IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
2225
Radon-Linear Canonical Ambiguity Function-Based Detection and Estimation Method for Marine Target With Micromotion Xiaolong Chen, Associate Member, IEEE, Jian Guan, Member, IEEE, Yong Huang, Ningbo Liu, and You He
Abstract—Robust and effective detection of a marine target is a challenging task due to the complex sea environment and target’s motion. A long-time coherent integration technique is one of the most useful methods for the improvement of radar detection ability, whereas it would easily run into the across range unit (ARU) and Doppler frequency migration (DFM) effects resulting distributed energy in the time and frequency domain. In this paper, the micro-Doppler (m-D) signature of a marine target is employed for detection and modeled as a quadratic frequency-modulated signal. Furthermore, a novel long-time coherent integration method, i.e., Radon-linear canonical ambiguity function (RLCAF), is proposed to detect and estimate the m-D signal without the ARU and DFM effects. The observation values of a micromotion target are first extracted by searching along the moving trajectory. Then these values are carried out with the long-time instantaneous autocorrelation function for reduction of the signal order, and well matched and accumulated in the RLCAF domain using extra three degrees of freedom. It can be verified that the proposed RLCAF can be regarded as a generalization of the popular ambiguity function, fractional Fourier transform, fractional ambiguity function, and Radon-linear canonical transform. Experiments with simulated and real radar data sets indicate that the RLCAF can achieve higher integration gain and detection probability of a marine target in a low signal-to-clutter ratio environment. Index Terms—Long-time coherent integration, marine target, micro-Doppler (m-D), quadratic frequency-modulated (QFM) signal, Radon-linear canonical ambiguity function (RLCAF).
I. I NTRODUCTION
M
ARINE or sea surveillance radars are extensively used in military and civil fields, such as maritime traffic monitoring, coastal surveillance tasks, remote sensing, and lowflying aircrafts striking, etc. [1]–[3]. One of the most important problems is related to the detection of low-observable marine targets. In marine environments, the radar echo generated by the sea surface is of great interest. It can be significantly stronger than the target, and it is characterized by a high variability. The Manuscript received January 18, 2014; revised July 25, 2014; accepted September 3, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 61471382, Grant 61401495, Grant 61201445, and Grant 61179017 and in part by the special funds of Taishan Scholars construction engineering of China. X. L. Chen, J. Guan, and Y. Huang are with the Department of Electronic and Information Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China (e-mail:
[email protected]; guanjian96@ tsinghua.org.cn). N. B. Liu and Y. He are with the Institute of Information Fusion, Naval Aeronautical and Astronautical University, Yantai 264001, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2014.2358456
complex sea surface usually leads to a major loss and false alarms in target detection. Therefore, one of the classical detection methods is based on the understanding, characterizing, and modeling of sea clutter [4], [5]. The analysis of clutter is traditionally performed from a statistical point of view, and typical models are Rayleigh, log-normal, Weibull, and compound-K distributions, etc. However, in modern radar systems operating at low grazing angles with high-resolution capabilities, sea clutter is often observed to be highly non-Gaussian, nonlinear, and nonstationary [6]. Therefore, the statistical-based detection methods cannot accurately fit the sea clutter in a complex environment. The introduction of fractal geometry provides a new method to describe natural rough structures [7]. Great efforts have been made to analyze radar signals from the sea surface by fractal methods, and a variety of concepts, such as fractal dimension, multifractal analysis [8], and fractal feature in the transform domain [9], have been introduced. However, the performance of fractal-based detection methods would be largely influenced by the complex sea environment. Sometimes, there are frequency modulations on the returned signal of a marine target that make sidebands on the Doppler frequency shift the target reflected [3]. This is usually due to the nonuniform motion, vibrations or rotations of structures on the target, and is commonly referred to as the micro-Doppler (m-D) effect [10]. The m-D effect can be observed in radar returns from objects with micromotion structures such as humans, animals, birds, wind turbines, helicopters, engines, etc. [11]. Many applications are still undiscovered since this is relatively new, but it is a very promising subject for classification and detection for space, air, ground, and sea surface target [12]. Therefore, m-D characteristics have recently been employed for small target detection and recognition as they can provide more detailed information. Under high oceanic conditions, the signalto-clutter ratio (SCR) of the returned signal may be reduced due to the heavy sea clutter. At the same time, due to the pushing and control effects caused by propeller, engine, and rudder, the attitude of target may vary with the fluctuation of sea surface, which induces the effect of power modulation on radar echo [3], [13]. Although the m-D signatures of a marine target are quite useful for target detection, it is rather difficult to extract and strengthen the time-varying m-D signals. Moreover, the Doppler spectrum of sea clutter may be broadened to cover the target’s spectrum. How to effectively accumulate the m-D signal to compete sea clutter still remains to be resolved. It is well-known that detection performance and SCR of radar returns can be greatly improved by means of incoherent or
0196-2892 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
2226
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
coherent integration among different pulses [14], [15]. For an incoherent integration method, such as the Radon transform (RT) [16] and Hough transform [17], they are easy to be realized, whereas the integration gain would be unsatisfactory since they only use the amplitude information. The coherent integration can provide more information of a target using both amplitude and Doppler. Therefore, it has the advantages of high integration gain, anticlutter ability, and can be applied to moving target detection in complex environments. With the development of radar technology, particularly for the invention of wideband radar and digital phased-array radar [18], we can obtain higher range resolution profiles [19] and longer observation time of a target, which is useful for long-time integration. However, the envelope of radar returns may easily migrate across several range bins during the integration time resulting in the across range unit (ARU) effect [14]. At the same time, the time-varying m-D signals of a marine target with frequency-modulated (FM) property would come across the unfavorable Doppler frequency migration (DFM) effect [20]. The target’s energy will be distributed among several range and Doppler bins, which is unfavorable for the expected detection performance. For the ARU effect, the commonly used methods include the envelope correlation and Keystone transform methods [21]. However, their performances are affected by the SCR and the Doppler frequency ambiguity. The newly developed coherent integration method, i.e., Radon–Fourier transform (RFT) can realize the long-time coherent integration for the uniformly moving target with range walk [14]. Unfortunately, it cannot be applied for the m-D signal of a marine target with nonuniform or rotational motions. Since the DFM is caused by the timevarying Doppler, it is an effective solution to find the changing rule of m-D with time. Therefore, the time–frequency techniques and high-order signal processing methods are employed to improve the ability of coherent integration, such as the fractional Fourier transform (FRFT) [22], chirplet transform [23], chirp-Fourier transform [24], high-order ambiguity function (HAF) [25], and fractional ambiguity function (FRAF) [26], etc. However, there are still several problems or disadvantages if they are applied to Doppler compensation of a marine target, such as the cross-terms for multicomponent signals, heavy computational burden, or the “picket-fence” effect. The sparse decomposition is another way, which decomposes a signal into waveforms that belong to a dictionary of functions [27]. It can provide superior resolution but is a more computationally intensive process. As can be seen, little work about the simultaneous compensations of range migration and DFM of a highly mobile target has been reported. Recently, we have induced the concept of long-time coherent integration for a maneuvering target, and the Radon-FRFT (RFRFT) [28] and Radon-linear canonical transform (RLCT) [29] methods are proposed for detection of the target modeled as the linear FM (LFM) signal. However, the LFM signal model is not accurate to describe the complex micromotion characteristic of a marine target during long observation time. Considering the higher order phase signal model, such as the fourth-order phase signal, is more accurate than the LFM model [30]. However, the Doppler migration compensation and
parameters estimation are much more complicated and difficult to be implemented; thus, it is not valuable in practice. This paper aims at introducing an effective and accurate detection and estimation method of a marine target with micromotion. A novel transform, i.e., Radon-linear canonical ambiguity function (RLCAF) is proposed to compensate the range and Doppler migration simultaneously for the micromotion target modeled as the quadratic FM (QFM) signal. Using the longtime instantaneous autocorrelation function (LIACF) and extra three degrees of freedom, the micromotion target would appear as an obvious peak in the corresponding RLCAF domain. In addition, this paper provides comparisons of RLCAF with Ambiguity function (AF), RFT, FRFT, FRAF, HAF, and RLCT methods, which indicates they have close relations. The performance of the proposed method is validated by numerical experiments, and the results indicate that the RLCAF can improve the detection probability with better ability of clutter suppression. The rest of this paper is organized as follows. The m-D signal model of a marine target is established in Section II, including the translational and 3-D rotational motions. In Section III, we give the definition of LIACF and RLCAF. The RLCAF representations for mono and multicomponent m-D signals are derived. We also demonstrate the relations between RLCAF and some popular coherent integration methods. Section IV presents the detailed detection and estimation procedure with some remarks and explanations. In Section V, the effectiveness of the RLCAF is validated by numerical experiments using both simulated and real radar data collected by popular intelligent pixel (IPIX) processing radar [31], Council for Scientific and Industrial Research (CSIR) [32], and a sea surveillance radar (SSR). The last section concludes this paper and presents its future research direction. II. M-D A NALYSIS OF M ARINE TARGET W ITH M ICROMOTION Due to the environment influence such as the wind and wave, as well as the pushing and control effects caused by propeller, engine, and rudder, the complex motion of a marine target consists of translations and rotations, which can be described by six degrees of freedom. The 3-D rotational motion includes the pitch, roll, and yaw movements, which makes the Doppler appear as a period modulated property [33]. In addition, the motion of radar itself is not considered or has been compensated. Therefore, the target’s kinematics, such as its velocities, accelerations, jerks, and angular momentums, can be used to describe the complex motion. Fig. 1 gives the observation geometry, where three common coordinate systems are employed, i.e., the global system (X, Y, Z), parallel to the reference system (X1 , Y1 , Z1 ), and the local system (x, y, z). The x-axis marks the heading of the marine target, the left side marks the y-axis, and the top side marks the z-axis. The global coordinate system is usually fixed on the radar, and the local system is fixed on the rotation center of the target. If the azimuth and elevation angles of the center point of the target with respect to the radar are α and β, the unit vector of radar line of sight (RLOS) is denoted as n = [cos α cos β, sin α cos β, sin β]T .
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2227
where v0 , as , gs are the radial components of target’s initial velocity, acceleration, and jerk, respectively. Then, the radar returns are written in the vector form, and the radial velocity can be expressed as vr = (v0 , as , gs )T . Therefore, the RLOS is the integral of vr .n during the time Tn T n Rs (tm ) = (vr · n)dtm .
(5)
0
The corresponding Doppler shift has the form of ft (tm ) = Fig. 1.
Observation geometry of a marine target with micromotion.
A. M-D Model of Marine Target With Translational Motions In the target local coordinate system, a target located at D(x0 , y0 , z0 ) moving with velocity v, will move with translational motion to a new place in the reference coordinate system defined by v.n, where “.” represents the inner product. The translational motion can be divided into tangential and radial components, i.e., vt and vr . The latter parallel to n, is useful for coherent processing. In practice, to obtain high-range resolution and far detection range, the LFM signal is employed as the transmitted waveform, i.e., (1) st (t) = rect(t/Tp ) exp(j2πfc t + jπγt2 ) 1, |u| ≤ 1/2 where rect(u) = , T , f , and γ denote the 0, |u| > 1/2 p c pulsewidth, carrier frequency, and chirp rate, respectively, and t is the fast time. Suppose there is a target at the RLOS distance Rs (tm ), where tm is the slow-time measuring the time among pulses within a coherent processing interval. Then, after pulse compression (PC), the returned signal has the following form [3]: 2Rs (tm ) 4πRs (tm ) s(t, tm ) = Ar sinc B t − exp −j c λ (2) where Ar is the complex amplitude of the compressed signal, sinc(x) = sin(πx)/πx, B is the bandwidth, the delay is τ = 2Rs (tm )/c, c is the speed of light, and λ = c/fc is the wavelength. From (2), the target’s envelope has been shifted away from its original position. If the offset exceeds the radar range resolution ρr , it will come cross the ARU effect with distributed energy among different range bins [14]. Rs (tm ) can be expanded with Taylor series Rs (tm ) = r0 − v0 tm −
v 2 v tm − t3m − · · · 2! 3!
(3)
where r0 is the initial range, v and v are higher order terms of velocity. Considering the Weierstrass approximation principle and the complexity, the nonuniformly translational motion of a maneuvering target can be well described by a cubic phase signal (CPS) [24], [34]. Then, rewriting (3), we have Rs (tm ) = r0 − v0 tm − as t2m /2 − gs t3m /6
(4)
2 k · (vr · n) = f0 + μtm + t2m λ 2
(6)
where f0 = 2v0 /λ, μ = 2as /λ is the chirp rate, and k = 2gs /λ is the nonlinear FM item caused by the acceleration changes. Equation (6) indicates that the Doppler shift is modulated with quadratic frequency during observation time, which can be modeled as a quadratic FM (QFM) signal. The time-varying property of the QFM signal will make the broadened Doppler and range curvature with the DFM effect. B. M-D Model of Marine Target With 3-D Rotational Motions The angular rotation velocity ω = (ωx , ωy , ωz )T with rotation angles θ = (θx , θy , θz )T in the reference coordinate system are used to describe the rotation of the target, which are defined as the counterclockwise rotation about the x-y-zaxis. When the target is rotating, a point on the target r0 = (x0 , y0 , z0 )T will move to a new place P defined in the reference system. This new location of the point can be obtained from its initial position vector by multiplying by a rotation matrix RI with the rotation angles θ [3], i.e., RP = RI .r0 . Similar to the translational motion, ω can be decomposed into the ω t and ω r . However, ω t may result in Doppler frequency by the rotation motion and thus is called the effective rotation vector. Then, the line velocity of scatterer P is denoted as the outer product of ω t and RP , i.e., ω t × RP , and the corresponding radial component is (ω t × RP ).n. ω t usually shows periodic and time-varying properties, and it can be approximated as follows over a period of time: ω t (tm ) ≈ ω 0 + ω 1 tm + ω 2 t2m /2
(7)
where ω 0 , ω 1 , and ω 2 are the constant term, first-order term and quadratic term coefficients of the angular velocity. Therefore, the m-D shift resulting from the 3-D rotational motion also has the form of a QFM signal 2 fr (tm ) = (ω t × RP ) · n λ 2 = [ω 0 · (RP × n) + ω 1 · (RP × n)tm λ + ω 2 · (RP × n)t2m /2
(8)
where (a × b).c = a.(b × c) is used. Accordingly, the RLOS from the scatterer P to the radar can be expressed as T n Rs (tm ) = [(ω t × RP ) · n] dtm . 0
(9)
2228
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
From the aforementioned analysis, the radar returns of a marine target with micromotion in different range bins can be modeled as a QFM signal after PC, whose amplitude and frequency relate to the SCR and the motion status. Then, the m-D signal of a marine target can be expressed as 2Rs (tm ) s(t, tm ) = Ar sinc B t − c 1 1 (10) · exp j2π f0 t + μt2m + kt3m 2 6 where tm ∈ [−Tn /2, Tn /2]. Therefore, it is necessary to accumulate the target’s energy distributed in range and Doppler bins for better integration gain and detection performance.
Rf (tm , τ ) in the (τ, u) plane. The LIACF intends to reduce the signal order and the m-D signal can be easily accumulated in the RLCAF domain by rotating, distorting, and stretching the time–frequency plane with flexible parameters M . Moreover, the energy of sea clutter cannot be integrated due to the mismatch with RLCAF, and hence, the SCR will be greatly improved. Sample the original function f (tm , Rs ) and transform function LM f (τ, u) spaced with Δtm and Δu, i.e., f (nΔtm , Rs ), and LM f (τ, mΔu). Then, the discrete form of RLCAF is LM f (τ, mΔu) (N −1)/2 d
= CM ej 2b m
A. Principle of RLCAF Without loss of generality, the RLCAF can be decomposed into three parts: data acquisition for long-time integration, LIACF, and the LCT calculation. First, we define a 2-D complex function extracted in the slow-time versus range plane, which is denoted by f (tm , Rs ). Rs (tm ) represents the motion trajectory of a micromotion target and is used for searching lines in the plane, which has the form of (4). Then, the LIACF of the signal f (tm , Rs ) is defined by
τ τ (11) Rf (tm , τ ) = f tm + , Rs f ∗ tm − , Rs 2 2 where “∗” is the complex conjugation, and τ is the time delay. This way, the radar returns of the m-D signal during observation time are extracted in the 2-D (tm , Rs ) plane according to the motion parameters and calculated with LIACF. Then, the LIACF of the signal f (tm , Rs ) associated with the LCT with parameter M = (a, b; c, d), and τ is defined as RLCAF RLCAF [f (tm , Rs )] (τ, u) ∞ =
=
Rf (tm , τ )KM (tm , u)dtm ,
(Δu)2
· f ∗ nΔtm −
III. RLCAF-BASED L ONG -T IME C OHERENT I NTEGRATION
LM f (τ, u)
2
b = 0
(12)
−∞
where La,b,c,d ( ) denotes the RLCAF operator, and M = (a, b, c, d) are real numbers satisfying det(M ) = 1. KM (t, u) is the transform kernel, which has the form of [35], i.e., 2 1 at + du2 KM (t, u) = CM exp j − j ut (13) 2b b
n=−(N −1)/2
τ f nΔtm + , Rs 2
a 1 τ 2 , Rs ej 2b (nΔtm ) −j b mnΔuΔtm 2
(14)
where N = Tn fs is the signal length. The proposed method is named as RLCAF because it has close relation with the RT [16], which is also an integration method of the signal amplitudes along a straight line. However, RT only employs the amplitude information resulting in poor integration gain in case of the complex sea environment. Furthermore, the RLCAF has close relationships with many popular coherent integration methods. 1) The AF is one of the tools used to evaluate range and Doppler resolution of signals for radar applications. According to the definition of RLCAF, the AF corresponds to the set of parameter M = (0, 1; −1, 0) when the signal is accumulated within one range bin, i.e., |Δrs | ≤ ρr L0,1,−1,0 (τ, u) |ΔRs |≤ρr = AF [f (tm )] (τ, u). f
(15)
2) The FRFT can be thought as rotating the original signal counterclockwise by and an angle α [22]. The LCT is a three-parameter class of linear integral transforms, which includes among its many special cases, such as FRFT, scaling operations, and Fresnel transform [35]. They are more suitable for target detection with accelerated motion due to the orthonormal basis consisting of chirp functions. Considering the generality, the RLCAF can accumulate the LFM signal, as well without the quadratic frequency modulation component. In this case, the integration and transform results (peak value) of an accelerated moving target using RLCAF are quite similar to those using FRFT and LCT within one range bin. Thus M Lf
LFM
√ where CM = 1/ j2πb. The case b = 0 is obtained as the limit of the previous case b = 0 and can be neglected. The amplitude distribution along u-axis denotes the RLCAF domain. The inverse RLCAF can be represented by M −1 . From the definition and the physical meaning of the RLCAF, it can be interpreted as the affine transform of the LIACF
·
(u) |ΔRs |≤ρr | ≈ |FRFT or LCT [fLFM (tm )] (u) . (16)
A detailed derivation can be found in the Appendix. 3) Recently, the FRAF has been proposed based on the FRFT and AF in order to solve the problem of the signal with cubic phase [26]. However, the performance of FRAF is also influenced by the ARU effect. In fact, it is
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2229
Fig. 3. RLCAF representation for the m-D signals with (a, b, c, d) = (−0.1253, 0.9921, −0.9921, −0.1253) (SNR = −2 dB, Tn = 1.024, fs = 1000 Hz). (a) RLCAF spectrum for x1 (t); (b) RLCAF spectrum for x1 (t) and x2 (t).
Fig. 2.
Diagram of numerical coherent integration processing methods.
easy to find that the RLCAF is equivalent to FRAF under some circumstances, i.e., α,sin α,− sin α,cos α (τ, u) |ΔRs |≤ρr =FRAF [f (tm )] (τ, u). Lcos f (17) 4) Based on the coupling relationship of radial velocity, acceleration, range walk, and Doppler frequency of a moving target during long integration time, we have proposed the RLCT for targets modeled as chirp signals [29]. Interestingly, the RLCAF can be regarded as the AF associated with the RLCT. The diagram of numerical coherent integration processing methods are compared and shown in Fig. 2. The x- and y-axis denote the range bin and slow time, respectively. There are three kinds of movements, i.e., the uniform motion, accelerated motion and high-order or rotated motion. We divide the existing methods into two kinds, i.e., the integration methods within one range bin and the long-time coherent integration methods. The RFT can be regarded as a generalized Doppler filter bank with ability of ARU compensation. i.e., [14] RFT [f (tm , Rs )] (u) |ΔRs |≤ρr = MTD [f (tm )] (u). (18) However, the range curvature makes the RFT and MTD fail to accumulate the target’s energy if only straight lines are searched for. Combining the LIACF and the kernel of LCT, the proposed RLCAF can jointly compensate the envelope migration, range curvature, the high-order phase modulation (DFM) for a micromotion target. Therefore, the aforementioned methods are all special cases of RLCAF in a sense. B. RLCAF Representation for the M-D Signal For a m-D signal modeled as a QFM signal 4π f (tm , Rs ) = σ0 exp j Rs (tm ) λ
= σ0 exp j2π a0 + a1 tm + a2 t2m + a3 t3m , |tm | ≤ Tn /2 (19) where ai , i = 0, 1, . . . , 3 is the coefficient of the cubic polynomial phase and according to the signal model, a0 = 2R0 /λ =
ϕ0 , a1 = 2v0 /λ = f0 , a2 = as /λ = μ/2, and a3 = gs /3λ = k/6. The corresponding RLCAF has the form of Tn /2
LM f (τ, u)
= −Tn /2
τ τ f tm + , R s f ∗ tm − , R s 2 2
× KM (tm , u)dtm = σ02 CM ejπ(2a1 τ +a3 τ Tn /2
· −Tn /2
3
d 2 /2)+j 2b u
a 2 t exp j 6πa3 τ + 2b m u tm dtm . (20) + j 4πa2 τ − b
We can see from (20) that, when 6πa3 τ + a/2b = 0, the LM f (τ, u) will get the maximum value as a sinc function, i.e., 2 jπ(2a1 τ +a3 τ LM f (τ, u) = σ0 CM e
3
d 2 /2)+j 2b u
· Tn sinc [(4πa2 τ − u/b)tn /2]
(21)
and the peak is located at u = 4πa2 τ b. Therefore, the parameters a2 and a3 can be estimated by searching peaks in the RLCAF domain, i.e., (τ0 , u0 ) = arg max LM f (τ, u)
(τ,u)
a2 = u0 /4πτ0 b a3 = −a/12πτ0 b.
(22)
Therefore, the RLCAF has the focusing ability of m-D signal, which can be used for detection and estimation. We give an example to demonstrate the effectiveness of RLCAF. The parameters of the m-D signal are as set as follows: a0 = 100, a1 = 1000, a2 = −500, and a3 = 200. The RLCAF spectrum for the signal is shown in Fig. 3(a). It is obvious that there is a peak in the (τ, u) plane, and its coordinate represents the value of the parameters of a2 and a3 . For finite-length multicomponent m-D signals such as s(tm , rs ) = =
K i=1 K i=1
si (tm , rs )
σi exp j2π Ai +Bi tm +Ci t2m +Di t3m (23)
2230
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
Fig. 4. Flowchart of the RLCAF-based detection and estimation algorithm.
where K is the number of signal components; and Ai , Bi , Ci , and Di are real coefficients. Then, the RLCAF of s(tm , rs ) can be decomposed into the auto-terms and the cross-terms, i.e., LM s (τ, u) =
K
LM si (τ, u)
i=1
K−1
K
auto-terms
+
i=1 j=i+1
M LM si sj (τ, u) + Lsj si (τ, u)
cross-terms
(24)
where each auto-term LM si (τ, u) has the form of (21). Calculation of the cross-terms is rather complex, and the approximated expression can be given as follows [16]: M 2 LM si sj (τ, u) + Lsj si (τ, u) = B [C(X1 ) + C(X2 )] cos(Aτ ) + [S(X1 ) + S(X2 )] sin(Aτ 2 ) (25) where A, B, X1 , and x of m-D sig x X2 relate to the parameters nals, and, C(x) = 0 cos(πt2 /2)dt, S(x) = 0 sin(πt2 /2)dt are the Fresnel integrals. We can see that the cross-terms are always at the center point between the corresponding auto-terms, and they have the sine or cosine oscillation structures, whose modulus are much smaller than the auto-terms. In case of longer integration time, i.e., Tn → ∞, the RLCAF representation for multicomponent mD signals can be approximated as ideal impulses. We consider the same m-D signal s1 (t) as Fig. 3(a), as well as s2 (t) with A2 = 20, B2 = 500, C2 = 300, and D2 = 150. It can be seen from Fig. 3(b) that there are two obvious peaks in the RLCAF domain representing the auto-terms, whereas the cross-terms are rather small, and their energy can be ignored compared with the distinct peaks. Therefore, with the increment of integration time, the RLCAF, on its own, can greatly “suppress” the crossterms without changing the peaks coordinates, which indicate the asymptotic linearity property of RLCAF. IV. D ETECTION AND E STIMATION A LGORITHM OF M ICROMOTION TARGET AT S EA VIA RLCAF A. Flowchart of the Proposed Algorithm The flowchart of the proposed algorithm is illustrated in Fig. 4, and the main steps are listed as follows.
Step 1—Parameters Initialization According to the Predicted Type of the Marine Target: The radar returns are sampled in range and in azimuth direction, and then, the sampled data are performed with demodulation and PC in range and slow-time domain. Since there are various kinds of targets at sea resulting in different searching parameters, we classify the targets into two types, according to the observation environment and the target itself. In case of high sea state (no less than sea state 3), the target at sea will fluctuate with the rough sea surface with 3-D rotational motions. The change of the target’s attitude would result in the Doppler modulation, and therefore, the m-D of rotation plays the major role compared with that of translational motion. In this case, the target is labeled as Type 1. As for the target belonging to the Type 2, such as the speedboat, hovercraft, and the sea-skimming missile or aircraft, the translational motion with nonuniform velocity counts for much during the maneuvering, turning, or defense penetration. The integration time Tn of RLCAF can be greatly extended unaffected to the ARU and DFM effects, and for the phasedarray radar, Tn is only restricted by the dwell time of antenna beam Tdwell . Considering the m-D signal model (10), the Tn of (1) (2) Type 1 and Type 2, i.e., Tn and Tn , are quite different, which will be explained in the following parts. In addition, according to the type of the observed target, we set the searching scopes of velocity [−vmax , vmax ], acceleration [−amax , amax ], and jerk [−gmax , gmax ] and their intervals depend on the Doppler resolution. Step 2—Long-time Coherent Integration via RLCAF: The trajectory of the micromotion target to be searched for can be determined by the preset parameters in Step 1, i.e., Rs (tm ) = ri − vj tm − al t2m /2 − gq t3m /6
(26)
(1)
where tm = nTl , n = 1, 2, . . . , Np for Type 1 and tm = (2) nTl , n = 1, 2, . . . , Np for Type 2, Tl is the pulse repetition period, Np is the number of pulses, ri ∈ [r1 , r2 ], vj ∈ [−vmax , vmax ], al ∈ [−amax , amax ], and gq ∈ [−gmax , gmax ]. The observation values are then extracted along the searching trajectory for long-time coherent integration in the (tm , Rs ) plane X1×Np = s(n, [Rs (nTl ) − r1 ]/ρr )( : integer operation). By searching for the preset moving trajectories of a target in the range and slow-time plane, the range walk compensation turns into the parametric matching problem. Then, we can perform the RLCAF of these observation values to compensate range and Doppler migrations simultaneously with preset transform parameters satisfying det(M ) = 1. The detailed procedure of RLCAF processing is presented in Fig. 5, which shows that RLCAF is a special kind of Doppler filter bank with different delays. Then, the micromotion target in the ith range bin will correspond to a peak value in (τ , u) domain according to (21), when 6πa3 τi0 + a/2b = 0 M Lr (τi , ui ) = σ02 CM Tn (27) 0 0 i where (τi0 , ui0 ) is the peak coordinate, i.e., (τi0 , ui0 )|ri = (−a/12πa3 b, −aa2 /3a3 ),
i = 1, 2, . . . , Nr (28)
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2231
TABLE I D ESCRIPTION OF D OUGLAS S EA S TATE
Fourier transform peak vˆ0 = a1 λ/2
λ = arg max FFT f (tm , Rs ) 2 f0 gˆs 3 2π 2 . (31) · exp −j a ˆ s tm + tm λ 3
Finally, the motion trajectory can be estimated by Rs (tm ) = rˆ0 − vˆ0 tm − a ˆs t2m /2 − gˆs t3m /6.
Fig. 5.
Detailed procedure of RLCAF-based long-time coherent integration.
where Nr is the number of range bins for searching. Step 3—Micromotion Target Detection Using the Detection Map in RLCAF Domain: If all the searching parameters are traversed, we will obtain the detection map in the RLCAF domain, |LM f (τi0 , ui0 )|ri , which means the peak value in the RLCAF domain for different searching ranges ri . We take the modulus as test statistic and compare with an adaptive threshold H1
> M Lf (τi , ui ) < η 0 0 r i
H0
(29)
where η is the threshold usually determined by a constant false alarm rate (CFAR) detector [36]. If the test statistic is bigger than the threshold, a micromotion target in the ri the range bin can be declared. Otherwise, go on with the other range bins. It should be noted that “CLEAN” method can be employed in case of multiple targets to reduce the effect of the stronger target on the weaker one [37]. Step 4—Micromotion Parameters and Trajectory Estimation: Since the searching range, initial velocity, acceleration, and jerk are connected with the peak coordinate of target in RLCAF domain, the micromotion parameters can be estimated according to (19) and (28). Suppose the initial range of the detected target is rl , and its corresponding peak coordinate is (τl0 , ul0 ). Then, the estimation method is as follows: ⎧ ⎨ rˆ0 = r1 + lρr a ˆs = a2 λ = ul0 λ/4πbτl0 (30) ⎩ gˆs = 3a3 λ = −aλ/4πbτl0 . The initial velocity vˆ0 can be estimated by dechirping the original signal with the estimated parameters and finding the
(32)
B. Remarks and Explanations Determination of Coherent Integration Time: The proposed algorithm is more appropriate for signal processing using modern radar, such as the wideband radar, phased-array radar, or multiple-input multiple-output radar, which can ensure longtime observation for the target. For the Type 2 target, we (2) only have to ensure its integration time Tn no less than Tdwell . However, for the Type 1 target, the m-D due to the rotational movement is periodically modulated, and it can be well approximated as the QFM signal within the rotation period (1) (1) Tr . Therefore, the Tn should satisfy the condition, Tn ≤ min(Tdwell , Tr ). Tr includes the period of yaw, pitch, and roll motions [38]. Generally, Tr is closely related with the sea state, and in case of limited prior information of the micromotion target to be detected, Tr can be determined by the sea state and equals to the average wave period show in Table I. In real applications, the long integration time is a relative value, which has relations with the dwell time of the antenna and the sampling frequency among the pulses interval. Moreover, we should consider the decorrelation time of sea clutter and the micromotion target. Sometimes, it won’t take very long time as long as the data number is sufficient for the expected performance. Calculation Complexity: Although high integration gain and detection performance can be achieved via RLCAF, it requires large quantities of searching calculations and long integration time. On the one hand, the integration performance and accuracy of parameters estimation depend on the searching intervals of the preset motion parameters, which would lead to a heavy computational burden. On the other hand, the RLCAF itself requires efficient discrete computational method. Fortunately,
2232
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
the proposed method can be efficiently implemented once the following techniques can be applied. (1) Several fast implementation methods for LCT have been proposed, which can be applied in the process of calculating RLCAF. The recursive fast algorithm for the LCT is achieved by using the periodicity and shifting properties of the DLCT to break down the original matrix transform into identical transforms of smaller sizes, which makes the computational burden as N log N [39]. In addition, the digital computation of LCT proposed by [35] computes LCT with a performance similar to that of the FFT algorithm in computing the FT. (2) Make use of the prior information of the target or the environment to reduce the searching area as far as possible. Moreover, the calculation burden can be reduced by half using the positive and negative symmetry of searching parameters. (3) Using some techniques such as the grading iterative search method, the RLCAF will save much of the searching time greatly [22]. CFAR Property in Sea Clutter Background: It is known that sea clutter is more complex, particularly the sea spikes in case of high sea state, which can influence the detection performance. In such case, we can employ the sea clutter suppression method in [3], where sea spikes are identified and eliminated before target detection to improve SCR. One thing for sure is that once the RLCAF matches the echo of the micromotion target, the integration gain of target will be much higher than that of clutter. Besides, whether the detection performance is the best or not depends on the CFAR methods, which should be designed and selected based on characteristics of the clutter, such as the amplitude distribution in RLCAF domain. V. S IMULATION AND E XPERIMENTAL R ESULTS In this section, some results with simulated and real data sets are presented to demonstrate the effectiveness of the proposed algorithm for detection of a low-observable marine target with micromotion. Comparisons with other popular coherent integration methods, i.e., MTD, FRFT, HAF, and RFT are also given, including the integration ability, SCR improvement, parameters estimation, computation time, and detection probability. The McMaster IPIX radar database [31] and the CSIR database [32] are employed to validate the detection performance of maneuvering marine target with translational motion. Moreover, the detection and estimation performances of a marine target with rotational motion are validated with the SSR data set. Descriptions of the three databases are shown in Table II, including radar setup parameters, experiment summary, and environmental parameters. A. Simulated Micromotion Target Detection With IPIX Data The X-280# data were collected in November 1993 conducted at a site in Osborne Head Gunnery Range (OHGR), Dartmouth, Nova Scotia, on the East Coast of Canada, with a moderate sea state. Although the cooperative target, i.e., a spherical block of Styrofoam wrapped with wire mesh, is very small (diameter is 1 m) and weak (SCR is about 0–6 dB), it exhibits little micromotion characteristics, which are not suitable for the performance verification. Therefore, we simulate two
TABLE II D ESCRIPTION OF N UMERICAL R EAL S EA C LUTTER DATABASES
TABLE III PARAMETERS OF THE S IMULATED M ARINE TARGETS W ITH M ICROMOTION
micromotion targets with pure sea clutter. The first target (#1) moves with high mobility, whereas its radar reflection is lower (SCR = −5 dB after PC) than the second target (#2) (SCR = −3 dB). Detailed simulation parameters are shown in Table III. Radar returns versus time of the two simulated micromotion targets are plotted in Fig. 6. The targets’ returns are covered by heavy sea clutter and cannot be directly figured out by the amplitudes. For further analysis, we give the relation between time and range bins. It can be found that during the long-time (Tn = 6 s), both of the two micromotion targets move across several range bins due to the acceleration and jerk motions. Fig. 6(b) also indicates that only signals within Tn = 0.6 s can be provided for the traditional coherent integration methods. Figs. 7–11 compare the coherent integration abilities using RFT, FRFT, HAF, and RLACF. We perform the long-time coherent integration via RFT with Tn = 2 s and the results are shown in Fig. 7. From the RFT spectrum, the energy of the two marine targets has been accumulated to one range bin, and hence, RFT is an effective tool for range migration compensation. However, the sea clutter interference results in an incorrect estimated initial distance of #1 (r01 = 12.9 Km). In addition, the targets’ energy is distributed in different frequency bins due to the DFM effect. Therefore, the standard RFT-based detection method is ineffective and not suitable for time-varying m-D signals. The two micromotion targets in FRFT domain [Fig. 8(a) and (b)] are more visible, whose energy is mainly accumulated around the popt1 = 1.277 and popt2 = 1.157. Although sea clutter still exists with several peaks, it can be separated from the target in different transform domains. Although, in the
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2233
Fig. 6. Radar returns versus time of the two simulated micromotion targets in sea clutter (X-280#). (a) Range-time intensity plot (the white lines are the true trajectories). (b) Relation between time and range bins.
Fig. 7. Coherent integration results of the marine targets with micromotion via RFT (X-280#, Tn = 2 s). (a) RFT spectrum (r01 = 12.9 Km, r02 = 13 Km). (b) Energy distribution in RFT domain.
Fig. 8. Coherent integration results of the marine targets with micromotion via FRFT (X-280#, Tn = 0.6 s). (a) FRFT spectrum (r01 = 13 Km, r02 = 13 Km). (b) Energy distribution in FRFT domain. (c) Slices of FRFT spectrum of #1 (popt1 = 1.277). (d) Slices of FRFT spectrum of #2 (popt2 = 1.157).
corresponding FRFT domain [Fig. 8(c) and (d)], the two targets can be separated, the peak width Δp is broadened due to the mismatch between FRFT and m-D signals, which is called
the mismatch loss. The mismatch loss of #1 is more obvious, indicating bigger acceleration or jerk components. Therefore, the estimated motion parameters are not accurate.
2234
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
Fig. 9. Coherent integration results of the marine targets with micromotion via HAF (X-280#, Tn = 0.6 s). (a) HAF spectrum (r01 = 13 Km, r02 = 13 Km). (b) Energy distribution along frequency axis (τ = 0.4 s).
Fig. 10. Coherent integration results of the marine targets with micromotion via RLCAF with (a, b, c, d) = (−0.0628, 0.998, −0.998, −0.0628) (X-280#, Tn = 2 s). (a) RLCAF spectrum (r01 = 13 Km, r02 = 13 Km). (b) Energy distribution in RLCAF domain. (c) Slices of RLCAF spectrum of #1. (d) Slices of RLCAF spectrum of #2.
Then, a kind of polynomial phase transform, i.e., HAF method is employed. For an M th-order polynomial phase signal, its HAF has the form of [25] THAF /2
HAF(τM −1 , f ) =
sM (tm , τM −1 ) exp(−j2πf tm )dtm
−THAF /2
(33) where sM (tm , τM −1 ) is the multilag high-order instantaneous moment (ml-HIM), which is performed (M − 1) times. From the HAF spectrum and the energy distribution along frequency axis (Fig. 9), the HAF is able to deal with m-D signals modeled as QFM signals with less mismatch loss. However, the HAF suffers from cross-terms. From Figs. 8 and 9, it can be concluded that the coherent integration abilities and detection
performances of FRFT and HAF are affected by the mismatch loss or the limited integration time within one range bin. In order to deal with the ARU and DFM effects with good matching ability to the m-D signals, the results of RLCAF are given in Fig. 10. We can see that the two micromotion targets are well accumulated in the RLCAF domain as expected with obvious peaks. The sea clutter is mostly suppressed and can be separated from the targets. There are few cross-terms due to the asymptotic linearity property. From Fig. 10(c) and (d), the peak side-lobe ratio is high with narrow width. In addition, parameters as and gs can be estimated according to (30). Although we may obtain better detection performance based on RLCAF, there are two shortcomings. One is the sea clutter interference, and the other is energy residue among multiple signals. For the first problem, we can rotate, distort, and stretch the time–frequency plane with different transform parameters M .
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2235
Fig. 11. Improved coherent integration and estimation of #1 and #2 with “CLEAN” method and (a, b, c, d) = (−0.1564, 0.9877, −0.9877, −0.1564) (X-280#, Tn = 2 s). (a) Energy distribution in RLCAF domain. (b) Energy distribution of #1 after “CLEAN” method. (c) Slices of RLCAF spectrum of #1. (d) Slices of RLCAF spectrum of #2.
Then, the distance of the peaks between sea clutter and micromotion target can be enlarged to reduce the impact of sea clutter. In addition, “CLEAN” method can be employed to eliminate the residue of the bigger m-D component [37]. Fig. 11 shows the improved integration results using “CLEAN” method and different M . The sea clutter and the cross-terms have been greatly suppressed far away from the micromotion targets. Moreover, using the “CLEAN” technique, the weaker m-D component can be easily extracted and estimated. Performances of the four methods are tested and compared in Table IV. The output SCR, i.e., SCRout , and the estimation error ε are defined and employed for quantitative comparisons ⎛ ⎞ 2 m+D Y (i) /2D m−D ⎜ ⎟ SCRout=10 lg⎝ ⎠ m−D 2 N 2 |Y (i)| + m+D |Y (i)| /(N−2D) 1
TABLE IV C OMPARISONS OF P ERFORMANCE AND C OMPUTING T IME U SING D IFFERENT M ETHODS (IPIX, X-280#)
(34) ε =|f − fˆ|
(35)
where Y (m) is the maximum value of the output in the transform domain, m denotes the peak location of the target and D is the peak width, and f and fˆ are the true and estimated value. It can be easily deduced that larger peak amplitude and less clutter may lead to higher SCRout and better detection performance. From Table IV, we can see that the proposed RLCAF can achieve higher SCRout due to the long-time coherent integra-
tion and good matching ability of m-D signal. It can improve the SCRout by about 5−6 dB compared with the popular coherent integration methods. One hundred Monte Carlo simulations are carried out to calculate the average computing time. The integration and searching process require more time, which would increase the computational burden. In this case, we should employ the methods introduced in Section IV to improve efficiency.
2236
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
Fig. 12. Descriptions of the X-17# dataset with a maneuvering Rotary Endeavour target. (a) Range line versus time plot; (b) Range walk, GPS trajectory, and its polynomial fitted curve of the Rotary Endeavour; (c) High Doppler resolution spectrogram of target range bin [32].
Fig. 13. Comparisons of detection and estimation results using RFT and RLCAF at different starting times. (X-17#, Tn = 5.12 s, Pfa = 10−4 ). (a1) RFT outputs (t0 = 22 s). (b1) RLCAF outputs (t0 = 22 s, τ = 0.85 s). (a2) RFT outputs (t0 = 35 s). (b2) RLCAF outputs (t0 = 35 s, τ = 0.75 s).
B. Real Micromotion Target Detection With CSIR Data The measurement trial was conducted on November 4, 2007 with an experimental monopulse radar deployed on top of Signal Hill in Cape Town and a cooperative target named as Rotary Endeavour. The range-time intensity plot for X-17# with a maneuvering Rotary Endeavour target is presented in Fig. 12(a). The Rotary Endeavour is a class 35.5-m rigid inflatable boat with two 60-hp Yamaha outboard motors, and its trajectory was estimated using a differential-processing GPS receiver, which is plotted in the white line. It is not clear to find the target’s returns only by the amplitudes. The range walk, GPS trajectory of the target, and its cubic polynomial fitted curve are shown in Fig. 12(b). It is found that during the observation time, the target moves across nearly ten range bins (green dotted line), according to the raw GPS range (red line), which can be well fitted by a cubic polynomial curve (blue line). Therefore, the established m-D signal model in Section II is effective
TABLE V C OMPARISONS OF P ERFORMANCE AND C OMPUTING T IME BY RFT AND RLCAF M ETHODS (CSIR, X-17#)
and suitable for real applications. The high Doppler resolution spectrogram of the Rotary Endeavour is plotted in Fig. 12(d) at the 51st range gate. The target has high mobility with timevarying narrow Doppler response. The local disturbance of the sea surface is strong and visible with broad Doppler bandwidth ranging from zero frequency to slightly higher than the speed of
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
2237
Fig. 14. Detection and estimation of the marine target with micromotion by MTD, RFT, FRFT, and RLCAF (S-02#). (a) Range-Doppler analysis of radar returns (Tn = 1 s). (b) STFT spectrum of the radar returns extracted by RFT (Tn = 5 s). (c) MTD outputs (Tn = 1 s). (d) RFT outputs (Tn = 5 s). (e) FRFT outputs in the best transform domain (Tn = 1 s, popt = 1.011) (f) RLCAF outputs along u-axis (Tn = 5 s, τ = 0.833 s).
the target. Moreover, the spectral intensity is much higher than the target signature. Hence, with such a low SCR, it becomes increasingly difficult to detect the target. We select two intervals to verify the proposed algorithm and make comparison with RFT method in Fig. 13. The two data sets start at t0 = 22 s, 35 s, and the integration time is 5.12 s with down sampling frequency fs = 200 Hz. From Fig. 13(a1) and (a2), although we can separate the sea clutter and the micromotion target by frequency, sea clutter is accumulated as well via RFT, making it difficult to judge a target by the CFAR threshold. Moreover, due to the acceleration and jerk, the spectrum of m-D signal is broadened resulting in poor estimation accuracy. The CFAR threshold is determined by the biparameter CFAR detector with false alarm probability (Pfa = 10−4 ), which is plotted in the red dotted line. It can be easily seen that after detection, there still remains quite a lot of false alarms. Fortunately, the ARU and DFM effects can be perfectly solved by the proposed RLCAF method, which is shown in Fig. 13(b1) and (b2). The peak of the target is more obvious and at the same time, we obtain lower amplitudes of sea clutter. According to the peak location, the motion parameters of the target can be estimated, which are in correspondence with the real motion status. Furthermore, we provide the comparisons between RFT and RLCAF in Table V, where ΔP denotes the absolute differ-
ence between the normalized peak of sea clutter and the target. It can be found that the SCRout of RLCAF outperforms RFT by 6 dB or so. It should be noted that in this experiment, the complex trajectory searching process is not necessary due to the GPS information, and hence the computing time of RLCAF is greatly reduced. C. Real Micromotion Target Detection With SSR Data The detection and estimation performances of a marine target (cargo ship) with rotational motion are validated using S-01#. Fig. 14(a) presents the range-Doppler image with a possible marine target at 35 nm. The Doppler spectra are broadened, indicating the DFM effect. Moreover, sea clutter and noise are surrounded around different range and Doppler bins. We obtain the short-time FT (STFT) spectrum of the target extracted by RFT during Tn = 5 s [Fig. 14(b)]. The micromotion target exhibits time-varying property and can be modeled as a QFM signal. The rotation period is about 9 s, which is in accordance with the sea state and wave period given in Table I. Then, according to the determination method of integration time in Section IV, Tn is set to 5 s. Comparing the outputs of MTD and RFT, i.e., Fig. 14(c) and (d), we can find that in spite of long integration time, the improvement of RFT is not obvious
2238
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
applied to detect and estimate the m-D signal of a marine target. The performances are validated by numerical experiments of real data, including the IPIX, CSIR, and SSR data sets, which show the excellent abilities of coherent integration and sea clutter suppression. It is believed that the RLCAF has promising applications in maneuvering target detection, clutter suppression, and can provide useful information for target tracking. The fast implementation of RLCAF is still a challenging problem for future engineering applications.
Fig. 15. Pd-SCR curves of the proposed method (X-17#, Pfa = 10−3 ).
accordingly. Then, the m-D signal is transformed into FRFT domain [Fig. 14(e)]. The peak coordination indicates a small transform order (popt = 1.011) with the estimated acceleration as = 0.915 m/s2 . However, due to the limited available pulses, the FRFT still cannot achieve better integration performance. Moreover, according to Fig. 14(a), the true motion status is a decelerated rotational motion rather than accelerated motion. Finally, the RLCAF outputs are obtained [Fig. 14(f)], showing the excellent abilities of integration, clutter suppression, and detection. The ΔP of RLCAF is 0.7881 and SCRout is improved by about 10, 8, and 7 dB compared with the MTD, RFT, and FRFT, respectively.
A PPENDIX A P ROOF OF (16) Suppose an LFM signal, i.e.,
f (tm , Rs ) = σ0 exp j2π a0 + a1 tm + a2 t2m , |tm | ≤ Tn /2 Its RLCAF is given as follows: Tn /2
LM f (τ, u)
= −Tn /2
VI. C ONCLUSION In this paper, a novel detection method for a target in sea clutter has been proposed, which not only makes use of the micromotion characteristic but also achieves long-time coherent integration without the ARU and DFM effects. After range compression, the model of the m-D of a marine target, resulting from the translational and 3-D rotational movements, can be approximated as a QFM signal. As a generalization of many popular coherent integration methods, e.g., AF, FRFT, FRAF, and RLCT, the proposed RLCAF has the ability of representation for mono and multicomponents m-D signals. Combined with the RLCAF technique, a new algorithm is illustrated and
τ τ f tm + , R s f ∗ tm − , R s 2 2
× KM (tm , u)dtm d
2
= σ02 CM ejπ2a1 τ +j 2b u Tn /2
· −Tn /2
D. Detection Performance Analysis The detection performance of the proposed method is then analyzed (Pfa = 10−3 ) in Fig. 15. An m-D signal is simulated embedded in the pure sea clutter of X-17#. The biparameter CFAR detector is combined with the four integration methods, i.e., FRFT, HAF, RFT, and RLCAF, as corresponding detectors. The detection probabilities (Pd ) versus SCRs are calculated by 105 times of Monte Carlo trials. From Fig. 15, it is clear that the proposed method is superior to the other three detection methods. An interesting point should be made that in case of lower SCR environment (SCR = −5 dB), the Pd of RFT is higher than the FRFT and HAF methods. It means that the longtime integration will play a major role. While the superiority of RFT on Pd improvement decreases as the increment of SCR due to the mismatch loss of the m-D signal.
(A1)
a u tm dtm . exp j t2m + j 4πa2 τ − 2b b (A2)
When a = 0, the LM f (τ, u) will get the maximum value as a sinc function, i.e., d
2
2 jπ2a1 τ +j 2b u LM f (τ, u) = σ0 CM e
· Tn sinc [(4πa2 τ − u/b)Tn /2] .
(A3)
The LCT is defined by means of the same transform kernel with RLCAF, and is expressed as ∞ f (t)K(a,b,c,d) (t, u)dt, b = 0. (A4) LCT [f (t)] = −∞
Thus, it is easy to calculate the LCT of (A1) LCT [f (tm )] d
2
d
2
= σ0 CM ej 2b u ∞ 2 · ej2π(a0 +a1 tm +a2 tm ) K(a,b,c,d) (tm , u)dtm −∞
= σ0 CM ej 2b u +j2πa0 ∞ u
a
− 2πa1 + jt2m + 2πa2 dtm . · exp −jtm b 2b −∞
(A5)
CHEN et al.: RLCAF-BASED DETECTION AND ESTIMATION METHOD FOR MARINE TARGET WITH MICROMOTION
When a/2b + 2πa2 = 0, the LCT[f (tm )] will also get the maximum value as a sinc function, i.e., d
2
LCT [f (tm )] = σ0 CM ej 2b u
+j2πa0
· Tn sinc [(u/b − 2πa1 )Tn /2] .
(A6)
Then, we can get the result of (16). From the aforementioned analysis, the RLCAF is quite different with LCT. However, the RLCAF can be regarded as the AF associated with the RLCT proposed in [29]. ACKNOWLEDGMENT The authors would like to thank the small boat detection team from CSIR for the valuable data sets, as well as the anonymous reviewers for their valuable comments and suggestions. R EFERENCES [1] L. Zuo, M. Li, X. W. Zhang, Y. J. Wang, and Y. Wu, “An efficient method for detecting slow-moving weak targets in sea clutter based on time–frequency iteration decomposition,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 6, pp. 3659–3672, Jun. 2013. [2] S. Panagopoulos and J. J. Soraghan, “Small-target detection in sea clutter,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 7, pp. 1355–1361, Jul. 2004. [3] X. L. Chen, J. Guan, Z. H. Bao, and Y. He, “Detection and extraction of target with micromotion in spiky sea clutter via short-time fractional Fourier transform,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 3, pp. 1002–1018, Feb. 2014. [4] K. D. Ward and S. Watts, “Use of sea clutter models in radar design and development,” IET Radar Sonar Navigat., vol. 4, no. 2, pp. 146–157, Apr. 2010. [5] L. Rosenberg, “Sea-spike detection in high grazing angle X-band seaclutter,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 8, pp. 4556–4562, Aug. 2013. [6] M. Greco, P. Stinco, and F. Gini, “Impact of sea clutter nonstationarity on disturbance covariance matrix estimation and CFAR detector performance,” IEEE Trans. Aerosp. Electron. Syst., vol. 46, no. 3, pp. 1502–1513, Jul. 2010. [7] F. Luo, D. T. Zhang, and B. Zhang, “The fractal properties of sea clutter and their applications in maritime target detection,” IEEE Geosci. Remote Sens. Lett., vol. 10, no. 6, pp. 1295–1299, Nov. 2013. [8] J. Guan, N. B. Liu, J. Zhang, and J. Song, “Multifractal correlation characteristic for radar detecting low-observable target in sea clutter,” Signal Process., vol. 90, no. 2, pp. 523–535, Feb. 2010. [9] X. L. Chen, J. Guan, Y. He, and J. Zhang, “Detection of low observable moving target in sea clutter via fractal characteristics in FRFT domain,” IET Radar Sonar Navigat., vol. 7, no. 6, pp. 635–651, Jul. 2013. [10] V. C. Chen, F. Y. Li, S.-S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst., vol. 42, no. 1, pp. 2–21, Jan. 2006. [11] Y. Luo, Q. Zhang, C. W. Qiu, X. J. Liang, and K. M. Li, “Micro-Doppler effect analysis and feature extraction in ISAR imaging with steppedfrequency chirp signals,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 4, pp. 2087–2098, Apr. 2010. [12] X. R. Bai, M. D. Xing, F. Zhou, G. Y. Lu, and Z. Bao, “Imaging of micromotion targets with rotating parts based on empirical-mode decomposition,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 11, pp. 3514–3523, Nov. 2008. [13] G. Hajduch, J. M. Le Caillec, and R. Garello, “Airborne high-resolution ISAR imaging of ship targets at sea,” IEEE Trans. Aerosp. Electron. Syst., vol. 40, no. 1, pp. 378–384, Jan. 2004. [14] J. Xu, J. Yu, Y. N. Peng, and X.-G. Xia, “Radon-Fourier transform for radar target detection, I: Generalized Doppler filter bank,” IEEE Trans. Aerosp. Electron. Syst., vol. 47, no. 2, pp. 1186–1202, Apr. 2011. [15] J. Tian, W. Cui, and S. Wu, “A novel method for parameter estimation of space moving targets,” IEEE Geosci. Remote Sens. Lett., vol. 11, no. 2, pp. 389–393, Feb. 2014.
