Moving target detection in over-the-horizon radar using adaptive chirplet transform

Authors


Abstract

[1] In over-the-horizon radar (OTHR) moving target detection, the signal to clutter ratio (SCR) is low for slow targets near the clutter, such as ships. One method to detect a moving target is to first reject the clutter and improve the SCR before the detection, such as the adaptive Fourier transform developed by Root [1998a, 1998b, 1998c] when a target moves uniformly. When a target does not move uniformly, the Fourier-based techniques for the target detection including superresolution techniques may not work well. In this paper, we propose an adaptive chirplet transform technique in the Doppler processing in OTHR as an alternative of the Fourier transform technique when a target moves nonuniformly.

1. Introduction

[2] Over-the-horizon radar (OTHR) has been used in the detection and tracking of aircraft targets and surface ship targets in wide-area surveillance at long ranges [see, e.g., Headrick and Skolink, 1974; Trizna and McNeal, 1985; Barnum, 1986; McNeal, 1995; Headrick and Thomason, 1996; Root, 1998a, 1998b, 1998c; Anderson and Krolik, 1998, 1999; Georges and Harlan, 1998]. In OTHR, target detection is performed at each radar dwell from the radar return signals, and target tracking is then performed by modeling target motions based on the detection across a sequence of dwells. The antenna array in OTHR is always used to detect the direction of a target, which helps the detection and tracking. The detection of slow targets is often difficult with OTHR, due to the spread of the ground or ocean clutter. The existing OTHR algorithms are based on the assumption that the Doppler frequency of each target is constant or approximately constant (i.e., the motion of the target is uniform) during each dwell. A two-dimensional Fourier transform is taken of the received signal. Targets are detected from amplitude peaks away from the zero frequency. The detection capability of an algorithm depends on the SCR or SNR and the Doppler resolution. Since the Doppler resolution depends on the length of the coherent integration time (CIT), if a short CIT is used, then the target spectral power cannot be separated from the clutter spectral power. In order to improve the SCR and Doppler resolution, some algorithms for clutter cancellation, such as the adaptive Fourier transform based clutter rejection method recently proposed by Root [1998a, 1998b, 1998c], and superresolution spectrum estimation algorithms have been used, for example, by Trizna and McNeal [1985], Barnum [1986], Root [1998b], and Barnum and Simpson [1997].

[3] For a maneuvering target, there is a trade-off between the CIT length, SCR, and the Doppler resolution in the existing Fourier-based techniques. For a slow or uniform moving target, such as a ship, the Fourier-based techniques work well, where a nonshort CIT can be chosen for suppressing the clutter spread. However, for a fast maneuvering target, such as an aircraft and a fast boat, the Fourier-based techniques may not work well as we will see later in simulations. In this paper, we propose an adaptive chirplet transform in the Doppler processing as an alternative of the Fourier transform, where the sinusoidal signal model is replaced by the chirplet signal model because the radar return signals from maneuvering targets have chirplike characteristics. With the adaptive chirplet transform technique, the CIT can be longer and therefore the Doppler resolution may be better than that in the Fourier transform techniques. Since the SCR is low, before implementing the adaptive chirplet transform, we first use the adaptive Fourier transform proposed by Root [1998a, 1998b, 1998c] to reject the clutter.

[4] For the chirplet transform, see, for example, Mann and Haykin [1995], and for the adaptive chirplet transform, see, for example, Wang et al. [1998], Bao et al. [1998], Qian et al. [1998], and Wang and Bao [1999]. The adaptive chirplet transform can be thought of as a time-frequency analysis (TFA) technique. TFA has been found useful in the inverse synthetic aperture radar (ISAR) imaging for a maneuvering aircraft by Chen [1994] and [1995], Chen and Qian [1998], Chen et al. [1996], and Trintinalia and Ling [1997] and has also been applied in SAR by Chen and Miceli [1998]. This paper is organized as follows. In Section 2, we briefly review the OTHR signal model described by Anderson and Krolik [1999] and describe the problem of interest in this paper in more detail. In Section 3, we propose the adaptive chirplet transform for OTHR. In Section 4, we present simulation results. In Section 5, we compare the adaptive chirplet transform with the conventional Fourier transform for the detection of moving targets by applying both of them to a set of real OTHR data received from 372 antenna array elements.

