Information matrix-based optimal configuration and fusion attitude determination for multi-fov star sensors
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摘要:
针对窄视场、长焦距星敏感器易出现滚动轴精度退化和观测几何病态的问题，本文建立含观测权重的全局Fisher信息矩阵模型，基于A、D、E最优性准则推导多视场最优指向关系，并提出多传感器Wahba融合（MSWF）定姿方法。理论分析表明，等权条件下双视场正交、三视场正交及四视场正四面体构型可优化三轴信息分布。以双视场离轴三反星敏感器为例的仿真表明，单视场病态轴误差约为其余两轴的38倍；正交双视场结合MSWF后，总体定姿误差较单视场降低95.4%，较简单平均融合降低29.2%，并能在稀疏星场、随机丢星和动态模糊条件下保持较好的三轴均衡性。结果说明，多视场构型优化与加权星矢融合可有效缓解单视场观测几何限制，为高精度姿态确定提供参考。
Abstract:Narrow-FOV, long-focal-length star sensors suffer from roll-axis degradation and ill-conditioned observation geometry. This paper builds a weighted global Fisher information matrix model. A-, D-, and E-optimality criteria are used to derive optimal multi-FOV pointing relations. A multi-sensor Wahba fusion (MSWF) method is then developed. The analysis shows that orthogonal two-FOV and three-FOV configurations, and a tetrahedral four-FOV configuration, improve three-axis information distribution under equal weights. Simulations with a dual-FOV off-axis TMA star sensor show that the ill-conditioned-axis error of a single FOV is about 38 times that of the other axes. The orthogonal dual-FOV configuration with MSWF reduces the total attitude error by 95.4% relative to a single FOV and by 29.2% relative to simple averaging. It also maintains balanced three-axis performance under sparse-star, random-loss, and motion-blur conditions. The results show that optimized multi-FOV geometry and weighted star-vector fusion can mitigate the geometric limitation of a single FOV.
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图 1 星敏感器矢量定姿缺陷的仿真
Figure 1. Simulation of defects in star tracker vector attitude determination.
图 3 分离角度和构型优化之间的关系
Figure 3. Relationship between separation angle and configuration optimization.
图 4 基于不同办法解算原理的星敏感器安装矩阵标定残差
Figure 4. Calibration residual of the star tracker mounting matrix based on different solution principles.
图 6 不同姿态解算方案的定姿精度对比与误差分布特性分析
Figure 6. Attitude accuracy comparison and error distribution analysis across different solution schemes.
表 1 三次蒙特卡洛仿真的星敏感器参数对比
Table 1. Comparison of star tracker parameters from three Monte Carlo simulations.
仿真参数 仅双矢量 增多星矢 提高星矢精度 焦距 75 mm 75 mm 150 mm 像元尺寸 5 μm 5 μm 5 μm 视场 15° 15° 15° 定姿矢量数量 2 5 2 星点提取误差(RMS) 0.1 pixel 0.1 pixel 0.05 pixel 
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表 2 不同仿真方案下的星敏感器光学参数与权重配置对比
Table 2. Comparison of optical parameters and weight configurations of star trackers under different simulation schemes.
仿真方案 星敏感器 焦距/mm 视场角/deg 质心误差/pixel 像元尺寸/μm 权重/% 情况一：
等权重双正交Sensor 1 75.00 15 × 15 0.10 5 × 5 50.00 Sensor 2 75.00 15 × 15 0.10 5 × 5 50.00 情况二：
不等权重双正交Sensor 1 75.00 15 × 15 0.10 5 × 5 35.92 Sensor 2 100.00 15 × 15 0.08 5 × 5 64.08 情况三：
不等权重三正交Sensor 1 75.00 15 × 15 0.10 5 × 5 25.12 Sensor 2 50.00 20 × 20 0.15 5 × 5 5.01 Sensor 3 100.00 10 × 10 0.08 5 × 5 69.87
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表 3 不同融合定姿方案性能对比
Table 3. Performance comparison of different fusion attitude determination schemes.
定姿方案 X (3σ) Y (3σ) Z (3σ) Total (3σ) 精度提升 单星敏感器 0.245″ 0.246″ 8.309″ 8.317″ — 平均融合 4.166″ 0.169″ 4.164″ 5.892″ 29.2% MSWF 0.251″ 0.159″ 0.239″ 0.381″ 95.4%
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表 4 稀疏星场及随机丢星工况下不同定姿方案的性能对比
Table 4. Performance comparison of attitude determination schemes under sparse star fields and random star loss.
