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光学大气数据测量的一般流程:系统向大气中发射多束彼此独立的激光束,用于测量激光视线方向飞行器与气溶胶粒子的相对速度(简称视线速度),多个独立的视线速度通过坐标反演可获得飞行器三轴真空速,通过三轴真空速可解算出攻角及侧滑角。
建立机体坐标系,x为机体横截面法线方向,y为机翼方向,z为机头方向,假设系统光学天线坐标与机体坐标重合(实际中可通过测量安装角度及坐标变化使其重合),则可定义激光束与z轴夹角为仰角θ,激光束在x-y平面上投影与x轴夹角定义为方位角φ,如图1所示。视线速度为三轴真空速在视线方向上的投影,因此视线速度V可表示为:
图 1 多波束测量空速反演坐标系
Figure 1. Inversion coordinate system with multi-laser beam for airspeed measurement
$$V = \left[ {\sin \theta \;\;\cos \varphi \mathop {}\nolimits^{} \;\;\sin \theta \;\;\sin \varphi \mathop {}\nolimits^{} \;\;\cos \theta } \right]\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right]$$ (1) 式中:Vx、Vy、Vz为三轴真空速。为了获得三轴真空速,需要测量至少三个独立不相关的视线速度V,因此需要至少分别向三个独立方向上发射激光,通过坐标反演算法解算出三轴空速。
N波束激光测量,其视线速度与三轴真空速的关系可表示为:
$$\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right] = \left[ \begin{gathered} \sin {\theta _1}\cos {\varphi _1}\mathop {}\nolimits^{} \sin {\theta _1}\sin {\varphi _1}\mathop {}\nolimits^{} \cos {\theta _1} \\ \sin {\theta _2}\cos {\varphi _2}\mathop {}\nolimits^{} \sin {\theta _2}\sin {\varphi _2}\mathop {}\nolimits^{} \cos {\theta _2} \\ \quad \vdots \quad \quad {\quad ^{}}\,\, \vdots \quad \quad \quad \vdots \\ \sin {\theta _N}\cos {\varphi _N}\mathop {}\nolimits^{} \sin {\theta _N}\sin {\varphi _N}\mathop {}\nolimits^{} \cos {\theta _N} \\ \end{gathered} \right]\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right] = M\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right]$$ (2) 反演出三轴真空速后,可由公式(3)解算出真空速
${V_{TAS}}$ 、攻角α、侧滑角β[3,10]:$$\left\{ \begin{gathered} {V_{TAS}} = \sqrt {V_x^2 + V_y^2 + V_z^2} \\ \alpha = \arctan \frac{{{V_x}}}{{{V_{\textit{z}}}}} \\ \beta = \arcsin \frac{{{V_y}}}{{{V_{TAS}}}} \\ \end{gathered} \right.$$ (3) 由公式(2)、(3)可知,三轴真空速、攻角及侧滑角反演精度取决于各视线速度的测量精度σ、θ及φ的角度选择。理论上,可计算任意空间分布的N束激光反演结果和精度。对于三波束及四波束测量,参考文献[7-8]给出了三轴反演风速(与三轴空速测量原理及方法相同)及反演精度的解析表达式。其中做以下假设:(1)各视线方向与z轴夹角θ相同;(2)各视线速度测量精度σ相同(决定于系统设计,可认为各束激光的光路、电路和信号解算一样);(3)
${\varphi _n} = \dfrac{{2\pi (n - 1)}}{N}$ ,N为激光总数目,n为激光束序号。但对于N束激光测量时(N>4),由于矩阵M为N×3矩阵,公式(2)为超定方程组,无法给出解析解,此时可通过求解方程的最小二乘解反演三轴真空速,表示为:$$\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right] = {({M^{\rm{T}}}M)^{ - 1}}{M^{\rm{T}}}\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right] = \left[ \begin{gathered} {m_{11}}\;{m_{12}} \cdots {m_{1N}} \\ {m_{21}}\;{m_{22}} \cdots {m_{2N}} \\ {m_{31}}\;{m_{32}} \cdots {m_{3N}} \\ \end{gathered} \right]\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right]$$ (4) 式中:
${({M^\rm T}M)^{ - 1}}{M^\rm T}$ 为3×N矩阵。由于公式(4)为线性方程,三轴真空速可表示为V1、V2、···VN的线性组合。根据线性无关变量的方差传递性质,三轴真空速的反演精度只决定于系数矩阵${({M^\rm T}M)^{ - 1}}{M^\rm T}$ ,可表示为公式(5),其中i代表x、y、z。$${\sigma _i} = \sqrt {m_{i1}^2 + m_{i2}^2 + \cdots + m_{iN}^2} \cdot \sigma $$ (5) 对公式(3)两端求微分,可推导出攻角及侧滑角反演精度表达式:
$${\sigma _\alpha } = \frac{1}{{1 + \tan {{(\alpha )}^2}}} \cdot \sqrt {{{\left( {\frac{{{\sigma _x}}}{{{V_{\textit{z}}}}}} \right)}^2} + {{\left( {\frac{{{\sigma _{\textit{z}}} \cdot {V_x}}}{{{V_{\textit{z}}}^2}}} \right)}^2}} $$ (6) $${\sigma _\beta } = \frac{1}{{\cos (\beta )}} \cdot \sqrt {{{\left( {\frac{{{\sigma _y}}}{{{V_{TAS}}}}} \right)}^2} + {{\left( {\frac{{{\sigma _V} \cdot {V_y}}}{{{V_{TAS}}^2}}} \right)}^2}} $$ (7) 式中:
${\sigma _V} = \dfrac{1}{{{V_{TAS}}}} \cdot \sqrt {{V_x}^2 \cdot {\sigma _x}^2 + {V_y}^2 \cdot {\sigma _y}^2 + {V_{\textit{z}}}^2 \cdot {\sigma _{\textit{z}}}^2}$ 。
Analysis of data inversion accuracy of airborne optical air data system
