A Pulsar Vector Observation-Based Link Acquisition Method for X-Ray Communications

Song, Shibin; Lu, Xiao; Wang, Haixia

doi:https://doi.org/10.1155/2023/5541338

International Journal of Aerospace Engineering

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Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 5541338 | https://doi.org/10.1155/2023/5541338

A Pulsar Vector Observation-Based Link Acquisition Method for X-Ray Communications

Shibin Song,¹Xiao Lu,¹and Haixia Wang¹

Academic Editor: Chuang Liu

Received24 Mar 2023

Revised15 Aug 2023

Accepted25 Nov 2023

Published14 Dec 2023

Abstract

X-ray communication (XCOM) is an emerging laser communication technique for deep space applications. Traditional link acquisition of laser communications depends significantly on Earth support and shows little autonomy. For XCOM, a pulsar vector observation-based link acquisition method is proposed, which utilizes noncooperative pulsars in deep space as beacons to acquire absolute attitude information and accomplish link acquisition. Firstly, a pulsar vector observation model was established based on the coordinate definition of the X-ray detector and X-ray collimator model. Secondly, a modified “success-failure” pulsar vector search algorithm with two degrees of freedom was proposed to acquire the pulsar vector. With the pulsar vector and the relative attitude obtained from inertial sensors, the link acquisition pointing vector could be determined. Finally, the performance of the proposed method was evaluated using numerical experiments, and factors that influence the performance are discussed and analyzed.

1. Introduction

X-ray communication (XCOM) is a revolutionary technique in space communication [1, 2], which takes advantage of the high energy and excellent penetrative properties of X-rays in deep space [3, 4] and is widely studied. In China, Zhao et al. first discussed the application of X-rays in space communication [5]. Zhao et al. extensively studied various aspects of XCOM, including transmission properties [6], frequency modulation [7], source design and testing [8–10], and XCOM applications [11–13]. These studies built a solid foundation for XCOM development. In addition, Tang et al. conducted a series of studies regarding XCOM, including the penetrative properties of X-rays [14], X-ray high frequency pulse emission characteristics [15], and collimating/focusing optical systems [16]. The potential applications of XCOM in the Mars scenario [3, 17] and during Earth re-entry [18–20] were also studied. These studies remarkably promoted the development of XCOM.

Though extensive research has been performed, the study of XCOM is ongoing and many problems remain unsolved. X-ray signal modulation, communication signal denoising, X-ray detector design and optimization, communication link acquisition, and establishment are main technical challenges for XCOM. X-ray transmission properties, X-ray source and detector design, and X-ray signal modulation are studied by researchers. Of current challenges, there is no literature concerning link acquisition of XCOM for deep space applications. In traditional laser communication, a master/slave pattern [21] is commonly used for link acquisition, which establishes an extra optical link between a transmitter (master) and a receiver (slave) [22], and the communication link acquisition is established by acquiring the beacon link between the master and slave station. The traditional acquisition system depends greatly on the beacon link and is time-consuming and complicated, and extra equipment is required for the beacon link. In addition, the beacon link is easily affected by other optical sources in deep space.

To eliminate the dependence on the beacon link and improve autonomy, a pulsar vector observation-based acquisition method is proposed. Pulsars are neutron stars in space and emit signals over a wide spectrum, which include radio waves, visible light, X-rays, and gamma rays [23, 24]. Of the emitted signals, X-ray pulsar signals show low attenuation and good radiation directivity [25, 26], making them suitable for attitude determination [27]. As regards the proposed acquisition method, pulsars serve as noncooperative beacons, and a pulsar vector observation method is proposed to acquire an accurate absolute attitude. With other supplementary information, such as the pulsar ephemeris, positions obtained from the navigation system, and other data, the link acquisition can be established. Compared with the master/slave pattern, the link acquisition reflected in this paper uses noncooperative pulsars as beacons and eliminates the dependence on the beacon link, providing a simple and autonomous method of link acquisition for XCOM. The main contribution of this research is that a pulsar vector observation-based XCOM link acquisition method is proposed, which utilizes X-ray pulsars in deep space as beacons and can establish X-ray communication link without extra optical link. This research paves a new way for XCOM link acquisition and contributes to the development of XCOM. Besides, the proposed approach can be potentially used in attitude system control. In the threatening space environment, attitude determination is vital for spacecraft navigation and communication, and accurate control of spacecraft attitude system is quite important [28]. The proposed approach could obtain attitude information based on pulsar signals. This attitude information depends on pulsar signals and is barely influenced by equipment drift, equipment noise, etc., which contributes to the better control of spacecraft attitude system.