(a). 单星敏感器 $ {P}_{loss} $ Stars X(3σ) Y(3σ) Z(3σ) Total 0.00 4 11.918″ 0.377″ 11.910″ 16.853″ 6 7.868″ 0.266″ 7.861″ 11.125″ 8 6.119″ 0.214″ 6.115″ 8.653″ 0.04 4 12.250″ 0.395″ 12.268″ 17.342″ 6 7.906″ 0.264″ 7.908″ 11.185″ 8 6.183″ 0.215″ 6.177″ 8.743″ 0.08 4 12.085″ 0.381″ 12.103″ 17.108″ 6 7.943″ 0.264″ 7.940″ 11.234″ 8 6.310″ 0.217″ 6.306″ 8.923″ (b). 双星跟踪器（MSWF） $ {P}_{loss} $ Stars X(3σ) Y(3σ) Z(3σ) Total 0.00 4 0.307″ 0.197″ 0.301″ 0.473″ 6 0.232″ 0.156″ 0.236″ 0.366″ 8 0.196″ 0.133″ 0.196″ 0.308″ 0.04 4 0.303″ 0.196″ 0.304″ 0.472″ 6 0.232″ 0.155″ 0.232″ 0.363″ 8 0.199″ 0.134″ 0.196″ 0.310″ 0.08 4 0.301″ 0.199″ 0.302″ 0.470″ 6 0.231″ 0.157″ 0.231″ 0.362″ 8 0.197″ 0.134″ 0.196″ 0.308″
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表 5 星敏感器仿真主要参数
Table 5. Main parameters for star tracker simulation.
参数名称 数值 参数名称 数值 焦距 375 mm 质心误差 0.1 pixel 视场角 5° 角速度 0.1–1.5°/s 最大探测星等 11 曝光时间 50 ms 像元尺寸 8 μm 去模糊因子 0.7 PSF 标准差 1.5 pixel 信噪比 SNR 10
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表 6 不同角速度下MSWF与单星姿态解算残差对比
Table 6. Comparison of attitude determination residuals between MSWF and single-star methods at different angular velocities.
(a). MSWF三轴残差 角速度 (°/s) X(3σ) Y(3σ) Z(3σ) Total(3σ) 0.1 0.202″ 0.144″ 0.203″ 0.321″ 0.2 0.255″ 0.182″ 0.259″ 0.407″ 0.5 0.469″ 0.341″ 0.463″ 0.742″ 1.0 0.870″ 0.620″ 0.844″ 1.361″ 1.5 1.254″ 0.886″ 1.271″ 1.993″ (b). 单星三轴姿态残差 角速度 (°/s) X(3σ) Y(3σ) Z(3σ) Total(3σ) 0.1 0.202″ 0.205″ 6.798″ 6.804″ 0.2 0.256″ 0.250″ 7.884″ 7.892″ 0.5 0.471″ 0.475″ 15.635″ 15.649″ 1.0 0.874″ 0.847″ 27.712″ 27.738″ 1.5 1.254″ 1.266″ 43.278″ 43.315″
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表 7 不同工作探头数下MSWF的定姿精度对比
Table 7. Comparison of attitude determination accuracy of MSWF under different numbers of active heads.
工作星敏数 X(3σ) Y(3σ) Z(3σ) Total(3σ) star number 4 0.191″ 0.190″ 0.189″ 0.330″ 528.51 3 0.231″ 0.209″ 0.234″ 0.390″ 396.85 2 0.310″ 0.220″ 0.351″ 0.517″ 262.77 1 0.312″ 0.311″ 3.392″ 3.420″ 132.99
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表 8 不同安装误差及工作探头数的姿态定姿精度对比分析
Table 8. Comparative analysis of attitude accuracy versus installation errors and active head count.
(a). 2个星敏感器工作（MSWF） 评价指标 0 0.1 0.5 1.0 2.0 5.0 X(3σ) 0.070″ 0.128″ 0.516″ 1.029″ 1.974″ 5.113″ Y(3σ) 0.051″ 0.091″ 0.354″ 0.726″ 1.435″ 3.654″ Z(3σ) 0.073″ 0.125″ 0.506″ 0.992″ 1.979″ 5.023″ Total(3σ) 0.113″ 0.201″ 0.804″ 1.603″ 3.142″ 8.045″ (b). 单星敏感器工作 评价指标 0 0.1 0.5 1.0 2.0 5.0 X(3σ) 0.072″ 0.129″ 0.518″ 1.030″ 1.974″ 5.116″ Y(3σ) 0.075″ 0.129″ 0.513″ 0.979″ 1.964″ 4.931″ Z(3σ) 2.486″ 2.524″ 2.512″ 2.658″ 3.101″ 5.543″ Total(3σ) 2.488″ 2.531″ 2.615″ 3.014″ 4.168″ 9.013″
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