• Infrared and Laser Engineering
  • Vol. 50, Issue 8, 20200429 (2021)
Bin Li and Hongjie Lei
Author Affiliations
  • Xi’an Flight Automatic Control Research Institute, AVIC, Xi’an 710065, China
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    DOI: 10.3788/IRLA20200429 Cite this Article
    Bin Li, Hongjie Lei. Analysis of data inversion accuracy of airborne optical air data system[J]. Infrared and Laser Engineering, 2021, 50(8): 20200429 Copy Citation Text show less

    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).
    $V = \left[ {\sin \theta \;\;\cos \varphi \mathop {}\nolimits^{} \;\;\sin \theta \;\;\sin \varphi \mathop {}\nolimits^{} \;\;\cos \theta } \right]\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right]$(1)

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    $\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right] = \left[ \begin{gathered} \sin {\theta _1}\cos {\varphi _1}\mathop {}\nolimits^{} \sin {\theta _1}\sin {\varphi _1}\mathop {}\nolimits^{} \cos {\theta _1} \\ \sin {\theta _2}\cos {\varphi _2}\mathop {}\nolimits^{} \sin {\theta _2}\sin {\varphi _2}\mathop {}\nolimits^{} \cos {\theta _2} \\ \quad \vdots \quad \quad {\quad ^{}}\,\, \vdots \quad \quad \quad \vdots \\ \sin {\theta _N}\cos {\varphi _N}\mathop {}\nolimits^{} \sin {\theta _N}\sin {\varphi _N}\mathop {}\nolimits^{} \cos {\theta _N} \\ \end{gathered} \right]\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right] = M\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right]$(2)

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    $\left\{ \begin{gathered} {V_{TAS}} = \sqrt {V_x^2 + V_y^2 + V_z^2} \\ \alpha = \arctan \frac{{{V_x}}}{{{V_{\textit{z}}}}} \\ \beta = \arcsin \frac{{{V_y}}}{{{V_{TAS}}}} \\ \end{gathered} \right.$(3)

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    $\left[ \begin{gathered} {V_x} \\ {V_y} \\ {V_{\textit{z}}} \\ \end{gathered} \right] = {({M^{\rm{T}}}M)^{ - 1}}{M^{\rm{T}}}\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right] = \left[ \begin{gathered} {m_{11}}\;{m_{12}} \cdots {m_{1N}} \\ {m_{21}}\;{m_{22}} \cdots {m_{2N}} \\ {m_{31}}\;{m_{32}} \cdots {m_{3N}} \\ \end{gathered} \right]\left[ \begin{gathered} {V_1} \\ {V_2} \\ \vdots \\ {V_N} \\ \end{gathered} \right]$(4)

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    ${\sigma _i} = \sqrt {m_{i1}^2 + m_{i2}^2 + \cdots + m_{iN}^2} \cdot \sigma $(5)

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    ${\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)

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    ${\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)

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    Bin Li, Hongjie Lei. Analysis of data inversion accuracy of airborne optical air data system[J]. Infrared and Laser Engineering, 2021, 50(8): 20200429
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