Real-Time Motion Compensation , Image Formation and Image Enhancement of Moving Targets in ISAR and SAR Using S-method Based Approach

The commonly used technique for ISAR/SAR signal analysis is a two dimensional Fourier transform, which results in an image of the target’s reflectivity mapped onto a range and cross-range plane. However, in cases where the line-of-sight projections of the target’s point velocities change or there is uncompensated movement within the coherent integration time, the Fourier transform produces blurred images. For target recognition applications, mainly those in military surveillance and reconnaissance operations, a blurred ISAR image has to be refocused quickly so that it can be used for real-time target identification. Two standard techniques used for improvement of blurred ISAR images are motion compensation and the use of quadratic time-frequency representations. Both are computationally intensive. In this paper, we present an effective quadratic time-frequency representation, the Smethod. This approach performs better than the Fourier transform method by drastically improving images of fast manoeuvring targets and by increasing the SNR in both low and high noise environments. These advantages are a result of the S-method’s ability to automatically compensate for quadratic and all even higherorder phase terms. Thus, targets with constant acceleration will undergo full motion compensation and their point-scatterers will each be localized. It should be noted that the source of the quadratic term can come from not only acceleration, but also non-uniform rotational motion and the cosine term in wide-angle imaging. The method is also computationally simple, requiring only slight modifications to the existing Fourier transform based algorithm. The effectiveness of the S-method is demonstrated through application to simulated and experimental data sets. IET Signal Processing, Vol. 2, No. 3, Aug. 2008. I. I Inverse synthetic aperture radar (ISAR) is a powerful signal processing technique that can provide a two-dimensional image of an area or target of interest. Being radar based, this imaging technique can be employed in all weather and day/night conditions. ISAR images are obtained by coherently processing the received radar echoes of the transmitted pulses. Commonly, the ISAR image is characterized by high resolution along both the range and cross range dimensions. High resolution in the range dimension is achieved by means of large bandwidth pulses, whereas high cross-range resolution is obtained by exploiting a synthetic aperture technique. In ISAR, the synthetic aperture can be generated by motion of the target as well as by motion of the radar platform. In contrast, the related imaging technique of synthetic aperture radar (SAR) has its synthetic aperture generated by means of radar platform motion only [1], [2]. The inverse synthetic aperture is formed by the coherent integration of signals obtained from the fixed aperture radar as the target translates and rotates “within the radar’s beam width”, creating the equivalent of a large circular aperture focused at the target’s center-of-rotation [3], [4]. The underlying concept in ISAR imaging is to use the Doppler information provided by the different velocities, relative to the radar, of individual scatterers to obtain high cross range resolution. That is, we decompose the target (spatially) into a set 1354 TIME-FREQUENCY SIGNAL ANALYSIS of individual “point” scatterers each of which has a different Doppler velocity represented by Doppler frequency shifts. Thus, the distribution of the target’s reflectivity function can be measured by the Doppler spectrum. Typically, the Doppler spectrum is obtained using conventional Fourier transform techniques implemented, computationally, using a fast Fourier transform (FFT) algorithm with the underlying assumption that the Doppler frequency is fixed or is time invariant. In ISAR scenarios, where the target is moving smoothly with respect to the radar and when the coherent integration time (CIT) is short, the Fourier transform represents the most effective solution. Nevertheless, in ISAR scenarios with fast manoeuvring targets or with sea-driven ship motion, the effectiveness of the Fourier approach is limited [1], [5], [6], [7]. For this reason, several other techniques have been proposed. One proven approach for achieving ISAR motion compensation and focused distorted ISAR images is the adaptive joint timefrequency (AJTF) algorithm [6], [7]. An adaptive time-frequency procedure is used to extract the phases of the prominent pointscatterers on the target. The extracted phase information is then used in conjunction with a prominent point processing (PPP) model to remove higher-order motion errors in the radar data. In this procedure, the phase of the resulting focused image is preserved and the Doppler resolution offered by the full coherent processing interval can be achieved. However, this algorithm is not without significant weaknesses. One of the problems is that the computational burden of the exhaustive search used to extract the motion compensation parameters, limits its usefulness in an operational situation. Another approach is based on the use of quadratic time-frequency representations [1], [8], [9], [10]. Time-frequency techniques are known to be successful in refocusing blurred ISAR images. This occurs because the images are obtained at a particular instant in time when the target’s motion can be considered uniform. However, the data is not collected instantaneously. Consequently, a large number of refocused ISAR images will be generated, spanning the entire CIT. For accurate target recognition, it is imperative to make use of only the best refocused image. It would be very impractical and inefficient to examine all of the images produced in order to identify which is the best. Such manual inspection, or even with the aid of an automated image searching algorithm, only adds extra complexity to the target recognition process [11]. The basic quadratic timefrequency representation is the Wigner-Ville distribution (WVD). In contrast to the Fourier transform, the WVD can produce a fully concentrated representation only if the signal frequency changes are linear. However, the WVD suffers from cross-terms if there is more than one point-scatterer at the same range in ISAR analysis. These were the reasons for introducing other quadratic time-frequency representations, with simplicity, efficiency and reduced interference as essential conditions. In this paper we propose that the S-method based calculation be used [12], [13], [14]. As with the WVD, the S-method can produce concentrated representations of linear frequency changes and has the added advantage of being cross-term free (or with significantly reduced cross-terms). In contrast to other reduced interference distributions, which are usually derived under the condition that the marginal properties are preserved (what inherently leads to auto-term degradation with respect to the WVD [15]), the S-method is derived with the goal of preserving the same auto-terms as in the WVD, while avoiding cross-terms [16], [17], [18]. In other words, the method automatically compensates for quadratic and all even higher-order terms in phase induced by the target’s complex motion, leading to well-focused images. The S-method is also numerically very simple and requires just a few more operations than the standard Fourier transform based algorithm. This method works on the whole set of data and it does not split the ISAR image into a time series of ISAR images, as in the case of common time-frequency techniques. These are significant advantages over other quadratic representations and over linear transforms based on REAL-TIME MOTION COMPENSATION, IMAGE FORMATION AND IMAGE ENHANCEMENT. 1355 signal dechirping and multiparameter search procedures. The objective of this paper is to demonstrate the effectiveness of the S-method for real-time image refocusing using both simulated and experimental targets exhibiting two and three-dimensional motion. Three numerical models were developed to simulate targets with complex rotational motion. This motion is that of in-flight aircraft in that it incorporates changes in pitch, roll and yaw. Experiments were conducted to gather data from a delta-wing shaped apparatus with six corner reflectors. These experiments were carried out in order to study severe distortions in ISAR images. The experimental data are then used for comparing and validating the simulated results. Statistical study of the results and achieved improvements are discussed.