• Infrared and Laser Engineering
  • Vol. 50, Issue 6, 2021G006 (2021)
Kexun Chen1,2, Deng'ao Li1,*, and Wei Qiu2
Author Affiliations
  • 1Institute of Information and Computer, Taiyuan University of Technology, Taiyuan 030600, China
  • 2Beijing Intensity Environment Institute, Beijing 100076, China
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    DOI: 10.3788/IRLA2021G006 Cite this Article
    Kexun Chen, Deng'ao Li, Wei Qiu. Design and verification of multi-mode GNSS pseudo-range combined positioning method[J]. Infrared and Laser Engineering, 2021, 50(6): 2021G006 Copy Citation Text show less

    Abstract

    In a complex geomorphic environment where satellite signals are severely interfered with, due to the small number of visible satellites and poor satellite signal quality, the accuracy of single-mode satellite positioning and navigation has been unsatisfactory, especially for dynamic navigation and positioning accuracy. In order to improve the accuracy of dynamic navigation and positioning, a multi-mode GNSS pseudo-range combined positioning algorithm was designed, which belonged to an iterative combined positioning algorithm. The initial iterative weight matrix was determined by the height angle priori weight model, and the weight was the smallest. In the process of the two multiplication method, the posterior model was estimated by the variance component, and the weight matrix was continuously updated iteratively to obtain the accurate position of the target. The algorithm needed to rely on the initial value and multiple iterations, but the positioning accuracy was better than the Gauss-Newton iterative algorithm and Helmert variance component estimation method. Experimental simulation results show that compared with Gauss-Newton iterative algorithm and Helmert variance component estimation method, the positioning accuracy of the algorithm designed in this paper is improved by 45.1% and 23%, respectively. Finally, combined with the actual airdrop test analysis, it is shown that the algorithm described in this paper can accurately calculate the drop point of the airdrop material, which can provide a reference for the aircraft navigation system designer, and has certain theoretical significance and practical value.
    $ ρi=(xixu)2+(yiyu)2+(zizu)2+ctu+δfi+δc+δri $(1)

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    $\Delta \rho = H\left[ {ΔxuTcΔtu} \right] + \delta $(2)

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    $ \delta _i^{real} = \delta _f^i + \delta _c + \delta _r^i $ (3)

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    $ δcom=1ni=1nδireal=1ni=1n(δfi+δc+δri)=δc+uδ+1ni=1n(δfi) $(4)

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    $ δi=δfi+δc+δriδcom=δfi+δc+δriδcom1ni=1n(δfi) $(5)

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    $\delta _{eig}^i = \delta _f^i + \delta _r^i - {u_\delta }$(6)

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    $\delta _{eig}^i = \delta _f^i + \delta _r^i - {u_\delta } = \delta _i$(7)

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    $ δeigi=δiδmid=δfi+δriuδδmid=δfi+δriuδδfmidδrmid $(8)

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    $P = \left[ {1σ0201σ2201σn2} \right]$(9)

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    ${P_0} = \left[ {sinθ1σ020sinθ2σ020sinθnσ02} \right]$(10)

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    $\left\{ {V1=B1ΔxL1V2=B2ΔxL2} \right.$(11)

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    $L = \left( {L1L2} \right)V = \left( {V1V2} \right)B = \left( {B1B2} \right)P = \left( {P100P2} \right){\rm{ }}$(12)

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    $\left\{ {σ0i=1n1i=1n(δi0)2σ0i=1n1i=1n(δiδmid)2} \right._{}i = 1,2$(13)

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    $\mathop S\limits_{2 \times 2} \cdot \mathop {\overset{\frown}\theta }\limits_{2 \times 1} = \mathop W\limits_{2 \times 1} $(14)

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    $\mathop S\limits_{2 \times 2} = \left[ {Missing \end{array} &{{k_3}TR\left( {{N^{ - 1}}{N_1}{N^{ - 1}}{N_2}} \right)} \ {{k_3}tr\left( {{N^{ - 1}}{N_2}{N^{ - 1}}{N_1}} \right)}&k1TR(N1N2N1N2)2k2TR(N1N2)+n2 \end{array}} \right]$(15)

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    $\mathop {\overset{\frown}\theta }\limits_{2 \times 1} {\rm{ = }}\left( {σ012σ022} \right)\;\;\mathop W\limits_{2 \times 1} {\rm{ = }}\left( {V1TP1V1V2TP2V2} \right)$(16)

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    $\mathop Y\limits^\frown P_1^i = \left\{ {exp(δi0σ01×h)2D<Texp(δiδmid1σ01×h)2DT} \right.\;i = 1,2, \cdots $(17)

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    $ P_2^i = \left\{ {exp(δi0σ02×h)2D<Texp(δiδmid2σ02×h)2DT} \right.i = 1,2, \cdots $(18)

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    $ f(Δx^)=j=1n1φ(Pij12(αijTΔx^Lij))αijPij12+j=1n2φ(Pij12(αijTΔx^Lij))αijPij12=0 $ (19)

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    $f(\Delta \hat x) = f(\Delta x) + {f'}(\Delta x)(\Delta \hat x - \Delta x) + \cdots = 0$(20)

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    $j=1n1φ(P1j12(α1jTΔxL1j))α1jP1j12+j=1n2φ(P2j12(α2jTΔxL2j))α2jP2j12+j=1n1φ(P1j12(α1jTΔx^L1j))α1jP1j12(Δx^Δx)+j=1n2φ(P2j12(α2jTΔx^L2j))α2jP2j12(Δx^Δx)+=0 $(21)

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    $f({\Delta _{{ij}}}) = {\left( {2\pi {\sigma _i}P_{ij}^{ - 1/2}} \right)^{ - 1}}\exp \left( { - \Delta _{ij}^2/\left( {2{\sigma _i}^2P_{ij}^{ - 1}} \right)} \right)$(22)

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    $f({\Delta _{i}}) = {\left( {2\pi {\sigma _i}} \right)^{ - 1}}\exp \left( { - \Delta _i^2/\left( {2{\sigma _i}^2P} \right)} \right)$(23)

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    $\left\{ {λ1i=E(φ(Pij1/2(bijΔxLij)))=E(φ(Pij1/2Δij))λ2i=E(φ(Pij1/2Δij)φ(Pij1/2))=E(φ2(Δi))λ3i=E(φ(Pij1/2Δij)(Pij1/2Δij))=E(φ(Δi)Δi)} \right.$(24)

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    Kexun Chen, Deng'ao Li, Wei Qiu. Design and verification of multi-mode GNSS pseudo-range combined positioning method[J]. Infrared and Laser Engineering, 2021, 50(6): 2021G006
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