2. Basic Concepts

Figure 1 presents the relation between the pulsar vector and the line of sight (LOS) of the XCOM link. In the figure, A and B are the communication terminals on different spacecraft, denotes the unit vector of the pulsar signal radiation direction, and is the desired pointing vector for XCOM link alignment. Let be the observation of and θ be the pulsar observation error. If denotes the error between and its observation , can be used to evaluate the acquisition error.

Assuming the remote end (terminal B) is a spacecraft, the pulsar vector can be observed through a pulsar vector observation system. The relation between the pulsar vector observation system and the spacecraft can be measured by the spacecraft’s onboard inertial sensors. The position of terminal B can be estimated by an X-ray pulsar-based navigation (XPNAV) system [29, 30]. Assuming the proximal end (terminal A) is a satellite and the position of terminal A is known, then, the pointing vector of the XCOM link can be estimated with the obtained information.

3. Pulsar Vector Observation Model

3.1. Coordinate Definition

The pulsar vector represents the direction of radiation of pulsar signals. A pulsar vector can be observed by acquiring X-ray photons with an X-ray detector. Collimators are well-type pipes, which are placed in front of an X-ray detector to mitigate background noises [31]. The X-ray detector is placed on a two-degree of freedom pan-tilt mechanism, and by controlling the rotation of the mechanism, the pointing direction of the detector and collimator is adjusted.

To describe the pulsar vector observation process, a detector/collimator coordinate system should be defined. In addition, the body-fixed coordinate system of the spacecraft where the X-ray detector is placed should also be considered. Figure 2 presents the collimator coordinate system (-coordinate) and the body-fixed coordinate system (-coordinate). The -coordinate is denoted by . is the central axis of the collimator. forms the bottom plane of the collimator, and , , and form a right-handed coordinate system. Let be the radiation direction of X-ray pulsar signals and the angle error between and be denoted by .

The -coordinate is a fundamental coordinate for a spaceborne system. In Figure 2, the -coordinate is denoted by . The origin of the -coordinate is generally at the barycenter of the spacecraft. As indicated in Figure 2, is along the longitudinal axis of the spacecraft and is vertical to the longitudinal plane of the spacecraft. , , and form a right-handed coordinate system.

Assuming that the -coordinate and -coordinate share the same origin, the relation between the two coordinate systems can be expressed by the angles and . is the horizontal rotation angle of the -coordinate relative to the -coordinate. denotes the rotation angle of the plane relative to the plane. can be calculated from the angle between and the projection of on plane . can be obtained from the angle between and the projection of on plane .

3.2. Pulsar Observation Model

Collimators are elongated wells placed in front of an X-ray detector. When observing X-ray pulsar signals, the incident X-ray photons that deviate from the collimator direction will hit the collimators’ sidewalls and not reach the detector. Thus, the pulsar vector observation result is closely related to the collimator model and direction.

Given its geometrical shape, a collimator can be regarded as a cylinder [32]. A model of a collimator is presented in Figure 3. In Figure 3, represents the radius of the collimator, is the length of the collimator, and is the pulsar vector. The effective area of the X-ray detector is defined as the area where X-ray pulsar signals can be detected by the detector after traveling through the collimators. When there is an error angle between and , the effective area is smaller than the collimators’ bottom area. According to the geometrical relation shown in Figure 3, satisfies

Notably, when , the effective area becomes 0. Thus, the range of is limited to .

As indicated in Figure 3, the solid line circle is the bottom of a collimator and the dotted line circle is the ideal photo arrival area. When , the solid line circle and the dotted line circle are totally overlapped.

