1. Efficient Estimation of Residual Trajectory Deviations from SAR data
Institute of Radio Astronomy of the National Academy of Sciences of Ukraine
Efficient Estimation of Residual Trajectory Deviations from SAR data
O.O. Bezvesilniy, I. M. Gorovyi, D.M. Vavriv

2. Description of the Approach
Outline
Problem of Uncompensated Trajectory Deviations
A New Idea for Stripmap SAR Autofocus
Description of the Approach
Experimental Results

3. Trajectory Instabilities in Real Flight
Residual uncompensated deviations
Trajectory instabilities are inevitably exist in
real flight conditions.
Trajectory is measured with navigation system
and compensated in the SAR data
PROBLEMS
Even expensive navigation systems often do not provide
the sufficient measurement precision
The residual trajectory deviations are still exist
Defocused SAR image

4. Conventional Map-Drift Autofocus: Problem Statement
Image 1
Image 2
Two SAR images are built from radar data
The relative shift between the images can be used to determine the quadratic phase error
Quadratic phase error
Data acquisition
Polynomial approximation can be inefficient
Conventional map-drift autofocus cannot handle time-varying phase errors
Time-varying phase error
GOAL – the estimation of a time-varying arbitrary phase error functions

5. New Approach for an Arbitrary Phase Error Estimation
- length of the short interval
IDEA
Phase error and local quadratic approximations
We use independent estimates
on short time intervals for an arbitrary
phase error reconstruction
Phase error and local quadratic approximations
RESULT
We obtain the sequence of the estimated residual phase error second derivatives
The phase error can be retrieved via double integration

6. SAR Processing on Short Time Interval
After SAR processing on short time interval
we obtain SAR image of whole antenna footprint
REAL EXAMPLE
Data acquisition on short time interval
Antenna footprints on the ground
Short time interval can be divided into two parts
In the presence of a phase error, there will be a shift between two SAR images
This shift can be measured with local Map-Drift Autofocus
SAR image of the antenna footprint

7. Local Map-Drift and Short Time Intervals
The local quadratic phase error in the signal:
SAR images are built as a convolution of the short signal with the long reference function:
The obtained synthetic patterns:
Shifted and defocused SAR images (looks) (accurate solution)
Shifted SAR looks (sinc-approximation)
The relative shift between synthetic patterns is

8. Calculation of SAR Images Correlation
Local Correlation
For better estimation of the local quadratic phase error we use the locally-centered images.
The correlation peak is well noticeable for the centered SAR images.
SAR images built on the short time interval

9. Processing of Range Blocks
PROBLEM – range dependence of the residual phase errors should be accounted
SAR images can be divided on several range blocks
Estimation of time-shift within the particular range block gives the value of Doppler rate error
The sequences of Doppler rate error estimates can be used for the
trajectory restoration

10. Evaluation of residual trajectory deviations
The Doppler rate error can be approximated as
One can construct the MSE:
REMARKS
Residual along-track acceleration can be neglected
Derivation of trajectory components from Doppler rate errors
We assume that residual velocity errors and residual trajectory deviations do not have any linear trends on considered interval T

11. Local-Quadratic Map-Drift Autofocus Scheme2 1 3 4 5
1. Input raw data buffer is divided on azimuth blocks
2. Each block is divided on two parts which are processed by SAR processing algorithm
3. Doppler rate errors are estimated within several range blocks
4. Cross-acceleration components are evaluated
5. Residual trajectory deviations are reconstructed via double integration

12. LQMDA Performance :Example I
Compensation of the estimated residual trajectory deviations leads to SAR image refocusing
Small-scale objects and shadows become well noticeable
SAR image before autofocusing
Refocused SAR image

13. LQMDA Performance :Example II
Refocused SAR image
SAR image before autofocusing
Refocused SAR image

14. CONCLUSIONS SAR autofocusing is necessary for high-resolution imaging.
Polynomial phase error approximation
can be often inefficient.
The proposed autofocus approach
can handle time-varying and range
dependent phase errors.
Local-Quadratic Map-Drift Autofocus
allows effective refocusing of SAR
images.

15. Thank you!