- Open Access
Moving Target Indication via Three-Antenna SAR with Simplified Fractional Fourier Transform
© Wang; licensee Springer. 2011
- Received: 25 January 2011
- Accepted: 24 November 2011
- Published: 24 November 2011
Ground moving target indiction (GMTI) is of great important for surveillance and reconnaissance, but it is not an easy job. One technique is the along-track interferometry (ATI) synthetic aperture radar (SAR), which was initially proposed for estimating the radial velocity of ground moving targets. However, the measured differential phase may be contaminated by overlapping stationary clutter, leading to errors in velocity and position estimates. As effective clutter suppression can be achieved by multiple aperture or phase center antennas, this article presents a simplified fractional Fourier transform (SFrFT) for three-antenna-based SAR GMTI applications. This approach cancels clutter with three-antenna-based methods and forms two-channel signals through which moving targets are detected and imaged. Next, the Doppler parameters of the moving targets are estimated with the SFrFT-based estimation algorithm. In this way, both target location and target velocity are acquired. Next, the moving targets are focused with one uniform imaging algorithm. The feasibility is validated by theory analysis and simulation results.
- Fractional Fourier transform (FrFT)
- Simplified FrFT
- Along-track interfer-ometry (ATI)
- Displaced phase center antenna (DPCA)
- Ground moving targets detection (GMTD)
- Synthetic aperture radar (SAR)
- Three-antenna SAR
Ground moving target indication (GMTI) is of great interest for surveillance and reconnaissance [1–4], but it is not an easy job because separating the moving targets' returns from stationary clutter is a technical challenge . Moving target indication is twofold : one is the detection of moving targets within severe ground clutter, and the other is the estimation of their parameters such as velocity and location. As such, radar clutter has received much recognition in recent years. Several clutter suppression approaches have been proposed , but they often require high pulsed repeated frequency (PRF), which is not desirable to avoid excessive data rate and PRF ambiguity problem.
It is well known that the moving target with a slant range velocity will generate a differential phase shift. This phase may be detected by interferometric combination of the signals from a two-channel along-track interferometry (ATI) synthetic aperture radar (SAR) system. The ATI SAR was initially proposed for detecting ground moving targets [8–10], which uses two antennas to detect targets by providing essentially two identical views of the illuminated scene but at slightly different time. Several interferometry SAR (InSAR)-based moving targets detection algorithms have been proposed previously [11–14]. However, the stationary clutter unavoidably corrupts the interferometric phase of the targets depending on its signal-to-clutter environment. Consequently, the imaged moving targets will be displaced in azimuth according to its radial velocity.
There have been several studies on the clutter effects on the intended signals [15, 16]. But there remains still many unresolved problems, e.g., how to reliably estimate the target's true interferometric phase from the clutter. Moreover, in a nonhomogeneous terrain, the degree of physical overlap of the target with a bright stationary point clutter may also influence the estimation accuracy. In order to accurately estimate the target's true velocity, clutter contamination on the signal must be minimized. Precise knowledge of the interferogram's phase and amplitude statistics is very important for distinguishing the moving targets from the clutter. A straightforward approach to clutter cancelation is the displaced phase center antenna (DPCA) technique . For one two-antenna DPCA system, the additional freedom provided by the second antenna can be used to cancel the clutter; however, it can no longer be used to estimate the moving targets' position information.
Moreover, estimating the moving targets' Doppler parameters is often required, but the Wigner-Vill distribution-based algorithms will generate cross-terms , particularly in the presence of multiple moving targets. In this case, the fractional Fourier transform (FrFT) is a powerful tool. But the conventional FrFT is redundant for moving targets detection . This article presents a simplified FrFT (SFrFT) and three-antenna SAR combined GMTI approach. After canceling the stationary clutter using three-antenna ATI SAR, two-channel signals through which moving targets can be detected are formed. Next, one SFrFT-based algorithm is presented to estimate the Doppler parameters of the moving targets. Finally, the moving targets are located through two-channel interferometric processing algorithm. The remaining sections are organized as follows. Section II introduces the SFrFT and its mathematical properties. Section III describes the system scheme of DPCA-based three-antenna ATI SAR for GMTI applications. Next, the SFrFT-based detection algorithm is detailed in Section IV, followed by decorrelation discussion in Section V. Finally, Section VI concludes the whole paper.
Zero rotation: rotation: .
Consistency with Fourier transform: .
Additivity of rotations: .
Additional properties can be found in the Ref. . The domains 0 < α < π/2 are called as the fractional Fourier domains. The FrFT of a function x(t), with an angle α, can be computed as the following steps.
where ⊛ denotes a convolution operator.
As the Steps 3 and 4 are redundant for signal detection, we name the FrFT without the Steps 3 and 4 as simplified FrFT (SFrFT). Note this SFrFT is different the simplified FrFT proposed in . The SFrFT is also a linear transform and continuous in the angle α. This provides us a powerful tool for detecting SAR moving targets, particularly when there are multiple moving targets.
where * denotes a conjugate operator. The first term is the moving target's interferogram that we are wanted. The second term is the stationary target's interferogram. Its phase should be equal to zero because a stationary scene does not change with time, i.e., Rc 1= Rc 2. The remaining two terms are cross-terms, which come from the clutter contamination at the SAR image formation stage. As the phase angle is 2π periodic, the two cross-terms may have different phase values; hence, the effects of cross-terms on the total along-track interferometric phase are not easily predictable.