As increases, parts of photons hit the side wall of the collimator and cannot reach the collimator bottom. The effective photon arrival area is the overlap area of the solid line circle and the dotted line circle. When is small (), the center of the solid line circle is covered by the effective area, which is case (b) in Figure 4. When increases (), the effective area is case (a) in Figure 4. The diamond drawn in Figure 4 case (b) is used to calculate the area of the shadow part.

(a)

(b)

Thus, the calculation of X-ray detector effective area can be divided into two cases: case (a) of shown in Figure 4(a) and case (b) of shown in Figure 4(b).

For case (a), as can be expressed by , can be calculated by

For case (b), there is

Therefore, for case (a), the effective area is expressed by where satisfies

With Eq. (5), Eq. (4) can be rewritten as

Similarly, for case (b), we get

Based on the above analysis, the effective area of a collimator can be described by where

Then, for a single collimator, the photo intensity received by the detector can be expressed by where is the detection efficiency and is the average flux intensity of the incident X-ray signals.

As the collimators are cylinders with a round bottom, the full area of the detector cannot be used. Figure 5(a) shows the layout of the collimators, and Figure 5(b) indicates the geometric dimensioning of collimator layout. Assume that the width of the detector is and the length . Along the widthwise direction, the number of collimators allowed is , where the symbol depicts rounding half down. If is an even number, the number of collimators for a detector of is

(a) Collimator layout

(b) Geometric dimensioning of collimator layout

If is an odd number, the number of collimators is

Using Eq. (9), the photo intensity received by the entire detector can be presented as

Besides, to guarantee the precision of the measurement, X-ray detector calibration and noise filtering should be considered. An X-ray detector calibration can be realized using “two-point calibration” [33]. For the calibration method, two scaling points, and , are set. represents the received energy when X-ray emitting source is turned off, and represents the received energy when X-ray emitting source is turned on. Under the two scaling points, the output signals of X-ray sense components are obtained. The output signals are used to calculate the offset parameter and gain parameter of X-ray sense components.

Though collimators can mitigate some background noises, there are still noise signals arriving at the detector. Through numerical experiments using date from on-orbit X-ray detector, the Wiener filter shows good filtering performance for the proposed method.

4. Pulsar Vector Observation

Pulsar vector observation is the determination of the radiation direction of X-ray pulsar signals, which is realized by adjusting the direction of the collimators. Based on the pulsar observation model, a pulsar vector search algorithm with two degrees of freedom is proposed.

The search algorithm is inspired by the “success-failure method” and is conducted using two degrees of freedom. For a complete search attempt, the and directions are found by rotating the collimator direction along the and directions, respectively. To describe the rotation of a vector, the quaternion is used. Assuming that rotates around the rotation axis and that is the rotation angle, a quaternion can be expressed by where , , and are imaginary units. Utilizing a quaternion to express gives

Then, the rotation process can be expressed by where is the conjugate of . The rotation result is the conjugate transformation of .

Let denote the direction of . Set and to be the search step of the and directions, respectively. denotes the initial direction of , and the observed photon flux intensity at this attitude is . Let the search accuracy to be set to , which is used to terminate the search algorithm. The detailed search algorithm can be described in pseudocode in Algorithm 1.

1 Rotate around by , and obtain a new pointing vector .
2 Calculate the cross product of and , which is denoted by .
3 Rotate by around , and obtain a new pointing vector, .
4 At , obtain based on Eq.(13).
5 If
Then, let and
Turn to step 10
6 Else
Rotate around by , and obtain a pointing vector .
Calculate the cross product of and , denoted by .
Rotate by around and obtain a new pointing vector, .
At , obtain based on Eq.(13).
7 If
Then, let and .
Turn to step 10.
8 Else
Rotate around by , and obtain a pointing vector .
Calculate the cross product of and , denoted by .
Rotate by , and obtain a new pointing vector, .
At , obtain based on Eq.(13).
9 If
Then, let and .
Turn to step 10
Else
Rotate around by , and obtain a pointing vector .
Calculate the cross product of and , denoted by .
Rotate by , and obtain a new pointing vector, .
At , obtain based on Eq.(13).
Let and .
Turn to step 10
10 If and
Then, end the search.
Else
, and .
Turn to step 1.

