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 深空探测学报  2019, Vol. 6 Issue (1): 88-95  DOI: 10.15982/j.issn.2095-7777.2019.01.013 0

### 引用本文

NING X L, GUI M Z, SUN X H, et al. A Novel Autonomous Celestial Navigation Method Using Solar Oscillation Time Delay Measurement[J]. Journal of Deep Space Exploration, 2019, 6(1): 88-95. DOI: 10.15982/j.issn.2095-7777.2019.01.013.

### 文章历史

1. 北京航空航天大学 仪器科学与光电工程学院，北京 100191;
2. 武汉科技大学 信息科学与工程学院，武汉 430081;
3. 探月与航天工程中心，北京 100191

A Novel Autonomous Celestial Navigation Method Using Solar Oscillation Time Delay Measurement
NING Xiaolin1, GUI Mingzhen1, SUN Xiaohan1, LIU Jin2, WU Weiren3
1. School of Instrument Science & Opto-electronics Engineering，Beihang University，Beijing 100191，China;
2. School of Information Science and Engineering，Wuhan University of Science and Technology，Wuhan 430081，China;
3. Lunar Exploration and Space Program Center，Beijing 100191，China
Abstract: Solar oscillation, causing a dramatic variation of the sunlight spectral central wavelengths and intensity during a short time, has been studied in detail over the years, both observationally and theoretically. Through detecting the sunlight spectral central wavelengths and intensity and recording the moment when solar oscillation occurs, the time delay between the sunlight coming from the Sun directly and the sunlight reflected by a celestial body such as the satellite of planet or asteroid can be obtained. Because the solar oscillation time delay is determined by the relative positions of the spacecraft, reflective celestial body and the Sun, it can be adopted as the navigation measurement to provide the spacecraft's position information. In this paper, a novel celestial navigation method using solar oscillation time delay measurement is proposed. The implicit measurement model of time delay is built, and the Implicit Unscented Kalman Filter （IUKF） is applied. Simulation results indicate that the position error and velocity error of the proposed method for the transfer orbit are about 3.55 km and 0.077 m/s respectively, and for the surrounding orbit are about 1.76 km and 1.57 m/s respectively. The impact of the three factors on the navigation performance is also investigated.
Key words: autonomous navigation    celestial navigation    solar oscillation    time delay    implicit UKF

Hight lights:

1. ●　A celestial navigation method using solar oscillation time delay measurement is proposed.
2. ●　The procedure for calculating the implicit measurement is given.
3. ●　The celestial navigation system using solar oscillation time delay measurement is designed.

1 太阳震荡时间延迟量测量及其量测模型 1.1 量测量的获取

 图 1 太阳振荡引起的He Ⅱ 30.4 nm的光谱线心波长的典型变化 Fig. 1 Typical variation of the spectral central wavelengths of He Ⅱ 30.4 nm caused by the solar oscillation

 图 2 太阳震荡时间延迟量测量的获取 Fig. 2 The acquisition of solar oscillation time delay measurement

 $\mathit{\boldsymbol{Z}} = \left[ {\Delta t} \right] = \left[ {{t_2} - {t_1}} \right]$ (1)
1.2 量测模型

 图 3 太阳震荡时间延迟量测模型 Fig. 3 Measurement model of solar oscillation time delay

 $\Delta t = \left( {\left| {{\mathit{\boldsymbol{{ r}}}_{rr}}} \right| + \left| {{\mathit{\boldsymbol{{ r}}}_2} - {\mathit{\boldsymbol{{ r}}}_{rr}}} \right| - \left| {{\mathit{\boldsymbol{{ r}}}_1}} \right|} \right)/c$ (2)

r2v2之间的关系可近似表示为

 $\left( {{\mathit{\boldsymbol{{ r}}}_1},{\mathit{\boldsymbol{{ v}}}_1}} \right) = f'\left( {{\mathit{\boldsymbol{{ r}}}_2},{\mathit{\boldsymbol{{ v}}}_2},\Delta t} \right)$ (3)

 ${t_0} = {t_1} - \frac{{\left| {{\mathit{\boldsymbol{{ r}}}_1}} \right|}}{c}$ (4)

 $c \cdot \left( {{t_r} - {t_0}} \right) = \left| {{\mathit{\boldsymbol{{ r}}}_{rr}}} \right|$ (5)

