• Infrared and Laser Engineering
  • Vol. 50, Issue S2, 20210066 (2021)
Yongjian Zhang, Lin Wang, Guo Wei, Chunfeng Gao, and Hui Luo
Author Affiliations
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
  • show less
    DOI: 10.3788/IRLA20210066 Cite this Article
    Yongjian Zhang, Lin Wang, Guo Wei, Chunfeng Gao, Hui Luo. Integrated navigation method of RLG INS/GNSS polar region[J]. Infrared and Laser Engineering, 2021, 50(S2): 20210066 Copy Citation Text show less

    Abstract

    When the aircraft is flying across the polar region, the transformation of navigation coordinate system will lead to the change of filter structure, which will affect the navigation accuracy. To solve this problem, a Ring Laser Gyroscope Inertial Navigation System/Global Navigation Satellite System (RLG INS/GNSS) polar region integrated navigation algorithm based on covariance transformation was proposed. The transformation relationship of the system error state and the covariance between the geographic coordinate system and the grid coordinate system was established. Then the integrated navigation filter with full latitude applicability was designed, and the effectiveness of the algorithm was verified by sports car experiment and semi-physical simulation experiment. The experiment results show that the covariance transformation algorithm can effectively solve the filtering instability caused by the transformation of the navigation coordinate system. Compared with the non-covariance transformation, the system state error decreases by one order of magnitude.
    $sinσ=sinLsinλ1cos2Lsin2λcosσ=cosλ1cos2Lsin2λ $(1)

    View in Article

    ${\boldsymbol{C}}_e^G = {\boldsymbol{C}}_n^G{\boldsymbol{C}}_e^n = \left[ {cosσsinλ+sinσsinLcosλsinσsinλcosσsinLcosλcosLcosλcosσcosλ+sinσsinLsinλsinσcosLsinσcosλcosσsinLsinλcosσcosLcosLsinλsinL} \right]$(2)

    View in Article

    $\dot {\boldsymbol{C}}_b^G = {\boldsymbol{C}}_b^G\left[ {{\boldsymbol{\omega}} _{ib}^b \times } \right] - \left[ {{\boldsymbol{\omega}} _{iG}^G \times } \right]{\boldsymbol{C}}_b^G$(3)

    View in Article

    $ {\dot{{\boldsymbol{v}}}}^{G}={\boldsymbol{C}}_{b}^{G}{\boldsymbol{f}}^{b}-\left(2{{\boldsymbol{\omega}} }_{ie}^{G}+{{\boldsymbol{\omega}} }_{eG}^{G}\right)\times {{\boldsymbol{v}}}^{G}+{\boldsymbol{g}}^{G}$(4)

    View in Article

    $\dot {\boldsymbol{C}}_e^G = - \left[ {{\boldsymbol{\omega}} _{eG}^G \times } \right]{\boldsymbol{C}}_e^G$(5)

    View in Article

    $\dot h = v_U^G$(6)

    View in Article

    ${\boldsymbol{\omega}} _{iG}^G = {\boldsymbol{\omega}} _{ie}^G + {\boldsymbol{\omega}} _{eG}^G = {\boldsymbol{C}}_e^G{\boldsymbol{\omega}} _{ie}^e + {\boldsymbol{\omega}} _{eG}^G$()

    View in Article

    ${\boldsymbol{\omega}} _{ie}^G{\rm{ = }}\left[ {ωiesinσcosLωiecosσcosLωiesinL} \right],{\boldsymbol{\omega}} _{eG}^G = \left[ {1τf1Ry1Rx1τfκτfκRy} \right]\left[ {vEGvNG} \right]$()

    View in Article

    $\left\{ {x=(RN+h)cosLcosλy=(RN+h)cosLsinλz=[RN(1f)2+h]sinL} \right.$(7)

    View in Article

    $\left\{ {x=(R(1+fc332)+h)c31y=(R(1+fc332)+h)c32z=[R(1+fc332)(1f)2+h]c33} \right.$(8)

    View in Article

    $\dot {\boldsymbol{\phi}} _{}^G = - {\boldsymbol{\omega}} _{iG}^G \times {\boldsymbol{\phi}} _{}^G + \delta {\boldsymbol{\omega}} _{iG}^G - {\boldsymbol{C}}_b^G\delta {\boldsymbol{\omega}} _{ib}^b$(9)

    View in Article

    $ δ\boldsymbolv˙G=fG×\boldsymbolϕG+\boldsymbolvG×(2δ\boldsymbolωieG+δ\boldsymbolωeGG)(2\boldsymbolωieG+\boldsymbolωeGG)×δ\boldsymbolvG+\boldsymbolCbGδ\boldsymbolfb $(10)

    View in Article

    ${\dot {\boldsymbol{\theta}} ^G} = - {\boldsymbol{\omega}} _{eG}^G \times {{\boldsymbol{\theta}} ^G} + \delta {\boldsymbol{\omega}} _{eG}^G$(11)

    View in Article

    $\delta \dot h = \delta {{v}}_U^G$(12)

    View in Article

    $\boldsymbolCbG=\boldsymbolCnG\boldsymbolCbn\boldsymbolCbn=\boldsymbolCGn\boldsymbolCbG $(13)

