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 www.radar.kharkov.com

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

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

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

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

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

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

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

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

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

Local-Quadratic Map-Drift Autofocus Scheme 2 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

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

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

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.

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