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    Journals >Infrared and Laser Engineering >Volume 49 >Issue 4 >Page 0403001 > Article
    • Infrared and Laser Engineering
    • Vol. 49, Issue 4, 0403001 (2020)
    Modeling and simulation of multi-detection point optimal initiation of synchronous scanning panoramic pulse laser fuze
    He Zhang, Hongxia Li, Libo Ding*, and Bingting Zha
    Author Affiliations
  • ZNDY of Ministerial Key Laboratory, Nanjing University of Science and Technology, Nanjing 210094, China
    • show less
    DOI: 10.3788/IRLA202049.0403001 Cite this Article
    He Zhang, Hongxia Li, Libo Ding, Bingting Zha. Modeling and simulation of multi-detection point optimal initiation of synchronous scanning panoramic pulse laser fuze[J]. Infrared and Laser Engineering, 2020, 49(4): 0403001 Copy Citation Text show less

    Abstract

    Panoramic laser fuze usually calculates the optimal initiation time and initiation azimuth only based on single measured target direction and distance, the calculation accuracy is low. On the other hand, fuze can not distinguish the authenticity of targets, it is easy to cause "false alarm" or accidental bombing. Based on the working principle of the synchronous scanning panoramic pulse laser fuze, the direction, distances and position coordinates of multiple detection points were analyzed. The target velocity model based on multiple detection points were established, which can calculate the target speed and judge whether the target was true. The geometric center position of the target feature was solved, and the optimal initiation time and azimuth calculation model were established to obtain the maximum damage effectiveness of the warhead. The influence factors of the optimal initiation time and azimuth were analyzed. The research can provide a reference for the target identification and directional initiation of the panoramic laser fuze.

    Keywords

    $\left[ {\begin{aligned} {{x_0}} \\ {{y_0}} \\ {{z_0}} \end{aligned}} \right] = C_0^m\left[ {\begin{aligned} {{x_m}} \\ {{y_m}} \\ {{z_m}} \end{aligned}} \right]$(1)

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    $C_0^m = \left[ {\begin{array}{*{20}{c}} {\cos {\beta _m}\cos {\psi _m}}&{ - \sin {\beta _m}\cos {\psi _m}}&{\sin {\psi _m}} \\ {\sin {\beta _m}}&{\cos {\beta _m}}&0 \\ { - \cos {\beta _m}\sin {\psi _m}}&{\sin {\beta _m}\sin {\psi _m}}&{\cos {\psi _m}} \end{array}} \right]$(2)

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    $\left[ {\begin{aligned} {{x_t}} \\ {{y_t}} \\ {{z_t}} \end{aligned}} \right] = C_t^0\left[ {\begin{aligned} {{x_0}} \\ {{y_0}} \\ {{z_0}} \end{aligned}} \right]$(3)

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    $C_t^0 = \left[ {\begin{array}{*{20}{c}} {\cos {\beta _t}\cos {\psi _t}}&{\sin {\beta _t}}&{ - \cos {\beta _t}\sin {\psi _t}} \\ { - \sin {\beta _t}\cos {\psi _t}}&{\cos {\beta _t}}&{\sin {\beta _t}\sin {\psi _t}} \\ {\sin {\psi _t}}&0&{\cos {\psi _t}} \end{array}} \right]$(4)

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    $\left[ {\begin{aligned} {{x_t}} \\ {{y_t}} \\ {{z_t}} \end{aligned}} \right] = C_t^m\left[ {\begin{aligned} {{x_m}} \\ {{y_m}} \\ {{z_m}} \end{aligned}} \right] = C_t^0C_0^m\left[ {\begin{aligned} {{x_m}} \\ {{y_m}} \\ {{z_m}} \end{aligned}} \right]$(5)

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    $\begin{split} ({}^{{m}}{{{x}}_k},{}^{{m}}{{{y}}_k},{}^{{m}}{{{z}}_k}) =\; & ({R_k}\cos {\alpha _t},{R_k}\sin {\alpha _t} \cos {\psi _k},\\ & {R_k}\sin {\alpha _t}\sin {\psi _k}) \end{split} $(6)

