Amaya Medrano Ortiz

A Bistatic Point Target Reference Spectrum for General Bistatic SAR Processing

A bistatic point target reference spectrum (BPTRS) based on Loffelds bistatic formula (LBF) is derived in this letter. For LBF, the same contributions of the transmitter and receiver to the total azimuth modulation are assumed. This assumption results in the failure of LBF in the extreme configuration (i.e., spaceborne/airborne configuration). For general bistatic configurations, the azimuth modulations are unequal for the transmitter and receiver due to the different slant ranges and velocities. Therefore, the azimuth time-bandwidth products (TBPs) from the transmitter and receiver are different; in some cases (e.g., spaceborne/airborne case), one of them might be very small, which might even result in a serious error of the principle of stationary phase. This letter uses TBP to weight the azimuth phase modulation contributions of the transmitter and receiver to the common azimuth spectrum to approximately obtain the point of stationary phase of the total azimuth phase history. Simulations show that the proposed BPTRS can work well for spaceborne/airborne configurations.

First steps to bistatic focusing

Although this work is a bit theoretical and contains lots of derivations, it leads to very explicit practical results in bistatic focusing. Our approach is based on Loffelds bistatic formula describing the point targets reference spectrum for arbitrary bistatic configuration. Based on various simulations the validity of LBF for both airborne and spaceborne configurations is demonstrated. Focusing for special bistatic configurations like: Tandem and Translationally Invariant constellations is considered. The focusing for the Tandem configuration is solved analytically. Focusing in the TI case is realized by blockwise processing. All focusing algorithms are developed in IDL and adequate simulation results are presented. In the end of the paper outlines the conceptual solution of the most difficult bistatic General Case and presents some first focusing results.

A Solution for Bistatic Motion Compensation

Bistatic synthetic aperture radar (SAR) missions have become attractive in the last years, because of their higher degree of freedom in choosing transmitter and (passive) receiver motion trajectories. In order to take advantage of this increased imaging flexibility, adequate processing algorithms have to be developed, implemented and verified with experimental data. Currently some promising approaches have been published in this area. A further step in improving the focusing results within a bistatic SAR constellation where transmitter and receiver are mounted on different platforms essentially comprises the bistatic motion compensation (MC). We present a geometrical MC approach which requires high accurate position and velocity information of transmitter and receiver.

Comparison of doppler centroid estimators in bistatic airborne SAR

In the last years, many advances in SAR processing have taken place, but especially when regarding bistatic processing it is implicitly clear that correct processing parameters such as the bistatic Doppler centroid are even more crucial to obtain precisely focused images. In this paper, two Doppler centroid estimators are compared with respect to bistatic SAR data. Starting from classical approaches (e.g. Correlation Doppler Estimator –CDE-), which make use the correlation of the power signal spectra with some weighting function, the analysis is performed on a two dimensional field of sampled rangecompressed data. Since these algorithms may present Doppler ambiguities, other results are obtained by means of the Radon transform which is a geometry-based Doppler Centroid Estimator (GDE). As it is known, this approach estimates an ambiguity-free Doppler centroid, and can be made computationally efficient. Since the GDE is a very new technique for the monostatic SAR geometry, our first results with bistatic airborne data are very positive and will be presented in this paper. Keywords— SAR, Doppler centroid, CDE, GDE, Radon transform, Squint angle

Focusing bistatic SAR data in the wavenumber domain using linearized weighted LBF

A weighting solution based on the original Loffelds bistatic formula (LBF) is addressed briefly in this paper to deal with the cases with noticeable difference between transmitter and receivers velocities. The published LBF-based approaches use range blocks to deal with the range variance. Alternatively, a new wavenumber domain algorithm is proposed by using the linearization of bistatic range, which follows the same routine of the monostatic Omega-K algorithm. The approximation in this range linearization is examined with space-surface hybrid and airborne bistatic configurations. Due to large phase error for the airborne case, a second phase multiply have to be used in its focusing. This approach results in a good focusing performance over simulated data.

Second-order motion compensation in bistatic airborne SAR based on a geometrical approach

Common efficient SAR processing algorithms are based on nominal operational conditions. Unfortunately, due to atmospheric turbulences and maneuvering errors, these conditions are often violated in real SAR systems. Hence, a crucial problem in most airborne SAR systems is the compensation of motion errors; if not corrected, the image quality will considerably degrade. A first-order motion compensation (MoCo) technique was developed at our institute, based on a precise knowledge of the position and the velocity of the transmitter and the receiver. The problem arose while proceeding with our processing algorithm, since the reconstructed image was better focused but not completely focused. Our paper proposes a second-order MoCo technique that will considerably improve the reconstruction of the SAR image. While the first-order MoCo considered the range and azimuth times, the second-order MoCo approximation will consider the frequencies. Experiments with different sets of bistatic airborne SAR data are performed based on this solution, and some promising results are given.

Second-Order Motion Compensation in Bistatic Airborne SAR based on the Windowed Fourier-Transformation

A crucial problem in most airborne Synthetic Aperture Radar (SAR) systems is the compensation of motion errors to prevent the image degradation. If these errors are not compensated, some undesired effects will appear, such as loss of geometric resolution and radiometric accuracy, reduction of image contrast, azimuth ambiguities and strong phase distortions. For the bistatic airborne SAR systems, the motion errors become more complex since two separate trajectory deviations contribute to these errors. This paper proposes an approach that will compensate the bistatic motion errors in the frequency domain.

Evaluation of analytic point target spectra for bistatic SAR

The 2-dimensional frequency domain formulation for Bistatic SAR image formation received intensive and continuous interests recently. Due to the double square roots in the range equation, additional efforts have to be taken in deriving its point target reference spectrum. Loffelds bistatic formula and the spectrum based on the method of series reversion are both derived for general bistatic geometries, and a few focusing algorithms have been developed by basing on them. Most recently, LBF was modified to accommodate both the motion difference of bistatic platforms and high squinted geometries. We present the numeric comparison of these two methods using the simulated bistatic data. The focusing performance of point targets and their capability of accommodating range variance are examined in this paper.