On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging
Abstract
Synthetic Aperture Radar (SAR) imaging is a class of coherent range and Doppler signal processing techniques applied to remote sensing. The aperture is synthesized by recording and processing coherent signals at known positions along the flight path. Demands for greater image resolution put an extreme burden on requirements for inertial measurement units that are used to maintain accurate pulsetopulse position information. The recently developed Phase Gradient Autofocus algorithm relieves this burden by taking a datadriven digital signal processing approach to estimating the rangeinvariant phase aberrations due to either uncompensated motions of the SAR platform or to atmospheric turbulence. Although the performance of this fourstep algorithm has been demonstrated, its convergence has not been modeled mathematically. A new sensitivity study of algorithm performance is a necessary step towards this model. Insights that are significant to the application of this algorithm to both SAR and to other coherent imaging applications are developed. New details on algorithm implementation identify an easily avoided biased phase estimate. A new algorithm for defining support of the point spread function is proposed, which promises to reduce the number of iterations required even for rural scenes with low signaltoclutter ratios.
 Authors:
 Publication Date:
 Research Org.:
 Sandia National Labs., Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE, Washington, DC (United States)
 OSTI Identifier:
 211363
 Report Number(s):
 SAND952364
ON: DE96008071; TRN: 96:002377
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Technical Report
 Resource Relation:
 Other Information: PBD: Jan 1996
 Country of Publication:
 United States
 Language:
 English
 Subject:
 44 INSTRUMENTATION, INCLUDING NUCLEAR AND PARTICLE DETECTORS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; RADAR; IMAGE PROCESSING; ALGORITHMS; CONVERGENCE; ANTENNAS; FOCUSING
Citation Formats
Hicks, M.J.. On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging. United States: N. p., 1996.
Web. doi:10.2172/211363.
Hicks, M.J.. On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging. United States. doi:10.2172/211363.
Hicks, M.J.. 1996.
"On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging". United States.
doi:10.2172/211363. https://www.osti.gov/servlets/purl/211363.
@article{osti_211363,
title = {On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging},
author = {Hicks, M.J.},
abstractNote = {Synthetic Aperture Radar (SAR) imaging is a class of coherent range and Doppler signal processing techniques applied to remote sensing. The aperture is synthesized by recording and processing coherent signals at known positions along the flight path. Demands for greater image resolution put an extreme burden on requirements for inertial measurement units that are used to maintain accurate pulsetopulse position information. The recently developed Phase Gradient Autofocus algorithm relieves this burden by taking a datadriven digital signal processing approach to estimating the rangeinvariant phase aberrations due to either uncompensated motions of the SAR platform or to atmospheric turbulence. Although the performance of this fourstep algorithm has been demonstrated, its convergence has not been modeled mathematically. A new sensitivity study of algorithm performance is a necessary step towards this model. Insights that are significant to the application of this algorithm to both SAR and to other coherent imaging applications are developed. New details on algorithm implementation identify an easily avoided biased phase estimate. A new algorithm for defining support of the point spread function is proposed, which promises to reduce the number of iterations required even for rural scenes with low signaltoclutter ratios.},
doi = {10.2172/211363},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1996,
month = 1
}

Comparison of synthetic aperture radar autofocus techniquesPhase gradient vs subaperture
Two methods of focusing synthetic aperture radar (SAR) images are compared. Both a conventional subaperture crosscorrelation method and a new phase gradient autofocus (PGA) algorithm developed at Sandia National Laboratories are shown to perform well if highorder phase errors are not present. With the introduction of significant highorder phase errors (e.g., due to uncompensated platform motion), both algorithms suffer a loss in performance. However, relative performance degradation is less for PGA than for the subaperture focusing technique. An explanation is presented for the observed behavior of the two autofocus techniques. 8 refs., 8 figs. 
Autofocus correction of excessive migration in synthetic aperture radar images.
When residual range migration due to either real or apparent motion errors exceeds the range resolution, conventional autofocus algorithms fail. A new migrationcorrection autofocus algorithm has been developed that estimates the migration and applies phase and frequency corrections to properly focus the image. 
The phase gradient autofocus algorithm: An optimal estimator of the phase derivative
The phase gradient algorithm represents a powerful new signal processing technique with applications to aperture synthesis imaging. These include, for example, synthetic aperture radar phase correction and stellar image reconstruction. The algorithm combines redundant information present in the data to arrive at an estimate of the phase derivative. In this report, we show that the estimator is in fact a linear, minimum variance estimator of the phase derivative. 7 refs.