 $\left( {{\mathit{\boldsymbol{{ r}}}_{rr}},{\mathit{\boldsymbol{{ v}}}_{rr}}} \right) = f({\mathit{\boldsymbol{{ r}}}_{r1}},{\mathit{\boldsymbol{{ v}}}_{r1}},{t_r} - {t_1})$ (6)

 $\left( {\left| {{\mathit{\boldsymbol{{ r}}}_{rr}}} \right| + \left| {{\mathit{\boldsymbol{{ r}}}_2} - {\mathit{\boldsymbol{{ r}}}_{rr}}} \right| - \left| {{\mathit{\boldsymbol{{ r}}}_1}} \right|} \right)/c - \Delta t = 0$ (7)

 $h\left( {{\mathit{\boldsymbol{{ r}}}_2},{\mathit{\boldsymbol{{ v}}}_2},\Delta t} \right){\text{ = }}0$ (8)

 $\mathit{\boldsymbol{0}}{\text{ = }}h\left( {\mathit{\boldsymbol{X}},\mathit{\boldsymbol{Z}} - \mathit{\boldsymbol{V}}} \right)$ (9)
2 基于太阳震荡时间延迟量测的天文导航方法

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{{{\dot r}}}} = \mathit{\boldsymbol{v}}\\ \mathit{\boldsymbol{v}} = - {\mu _s}\displaystyle\frac{\mathit{\boldsymbol{{ r}}}}{{{{\left| \mathit{\boldsymbol{{ r}}} \right|}^3}}} - {\mu _m}[\dfrac{{{\mathit{\boldsymbol{{ r}}}_{sm}}}}{{{{\left| {{\mathit{\boldsymbol{{ r}}}_{sm}}} \right|}^3}}} + \dfrac{{{\mathit{\boldsymbol{{ r}}}_m}}}{{{{\left| {{\mathit{\boldsymbol{{ r}}}_m}} \right|}^3}}}] - {c_R}{p_{SR}}(\dfrac{A}{m})\dfrac{\mathit{\boldsymbol{{ r}}}}{{\left| \mathit{\boldsymbol{{ r}}} \right|}} + {\mathit{\boldsymbol{{ w}}}_v} \end{array} \right.$ (10)

3 仿真验证 3.1 仿真条件

$\left[ {5\;{\rm{km,}}\;{\rm{5}}\;{\rm{km,}}\;5\;{\rm{km,}}\;0.1\;{\rm{m}}/{\rm{s,}}\;0.1\;{\rm{m}}/{\rm{s,}}\;0.1\;{\rm{m}}/{\rm{s}}} \right]$

${\rm{diag}}\left[ {25\;{\rm{k}}{{\rm{m}}^2},\;25\;{\rm{k}}{{\rm{m}}^2},\;25\;{\rm{k}}{{\rm{m}}^2},\;0.01{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2},\;0.01{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2},\;0.01{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2}} \right]\text{。}$

${\rm{diag}}\left[ {{{10}^{ - 3}}\;{{\rm{m}}^2},\;{{10}^{ - 3}}\;{{\rm{m}}^2},\;{{10}^{ - 3}}\;{{\rm{m}}^2},\;{{10}^{ - 7}}{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2},\;{{10}^{ - 7}}{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2},\;{{10}^{ - 7}}{{\left( {{\rm{m}}/{\rm{s}}} \right)}^2}} \right]\text{。}$

3.2 结果分析 3.2.1 两种轨道下的导航结果

 图 4 转移轨道导航结果 Fig. 4 Navigation results of the proposed method for the transfer orbit

 图 5 火卫一的可见性 Fig. 5 Visibility of Phobos during the simulation period
 图 6 环绕轨道导航结果 Fig. 6 Navigation results of the proposed method for the surrounding orbit
3.2.2 影响因素分析

1）太阳震荡时间延迟量测误差

 图 7 不同量测误差下的导航结果 Fig. 7 Comparison of the navigation results with different measurement errors

2）相邻两次太阳震荡间的时间间隔

 图 8 不同Ti下的导航结果 Fig. 8 Comparison of the navigation results with different Ti

3）火卫一星历误差

 图 9 火卫一不同星历误差下的导航结果 Fig. 9 Comparison of the navigation results with Phobos ephemeris errors

4）探测器与反射天体间的距离

 图 10 探测器与反射天体间不同距离下的导航结果 Fig. 10 Navigation results of the different spacecraft and the reflective celestial body
4 结　论

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