# Target Maneuver Discrimination Using ISAR Image In .

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Fan et al. EURASIP Journal on Advances in Signal Processing (2016) 2016:24Page 3 of 13Fig. 1 Interception scenario geometryrelationship between motion parameters and relativeorientation of missile-to-target in a three-dimensionalinterception scenario has been derived in [11]. A twodimensional simplified analysis is presented to establishthe ISAR imaging model as follows.2.1 Imaging modelA right-handed coordinate system is attached to thetarget where the x-axis is pointing out of the nose, they-axis to the left, and the z-axis to the top. Assumingthe target velocity is along the x-axis, the pose angle ψ,relative to LOS, and its rates ω are formulated asψ ¼ γ T q: : :ω ¼ ψ ¼ γT qð2ÞThe positive pose angle is prescribed to the left andthe positive turn is also to the left. The considerable disparities of ψ and ω in MDS are the basis of maneuver::::discrimination. In (2), γ T and q represent the pose anglevariety introduced by the target motion and relativemotion of missile-to-target, respectively. It has beendemonstrated in [11] that: : : ð3Þj qj γ T :This conclusion also can be explained by the expression of :q: in proportional navigation (PN) guidance law [19]: : V T sinðγ T qÞ V M sin γ M q:ð4Þq¼RIn fact, the numerator of (4) is the “collision triangle”(the dotted triangle in Fig. 1) condition [19]. If the relative motion keeps the condition satisfied in the whole :interception, i.e., V T sinðγ T qÞ ¼ V M sin γ M q ; q ¼ 0:is straightforward. In real interception scenario, q is influenced by many factors, including target maneuver, guidance law adopted, initial heading error, and estimation:error. But the guidance law always keeps q within a smallneighborhood of zero before the seeker head reaches itsblind range. Hence, after translational motion compensation, the imaging model in two-dimensional interceptioncan be approximated as a planar rotating object in Fig. 2,where rotation angular velocity is equal to the pose anglerate,: :ω ¼ ψ γTð5ÞFurthermore, assuming target centroid O as the origin,the scatterer on target of radial distance L is mapped onto the range-Doppler plane as follows under the far-fieldcondition:X ¼ L cosψ ηr 2v 2ωL sinψY ¼ ηf ¼ ηf ;λλð6Þwhere v is the rotation linear velocity, λ is the wavelength, and ηr and ηf are the range and Doppler resolutions, respectively, defined byηr ¼ c ð2BÞηf ¼ 1 T img :ð7ÞIn (7), c is the velocity of light, B is the signal bandwidth, and Timg is the imaging time. A typical targetISAR image is also illustrated in Fig. 2 which shows thescatterer distribution in the range-Doppler plane.The above imaging model in interception differs significantly from that in surveillance of the ground-basedradar (or other location-fixed radar) [6, 16]. In the lattersituation, an ISAR image also can be obtained even ifthe target does not maneuver. However, from Fig. 2, wecan see that only when the target takes the lateralmaneuver (perpendicular to velocity), i.e., rotation, theimaging condition could be satisfied. This disparity provides the feasibility of maneuver discrimination usingISAR images in interception.2.2 Relationship between maneuver parameters andimagesThe changes of target acceleration aT and accelerationcommand acT in type II maneuver are showed in Fig. 3.

Fan et al. EURASIP Journal on Advances in Signal Processing (2016) 2016:24Page 4 of 13Fig. 2 Imaging model in two-dimensional interceptionIn maneuver discrimination, we focus on the acceleration command switch instant tsw and the accelerationdirection switch instant tdir. tsw is usually set to be thestarting instant which is the reference to the discrimination delay evaluation. We follow this metric in ourpaper. By substituting (1) into (5), ω and its time derivative can thus be expressed asω ¼ aT V T : ω ¼ acT aT V T τ T :ð8ÞFrom (8), ω and :ω: encapsulate the full information oftarget maneuver. On the other hand, from (6), ω can bederived by the scatterer position in the range-Dopplerplane. Consequently, the maneuver information can beextracted theoretically by matching the target scatterersin ISAR images of different instants [13, 14]. Forexample [14], ω of airplane rotation is estimated bycomparing the geometrical relationship differences ofrelative scatterers in two adjacent images. Actually, theequivalent scatterer number of missile-class target is significantly fewer than ship or airplane due to its smallersize. So the matching process needs the high-resolutionimages, and the scatterer association in different imagesmust be well-handled. Fortunately, a “shaft-like” shape isavailable for extracting the line features from targetISAR images.From (6), the slope of the target ISAR image can beexpressed ass¼XfsK¼ ;¼YT img f 0 ω tanψ ω tanψð9Þwhere f0 is the center frequency and K fs/Timgf0 is aknown constant. By substituting (8) into the time derivative of s, we obtain!: K ω1::s¼cosψ þsinψ ω2sinψð10ÞThus, the relationship between s and ω, also their timederivatives, is established. It is noted that these relationships are also related to the pose angle ψ. We firstly assume ψ 0 in the following analysis and other situationsare discussed later.For the sake of clarity, type II maneuver is further divided into two types considering the different switch directions, i.e., type P and type N. According to Fig. 3, adetailed summary of maneuver parameters and slopefeatures in type II maneuver is listed in Table 1.sin2ψ Fig. 3 The changes of aT and acT in type II maneuver 2a2T τ T ; amaxT aT V Tψ 0ð11ÞAccording to the results summarized in Table 1, we:can see that the value of s and the sign of s willchange after the time instants tsw and tdir, respectively. Especially, if ψ satisfies (11) in the type P

