A Multi -scale Sub-Aperture interferometry scheme for Estimating Target Velocity with SAR

A moving target will cause changes in the chirp signal coefficients of signals received by synthetic aperture radar (SAR). By computing these coefficients, we can find the speed of a moving target speed. This paper describes a new approach for estimating the doppler coefficients. The approach uses the sub-aperture interferometry scheme to estimate the chirp signal coefficients. A closed-form expression that describes the relationship between the phase differences and the chirp signal parameters is also derived. It is well known that the radar interferometry can provide the phase differences, but contains the inherent noise. Multi-looking process is one way to reduce the noise deviations, but the measurable spans will become smaller. This can be improved by adopting multi-scale sub-aperture interferometry scheme, as proposed in this paper. Unwrapping the phase differences, we will thus be able to recover the chirp signal coefficients from alias estimates. The maximum measurable span of the coefficients will be significantly larger. Numerical illustrations of the effectiveness of our method are provided. ? . Introduction By using match filters, the SAR process the chirp signal producing an accurate, high resolution images. The presence of moving targets induces unwanted phase variations, range migration and image degradations. In other words, images that are smeared and ill-positioned with respect to the stationary background are caused. Hence, it is necessary to estimate the relationship between a moving target and the antenna, to improve the SAR imaging (Patrick, 1988; Soumekh, 1994). These estimates also allow us to determine a moving target’s velocity, which is the purpose of this paper. There has been much work on how to estimate the phase coefficients. Based on the fact that a moving target and its stationary background will induce different doppler spectra, some detection methods were proposed (Raney, 1971; Freeman 1987). These methods require the use of a high pulse repetition frequency (prf). They perform poorly, as moving targets have only small velocity components in range direction. Werness et al.(1990) proposed an algorithm that can produce a fine resolution SAR image of moving targets by assuming multiple prominent points, which can be separated and have no phase interference with each other. These requirements are generally not met when range migration occurs or the spatial resolution is not fine enough. Chen et al.(1992) and Soumekh(1994) have described the relationship between the phase coefficients and the center frequency of doppler spectra based on the short time Fourier transform(STFT). It is well known that the STFT resolution is limited, in both the time and in the frequency domain. Furthermore this method suffers from smearing and side-lobe leakage. Other methods using maximum likelihood estimation perform well at low SNR(Besson, 1999; Peleg, 1991; Barbarossa, 1992), but they have a highly computational complexity. We can obtain the phase differences by the interferometry operation,. Then we can derive the signal coefficients from these phase differences(kuo, 2000). However, the interferometry operation causes the noise deviations to become larger, which leads the estimation to fail. Lee et al.(1994) have proved that multi-look processing can improve the phase accuracy, and we have determined that the sub-aperture interferometry scheme can decrease the noise deviation. This paper describes an estimation algorithm to find the chirp signal coefficients, based on sub-aperture interferometry scheme. Basically, the phase of the observed signal sequence may be modeled as a polynomial signal embedded in complex Gaussian noise. Since the received signals are wrapped by 2p , which results in aliases for the estimates when the phase differences are larger than 2p , this can come from the sub-apertures sizes, the moving target speed and the SAR system (i.e. wave length, sample spacing and SAR velocity). Thus, the speed of moving targets can only be estimated within some range, hence the measurable span becomes smaller, the reduction of which comes from the sub-aperture size being used. The above dilemma is easily resolved by using a multi-scales sub-apertures interferometry scheme, followed by unwrapping the difference of wrapped phase. The use of this method can effectively reduce the effect of the sub-aperture sizes. We were able to recover the chirp signal coefficients from the alias estimates. Therefore, the maximum measurable span of the coefficients were larger than when only the interferometry operation is used. ? . Joint parameter estimation using multi-scale sub-aperture interferometry 2.1. Multi-scale sub-aperture interferometry A stationary target area is assumed, for a broadside SAR geometry. During data acquisition, a dynamic target with a constant velocity is assumed to move with respect to a stationary background. We denote the target’s velocity vector as (vx, vy), which represents the components of the velocity in the directions of the range and the azimuth respectively. We denote the speed along the direction of the radar track to be U. Then the relation between those variables can be expressed as: (vx, vy)=(aU, bU) (1) where (a, b) are ratios between two vectors, normally, |a| and |b| <<1. As mentioned above, we know that (a,b) is nearly constant during the integration time of the azimuth compression processing. The relationship between an antenna and a moving target can be expressed as a function of distance(kuo,2000): [ ] { } { } ) ( ) ( exp ) ( ) ( exp ) ( ) ( ) 1 ( 2 4 4 exp ) ( ) (