As ATI SAR output is signal power, slowly moving targets will not attenuated along with the stationary clutter when we utilize magnitude and phase information for target extraction. In the case of low signal-to-clutter ratio (SCR), the ATI SAR will lose its ability to detect slowly moving targets and to correctly estimate their velocities because the system noise (additive thermal noise and multiplicative radar phase noise) scatters the stationary clutter signal around the real axis in the complex plane. If the clutter contribution is not negligible when compared to the signal power, the estimation of the target radial velocity from the contaminated interferometric phase may lead to erroneous results. When the SCR is small, this effect will become more serious for slowly moving targets and the moving targets will be indistinguishable from the clutter. Moreover, in this case, the targets' impulse responses are not normal delta functions, particularly for the moving targets which are poorly focused because of the unmatched azimuth-compression filter. This leads to a point target's response overlaps with several neighboring resolution cells. This also means a varying SCR across the target's response, which in turn affects its interferometric phase. Therefore, the ATI SAR is a clutter limited moving targets detector and applying some efficient clutter suppression or cancelation techniques is necessary.
3.2 Three-Antenna ATI SAR Scheme
When the DPCA condition is matched, the clutter cancelation can then be performed by subtracting the samples of the radar returns received by two-way phase centers in the same spatial position, which are temporally displaced. The radar returns corresponding to stationary objects like the clutter from natural scenes are canceled, while the returns backscattered by moving targets have a different phase in the two acquisitions and remain uncanceled. Therefore, all static clutter scatterers are canceled, leaving only moving targets and a much simplified target detection problem (which is detailed in the next section). If the DPCA condition is not matched, the collected azimuth samples will be spaced nonuniformly. This problem can be solved using the reconstruction filtering algorithm detailed in .
3.3 Signal Models
where ξl = (R l (t a ) + R c (t a ))/c o , ξ c = 2R c (t a )/c o and ξ r = (R c (t a ) + R r (t a ))/c o , with c o is the speed of light.
From Eq. (22) we can notice that, if v y = 0, there is |S cl (t r ,t a )| = 0; hence, the clutter has been successfully canceled by this method. The remaining problem is to detect the moving targets.
The interferometric phase Φ ∈ [-π, π] is unambiguous; hence, the unambiguous x o can be obtained in this way. Once R o and x o are determined, the y o can then be derived from the Eq. (14) because the h is known from the inboard motion sensors.
This condition forms the basis for estimating the moving targets' parameters. In the SFrFT domain with a proper α, the spectra of any strong moving target will concentrate to a narrow impulse, and that of the clutter will be spread. If we can construct a narrow band-stop filter in the SFrFT domain whose center frequency around at the center of the narrowband spectrum of a strong moving target, then the signal component of this moving target can be extracted from the initial signal. With this method, the strong moving targets can be extracted iteratively, thereafter the weak moving targets may be detectable. This method can be regarded as an extension of the CLEAN algorithm  to the SFrFT.
Therefore, after canceling the stationary clutter, the identification of moving targets can be implemented with SFrFT in the following steps:
Step 1. Apply one SFrFT to the data in which the clutter has been canceled with different α, and from the maximal peak get the numerical estimation of .
Step 4. The filtered signals are then rotated back to time-domain by an inverse SFrFT.
Step 5. Repeat the operations from Step 1 to Step 4 until all the desired moving targets are identified.
4.1 Simulation Results
pulse repeated frequency
antenna length of each aperture
position of the target A
(x = 50,y = 12000)
position of the target B
(x = 58,y = 12000)
position of the target C
(x = 50,y = 12250)
In this article, the clutter cancelation is performed between two DPCA antennas. Hence, the clutter cancelation performance mainly depends on the correlation characteristics of the signals from fore and aft antennas. But phase center offset and antenna deformation may cause decorrelation. So, decorrelation analysis is necessary.
In this article, one SFrFT and DPCA combined approach is proposed for GMTI applications. This approach realizes target location and velocity estimation with three antennas. After canceling by the three antennas, two-channel signals through which moving targets can be detected are formed. Next, the Doppler parameters of the moving targets are estimated with the SFrFT algorithm. Finally, the moving targets are focused with one uniform image formation algorithm. In this way, both target location and target velocity are acquired, and high-resolution moving target SAR images are obtained. Simulation results show its validity. While compared to conventional approaches, this approach is more effective and robust. In particular, it is not dependent on a target's across-track velocity component or its Doppler shift, which is difficult to determine due to insufficient freedom degrees. This approach depends only on target's Doppler rate, and this is shown to be measurable with a high degree of robustness. In contrast, the conventional approaches like ATI SAR depend not only on a target's Doppler rate but also on its across-track velocity component. Moreover, the selection of matched filter length directly affects the measured ATI phase. These additional unknowns make the SAR ATI a less desirable method for estimating target parameters than the SFrFT and DPCA combined approach, which also allows the estimation of target's true azimuth position directly from its measured position in the final SAR images, particularly when there are multiple moving targets. Therefore, the SFrFT and DPCA combined method is elegant and effective in moving target identification.
This work was supported in part by the Specialized Fund for the Doctoral Program of Higher Education for New Teachers under Contract number 200806141101, and the open funds of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences under contract number KLOCAW1004.
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