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    $C_{{m}}^l = \left[ {\begin{array}{*{20}{c}} {\cos \varphi \cos {\alpha _t}}&{ - \sin {\alpha _t}}&{ - \sin \varphi \cos {\alpha _t}} \\ {\cos \varphi \sin {\alpha _t}}&{\cos {\alpha _t}}&{ - \sin \varphi \sin {\alpha _t}} \\ {\sin \varphi }&0&{\cos \varphi } \end{array}} \right]$(7)

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    $\left[ {\begin{aligned} {{x_m}} \\ {{y_m}} \\ {{z_m}} \end{aligned}} \right] = C_{{m}}^{{l}}\left[ {\begin{aligned} {{x_l}} \\ {{y_l}} \\ {{z_l}} \end{aligned}} \right]$(8)

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    $\left[ {\begin{aligned} {{x_0}} \\ {{y_0}} \\ {{z_0}} \end{aligned}} \right] = C_0^{{m}}C_{{m}}^{{l}}\left[ {\begin{aligned} {{x_l}} \\ {{y_l}} \\ {{z_l}} \end{aligned}} \right]$(9)

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    $ {{{v}}_{{t}}} = \frac{{{{\rm{d}}{{{r}}}_t}}}{{{\rm{d}}t}},{{{{v}}}_{{m}}} = \frac{{{\rm{d}}{{{{r}}}_m}}}{{{\rm{d}}t}},{{{{v}}}_{{{mt}}}} = \frac{{{\rm{d}}{{{{r}}}_{mt}}}}{{{\rm{d}}t}} $ (10)

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    ${}^{{l}}{{{{v}}}_{{{mt}}}} = {(C_0^mC_m^l)^{\rm{T}}}({}^0{{{{v}}}_t} - {}^0{{{{v}}}_m})$(11)

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    ${}^{{l}}{{{v}}_{{{mt}}}} = \left\{ {\begin{aligned} {{}^{{l}}{v_{{{mtx}}}}} \\ {{}^{{l}}{v_{{{mty}}}}} \\ {{}^{{l}}{v_{{{mtz}}}}} \end{aligned}} \right\},{}^{{0}}{{{v}}_{{t}}} = \left\{ {\begin{aligned} {{}^{{0}}{v_{{{tx}}}}} \\ {{}^{{0}}{v_{{{ty}}}}} \\ {{}^{{0}}{v_{{{tz}}}}} \end{aligned}} \right\},{}^{{0}}{{{v}}_{{m}}} = \left\{ {\begin{aligned} {{}^{{0}}{v_{{{mx}}}}} \\ {{}^{{0}}{v_{{{my}}}}} \\ {{}^{{0}}{v_{{{mz}}}}} \end{aligned}} \right\}$(12)

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    ${}^{{l}}{v_{{{mtx}}}} = \frac{{{R_{{{k}} + {{1}}}} - {R_k}}}{{\Delta t}}$(13)

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    $L = {(C_0^mC_m^l)^{\bf{T}}} = \left[ {\begin{aligned} {{l_{11}}}\quad {{l_{12}}} \quad {{l_{13}}} \\ {{l_{21}}}\quad {{l_{22}}} \quad {{l_{23}}} \\ {{l_{31}}}\quad {{l_{32}}} \quad {{l_{33}}} \end{aligned}} \right]$(14)

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    $\left\{ {\begin{aligned} {{}^{{l}}{v_{{{mtx}}}}} \\ {{}^{{l}}{v_{{{mty}}}}} \\ {{}^{{l}}{v_{{{mtz}}}}} \end{aligned}} \right\} = \left[ {\begin{aligned} {{l_{11}}}\quad {{l_{12}}}\quad {{l_{13}}} \\ {{l_{21}}}\quad {{l_{22}}}\quad {{l_{23}}} \\ {{l_{31}}}\quad {{l_{32}}}\quad {{l_{33}}} \end{aligned}} \right]\left\{ {\begin{aligned} {{}^0{v_{tx}} - {}^0{v_{mx}}} \\ {{}^0{v_{ty}} - {}^0{v_{my}}} \\ {{}^0{v_{tz}} - {}^0{v_{mz}}} \end{aligned}} \right\}$(15)

