COMPARISON OF GEOMETRY-BASED DOPPLER
AMBIGUITY RESOLVER IN SQUINT SAR
AN INDIRECT DOPPLER RATE ESTIMATION
SCHEME OF SAR IN LOW-CONTRAST SCENE
Wenchao Li
University of Electronic Science and Technology of China

Introduction
An important remote sensing tool.
• Monostatic SAR
• Bistatic SAR
• Stripmap SAR
• Scan SAR
• Spotlight SAR
• Side-looking SAR
• Squint-looking SAR
……

Introduction
z v

R
B y
O
Geometry model
P
Squint angle x

Introduction
Range History ：
R t

R t
0
 v sin

( t t
0
)
 v
2 cos
2

R t
0
( )
0
2
 The linear term is range walk
 The quadratic term is range curvature

Introduction
After range walk correction, the azimuth data can be modeled as a linear frequency modulated (LFM) signal,
( )
  dc

1 j f t f t
2 dr
2
)]
• f dc
• f dr

Introduction
In principle, it is possible to compute Doppler parameter from prior information provided by GPS/INS, but measurement uncertainties on the information will limit the accuracy. f dc

2 v
 sin
 f dr
  v
2
2 cos
2

R


Introduction
An incorrect Doppler centroid
• a loss of SNR;
• an increase in the azimuth ambiguity level;
• a shift in the location of the target;
…...
An incorrect Doppler rate would blur the image.
Incorrect Doppler rate
Correct Doppler rate

Introduction

Doppler centroid estimation
As azimuth data are sampled by pulse repetition frequency (PRF), there is always Doppler centroid ambiguity, and the bigger the squint angle is, the more serious the doppler ambiguity will be.
Doppler centroid is usually expressed in two parts: the baseband Doppler centroid and Doppler ambiguity number . f dc

M amb

PRF
 f

Doppler centroid estimation
• Multiple PRF
• Wavelength diversity algorithm (WDA)
• Multilook algorithms (MLCC,MLBF)
• Geometry-based algorithms

Geometry-based algorithms
The relationship between Doppler centroid and range walk slope, f dc
 
2 ( )
 dt

0
 
2

K
Then Doppler centroid can be computed via estimating the range walk slope.
Since this method is based on the geometric characteristics of the range compressed data, it is named as a geometry-based Doppler ambiguity resolver.

Geometry-based algorithms
Range compressed data
Radon transform
Calculate the range walk slope
Output the Doppler centroid
Radon transform:
• A well-known tool for detecting slope.
• It integrates intensity along every possible direction in the image and maps this information into a feature space.
• It involves two-dimensional search.

Geometry-based algorithms
Range compressed data
Initialize the range walk slope
Range walk correction
Integrate energy over azimuth
Compute waveform entropy
Has minimum entropy been obtained ?
Yes
Output the corresponding range walk slope
Output Doppler centroid
No
The slope is seen as a searching variable, and entropy is used to measure the robustness of signal.
Update the range walk slope
It utilizes the prior information of platform, and replaces the Radon transform with a simple integration of image intensity over azimuth.

Geometry-based algorithms
Range compressed data
Edge detection
Set transform region and step size, and do the coarse Radon transform
Update the transform region and step size, and do the fine Radon transform
Calculate the range walk slope
Output the Doppler centroid
This scheme utilizes prior information of platform, convert the data into binary data, and conduct two-step Radon transform, which would make it is sparse and reduce the need to search the whole feature space .

Comparisons
C OMPARISONS FOR DIFFERENT DOPPLER AMBIGUITY NUMBER
Geometry-based
Doppler resolver
Conventional Radon transform
Iterative scheme
Improved Radon transform scheme
True value
6
6
6
Estimated value
6
6
6
Computation time
14.57
1.48
0.62
s s s
It is obviously that they can give the accurate Doppler ambiguity number. While the speed of the iterative scheme and the improved Radon transform scheme is much faster than conventional Radon transform.

(Autofocus)

Doppler rate estimation
Parametric Method
• Metric-based Autofocus
(Entropy/Contrast)
•
• Map Drift (MD)
Nonparametric Method
• Prominent Point Processing (PPP)
• Phase Gradient Autofocus (PGA)
• Time-Frequency Analysis

Doppler rate estimation
• Low SNR
• Without prominent point

Estimation Scheme
According to the fact that Doppler rate is inversely proportional to range, f dr 1
  v
2
2 cos
2


R
1 f dr 2
 
2 v
2 cos
2


R
2 f dr 2

R f dr 1
R
2
1
It indicates that the Doppler rate in lowcontrast scene can be estimated indirectly.

Estimation Flowchart
Range compressed data
Range walk correction
Choose the range bin that contains bright line
Wigner-Ville distribution
Radon transform
Output the Doppler rate of the range bin
Doppler rate in highcontrast scene is estimated first using Radon-Wigner transform, and then using the fact that Doppler rate is inversely proportional to range, Doppler rate in lowcontrast scene is estimated indirectly.
Fit the Doppler rate of the range bin in low-contrast scene

Results
Time frequency analysis
Time frequency analysis
High Contrast Scene
With Prominent Point
Radon transform
Radon transform
Low Contrast Scene
Without Prominent
Point

 The geometry-based scheme can be used to resolve
Doppler ambiguity of SAR with large migration.

The speed of improved Radon transform scheme and the iterative scheme is about ten times faster than conventional Radon transform scheme.

An indirect estimation scheme of Doppler rate for low contrast scene is developed.

The indirect scheme is effective, and it can reduce computation time greatly.