Doppler Coefficient Estimation for Synthetic Aperture Radar Using Sub-Aperture Interferogram
Keywords : Synthetic Aperture Radar, Sub-Aperture Interferogram, chirp signal
Abstract
A moving target will change the doppler coefficients of the received signal of Synthetic aperture radar(SAR), so we need to compute the coefficients, then we can obtain the moving targets speed or avoid smear of SAR images. This paper describes a new approach for estimating the doppler coefficients. Our approach uses the sub-aperture Interferogram scheme to estimate the doppler coefficients. Closed-form expressions are derived, and simulation results show this method can estimate the coefficients accurately. Less computation and a smaller amount samples of the signals are the characteristics of the Sub-Aperture Interferogram than other algorithms.
1. Introduction
Synthetic aperture radar (SAR) uses match filters to process the chirp signal to produce an accurate, high resolution images. A presence of moving targets, however, induces unwanted phase variations, resulting image degradations due to range migration. In addition, smeared and ill-positioned images with respect to the stationary background are caused as well. Hence, an estimate of the moving target relation to the antenna is necessary in order to improve the SAR images[1]. On the other hand, these estimates allows us to determine the moving targets velocity. The later is the purpose of this paper.
There are many works on how to estimate the phase coefficients. Based on the fact that the moving target and stationary background induce different doppler spectra, a detecting method was proposed in [2]. The method requires the use of a high pulse repetition frequency (prf) and performs poorly as the moving targets have a small range velocity components. Soumekh et al.[3] described the relation of the phase coefficients and the center frequency of doppler spectrum based on the short time Fourier transform (STFT). But as is well known, in STFT the resolution was limited either in time or in frequency domain, and it suffers from smearing and side-lobe leakage. Some methods use regression on the unwrapping signal phase [4] to estimate the polynomial phase coefficients of a constant amplitude signal, which requires to use a phase unwrapping algorithm prior to coefficient estimation. The algorithms is based on accumulate the phase difference, but it can be fooled by spare, rapidly changing phase values, and phase unwrapping errors cause inaccurate coefficient estimates. Another method by maximum likelihood estimation[5], it performs well at low SNR, but its cost is high computational complexity.
An estimation algorithm based on sub-aperture interferometric scheme and phase shift measurement to estimate the doppler coefficients is proposed in this paper. This paper also addresses the relation of target speed with the phase shift. Basically, the phase of the observed sequence is model as a polynomial embedded in white noise, which implies that, first, select an appropriate sub-aperture size and then segment recorded data to a finite number of subsets with the same size. Second, we can estimate the doppler parameters from the phase shift.
The presentation of the paper is as follows. First the problem of moving target velocity estimation in SAR signal is stated. Then a SAR signal model of a moving target velocity estimation is given in section II. Then a method for estimate doppler parameters is proposed in section III, which based on the application of interferometric scheme. And simulation results is shown in section IV. Finally, a conclusion is provided.
2. SAR Signal Model of A Moving Target
A moving target will alter the coefficients of the phase function of observed signals and target motion is generally unknown. When a conventional SAR processing algorithm is applied to scene with moving targets, the images of a moving targets are typically mislocated and smeared due to phase errors induced by the motion. The relation between antenna and a moving target can be express as a function of time and distance[1],[3]
Where A(t) is the amplitude of the signal,
is the distance vector between target and antenna, and
l is the wave length of SAR. This magnitude of
will be denoted as
½½.
For small time variations,
½½ is large relative to the magnitudes of the velocity and acceleration vectors, and neglecting terms higher than t
3 in a Taylor series expansion of the magnitude, then we can obtain the expansion:
where V is the velocity contains both radar and moving target. We denote the moving target velocity vector as (v
x,v
y), which is the components of moving target velocity in range and azimuth respectively, and the along track's speed of the radar symbolized as U. The relation of moving speed to antenna speed can be expressed as:
(vx, vy)=(aU, bU)
(3)
Where (a,b) is the dimensionless of target's velocity scaled to the speed of the radar, and Normally, |a| and |b| <<1. From above mention we can assume that (a, b) is nearly constant during the integration time in the azimuth.
Using equation (2) and (3), (2) can be rewritten as follows:
