• Journal of Geo-information Science
  • Vol. 22, Issue 9, 1878 (2020)
Yonghong HE*, Pengwei JIN, and Min SHU
Author Affiliations
  • School of Civil and Environmental Engineering, Hunan University of Science and Engineering, Yongzhou 425199, China
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    DOI: 10.12082/dqxxkx.2020.200061 Cite this Article
    Yonghong HE, Pengwei JIN, Min SHU. InSAR Tropospheric Delay Error Correction Algorithm based on Multi-Scale Correlation Analysis[J]. Journal of Geo-information Science, 2020, 22(9): 1878 Copy Citation Text show less

    Abstract

    Tropospheric delay error in synthetic aperture radar interferometry can affect DEM accuracy. This study adopts wavelet multi-scale correlation analysis to reduce the influence of tropospheric delay error on DEM estimation. This method is based on the wavelet multi-resolution analysis theory and the frequency characteristics of different components in differential interference phases. Firstly, the wavelet decomposition reconstruction RMS error rate is used to determine the decomposition layers. The terrain residual phase and noise phase are reduced to extract the frequency band where the troposphere delayed error phase is located. Secondly, we quantify the correlation between tropospheric delay error phase and DEM in radar coordinates and further down-weight the correlated coefficients. Lastly, the differential interferogram is reconstructed which reduces the influence of elevation-related tropospheric delay in InSAR. In this study, the ENVISAT ASAR data in Yima, Henan province are processed using the method proposed in this study. The differential interferogram with tropospheric delay error corrected are obtained to estimate elevation. The estimated tropospheric delay phase correlated with elevation is consistent with the topographic changes. Results show that the standard deviation of DEM error compared to Aster GDEM decreases from 30.7 m to 26.37 m, which indicates an increased accuracy of InSAR DEM.
    ϕ=ϕflat+ϕtopo+ϕorbit+ϕatm+ϕnoise(1)

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    ϕflat=-4πλ(R2-R1)(2)

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    ϕtopo=4πBcos(θ-α)λRsin(θ)h(3)

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    Δϕ=Δϕtopo+ϕorbit+ϕatm+ϕnoise(4)

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    ϕorbit(x,y)=a+bx+cy(5)

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    Δϕ=Δϕtopo+ϕatm+ϕnoise(6)

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    f(x1,x2)=k1p-1k2q-1vjk1k2φjk1k2(x1,x2)+jJk1p-1k2q-1ε3wjk1k2εψjk1k2ε(x1,x2)=AJ+jJε3Djε(7)

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    vjk1k2=<f(x1,x2),φjk1k2(x1,x2)>(8)

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    wjk1k2ε=<f(x1,x2),ψjk1k2ε(x1,x2)>,ε=1,2,3(9)

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    φjk1k2(x1,x2)=φjk1(x1)φjk2(x2)(10)

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    ψjk1k2ε(x1,x2)=φjk1ε(x1)ψjk2ε(x2),ε=1ψjk1ε(x1)φjk2ε(x2),ε=2ψjk1ε(x1)ψjk2ε(x2),ε=3(11)

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    U(x1,x2)=k1p-1k2q-1uvjk1k2φjk1k2(x1,x2)+jJk1p-1k2q-1ε3uwjk1k2εψjk1k2ε(x1,x2)(12)

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    D(x1,x2)=k1p-1k2q-1dvjk1k2φjk1k2(x1,x2)+jJk1p-1k2q-1ε3dwjk1k2εψjk1k2ε(x1,x2)(13)

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    cjε=<(wuwjk1k2ε-w̅uw̅jk1k2ε)(wdwjk1k2ε-w̅dw̅jk1k2ε)>(wuwjk1k2ε-w̅uw̅jk1k2ε)2(wdwjk1k2ε-w̅dw̅jk1k2ε)2(14)

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    $\overline{^{u}w^{\varepsilon}_{j k_{1}k_{2}}}=^{u}w^{\varepsilon}_{j k_{1}k_{2}}*(1-c^{\varepsilon}_{j})$ (15)

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    $\overline{U(x_{1},x_{2})}=\sum_{k_{1}}^{p-1}\sum_{k_{2}}^{q-1} {^{u}v_{j k_{1}k_{2}}} \varphi_{j k_{1}k_{2}}(x_{1},x_{2})+\sum_{j}^{J}\sum_{k_{1}}^{p-1}\sum_{k_{2}}^{q-1}\sum_{\varepsilon}^{3}\overline{^{u}w^{\varepsilon}_{j k_{1}k_{2}}}\psi^{\varepsilon}_{j k_{1}k_{2}}$ (16)

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    RMSEk=1m×nx=1,y=1m,n(ϕ(x,y)-ϕˆk(x,y))2(k=1,2,,n)(17)

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    rk+1=RMSE(k+1)RMSE(k)(k=1,2,,n)(18)

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    Yonghong HE, Pengwei JIN, Min SHU. InSAR Tropospheric Delay Error Correction Algorithm based on Multi-Scale Correlation Analysis[J]. Journal of Geo-information Science, 2020, 22(9): 1878
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