    View in Article

    $\boldsymbolvG=\boldsymbolCnG\boldsymbolvn\boldsymbolvn=\boldsymbolCGn\boldsymbolvG $(14)

    View in Article

    $ \boldsymbolxn(t)=[ϕEn,ϕNn,ϕUn,δvEn,δvNn,δvUn,δL,δλ,δh,εxb,εyb,εzb,xb,yb,zb]T $(15)

    View in Article

    $\tilde {\boldsymbol{C}}_e^G{\rm{ = }}\left[ {{\bf{I}} - {{\boldsymbol{\theta}} ^G} \times } \right]{\boldsymbol{C}}_e^G$(16)

    View in Article

    $\tilde {\boldsymbol{C}}_e^G - {\boldsymbol{C}}_e^G{\rm{ = }} - \left[ {{{\boldsymbol{\theta}} ^G} \times } \right]{\boldsymbol{C}}_e^G$(17)

    View in Article

    $\boldsymbolθG=[θEGθNGθUG]T=[cosσsinσsinσcosσcosσsinσtanLsin2σtanL][δLδλcosL] $(18)

    View in Article

    $θUG=[cosσsinσtanLsin2σtanL][δLδλcosL]=[sinσtanL0][θEGθNG] $(19)

    View in Article

    ${{\theta}} _U^G = \left[ {c13c330} \right]\left[ {θEGθNG} \right]$(20)

    View in Article

    $ \boldsymbolxG(t)=[ϕEG,ϕNG,ϕUG,δvEG,δvNG,δvUG,θEG,θNG,δh,εxb,εyb,εzb,xb,yb,zb]T $(21)

    View in Article

    $\delta {\boldsymbol{C}}_b^G = - [{\boldsymbol{\phi}} _{}^G \times ]{\boldsymbol{C}}_b^G$(22)

    View in Article

    $ δ\boldsymbolCbG=δ\boldsymbolCnG\boldsymbolCbn+\boldsymbolCnGδ\boldsymbolCbn=[\boldsymbolϕnGG×]\boldsymbolCnG\boldsymbolCbn\boldsymbolCnG[\boldsymbolϕn×]\boldsymbolCbn $(23)

    View in Article

    $\delta {\boldsymbol{C}}_n^G = \tilde {\boldsymbol{C}}_n^G - {\boldsymbol{C}}_n^G = - \left[ {{\boldsymbol{\phi}} _{nG}^G \times } \right]{\boldsymbol{C}}_n^G$(24)

    View in Article

    ${\boldsymbol{\phi}} _{nG}^G = {\left[ {00δσ} \right]^{\rm{T}}}$(25)

    View in Article

    $δσ=sinσcosσcosLsinLδL+1cos2σcos2LsinLδλ $(26)

    View in Article

    $\left[ {{\boldsymbol{\phi}} _{}^G \times } \right] = {\boldsymbol{C}}_n^G\left[ {{\boldsymbol{\phi}} _{}^n \times } \right]{\boldsymbol{C}}_G^n + \left[ {{\boldsymbol{\phi}} _{nG}^G \times } \right]$(27)

    View in Article

    ${\boldsymbol{\phi}} _{}^G = {\boldsymbol{C}}_n^G{\boldsymbol{\phi}} _{}^n + {\boldsymbol{\phi}} _{nG}^G$(28)

    View in Article

    $δ\boldsymbolvG=\boldsymbolCnGδ\boldsymbolvn+δ\boldsymbolCnG\boldsymbolvn=\boldsymbolCnGδ\boldsymbolvn[\boldsymbolϕnGG×]\boldsymbolCnG\boldsymbolvn $(29)

    View in Article

    $\left[ {θEGθNG} \right] = \left[ {cosσsinσcosLsinσcosσcosL} \right]\left[ {δLδλ} \right]$(30)

    View in Article

    ${{\boldsymbol{x}}^G}(t) = {\boldsymbol{\varPhi}} {{\boldsymbol{x}}^n}(t),{{\boldsymbol{x}}^n}(t) = {{\boldsymbol{\varPhi}} ^{ - 1}}{{\boldsymbol{x}}^G}(t)$(31)

    View in Article

    $ \boldsymbolPG(t)=E{(\boldsymbolx~G(t)\boldsymbolxG(t))(\boldsymbolx~G(t)\boldsymbolxG(t))T}=E{\boldsymbolΦ(\boldsymbolx~n(t)\boldsymbolxn(t))(\boldsymbolx~n(t)\boldsymbolxn(t))T\boldsymbolΦT}=\boldsymbolΦE{(\boldsymbolx~n(t)\boldsymbolxn(t))(\boldsymbolx~n(t)\boldsymbolxn(t))T}\boldsymbolΦT=\boldsymbolΦ\boldsymbolPn(t)\boldsymbolΦT $(32)

    View in Article

    ${{\boldsymbol{P}}^n}\left( t \right) = {{\boldsymbol{\varPhi}} ^{ - 1}}{{\boldsymbol{P}}^G}\left( t \right){{\boldsymbol{\varPhi}} ^{ - {\rm{T}}}}$(33)

    View in Article

    Yongjian Zhang, Lin Wang, Guo Wei, Chunfeng Gao, Hui Luo. Integrated navigation method of RLG INS/GNSS polar region[J]. Infrared and Laser Engineering, 2021, 50(S2): 20210066
    Download Citation