaries.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Please find attached the commented file.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf