Estimation of Uncompensated Trajectory Deviations and Image Refocusing for High-Resolution SAR Ievgen M. Gorovyi, Oleksandr O. Bezvesilniy and Dmytro M. Vavriv Department of Microwave Electronics, Institute of Radio Astronomy of NAS of Ukraine 4 Chervonopraporna Str., Kharkov 61002, Ukraine gorovoy@rian.kharkov.ua, obezv@rian.kharkov.ua, vavriv@rian.kharkov.ua Abstract— The accuracy of trajectory measurements is one of the crucial factors in high-resolution SAR imaging. Common navigation systems often do not fulfill the requirements that results in significant image quality degradation. In the paper, a new autofocus algorithm for the reconstruction of the SAR platform trajectory deviations is proposed. The approach is based on the estimation of the Doppler rate errors on a sequence of short-time intervals. The method is capable of estimation of time-varying and range-dependent phase error functions. The key steps of the developed technique are illustrated. The method is demonstrated on experimental data obtained with an X-band airborne SAR system. Keywords—synthetic aperture radar; autofocus; phase errors; residual trajectory deviations I. INTRODUCTION Synthetic aperture radar (SAR) is a well-known instrument for high-resolution imaging of the Earth surface [1]-[3]. The quality of obtained images strongly depends on the precision of SAR platform trajectory measurements [1], [4]-[7]. The problem is that the navigation systems have a limited precision and often do not fulfill the existing requirements. This results in uncompensated residual trajectory deviations, which lead to a significant SAR image quality degradation [2], [4]. In order to compensate the residual trajectory deviations, autofocus techniques are commonly applied [1]-[3]. The challenge is that there is no a universal autofocus algorithm. Some methods require the existence of bright targets on a scene, while other techniques are based on different analytical models for the residual phase error function. Recently a novel autofocus method called local-quadratic map-drift autofocus (LQMDA) was developed [8]. The approach is based on the estimation of local-quadratic phase errors on short-time intervals which are used for an arbitrary phase error reconstruction. The problem is that the residual phase errors can demonstrate considerable range dependence as the projection of the trajectory deviations on the radial direction considerably changes across the swath. Such range dependence should be carefully accounted. In the paper, we propose several important ideas that allow to improve the efficiency of the residual phase error estimation and successfully account its range dependence. In Section II, peculiarities of the SAR image formation on a short-time interval and ideas of the local quadratic phase error estimation are described. Important SAR image pre-processing steps that are applied before the cross-correlation calculation are introduced in Section III. An efficient trajectory restoration scheme with specifically chosen weighting coefficients is also described in this section. In Section IV, practical results of the application of the autofocus technique to the real SAR data obtained with an X-band airborne SAR system are provided. II. SAR PROCESSING AND LOCAL PHASE ERROR ESTIMATION ON A SHORT-TIME INTERVAL Generally, the residual uncompensated phase error ) , ( t R E ϕ in the backscattered radar signal is an arbitrary function. In airborne SAR systems, low-frequency phase errors are more critical [2], while the impact of fast-varying phase errors can be neglected in many cases. Recently, it has been shown that the phase error function can be efficiently described by using the local approximation principle [4]. According to this idea, the phase error on a short-time interval at a range gate R can be described in the following way: 2 / ) , ( ) , ( ) , ( ) , ( 2 τ ϕ τ ϕ ϕ τ ϕ n E n E n E n E t R t R t R t R ′ ′ + ′ + ≈ + , (1) where n t is the center of the considered short-time interval of duration S T , τ is the time within the short interval, 2 / 2 / S S T T < < − τ . In the approximation (1), the linear phase term τ ϕ ) , ( n E t R ′ causes the shift of the SAR image in the azimuth direction, while the quadratic phase error term 2 / ) , ( 2 τ ϕ n E t R ′ ′ leads to the image defocusing. Since the final SAR image represents only the intensity, the constant phase term ) , ( n E t R ϕ can be neglected. The length of the short-time intervals can be chosen to provide the sufficient precision of the local phase error approximation [8]. The key thing is that the local quadratic phase error ) , ( n E t R ϕ ′ ′ can be estimated with the map-drift principle via the formation of a pair of SAR images from two halves of a short- time interval [8]. For the formation of such images, a specifically modified version of the range-Doppler algorithm [9] can be used. Another option for the SAR synthesis on a short-time interval is the dechirp algorithm [2]. In this case, the computation burden can be significantly reduced and each of the SAR images can be obtained using a single short Fourier transform: 186 ISBN 978-3-9812668-6-3 © IMATech e.V. • Ratingen, Germany GeMiC 2015 • March 16–18, 2015, Nürnberg, Germany