2. OTHR Signal Model and Problem Description

[5] In this section, we first describe the OTHR signal model presented by Anderson and Krolik [1999] and the radar signal model in Barrick [1973], the conventional OTHR processing for uniform moving targets, and then the problem of interest in this paper for maneuvering targets.

2.1. OTHR Signal Model and OTHR Processing

[6] An OTH radar transmits frequency modulated continuous waves (FM/CW) in a series of chirp signals to determine the time delay and Doppler information of a target. The transmitted chirp signal has the form of

equation image

where T and equation image are the waveform repetition interval and waveform repetition frequency, respectively, and B is the bandwidth of the chirp. In each revisit, M such chirp signals are transmitted:

equation image

where A includes the transmit signal amplitude and phase, and ωc is the radar operating frequency. The signal duration Tc = MT is the coherent integration time (CIT). Since in this paper we only deal with target detection, in what follows, we focus on one revisit.

[7] After the low-pass filtering and the sampling in the time interval, the received signal s(n, m) for a target p with ground range r is [see, e.g., Anderson and Krolik, 1999]

equation image

where n is the fast time sample index, m is the chirp pulse index, equation image is the fast sampling time interval length, equation image is (or higher) the Nyquist sampling rate of the chirp bandwidth B, Ap is the phase and amplitude of the signal coming from the reflection of the target p, T0 is the minimum delay or the start range to the dwell illumination region (DIR),

equation image

is the Doppler frequency shift, βT and βR are the transmit elevation angle and receive path elevation angle, dp is the two way slant range of radar to target p, λ is the radar wavelength, and ξn,m is the additive noise. It should be noticed that ωp is usually not a function of the fast time index n, or in other words, it is usually constant over a time interval of length T.

[8] From (3), we find that the signal part in s(m, n) in terms of index n is a complex sinusoidal signal. It is also a sinusoidal signal in terms of index m if the Doppler frequency ωp is constant (with index m). In this case, a two-dimensional discrete Fourier transform over m and n provides the range-Doppler surface S(m′, n′). The index n′ represents the n′th range cell with resolution equation image, and the index m′ represents the m′th Doppler bin with resolution equation image. Targets and ground/sea clutter within distance less than Δr in the range slant direction are located in the same range cell but are separated by their Doppler frequencies if the Doppler differences are larger than Δω (i.e. the velocity differences are larger than equation image) under the condition that the SCR due to the clutter at target Doppler frequencies is not too low. For a particular OTHR processing algorithm, the target detection capability depends on the SCR. Therefore, in order to improve the target detection performance, one can increase the range and Doppler resolution and the SCR. The range resolution, equation image, depends on the radar system (the bandwidth B of radar), which is fixed for a fixed radar. However, the Doppler resolution, equation image, depends on the CIT Tc, which is chosen at the receiver. Targets and clutter with a Doppler difference less than Δω are located in one Doppler cell. One Doppler cell will be divided into l smaller cells and the SCR is then increased by l times if the CIT increases l times. A series of processing results for simulated OTHR data is shown in Figure 1. The data in Figure 1 are obtained by adding a simulated target data to real OTHR data. The simulated target moves uniformly with velocity v = 35 m/s. In Figure 1, the effect of the CIT is shown: Figures 1a, 1b, 1c and 1d are the Fourier transform results of the data with CIT Tc = 24 s, Tc = 12 s, Tc = 6 s, and Tc = 3 s, respectively, where one can clearly see the differences. The assumption here is that the target moves uniformly within the CIT interval, which may not hold when the CIT is too long. For a relatively short CIT, Root [1998a, 1998b, 1998c] recently proposed the adaptive Fourier transform method to reject the clutter and therefore increase the SCR.

Figure 1.

CIT and target detection for a uniform moving target.

2.2. Problem Description on Maneuvering Target Detection

[9] For a maneuvering target, the signal Doppler frequency in (4) due to the target motion is no longer constant but time varying. As an example, some joint time-frequency distributions of real OTHR data in a range cell of CIT Tc = 24.6 s are shown in Figure 2, where the Wigner-Ville distribution (WVD) is shown in Figure 2a and its cross term deleted version is shown in Figure 2b. WVD will be described later. In Figure 2, the x-axis is the time variable and the y-axis is the frequency variable of the signal in a range cell. One can clearly see that one of the components in Figure 2b depends linearly on the time, i.e., it is a linear chirp, and it may come from a moving target, while the other component in Figure 2b is a constant and may come from the clutter. We next show, by an example, why in this case the conventional Fourier transform based techniques may not work well, in particular why the increase of CIT may not imply the increase of the SCR as explained in the end of Section 2.1.

Figure 2.

Time-frequency distribution of an OTHR in a range cell.

[10] Consider a moving target with velocity v and acceleration a in the direction of slant range. The Doppler frequency ωp in (4) is

equation image

The Doppler spread length is

equation image

and therefore, the number of Doppler cells that the target energy spreads over is

equation image

From (7), one can see that when the target moves uniformly, i.e., a = 0, the target energy using the Fourier transform is always concentrated in a single Doppler cell. It is, however, different when the target moves nonuniformly, i.e., a ≠ 0. As an example, let us assume a/(2λ) = 1. In this case, the target energy spreads over Tc2 Doppler cells. This implies that, if the CIT Tc increases l times, the number of Doppler cells over which the target energy spreads increases l2 times. Therefore, in this case, the SCR in Doppler reduces l2 times compared to that in the uniform moving target case. This is illustrated by the simulation results shown in Figure 3, where the data are simulated similar to that in Figure 1 but the target is moving nonuniformly with velocity v = 35 m/s and acceleration a = 0.3 m/s2. Figures 3a, 3b, 3c, and 3d are the Fourier transform results with CIT 24 s, 12 s, 6 s and 3 s, respectively. From Figure 3, we see that the SCR does not increase when the CIT increases. This tells us that, for a maneuvering target, the CIT increase does not benefit the OTHR target detection if the Fourier transform based technique is used in the Doppler processing. We next want to propose an adaptive chirplet transform in the Doppler processing that may take advantage of the long CIT no matter whether the target moves uniformly or not, which can be thought of as a generalization of the adaptive Fourier transform method proposed by Root [1998a, 1998b, 1998c].

Figure 3.

CIT and target detection for a maneuvering target.

3. Chirp Signal Detection and Adaptive Chirplet Transform

[11] In OTHR, the received signal in a range cell is usually a multicomponent signal with time-varying frequency since there may be multiple targets and clutter with different velocities in a range cell. In this section, we first review the WVD and Radon-Wigner transform (RWT) for multiple chirp detection. We then describe an adaptive chirplet transform. For more details about WVD and RWT, see, for example, Cohen [1995], Qian and Chen [1996], and Wood and Barry [1994]. Adaptive chirplet transform has appeared in, for example, Wang et al. [1998], Bao et al. [1998], Qian et al. [1998], and Wang and Bao [1999].

3.1. Chirp Signal Detection Using Radon-Wigner Transform

[12] Let us first review the WVD, which has the highest resolution for a single chirp signal but has undesired cross terms for multicomponent chirp signal s(t). Consider a signal s(t). Its WVD is defined as

equation image

where variable t represents the time and ω represents the frequency. The above WVD is a joint time-frequency distribution and shows how the frequency of a signal changes with time. The two-dimensional plane (t, ω) is called the Wigner plane. The WVD of a two-component signal is illustrated in Figure 2a. The disadvantage of the WVD is its artificial cross terms caused by the quadratic multiplication in its definition as shown above. For a signal containing multiple linear chirps (corresponding to radar return signals containing multiple constant accelerating moving targets), the desired signal terms (or parts) in the WVD are the straight lines in the Wigner plane corresponding to the chirp rates in the signal while the undesired cross terms are manifested as the high frequency oscillating characteristics that may affect the chirp detection if they are not suppressed. The RWT takes advantage of the above properties of a multiple linear chirp WVD by integrating the WVD along lines, which happens to increase the signal-to-noise ratio (SNR). The cross terms can be suppressed in the WVD by the inverse Radon transform, which transforms the RWT back to the Wigner plane after the cross terms have been detected and reduced in the RWT domain [see, e.g., Bao et al., 1998]. An example of cross term deletion in the WVD using the RWT is shown in Figure 2b.

[13] Let us define the RWT and explain the above argument in more detail. The RWT Ds0, α) of a signal s(t) can be calculated by integrating Ws(t, ω) along a straight line in the Wigner plane, i.e.,

equation image

where the right-hand side is the integration along the straight line L: ω = ω0 + αt, and for convenience we use intercept ω0 and slope α of a straight line as parameters in (8). The RWT Ds0, α) can also be calculated from s(t) directly by dechirping as

equation image

Equation (9) is equivalent to (8) and is easy to calculate. Furthermore, the physical meaning of (9) is clear, and there will be a sharp peak appearing at the point when parameters ω0 and α match those of signal s(t). So the parameters of a chirp signal can be detected by the position of the peak in the RWT domain.

[14] To discuss the cross terms and their behavior in the Radon-Wigner plane, let us consider a two-component signal s(t) = s1(t) + s2(t). The RWT of the signal is

equation image

where the first two terms are the (desired) auto-terms of signals s1(t) and s2(t), respectively, and the last two terms are the cross terms , which are conjugate to each other and

equation image

We will see in Figure 4 that the characteristics of the cross terms and the auto terms in the RWT are different. The mask algorithm can be used to reduce the cross terms and keep the auto terms, and then the masked (or filtered) RWT coefficients can be transformed back to the Wigner plane by using the filtered-back projection algorithm. It is proved by Bao et al. [1998] that the auto terms after the inverse Radon transform of the masked coefficients are the same as those in the original WVD. These auto terms in the WVD are used to estimate the instantaneous Doppler frequencies of targets at the time instant t = 0. For other instantaneous Doppler frequency estimation methods, see, for example, Boashash [1992]. The main steps of the filtered-back projection algorithm are listed as follows, and the details are given by, for example, Bao et al. [1998]. Let P(α, ω0) be the masked RWT, i.e., P(α, ω0) = P(Ds0, α)), where P is a mask in the RWT plane. Then, in step 1, taking the Fourier transform of P(α, ω0) in terms of the variable ω0, we obtain

equation image

In step 2, filter Qα(Ω) saccording to the following equation:

equation image

In step 3, taking the inverse Fourier transform of Hα(Ω), we have

equation image

From these equations, we know that hα0) is the filtered P(α, ω0) in the filtered-projection algorithm. It is proved by Wang et al. [1998] that the slice Ws(0, ω0) of the WVD at the time instant t = 0 can be obtained by integrating hα0) along α, i.e.,

equation image
Figure 4.

Radon Wigner transform results of two chirp component signals.

[15] Figure 4 shows the characteristics of the auto-terms and the cross terms in Ds(α, ω0). The RWT of a two-component linear chirp signal with equal magnitudes is shown in Figure 4a, and the corresponding cross terms are shown Figure 4b. Their three-dimensional mesh figures are shown in Figures 4c and 4d, respectively. From the above figures, we can see that the auto-terms look like butterflies in Figures 4a and 4c with higher sharp peaks. The magnitudes of the cross terms are lower and distributed in a wide area. According to (15), the principal components of the signal with reduced cross terms can be obtained by masking the sharp peaks of the signal terms (set the values outside the peak regions to be zero). For multiple component signals with approximately equal magnitudes, the RWT filtering in the Radon-Wigner plane is effective from our numerous simulation results. However, for signals with significantly different magnitudes, it may not be effective because the cross terms may be larger than the auto-terms of weaker components. Figure 4e shows the case of two chirp signals where the magnitude of the weaker component is half of that of the stronger one. The weaker signal may be covered by the cross terms and cannot be detected. In OTHR, the signals coming from small targets, such as small boats and aircrafts, are often much weaker than that of clutter even after the clutter cancellation. We will discuss this issue in the next subsection.

3.2. Weak Signal Component Detection

[16] Let

equation image

be a multiple linear chirp component signal with different magnitudes Ai, parameters ω0i, and αi, where

equation image

and si(t) are sorted from the strongest to the weakest in their magnitudes, i.e.,

equation image

In the (α, ω0) plane of the RWT of s(t), the peak of the first component s1(t) (i.e., the strongest component) with parameter (α1, ω01) can be detected easier. We then mask Ds0, α) with the center (α1, ω01) and calculate the corresponding component in Ws(0 ω0). In general, the next component s2(t) cannot be determined accurately because the stronger component suppresses the weak one. If the first component s1(t) can be eliminated from s(t), then it will be easier to detect the second component. We next show how to eliminate s1(t).

[17] The dechirping operation is used to signal s(t), i.e., multiplying the signal s(t) with exp(−jequation imageα1t2) as follows:

equation image

After the dechirping, the chirp rates of the linear chirp components are changed correspondingly. The first component becomes a complex sinusoidal signal (or approximately complex sinusoidal signal or narrowband signal). The Fourier transform or other spectrum analysis method is used to the dechirped signal in (16) to estimate its amplitude and frequency ω01. The narrow spectrum of signal s(t)exp(−jequation imageα1t2) around ω01 is filtered out with a band-pass filter. By doing so, the mainlobe of the first component is eliminated and only some of its sidelobes may possibly remain. Because the bandwidth of the signal s1(t)exp(−jequation imageα1t2) is narrow, the filtering may not affect the remaining signal. After the filtering, the remaining signal is

equation image

which is multiplied by exp(jequation imageα1t2) to obtain the sum of the remaining components, i.e.,

equation image

This process is repeated until all the signal components are detected.

3.3. Adaptive Chirplet Transform for High-Order Time-Varying Frequency Signals

[18] If the CIT is not short, the received signal from a maneuvering target may not be a linear chirp but a higher-order time-varying frequency signal, i.e., high-order chirp. The idea in what follows is quite simple, i.e., a high-order chirp from a target is expressed as a combination of several linear chirps over different time intervals called chirplets introduced by Mann and Haykin [1995].

[19] Let us show how a signal s(t) is decomposed. The procedure is that we first estimate chirp rates α1, α2, …, equation image of s(t) and their corresponding different segments, we then define ui = exp(j(equation imageαit2)). For a given frame {hk, kZ} of all 0 chirp rates, a new frame {hkui, kZ} is obtained. Based on this new frame {hkui, kZ}, s(t) is divided as

equation image

where Ci,k = 〈s, hkui〉 are the frame decomposition coefficients and {hk′, kZ} is dual frame of {hk, kZ}, 〈•, •〉 represents the inner product, λi are arbitrary weights satisfying

equation image

For details about (17), see Wang and Bao [1999]. For more about frames, see, for example, Vetterli and Kovacevic [1995]. To have an efficient frame decomposition, {hk, kZ} should include functions with different time and frequency width and center (mean) locations. For example, the following modulated Gaussian functions are usually used:

equation image

where there are basically four indexes γk, ωk, βk, and tk corresponding to the envelope, phase, frequency and time centers, respectively. For convenience, these four indexes simplified into an index k by noticing that some of the four indexes may duplicate each other.

[20] We next present how the chirp rate parameters αi in ui = exp(jequation imageαit2) and the corresponding hk of the form (18) are estimated. A linear chirp in the Radon-Wigner plane has a “butterfly bow” shape, and the parameters can be estimated by searching the peak of the net. For a given signal s, chirp rate α1 is obtained by searching the largest peak in the Radon-Wigner plane after taking the RWT of the signal. We then obtain frame {hku1, kZ} by modulating frame {hk, kZ} in (18) with u1(t) = exp(jequation imaget2). We next estimate which element in the modified frame {hku1, kZ} optimally matches the signal s and denote the element as u1hk1 where

equation image

Define signal s1 as

equation image

By repeating the same procedure to s1 as to s, we obtain the following things: parameter α2 with the second largest component of s is estimated by the RWT of s1, and let u2(t) = exp(jequation imaget2), then

equation image

and define

equation image

Repeating the above procedure, signal s can be expressed as

equation image

Based on the above decomposition, the instantaneous frequencies of the signal's auto-terms can be obtained and then used for the OTHR target detection.

[21] One can see that the search in (19) and (21) is in fact four-dimensional, which has a high computational complexity. In order to reduce the complexity, a suboptimal algorithm is given by Wang and Bao [1999] as follows:

[22] The adaptive chirplet transform consists of steps 1–6. In step 1, chirp rate and frequency are estimated by

equation image

where Ds(α, ω) is the RWT of s(t). In step 2, let g(t) be a narrowband filter with center frequency ω1, u1 = exp(jequation imaget2), and h1(t) = g(t) ○ (s(t)u1*(t)) where ○ is the convolution operation. In step 3, the coefficient c1,1 in (17) is obtained as follows:

equation image

In step 4, let

equation image

In step 5, set s = s1. In step 6, stop if the energy of s is small enough; otherwise go to step 1. The above adaptive chirplet transform is used in the following simulations.

3.4. Clutter Rejection

[23] Because the SCR is low (about −30 dB to −60 dB) in the OTHR data, the above algorithm cannot be directly used to detect targets. Before using the adaptive chirplet transform, the clutter rejection algorithm using the adaptive Fourier transform in Root [1998a, 1998b, 1998c] is applied to remove clutter, which is possible because clutter is usually composed of sinusoidal signals. After most of the clutter energy is removed, the above adaptive chirplet transform is then used to detect targets.

3.5. Instantaneous Frequency Estimation and Target Detection

[24] The separated part y1 in step 5 in the adaptive chirplet transform is a mono-component chirp signal with finite time duration. The amplitude and instantaneous frequency of signal y1 can be used to estimate the reflectivity of the target and therefore to detect the target.

4. Simulation Results

[25] In this section, two sets of simulation results are presented. In the first set of simulations, we use the OTHR signal model for both clutter and target described in Section 2, and different CITs. In the second set of simulations, we use a real OTHR data as clutter, i.e., the background, and a simulated aircraft target with different motions, where the CIT is Tc = 24.6 s.

[26] Figures 5–8 show the first set of simulation results using the OTHR model described in Section 2 with the following parameters. There are 64 range cells in the received data. In each range bin, there are 100 clutter cells with random reflectivity to the radar-transmitted signals. The distance of the target to the radar is about 1500 km. The radar working frequency is 10 MHz. The moving target is located in the 30-th range cell with velocity 50 m/s and acceleration 2 m/s2 in the range slant direction. The SCR is about −20 dB. Each clutter in a range cell moves randomly of the uniform distributions in both velocities and accelerations of mean 0 and variance 0.3 m/s and 0.02 m/s2 in velocity and acceleration, respectively. Four different CITs, Tc = 5, 8, 10, 12 s, are tested, and the corresponding test results are shown in Figures 5–8, respectively.

Figure 5.

CIT Tc = 5 s.

Figure 6.

CIT Tc = 8 s.

Figure 7.

CIT Tc = 10 s.

Figure 8.

CIT Tc = 12 s.

[27] In Figures 5a, 6a, 7a, and 8a the WVDs of the 30th range cells with Tc = 5, 8, 10, 12 s are shown, respectively. It is hard to see the chirp from the moving target because of the low SCR. The corresponding Figures 5b, 6b, 7b, and 8b show the WVDs after the clutter rejection using the adaptive Fourier transform proposed by Root [1998a, 1998b, 1998c] with the iteration numbers 8, 10, 10, 10, respectively, where one can see the linear chirp characteristics of the radar signals from the moving target and it is clearer when the CIT is longer. Figures 5c, 6c, 7c, and 8c show the processing results using the conventional Fourier transform, where one cannot see the target. Figures 5d, 6d, 7d, and 8d show the processing results using the conventional Fourier transform but after the adaptive Fourier transform clutter rejection proposed by Root [1998a, 1998b, 1998c] with the iterations 8, 10, 10, 10, respectively. One can see that, although the clutter is significantly rejected in the middle columns in Figures 5d, 6d, 7d, and 8d, the target is not clearly seen. Figures 5e, 6e, 7e, and 8e show the processing results using the adaptive chirplet transform mentioned in Section 3 and after using the adaptive Fourier transform clutter rejection in Root [1998a, 1998b, 1998c] with the same iteration numbers as before. Figures 6f, 7f, and 8f correspond to Figures 6e, 7e, and 8e by adding the rejected clutter back to parts e. The target cannot be seen in Figures 5e and 5f since the CIT is too short and therefore the Doppler resolution is not high enough to separate the clutter as we mentioned in Section 2. The target starts to be seen clearly from Figures 6e and 6f when the CIT increases to 8 s and the Doppler resolution increases when the CIT increases as we can see from Figures 6e, 6f, 7e, 7f, 8e and 8f.

[28] In summary of Figures 5–8, the Doppler frequency of a moving target cannot be separated from that of clutter if a short CIT is used and as a result the target cannot be detected. On the other hand, the energy of a maneuvering target is spread if a long CIT and a Fourier transform based algorithm are used. In this case, the target cannot be detected either. Our proposed adaptive chirplet transform is able to accumulate a maneuvering target's energy and separate its “spectrum” from the clutter by using a longer CIT.

[29] In the second set of simulations shown in Figures 9–12, the background data is a real OTHR data of total 54 range cells and fixed, but the moving target is a simulated one added to the background data in the 30th range cell, where several velocities, v = 10, 15, 25, 35 m/s, of the target with the same acceleration a = 0.3 m/s2 are tested. The target signal is generated with SCR = −30dB. The CIT of the real OTHR data is Tc = 24.6 s. The figure structure of parts a–f in Figures 9–12 is the same as that in Figures 5–8. The number of iterations in the adaptive Fourier transform clutter rejection is 25 in parts b, d, and e in Figures 9–12. From these figures, one may find that the effect of the increase of the velocity of a target of a fixed CIT is similar to that of the increase of the CIT of a fixed velocity of a target, which degrades the performance of the conventional Fourier transform based methods but improves the performance of the adaptive chirplet transform method proposed in this paper.

Figure 9.

CIT Tc = 24.6 s, and target velocity v = 10 m/s.

Figure 10.

CIT Tc = 24.6 s, and target velocity v = 15 m/s.

Figure 11.

CIT Tc = 24.6 s, and target velocity v = 25 m/s.

Figure 12.

CIT Tc = 24.6 s, and target velocity v = 35 m/s.

5. Processing Results to Real Over-the-Horizon Radar Array Data

[30] In this section, the adaptive chirplet transform is applied to a real OTHR data. The radar frequency is 21.521 MHz. There are 372 receive elements. The data are prebeam formed IQ (PBIQ), recovered after the range processing. The number of range bins is 57, and the number of Doppler bins (time samples) is 64. The data include a set of beam forming factors (BFF) that are the product of the RF calibration factors, the azimuth weights and the azimuth rotation factors.

[31] The first step in the processing is to extract the RF calibration factors from the BFF and to apply them to the PBIQ. Using the estimated beam-forming factors across 372 receivers, 18 beams are generated. The 18 beams separate the radar echoes into 18 parts in the azimuthal direction. Thus, targets and clutter in a range bin may be separated by these 18 beams if they are in different azimuthal directions. Therefore, the signal (target) to clutter ratio (SCR) is higher after using beam forming than that obtained by one antenna alone. Next, Doppler spectrum methods are applied to each range and each beam, where the Fourier transform based methods, such as high resolution spectrum estimation methods, are the conventional processing method. After the Doppler spectrum is processed in each range and each beam, the largest component is used to represent the echo of an object (target or clutter) in that region (range and azimuth).

[32] The available algorithms (FFT or high resolution spectrum algorithms) are based on the assumption that received target signals are stationary. From the analysis in Section 3 and the real radar data shown in Figures 1 and 2, we find that the above assumption is not always true. Signals of moving targets are sometimes nonstationary. Below, the adaptive chirplet transform is used to replace the Fourier transform in the target detection after beam forming is implemented. The algorithm used in the processing is as follows: (1) extract the RF calibration factors from the BFF, (2) beam form, (3) reject clutter using Root's algorithm in each range and each beam, (4) apply the adaptive chirplet transform to the data after the clutter rejection, and (5) choose the largest component of the result in step 4 as the echo in the region. For the purpose of illustration, all results in these figures are scaled by 10−4 in the magnitudes.

[33] Figure 13 shows the WVD results of Data 2983, Beam 3, Range 45 and Range 46 with 5 iterations for the clutter rejection. This figure shows that there are some signal components with time-varying frequencies in the received signals. Figure 14 shows the WVD results of Beam 2, Range 44 and Range 45 with 5 iterations for the clutter rejection of Data 3013, which is the data after Data 2983 (received about 2 min later). Figure 14 has the same characteristics as that in Figure 13 with similar time-varying frequency components. In particular, the frequency rates in Figure 14 are almost the same as those in Figure 13. Therefore, we conclude that the signals shown in Figures 13 and 14 come from the same moving target. The reason why these signals are spread over two range cells and the locations of the signals in Data 2983 and Data 3013 have a slight difference is most likely due to multipath, which will be a future research topic.

Figure 13.

WVDs of Data 2983, Beam 3, Range 45 and Range 46.

Figure 14.

WVDs of Data 3013, Beam 2, Range 44 and Range 45.

[34] Figure 15 shows the processing results of Data 2983, Beam 3, Range 45 and Range 46, using the Fourier transform and the adaptive chirplet transform, where the processing results with 1 to 8 iterations of clutter rejection are given. It is shown that the clutter energy near zero frequency (centered at bin 32) is large even after the first iteration. The energy in the negative (left of center) frequencies is small, and the spectrum of this part spreads with the Fourier transform due to the time-varying frequencies, which can be explained by Figure 13. In contrast, the adaptive chirplet transform (ACT) accumulates the energy in the negative frequencies. However, the amplitude of the “target” is still not high enough compared with that of clutter. When the iteration number of the clutter rejection increases, more clutter is removed. After 5 iterations, the target energy is larger than that of the residue from clutter. It is interesting to note that, although the target energy is larger than the clutter energy, further iterations in the clutter rejection algorithm do not remove much energy of the target signal with time-varying frequency, which can be seen in the 6th to the 8th iterations from Figure 15. Similar to Figure 15, Figure 16 shows the processing results for Data 3013, Beam 2, Range 45 and Range 44.

Figure 15.

Processing results to Data 2983, Beam 3, Range 45 and Range 46 with different iterations.

Figure 16.

Processing results to Data 3013, Beam 2, Range 44 and Range 45 with different iterations.

[35] Figure 17 shows the detection results for Data 2983 using the Fourier transform and the adaptive chirplet transform with different numbers of clutter rejection iterations. The target can be detected in the ACT result with 8 iterations, which is circled. Although the “target” can be seen in the FFT result with 5 iterations, from the FFT processing results with iteration 5 shown in Figure 15, we can see that the “target” in the FFT result in Figure 17 is from the sidelobe of the clutter, and it is a fake.

Figure 17.

Processing results to Data 2983.

[36] Figure 18 shows the processing results for Data 3013 using the Fourier transform and the adaptive chirplet transform with 1 to 8 iterations of clutter rejection. The target can be detected in Beam 2, Ranges 44 and 45, with the ACT result of iteration 6 and 7, which are circled. However, the target cannot be detected in the FFT results. In summary, the processing results show that the ACT algorithm we proposed can detect some moving targets that the Fourier transform cannot.

Figure 18.

Processing results to Data 3013.

6. Conclusion

[37] In this paper, we proposed an adaptive chirplet transform method for Doppler processing in the OTHR detection of a maneuvering target. Since the SCR is low in OTHR, we proposed first to use the adaptive Fourier transform method for the clutter rejection proposed by Root [1998a, 1998b, 1998c] and then to use the adaptive chirplet transform for the Doppler processing in the maneuvering target detection. As we can see from the simulation results presented in this paper, the long CIT is an advantage of our proposed method, while it is a disadvantage of the Fourier transform based methods.

Acknowledgments

[38] The work of G. Wang and X.-G. Xia was partially supported by the Office of Naval Research (ONR) under grant N00014-0-110059.

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