使用CS算法机载SAR高精度成像处理的运动补偿

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,

VOL.

32, NO.

SEPTEMBER 1994

I029

Airbome SAR Processing

Highly Squinted Data

Using

Chirp Scaling Approach with Integrated

Motion Compensation

Albert0 Moreira,

Member,

IEEE,

and Yonghong Huang

Abstract-This paper proposes a new approach for high-res-

olution airborne

SAR

data processing, which uses a modified

chirp scaling algorithm to accommodate the correction of mo-

tion errors, as well

the variations of the Doppler centroid in

range and azimuth. By introducing a cubic phase term in the

chirp scaling phase, data acquired with a squint angle up to

30"

can be processed with no degradation of the impulse re-

sponse function. The proposed approach is computationally

very efficient, since it accommodates the variations of Doppler

centroid without using block processing. Furthermore, a mo-

tion error extraction algorithm can be incorporated into the

proposed approach by means of subaperture processing is azi-

muth. The new approach, denoted as extended chirp scaling

(ECS),

is considered to be a generalized algorithm suitable for

the high-resolution processing of most airborne

SAR

systems.

I. INTRODUCTION

raw data consist of a coherent superposition of the

backscattered echoes from the imaged scenario. The

backscattered echoes are modulated by the transmitted

pulse (Le., chirp signal) and by the natural movement of

the sensor (Doppler effect). The image formation process

consists of compressing the signal of each scatter, which

is time dispersed (modulated) in the along-track (azimuth)

and cross-track (range) directions. The first direct step in

a time-domain SAR processor consists of the range

compression, which is a one-dimensional correlation of

each received echo with the complex-conjugated time-in-

verted replica of the transmitted pulse. Then, azimuth

compression is performed. Due to the range migration of

each target during the azimuth illumination time and due

to the variation of the Doppler modulation as a function

the range distance, the azimuth compression consists

of a two-dimensional correlation of the range-compressed

signal with a space-variant reference function. The final

amplitude image can be calibrated in order to give a re-

flectivity map of the scenario for a given frequency and

polarization. Furthermore, if the phase of the final image

is also calibrated, a full polarization matrix can be formed

Manuscript received November

1993; revised March 17, 1994.

A. Moreira is with the Institute

for

Radio Frequency Technology, Ger-

man Aerospace Research Establishment (DLR), D-82230 Oberpfaffenho-

fen, Germany.

Huang is with the Department

Electronic Engineering, Beijing

100083,

People's

Republic

China.

IEEE Log Number 9403635.

that allows a better classification and interpretation of the

image.

In practical cases, the range and azimuth frequency

modulations consist of several hundred points,

that the

correlation process is carried out with reduced computa-

tional effort in the frequency domain by means of a fast

Fourier transform (FFT). This is the basic concept of the

hybrid algorithm

[24],

which performs a one-dimensional

frequency-domain correlation for range processing and

then generates a two-dimensional time-domain azimuth

reference function that is correlated in the Doppler-fre-

quency domain with the azimuth signal. This approach is

very accurate with a limitation concerning the update of

the azimuth reference function with range. This update is

done according to the required depth of focus in azimuth.

Otherwise, a new two-dimensional azimuth reference

function should be generated for each range position. The

update of the azimuth reference function decreases the

phase accuracy of the final image, although it has a minor

effect in the image intensity. The phase accuracy is very

important as far as polarimetric and interferometric appli-

cations are concerned.

The computational efficiency of the hybrid algorithm is

very low if the range migration (especially the range walk)

becomes large. In order to increase the efficiency, the

range migration can be corrected after range compression

by means of an interpolation,

that the azimuth corre-

lation in the frequency domain becomes a one-dimen-

sional process. Due to the fact that the range migration of

all targets located at the same range distance is equal, the

interpolation can efficiently be performed in the range-

time Doppler-frequency domain. The range-Doppler al-

gorithm

[5],

[ll]

uses an interpolation kernel (e.g., sinc

function) to correct the range migration in this domain.

For high squint angles, some complications arise in the

range-Doppler algorithm due to the coupling of the range

and azimuth signals

[ll].

Briefly, the range frequency

modulation is altered in the range-Doppler domain ac-

cording to the amount of squint angle. Several methods

have been proposed to correct this change

[4],

[20],

which

causes a defocusing of the range impulse response func-

tion (IRF). The correction of this change has been called

secondary range compression

(SRC).

A more accurate algorithm is the wavenumber algo-

0196-2892/94$04.00

1994 IEEE

rithm

[18],

which is based on wave propagation theory

commonly used in seismic processing. This algorithm can

also be interpreted as a two-dimensional frequency cor-

relation, whereby a two-dimensional FFT is used to trans-

form the signal from the time domain to the wavenumber

domain. The spatial variation of the azimuth signal is cor-

rected by the so-called Stolt interpolation. After adequate

phase correction, a two-dimensional IFFT (inverse FFT)

is used to form the final image. Several different imple-

mentations of this algorithm have been proposed in the

last few years

[3],

[8],

[9]

and are summarized and ana-

lyzed in terms of processing accuracy in

[

l].

The range-Doppler and the wavenumber algorithm have

mostly been used for efficient SAR processing. However,

both algorithms need interpolation for the range cell mi-

gration correction (RCMC) or for the Stolt change of vari-

ables. In general, the interpolation not only causes phase

errors and amplitude artifacts in the SAR image, but also

decreases the computational efficiency.

The chirp scaling (CS) algorithm has recently been pro-

posed for high-quality SAR processing

[6], [19].

This al-

gorithm avoids any interpolation in the SAR processing

chain and is suitable for the high-quality processing of

several spaceborne SAR systems (e.g., SEASAT, ERS-

RADARSAT). It consists basically of multiplying the

SAR data in the range-Doppler domain with a quadratic

phase function (chirp scaling) in order to equalize the

range cell migration for a reference range, followed by an

azimuth and range compression in the wavenumber do-

main. After transforming the signal back to the range-

Doppler domain, a residual phase correction is carried out.

Finally, azimuth IFFT's are performed to generate the fo-

cused image. It has been shown in

[17]

and

[22]

that the

image quality and the phase accuracy of the chirp scaling

algorithm is equal or superior to that of the range-Doppler

algorithm.

For spaceborne SAR systems, the CS algorithm can be

used to process data with up to approximately

20"

squint

angle in L-band without deterioration of the IRF

[7].

The

SRC is corrected for a reference range in the range-Dopp-

ler domain before range compression and it is updated

with the azimuth frequency. In order to accommodate

higher squint angles, a nonlinear phase term can be intro-

duced into the processing or into the transmitted pulse

[7].

In the former case, the nonlinear phase term is added in

the wavenumber domain before applying the quadratic

chirp scaling phase function. The image quality provided

by the chirp scaling algorithm in the case

spaceborne

SAR processing is excellent.

However, airborne SAR processing requires an update

of the Doppler centroid as a function of the range distance

and an accurate time-domain motion compensation, which

must also be updated with the range distance. The above-

mentioned requirements cannot be included in the original

chirp scaling algorithm, since it is basically a frequency

domain focusing approach. Some alternative methods can

be implemented in the original chirp scaling algorithm in

order to incorporate the Doppler centroid variations (e.g.,

block processing, increase of the azimuth FFT size with

adaptive bandpass filtering of the processed image

[

151).

In this case, the computational efficiency

the chirp scal-

ing algorithm decreases considerably, and no accurate

motion compensation can be performed.

The new algorithm, denoted as extended chirp scaling

(ECS), has been developed for the processing of airborne

data with strong motion errors (e.g., E-SAR system,

[lo])

and with variable Doppler centroid in range and/or azi-

muth.

One unique characteristic of the ECS algorithm is the

extension of the azimuth spectrum in the range-Doppler

domain for accommodating the variations of the Doppler

centroid in range. Additionally, short azimuth spectra

(subaperture processing) allow the inclusion of the Dopp-

ler variation in azimuth as well as the incorporation of the

so-called reflectivity displacement method (RDM) in the

processing for second-order motion compensation.

Unlike other chirp scaling implementations, a deter-

ministic cubic phase term

added by the extended chirp

scaling method during the equalization of the range cell

migration,

that no deterioration of the geometric res-

olution is measured up to a

30"

squint angle in the C-band

mode of the E-SAR system.

This paper is organized as follows. The next section

shows the mathematical formulation of the extended chirp

scaling (ECS) algorithm, including the accurate motion

compensation and the highly squinted data processing.

Several simulation results are presented in order to vali-

date the proposed approach. Section I11 extends the ECS

algorithm to include the update of the Doppler centroid

with range. The proposed azimuth spectral extension is

extremely accurate, and is based on the fact that the vari-

ation of the Doppler centroid as a function

the range

distance can be precisely accommodated if the chirp scal-

ing phase function is extended in the azimuth frequency

by the amount of the Doppler centroid variation. Section

IV describes the azimuth subaperture processing, which

allows the Doppler centroid to be updated in each sub-

aperture. In addition, the frequency displacement of the

cross-correlation result between adjacent subapertures

gives information about the acceleration in line of sight

[

141,

which

used for the second-order motion compen-

sation. In Section

the results of the image processing

with strong motion errors are presented and analyzed.