2239
[16] M. S. Wang, A. K. Chan, and C. K. Chui, “Linear frequency-modulated signal detection using Radon-ambiguity transform,” IEEE Trans. Signal Process., vol. 46, no. 3, pp. 571–586, Mar. 1998. [17] Q. Zhang, T. S. Yeo, H. S. Tan, and Y. Luo, “Imaging of a moving target with rotating parts based on the Hough transform,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 1, pp. 291–299, Jan. 2008. [18] P. W. Moo and Z. Ding, “Tracking performance of MIMO radar for accelerating Targets,” IEEE Trans. Signal Process., vol. 61, no. 21, pp. 5205–5216, Nov. 2013. [19] L. Du et al., “Bayesian spatiotemporal multitask learning for radar HRRP target recognition,” IEEE Trans. Signal Process., vol. 59, no. 7, pp. 3182–3196, Jul. 2011. [20] R. Tao, N. Zhang, and Y. Wang, “Analysing and compensating the effects of range and Doppler frequency migrations in linear frequency modulation pulse compression radar,” IET Radar Sonar Navigat., vol. 5, no. 1, pp. 12–22, Jan. 2011. [21] G. C. Sun, M. D. Xing, X.-G. Xia, Y. R. Wu, and Z. Bao, “Robust ground moving-target imaging using deramp–Keystone processing,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 2, pp. 966–982, Feb. 2013. [22] J. Guan, X. L. Chen, Y. Huang, and Y. He, “Adaptive fractional Fourier transform-based detection algorithm for moving target in heavy sea clutter,” IET Radar Sonar Navigat., vol. 6, no. 5, pp. 389–401, Jun. 2012. [23] F. Millioz and M. Davies, “Sparse detection in the chirplet transform: Application to FMCW radar signals,” IEEE Trans. Signal Process., vol. 60, no. 6, pp. 2800–2813, Jun. 2012. [24] L. Wu, X. Z. Wei, D. G. Yang, H. Q. Wang, and X. Li, “ISAR Imaging of targets with complex motion based on discrete chirp Fourier transform for cubic chirps,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 10, pp. 4201–4212, Oct. 2012. [25] S. Barbarossa, A. Scaglione, and G. B. Giannakis, “Product highorder ambiguity function for multicomponent polynomial-phase signal modeling,” IEEE Trans. Signal Process., vol. 46, no. 3, pp. 691–708, Mar. 1998. [26] T. S. Qiu and L. Li, “A novel joint parameter estimation method based on fractional ambiguity function in bistatic multiple-input multiple-output radar system,” Comput. Elect. Eng., vol. 39, no. 4, pp. 1248–1259, May 2013. [27] A. Gholami, “Sparse Time–Frequency DecBiparametric CFAR procedures for lognormal clutteromposition and some applications,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 6, pp. 3598–3604, Jun. 2013. [28] X. L. Chen, J. Guan, N. B. Liu, and Y. He, “Maneuvering target detection via Radon-fractional Fourier transform-based long-time coherent integration,” IEEE Trans. Signal Process., vol. 62, no. 4, pp. 939–953, Apr. 2014. [29] X. L. Chen, J. Guan, N. B. Liu, W. Zhou, and Y. He, “Detection of low observable sea-surface target with micromotion via Radon-linear canonical transform,” IEEE Geosci. Remote Sens. Lett., vol. 11, no. 7, pp. 1225–1229, Jul. 2014. [30] Y. Wang and Y. C. Lin, “ISAR imaging of non-uniformly rotating target via range-instantaneous-Doppler-derivatives algorithm,” IEEE J. Sel. Topics Appl. Earth Observ., vol. 7, no. 1, pp. 167–176, Jan. 2014. [31] A. Drosopoulos, “Description of the OHGR database,” Defence Research Establishment, Ottawa, ON, Canada, Tech. Rep. 94-14, Dec. 1994. [32] H. J. de Wind, J. C. Cilliers, and P. L. Herselman, “DataWare: Sea clutter and small boat radar reflectivity database,” IEEE Signal Process. Mag., vol. 27, no. 2, pp. 145–148, Mar. 2010. [33] Y. Li, R. Wu, M. Xing, and Z. Bao, “Inverse synthetic aperture radar imaging of ship target with complex motion,” IET Radar Sonar Navigat., vol. 2, no. 6, pp. 395–403, Dec. 2008. [34] X. Bai, R. Tao, Z. J. Wang, and Y. Wang, “ISAR imaging of a ship target based on parameter estimation of multicomponent quadratic frequencymodulated signals,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 2, pp. 1418–1429, Feb. 2014. [35] A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2383–2394, Jun. 2008. [36] M. Guida, M. Longo, and M. Lops, “Biparametric CFAR procedures for lognormal clutter,” IEEE Trans. Aerosp. Electron. Syst., vol. 29, no. 3, pp. 798–809, Jul. 1993. [37] J. Misiurewicz, K. S. Kulpa, Z. Czekała, and T. A. Filipek, “Radar detection of helicopters with application of CLEAN method,” IEEE Trans. Aerosp. Electron. Syst., vol. 48, no. 4, pp. 3525–3537, Oct. 2012.
2240
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 4, APRIL 2015
[38] A. W. Doerry, “Ship dynamics for maritime ISAR imaging,” Sandia Nat. Lab., Livermore, CA, USA, Tech. Rep. SAND2008-1020, Feb. 2008. [39] B. M. Hennelly and J. T. Sheridan, “A recursive fast algorithm for the linear canonical transform,” in Proc. SPIE, 2005, vol. 5823, pp. 1–12.
Xiaolong Chen (A’14) was born in Shandong, China, in 1985. He received the B.S. degree in 2008, the M.S. degree in 2010, and the Ph.D. degree in 2014, all in information and communication engineering from the Naval Aeronautical and Astronautical University, Yantai, China. He is currently a Lecturer with the Department of Electronic and Information Engineering, Naval Aeronautical and Astronautical University. He has published about 30 academic articles and applied for 13 national invention patents. He is the coauthor of Radar Target Detection–Fractal Theory and Its Application (in Chinese, Beijing: Publishing House of Electronics Industry, 2011). His current research interests include time–frequency analysis, micro-Doppler, and moving target detection at sea. Dr. Chen is a Member of the Chinese Institute of Electronics. In 2012, he received the Army Excellent Master Dissertation. He is frequently a Reviewer for IET Radar Sonar and Navigation, IEEE S IGNAL P ROCESSING L ETTERS, IEEE J OURNAL OF S ELECTED T OPICS IN A PPLIED E ARTH O BSERVATIONS AND R EMOTE S ENSING , and many international conferences.
Jian Guan (M’07) was born in Liaoning, China, in 1968. He received the Ph.D. degree in electronic engineering from Tsinghua University, Beijing, China, in 2000. He is currently a Professor with the Naval Aeronautical and Astronautical University, Shandong, China. He has published over 140 academic articles and declared 13 national invention patents. He is the coauthor of Radar Target Detection and CFAR Processing (in Chinese, Beijing: Tsinghua University Press, 1st ed., 1999, 2nd ed., 2011) and the author of Radar Target Detection–Fractal Theory and Its Application (in Chinese, Beijing: Publishing House of Electronics Industry, 2011). His current research interests include radar target detection and tracking, image processing, and information fusion. Dr. Guan is a Senior Member of the Chinese Institute of Electronics. He is frequently a Reviewer for a number of international technical journals. He has served in the technical committees of many international conferences on radar systems and remote sensing.
Yong Huang was born in Shandong, China, in 1978. He received the M.S. and Ph.D. degrees in information and communication engineering from the Naval Aeronautical and Astronautical University, Shandong, in 2005 and 2010, respectively. He is currently a Lecturer with the Department of Electronic and Information Engineering, Naval Aeronautical and Astronautical University. His current research interests include radar signal processing and clutter modeling.
Ningbo Liu was born in Shandong, China, in 1983. He received the B.S. and Ph.D. degrees in electronic engineering from the Naval Aeronautical and Astronautical University, Shandong, in 2009 and 2012, respectively. Since 2013, he has been with the Institute of Information Fusion, Naval Aeronautical and Astronautical University, where he is currently a Lecturer. He is the author of Radar Target Detection–Fractal Theory and Its Application (in Chinese, Beijing: Publishing House of Electronics Industry, 2011). His current research interests include radar signal processing and fractal analysis.
You He was born in Jilin, China, in 1956. He received the Ph.D. degree in electronic engineering from Tsinghua University, Beijing, China, in 1997. He is currently a Professor with the Naval Aeronautical and Astronautical University, Shandong, China. He has published over 200 academic articles. He is the author of Radar Target Detection and CFAR Processing (in Chinese, Beijing: Tsinghua University Press, 1st ed., 1999, 2nd ed., 2011), Multisensor Information Fusion With Applications (in Chinese, Beijing: Publishing House of Electronics Industry, 2000), and Radar Data Processing With Applications (in Chinese, Beijing: Publishing House of Electronics Industry, 2006). His current research interests include detection and estimation theory, digital signal processing, CFAR processing, distributed detection theory, pattern recognition, multiple target tracking, and multisensor information fusion. Dr. He is a Fellow Member of the Chinese Institute of Electronics. He is currently a Member of the Chinese Academy of Engineering. He serves on the editorial boards of the Journal of Data Acquisition and Processing, Modern Radar, Fire Control and Command Control, Ship Electronic Engineering, and Radar Science and Technology.
