SCIENCE CHINA Information Sciences, Volume 64 , Issue 1 : 112209(2021) https://doi.org/10.1007/s11432-019-2824-y

## Angular velocity estimation using characteristics of star trails obtained by star sensor for spacecraft

• AcceptedFeb 29, 2020
• PublishedDec 24, 2020
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### Abstract

Many studies have been conducted about angular velocity estimation using star sensors, and fairly good performance is achieved when the spacecraft is working at low-dynamic environments. However, when the spacecraft rotates at a large angular velocity, the star image will become blurred, which makes it difficult to identify and recognize star centroids, which, in turn, reduces the accuracy of angular velocity estimation. Therefore, to solve the problem with angular velocity estimation in highly dynamic situations, this research studies a method of angular velocity estimation using blurred star images. The length and ending point coordinates of star trails obtained from these blurred star images are used for a series of processes, which includes the pre-processing of blurred star images, determination of starting and ending points, thinning and selection of star trails, and calculation of trail lengths. Simulations show that the effectiveness of the proposed method in highly dynamic situations and the angular velocity estimation errors in constant and sinusoidal variation are reduced by at least 66% and 62%, respectively, compared with those of the traditional method.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61722301). The authors wish to express their gratitude to all members of the Science Technology on Inertial Laboratory and the Fundamental Science on Novel Inertial Instrument Navigation System Technology Laboratory for their valuable comments.

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• Figure 1

Flowchart of the process of obtaining the characteristics of star trails, and diagram of the filter schematic.

• Figure 2

(Color online) Simulated values of (a) three-axis body angular velocity and (b) angular acceleration angular velocity in case 1.

• Figure 3

(Color online) Simulated values of (a) three-axis body angular velocity and (b) angular acceleration angular velocity in case 2.

• Figure 4

Sequential blurred star images in case 1 with labeled star trails. (a) time = 0.5 s, (b) time = 1.0 s, and (c) time=1.5 s with $w(t)=[0^{\circ}/\textrm{s},0^{\circ}/\textrm{s},20^{\circ}/\textrm{s}]^{\rm~T}$ and 0.5 s exposure time.

• Figure 5

Sequential blurred star images in case 2 with labeled star trails. (a) time = 0.5 s, (b) time = 1.0 s, and (c) time=1.5 s with $w(t)=[8\sin(\frac{2\pi}{85}+\frac{\pi}{2})^{\circ}/\textrm{s},~8\sin(\frac{2\pi}{65}+\frac{\pi}{2})^{\circ}/\textrm{s},~8\sin(\frac{2\pi}{45}+\frac{\pi}{2})^{\circ}/\textrm{s}]^{\rm~T}$ and 0.5 s exposure time.

• Figure 6

(Color online) Number of available star trails in (a) case 1 and (b) case 2.

• Figure 7

(Color online) Estimation results of proposed method for case 1. (a) Estimated angular velocity; (b) estimated angular acceleration; (c) estimated angular velocity errors; (d) estimated angular acceleration errors.

• Figure 8

(Color online) Angular velocity estimation results of Accardo's method for case 1. (a) Estimated angular velocity; protectłinebreak (b) estimated angular acceleration; (c) estimated angular velocity errors; (d) estimated angular acceleration errors.

• Figure 9

(Color online) Angular velocity estimation results of proposed method for case 2. (a) Estimated angular velocity;protectłinebreak (b) estimated angular acceleration; (c) estimated angular velocity errors; (d) estimated angular acceleration errors.

• Figure 10

(Color online) Angular velocity estimation results of Accardo's method for case 2. (a) Estimated angular velocity;protectłinebreak (b) estimated angular acceleration; (c) estimated angular velocity errors; and (d) estimated angular acceleration errors.

• Table 1

Table 1Comparison of angular velocity and angular acceleration errors in case 1

 Method Mean angular velocity Mean angular acceleration Filtering time (one error on three axes ($^{\circ}$/s) error on three axes ($^{\circ}/{\rm~s}^2$) sampling interval) (s) $x$ $y$ $z$ $x$ $y$ $z$ Proposed method 0.005 0.005 0.035 0.007 0.007 0.047 0.025 Accardo's method 0.050 0.050 0.104 0.018 0.018 0.045 0.001
• Table 2

Table 2Comparison of angular velocity and angular acceleration errors in case 2

 Method Mean angular velocity Mean angular acceleration Filtering time (one error on three axes ($^{\circ}$/s) error on three axes ($^{\circ}/{\rm~s}^2$) sampling interval) (s) $x$ $y$ $z$ $x$ $y$ $z$ Proposed method 0.013 0.013 0.025 0.020 0.034 0.107 0.027 Accardo's method 0.138 0.159 0.001 0.378 0.489 0.729 0.001

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