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摘要: 通过分析误差传递规律,仿真分析了多波束激光反演三轴真空速、攻角及侧滑角的精度变化规律,并对反演精度变化规律进行了实验验证,实验与仿真结果吻合得较好。结果表明:三轴真空速反演精度随测量激光数目的增加而提高;x、y轴与z轴真空速精度随仰角变化具有不同的趋势,为保证三轴真空速反演精度小于2倍的测量精度,仰角取值范围应在20°~70°;角度反演精度与真空速、侧滑角的取值相关,与攻角取值无关,并随着真空速增大而提高;给定反演精度下,侧滑角的取值范围随着空速的增大而增大。文中的分析结论有助于光学大气数据测量系统的优化设计。Abstract: The inversion accuracy of three-axis true air speed (TAS), angle of attack (AOA), angle of sideslipe (AOS) was analyzed by analyzing the error transmission rules of multi-beam laser measurement. In addition, experiments were carried out to verify the law of inversion accuracy change, and the experimental and simulation results were well consistent. The results show that the inversion accuracy of three-axis TAS are higher when the number of laser beams increase. The inversion accuracy of TAS in the x, y and z directions has different trends with the elevation angle. In order to ensure the three-axis TAS inversion accuracy less than 2 times the measurement accuracy, the elevation angle should be within the range of 20°-70°. The inversion accuracy of angle is related to the values of TAS and AOS rather than AOA, and it become higher as TAS increase. the range of AOS become larger as TAS increase when the inversion accuracy is given. The conclusions of this paper are useful for the optimal design of optical air data system (OADS).
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Key words:
- OADS /
- atmospheric data /
- data invertion method /
- inversion accuracy /
- precision analysis
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[1] Xiong L, Liu Y M, Huang Q P. Research progress in air data sensor technology for attack helicopter [J]. Transducer and Microsystem Technologies, 2015, 34(2): 5-8. (in Chinese) [2] Smart A E. Optical velocity sensor for air data applications[C]//Proceedings of SPIE - The International Society for Optical Engineering, 1991, 31(1): 166-173. [3] Mocker H W, Wagener T J. Laser Doppler optical air-data system: feasibility demonstration and systems specifications [J]. Appl Opt, 1994, 33(27): 6457-6471. doi: 10.1364/AO.33.006457 [4] McGann R L. Flight test results from a low-power Doppler optical air data sensor[C]//Proceedings of SPIE - The International Society for Optical Engineering, 1995, 2464: 116-124. [5] Spuler S M, Richter D, Spowart M P. Optical fiber-based laser remote sensor for airborne measurement of wind velocity and turbulence [J]. Appl Opt, 2011, 50(6): 842-851. doi: 10.1364/AO.50.000842 [6] Mamidipudi P, Dakin E A, Dakin D C. LandSafe precision flight instrumentation system: the DVE solution[C]//Proceedings of SPIE - The International Society for Optical Engineering, 2012, 8360: 83600N. [7] Pan Jingyan, Wu Shuangyang, Liu Guo, et al. Wind measurement techniques of coherent wind lidar [J]. Infrared and Laser Engineering, 2013, 42(7): 1720-1724. (in Chinese) [8] Li Ce, Zhao Pei’e, Peng Tao, et al. Technical research of 3-D wind lidar [J]. Laser Technology, 2017, 41(5): 703-707. (in Chinese) [9] 丘祖京. 相干激光雷达风场测量及数据反演方法[D]. 南京信息工程大学, 2016. Qiu Zujing. Studies on wind field measurement and data inversion method of the coherent LIDAR[D]. Nanjing: Nanjing University of Information Science and Technology, 2016. (in Chinese) [10] Long Yanzhi, Liang Yingjian, Huang Qiapping, et al. Design of optical airspeed measurement system based on Doppler shift [J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44C(12): 2521-2527. (in Chinese)