Fan et al. EURASIP Journal on Advances in Signal Processing (2016) 2016:24Page 5 of 13Table 1 The summary of maneuver parameters and slope features in type II maneuver (ψ 0)tswType PType Nac:ωBeforeþamaxT0After amaxT maxBefore amaxT0AfterþamaxT maxmaneuver, the MDS can be easily discriminated only:by the sign of s .Notice that the above derivation entails the assumption that the rotation center of the target is knownwhich is very difficult to fulfill in reality. As a matter offact, the slope estimation can be realized by any twoscatterers along the target radial axis or by some elaborate line-extraction algorithms in image processing. Bothof them are independent of the position of rotation center. More detailed scheme will be given in the nextsection.2.3 DiscussionWe discuss the influence of ψ on the maneuver discrimination performance herein. As we know, most of themissile targets are of axial symmetry. The ISAR imageacquired when ψ 0 and ω 0 is the same as that whenψ 0 and ω 0 according to Fig. 2. In other words, weonly have the information of ψ and ω from the ISARimages. Thereupon, some further remarks are made asfollows (the sign of variable is denoted as sgn[ ] forsimplicity):First of all, conclusions in Table 1 are contrary whenψ 0 according to (9) and (10). It does not affect the detection of tsw but misleads the MDS discrimination. Actually, sgn[s] only indicates whether the target is turningtoward or away from the LOS without the knowledge ofsgn[ψ].Secondly, if ψ traverses zero in interception, either 0 or 0 , a “ghost phenomenon” is produced which means ω changing from ω 0 to ω 0. As:a result, both sgn[s] and the value of s vary even thoughno MDS occurs. In this instance, the discrimination oftype N maneuver suffers from the invalidation orambiguity.:Thirdly, from the expression of s before the MDS oc:: Kcurs, i.e., s ¼ sin2 , we know that the value of s variesψ:along with ψ even there is no MDS. If the value of s isused as the test statistic, a float threshold is neededwhich is generated by a large amount of statistics at different ψ. But it is very hard to be realized in reality.Finally, the performance of line extracting from theimages strongly depends on the value of ψ. For example,tdir:s K 0sin2 ψ K sin2 ψ; if K 0sin2 ψ K sin2 ψ(11) is satisfied, 0αωs 0 0 0 0 0 0 0 0 0 0 0 0within a small neighborhood of ψ 0, the target imageapproximately remains perpendicular to the Doppleraxis even if there is a rotation. The reason is thatDoppler frequencies developed in both sides of a targetfrom the front to the rear have the same small valueswith different signs. At the same time, the ISAR imagespreads in several Doppler resolution bins due to the::target width. Therefore, both sgn[s] and the value of svariations are unpredictable results from the line extracting errors.In summary, the estimation of sgn[ψ] and a deambiguity processing are necessary for the former twosituations in maneuver discrimination. From the point of:an implementation view, only sgn½s and sgn[s] are selected in our paper as the indications of MDS. Although(11) should be satisfied in type P maneuver, it holds inmost cases during [tsw,tdir]. This situation will be testified in Section 4 where the effect of ψ on discriminationperformance is also explained more thoroughly.3 Discriminator design3.1 Image pre-processingThe ISAR image series can be obtained by the slidingwindowing method. The window length, i.e., Timg, determines the accumulated rotating angle for each ISARimage, and thus determines its Doppler resolution(inversely proportional to Timg in (7)). But long Timg implies great delay in discrimination. Hence, a tradeoff between delay and resolution should be considered. Onthe other hand, the sliding step length (denoted as ΔT)determines the aspect angle difference between neighboring ISAR images with a given ω. In reality, ΔT shouldbe less than the missile control period but not too small.If so, the estimation of :s: is not reliable due to the slightdifference between neighboring aspect angles.Then, a target image is segmented out from thescene that is indicating which pixels are on-target.This usually can be done using CFAR detectionfollowed by a sequence of binary morphological operations [16]. For the air-to-air endgame application inour paper, the signal-to-noise ra

lution (HRR) or inverse synthetic aperture radar (ISAR) images gain more advantages in maneuver information extraction. As stated in [11], the relative orientation of missile-to-target in interception can be approximated by a turntable model, which makes the maneuver discrim-ination using ISAR images possible. In fact, the estima-

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