Section VI concludes the paper and gives some sugges-

tions for future work.

11. EXTENDED CHIRP SCALING ALGORITHM

Modeling the Received Signal

We consider in this section an airborne-side-looking

geometry with constant squint angle.

The hyperbolic

equation of the range history for a point target is ex-

pressed as

~(t;

ro>

Jri

tCl2

(1)

where

is the range to target at the closest approach,

is the aircraft velocity,

is the azimuth time measured in

I030

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,

VOL.

32,

NO.

SEPTEMBER

1994

~~~ ~~

the flight direction, and

is the time at the center of the

azimuth illumination path, which is related to the Doppler

centroid

fdc

by the following equation:

where is the radar wavelength. After demodulation, the

two-dimensional received SAR signal

s(7,

ro)

of a point

target can be written as

R(t; ro)

exp

[-j

(3)

The azimuth antenna pattern

and the envelope

of the

transmitted pulse are slowly varying functions relative to

the signal variations in the azimuth time

and range time

(range delay)

(3),

the first exponential term accounts

for the range chirp with frequency modulation rate

and

for the range migration. The last term in

(3)

is the azimuth

(Doppler) modulation. In a special case, where the squint

angle and azimuth illumination time are small, the range

migration in the first exponential term of

(3)

can be ne-

glected and the received signal is approximated to two

one-dimensional functions. In practical cases, however,

the range migration leads to a coupling between the range

and azimuth modulations,

that the received SAR signal

of each target becomes a two-dimensional space-variant

function.

Due to the large time-bandwidth product of the re-

ceived SAR signal, the principle of the stationary phase

[16] can be used to obtain a signal formulation in the

wavenumber domain. In this domain, the form of the azi-

muth antenna pattern and the envelope of the transmitted

pulse remains the same. By performing a series expansion

in the range frequency and an inverse Fourier transfor-

mation in range, the signal formulation in the range-

Doppler domain is given by

[

161

S(7,fa;

ro)

(

";fa;

ro))

)

*.tu

[(

.fa)l(2

v)I2

..,(

exp

[

-j

k(f,;

ro)

where

is a complex constant andf, is the azimuth fre-

quency, which varies within the following range:

(5)

PRF PRF

+fdC%t3fdC+F.

The last term in

(4)

corresponds to the azimuth modula-

tion in the frequency domain. The first exponential term

(4)

shows that the frequency modulation of the range

chirp is now dependent on the azimuth frequency and the

range distance. If this variation

not considered, the

range IRF for high squint data processing will be defo-

cused. The modified range-frequency modulation basi-

cally consists

two terms:

where

(2)2.

(7)

MOREIRA AND HUANG. SAR PROCESSING USING CHIRP SCALING WITH

MOTION

COMPENSATION

1031

-~~I

The correction of the term

k,,

in the range processing is

called secondary range compression (SRC). The tradi-

tional chirp scaling algorithm assumes one reference range

for the SRC and updates it with the azimuth frequency.

The missing update of the SRC with range causes a phase

error in the range compression for ranges different from

the reference range. This phase error

insignificant for a

squint angle up to approximately

20"

in the case of

L-band spaceborne SAR systems

[7].

Chirp Scaling with Cubic Phase Term

The range migration in the range-Doppler domain can

be expressed as

where

a(f,)

is the linear chirp scaling factor given by

In the case of airborne SAR, the scaling factor

fa)

not

independent on range,

that a linear scaling in range

leads to a perfect equalization of the RCMC, if the SRC

term can be neglected. The traditional chirp scaling

method performs this equalization by means of a qua-

dratic phase term in the range-Doppler domain. Actually,

the scaling consists of changing the position of the phase

minimum of each chirp signal.

explicit interpolation

is carried out.

The quadratic phase term of the chirp scaling intro-

duces a frequency offset in the range chirp signal, which

can assume values as high as several megahertz for high

squint angle. If the frequency offset is high enough

that

the signal bandwidth is aliased or shifted outside of the

剩余11页未读，继续阅读

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zyx263

2012-12-22

很好的文章。。关于CS算法
raymond2464

2014-09-13

看这个学习材料，有收获！
likun8999

2012-12-03

本领域一篇十分经典的文献，很有收获。

raferpy

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