A WEIGHTED CALIBRATION METHOD OF INTERFEROMETRIC

SAR DATA

Yongfei MaoMaosheng Xiang

Lideng Wei Daojing Li

Bingchen Zhang

Institute of Electronics, Chinese Academy of Sciences, Beijing, China

Contents

Abstract

Calibrate method based on sensitivity equations

Weighted calibrate method

Derivation of the weightings

Experimental results

Abstract

The accuracy of DEM generated by InSAR partly

depends on the accuracy of system parameters, so it is necessary to calibrate the system parameters.

The traditional calibration method models the elevation error as a linear function of parameter biases, and solves the biases through the sensitivity equations.

This paper presents a weighted calibration method. It introduces weightings to the sensitivity equations to discriminate the ground control points with different correlation coefficients and locations

This weighted calibration method can improve the DEM accuracy.

Calibrate method based on sensitivity equations

[ ][ ]T

h h h h hh B r H

B r H

h h h h hB r H

B r H

The elevation error can be modeled as a linear function of parameter errors.

It is a good approximation for small parameter errors.

Baseline lengthBaseline anglePhase offsetSlant rangeFlight altitude H

r

B

Calibrate method based on sensitivity equations

All of the control points have sensitivity equations, and they can be written as

where

H = F X

1 1 1 1 11

NN N N N N

h h h h h

B r H

h h h h h

B r H

F

F

F

TB r H X

1

T

Nh h H =

Calibrate method based on sensitivity equations

To acquire the biases of interferometric parameters , the equation below needs to be solved.

It is equal to make minimum.

The biases given below is the solution.

This calibration technique is iterative.

H = F X

X = F H

X

F X - H

2

1

min minN

n nn

h

X XF X - H F X

Weighted calibrate method

The error of interferometric phase varies from point to point, so the sensitivity equations of each control point have different errors.

Therefore, it is reasonable to introduce different weightings to the sensitivity equations of different control points.

Weighted calibrate method

With the weightings, solving

is equal to make minimum.

where .

Therefore, the solution is given below.

The weighted calibration technique is iterative.

22

1

2

1

min min

min

min

N

n n nn

N

n n n nn

k h

k k h

ΛX X

X

X

F X - H F X

F X

ΛF X - Λ H

1, ..., Ndiag k kΛ

X = ΛF Λ H

H = F X

ΛF X - H

Derivation of the weightings

The error of interferometric phase due to

decorrelation can be calculated by

where is the "number of looks", is the correlation coefficient.

The elevation error due to phase errors can be calculated by

where is the sensitivity of the elevation to the interferometric phase.

2

2

11

2n

nnLN

h

2

2

11

2n

n n n nnL

h hh

N

LN n

Derivation of the weightings

The elevation error makes a linear contribution to . To remove this linear contribution, we can design the weighting as a inverse proportion function of .

where is the constant coefficient and can be solved from the unitary equation bellow.

Then we can get the constant coefficient

nn

pk

h

1

N

nn

k N

1

1N

n n

Np

h

F X - H

nh

p

Derivation of the weightings

The weighting of No. control point can be written as

Therefore, using weighted calibrate method the biases of interferometric parameters can be acquired from the equation bellow.

where .

1

1n N

nn n

Nk

hh

n

1, ..., Ndiag k kΛ

X = ΛF Λ H

Experimental results

The weighted calibration method has

been applied to airborne InSAR data.

Methods RMS error (m)weighted calibration 0.9351traditional calibration 1.0834

Fig.1 SAR image Fig.2 DEM image

The elevation error of check points by

using weighted calibration method and traditional calibration method is shown below.

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