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    ${l_{11}}{}^0{v_{tx}} + {l_{12}}{}^0{v_{ty}} + {l_{13}}{}^0{v_{tz}} = {}^lv{}_{mtx} + {l_{11}}{}^0{v_{mx}} + {l_{12}}{}^0{v_{my}} + {l_{13}}{}^0{v_{mz}}$(16)

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    $\left\{ {\begin{aligned} & {l_{11}^1{}^0{v_{tx}} + l_{12}^1{}^0{v_{ty}} + l_{13}^1{}^0{v_{tz}} = {}^lv_{{}_{mtx}}^1 + l_{11}^1{}^0{v_{mx}} + l_{12}^1{}^0{v_{my}} + l_{13}^1{}^0{v_{mz}}} \\ & {l_{11}^2{}^0{v_{tx}} + l_{12}^2{}^0{v_{ty}} + l_{13}^2{}^0{v_{tz}} = {}^lv_{{}_{mtx}}^2 + l_{11}^2{}^0{v_{mx}} + l_{12}^2{}^0{v_{my}} + l_{13}^2{}^0{v_{mz}}} \\ & {l_{11}^3{}^0{v_{tx}} + l_{12}^3{}^0{v_{ty}} + l_{13}^{31}{}^0{v_{tz}} = {}^lv_{{}_{mtx}}^3 + l_{11}^3{}^0{v_{mx}} + l_{12}^3{}^0{v_{my}} + l_{13}^3{}^0{v_{mz}}} \end{aligned}} \right.$(17)

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    $\frac{{\left| {{{{{r}}}_{t{{2}}}}{{ - }}{{{{r}}}_{t{{1}}}}} \right| + L}}{{\left| {{}^{{0}}{{{{v}}}_{{t}}}} \right|}} = t$(18)

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    ${{{r}}_c} = {{{r}}_{{{t}}2}} + \frac{L}{2}\frac{{{}^0{{{v}}_t}}}{{\left| {{}^0{{{v}}_t}} \right|}}$(19)

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    ${{{{v}}}_h} = {{{v}}} + {{{{v}}}_m}$(20)

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    ${{{{v}}}_{{h}}} = \left[ {\begin{array}{*{20}{c}} {\left| {{{{{v}}}_m}} \right|} \\ {\left| {{{v}}} \right|\cos {\alpha _m}} \\ {\left| {{{v}}} \right|\sin {\alpha _m}} \end{array}} \right]$(21)

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    ${{{{r}}}_{t3}} = {{{{r}}}_{{c}}} + (\Delta T + \Delta {T_h}){{{{v}}}_t}$(22)

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    ${{{{r}}}_{m3}} + \Delta {T_{{h}}}{}^0{{{{v}}}_h} = {{{{r}}}_{{c}}} + (\Delta T + \Delta {T_h}){}^0{{{{v}}}_t}$(23)

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    ${{{{r}}}_{m3}} = {{{{r}}}_{m2}} + \Delta T{{{{v}}}_m}$(24)

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    $({{{{v}}}_{{m}}} - {{{{v}}}_t})\Delta T + (C_0^m\left[ {\begin{aligned} {\left| {{{{{v}}}_{{m}}}} \right|}\;\;\;\\ {\left| {{{v}}} \right|{{\cos}}{\alpha _{{m}}}} \\ {\left| {{{v}}} \right|\sin {\alpha _{{m}}}} \end{aligned}} \right]{{ - }}{{{{v}}}_t})\Delta {T_{{h}}} = \frac{L}{2}\frac{{{{{{v}}}_t}}}{{\left| {{{{{v}}}_t}} \right|}} + {{{r}}}_{mt2}^{}$(25)

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    ${{{{v}}}_{{m}}} = C_0^m{\left[ {\begin{array}{*{20}{c}} {\left| {{{{{v}}}_m}} \right|}&0&0 \end{array}} \right]^{\bf{T}}}$(26)

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    Abstract
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    He Zhang, Hongxia Li, Libo Ding, Bingting Zha. Modeling and simulation of multi-detection point optimal initiation of synchronous scanning panoramic pulse laser fuze[J]. Infrared and Laser Engineering, 2020, 49(4): 0403001
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