相位高程转换有理函数模型Rational Function Model for Conversion of InSAR Unwrapped Phases to Heights

+b12 y2φ + b13φ 2 x + b14 y2 x + b15φ x2
+b16 yφ 2 + b17 x3 + b18 y3 + b19φ 3
The coefficients a0 ，……， a19 ， b0 ，……， b19 are
named as Rational Function Coefficients (RFCs). In order to reduce the errors induced by rounding in
（4）
⎡1
vh
=
⎢ ⎣
Q
xn Q
yn Q
φn L yn3 φn3
Q
QQ
− hn xn Q
− hn yn Q
L − hn yn3 Q
Considering that RFM has been used broadly, it is proposed to use RFM as a new model for conversion of unwrapped phases to heights. It can be used in deriving accurate heights, even if there are unknown SAR system parameters, including resolutions, close time delay, wavelength, etc. RFM is universal in conversion of unwrapped phases to heights.
calculation and to get robust results, in formula
(1), hn , xn , yn ,φn were the standard values, their values are
[ ] in region − 1.0,+1.0 . The calculation formula is:
II. RFM FOR CONVERSION OF UNWRAPPED PHASES TO HEIGHTS
RFM for conversion of unwrapped phases to heights describes height as a ratio formula of two polynomials with
Abstract—Interferometric Synthetic Aperture Radar (InSAR) has become one of most potential technologies of earth observation. It has some prominent advantages, such as fast, high accuracy, all-daytime and all-weather, etc. In the processing of InSAR, the accuracy of derived height is highly related to the accuracy of estimated baseline parameters. Minor errors in baseline estimation can induce a major slope in derived DEMs (Digital Elevation Models). In order to get accurate heights from unwrapped interferometric phases, the rational function model for conversion of InSAR unwrapped phases to heights was proposed. It was used as a new model for conversion of unwrapped interferometric phases to heights. The interferometric data of SIR-C/X-SAR and of an airborne dual-antenna InSAR were employed to do experiments. And the unwrapped interferometric phases were converted accurately to heights, as showed that the rational function model is valid for unwrapped phases converting to heights.
Keywords-Interferometric Synthetic Aperture Radar, Baseline Estimation, Rational Function Model, Phase, Height
I. INTRODUCTION
Rational Function Model (RFM) or Rational Polynomial Coefficients (RPC) is often used to solve nonlinear fitting problems in natural science and technology [1]. RFM is a simple function. Though it is more complex than polynomial, it can describe functions flexibly and effectively. It is applied broadly in image restoration, curve or surface construction, target orientation in optical and SAR photogrammetry, etc.
Jin Guowang, Xu Qing, Qin Zhiyuan
Institute of Surveying and Mapping Information Engineering University
Zhengzhou, China
algorithm[5], matching parameters algorithm[6], FFT baseline estimation algorithm[8], phases of flat earth algorithm[9], etc.
Jin Guowang
National Key Laboratory of Science and Technology on Microwave Imaging
Institute of Electronics Chinese Academy of Science, Beijing, China
guowang_jin@
2011 International Conference on Communication and Electronics Information (ICCEI 2011)
Rational Function Model for Conversion of InSAR Unwrapped Phases to Heights
hn
=
(1 (1
xn xn
yn φn L yn3 φn3) ⋅ (a0 yn φn L yn3 φn3) ⋅ (1
Supposing that:
a1 L a19 )T b1 L b19 )T
（3）
( ) X = a0 a1 L a19 b1 b2 L b19 T
Then, the error equation can be described as:
In orientation and processing of photogrammetry, RFM has been studied and applied by many researchers. It is used in photogrammetry with high resolution optical images, such as IKONOS. Liu Jun researched RFM in positioning with stereo CCD images in 2003[2]. Qin Xuwen used RFM as SAR geometric model, his research showed that RFM can reduce the difficulty in processing of SAR photogrammetry in 2006 [4].
In order to improve the accuracy of derived heights, it needs to improve the accuracy of estimated baseline parameters or to convert unwrapped phases to heights with better models in processing of Interferometric Synthetic Aperture Radar (InSAR). The baseline parameters were often estimated by orbit parameter algorithm, ground control points algorithm, JPL baseline estimation
+a12 y2φ + a13φ 2 x + a14 y2 x + a15φ x2
+a16 yφ 2 + a17 x3 + a18 y3 + a19φ 3 Q(x, y,φ) = b0 + b1x + b2 y + b3φ + b4 xy + b5 yφ + b6φ x