At the proximal end (terminal A), is obtained by the proposed pulsar vector observation method, and the rotation relation between the pointing vector of its communication terminal and the pulsar vector is known between the two terminals. At the remote end (terminal B), the pulsar vector can also be obtained by the proposed pulsar vector observation method. Using this information, the pointing vector of link acquisition at the remote end (terminal B) can be estimated.

As the acquisition error is related to the pulsar vector observation error, the acquisition error is expressed by where is the pointing vector of the collimators and is the pulsar vector observed at the remote end (terminal B).

5. Experiment Results

5.1. Simulation Conditions

To evaluate the performance of the proposed acquisition method, a series of numerical simulations was conducted. For the simulation, the size of the X-ray detector was set to 1 m². The background flux intensity was set to be 5-3 ph/cm²/s. The parameters of the pulsar are listed in Table 1.

5.2. Link Acquisition Simulation

The link acquisition procedure was simulated in this section. For simulation conditions, the search accuracy was set to be rad, and the initial searching step was set as . To simulate different initial pointing directions of the collimators, the initial error, , was set to different values.

In Figure 6, the horizontal axis denotes the search attempts required during the search procedure, and the vertical axis is the link acquisition error. As can be seen in Figure 6, the acquisition error decreases almost to zero, but not monotonously. The reason is that not all search attempts are successful during the search procedure. When searching in the wrong direction, the acquisition error will deviate from the decreasing trend.

5.3. Acquisition Error Analysis

In this section, the acquisition error is analyzed by numerical experiments. The search procedure was simulated under different search accuracy settings, , and the same initial pointing error .

Figure 7 presents the acquisition error and the number of search steps required under the simulated conditions, and it can be seen that with a smaller search accuracy set, a better acquisition error is obtained. However, more search attempts are required during the search procedure. Thus, when choosing search accuracy settings, the balance between the acquisition error and the number of search attempts should be considered.

5.4. Influences of the Initial Errors and the Search Accuracy Settings

The influence of the initial pointing error and the search accuracy setting on the acquisition performance is analyzed in this section.

Figure 8 presents the acquisition errors using different search accuracy settings and initial pointing errors. In Figure 8, the horizontal axis represents different initial pointing errors, and the vertical axis represents the acquisition errors. It is shown from Figure 8 that for a given search accuracy, the initial error has little impact on the acquisition error results. Moreover, with smaller search accuracy settings, better acquisition errors are obtained.

Figure 9 shows the number of search attempts required under different search accuracy settings and initial pointing errors. The axis definitions are the same as that of Figure 8. As indicated in Figure 9, the number of search attempts required shows little connection with the initial errors. This is because during the search procedure, the search steps and are dynamically changing after each search attempt. It is shown in the figure that with a smaller search accuracy, more search attempts are required for the proposed acquisition system.

6. Conclusions

In this paper, a pulsar vector observation-based XCOM link acquisition method is presented. A pulsar vector observation model was established based on the collimator model and coordinate definition, and a pulsar vector search method is proposed. With pulsar vector observation and prior knowledge, the link acquisition vector could be obtained. Numerical experiments indicated that the proposed method could gradually obtain the acquisition pointing vector, and the search accuracy settings directly influence the acquisition accuracy and number of search attempts required. Using noncooperative pulsars as beacons, the proposed vector observation-based link acquisition method provides a more independent way of XCOM link acquisition, contributing to the further application of XCOM in deep space.

Data Availability

The simulation data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Acknowledgments

The authors would like to thank Hua Zhang of Xidian University for helpful discussions on topics related to this work. This work was supported by the National Natural Science Foundation of China (62103245 and 62273213), the Natural Science Foundation of Shandong Province (ZR2020MF095), and Taishan Scholarship Construction Engineering.

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Copyright © 2023 Shibin Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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