Target Turning ManeuverDetection using HighResolution Doppler Profile

YILONG ZHU, Student Member, IEEEHONGQI FAN, Member, IEEEJIANPENG FANZAIQI LUQIANG FUNational University of Defense Technology

Target turning maneuvering is always accompanied with

the rapid attitude variations, which are helpful to achieve

high cross-range resolution for pulsed coherent radar. Thus,

it is feasible to detect target turning maneuver using the high

resolution Doppler profile (HRDP). The preliminaries concerning

the HRDP are first introduced, including its formulation,

extraction requirements, and procedure. The principle of turning

maneuver detection using the HRDP is then fully explored. A

novel detector is developed based on the back propagation (BP)

neural network. Two novel indices for performance evaluation

are proposed. Finally, a simulation environment with software

tools capable of generating target dynamic echoes with realistic

features is developed. The simulation results demonstrate that the

proposed detector performs better than the other three up-to-date

feature-based detectors as a whole.

Manuscript received March 30, 2010; revised December 7, 2010;released for publication February 17, 2011.

IEEE Log No. T-AES/48/1/943647.

Refereeing of this contribution was handled by D. Salmond.

Authors address: ATR Key Laboratory, National University ofDefense Technology, Changsha, Hunan 410073, P.R. China, E-mail:(fhongqi@gmail.com).

0018-9251/12/$26.00 c 2012 IEEE

I. INTRODUCTION

Maneuvering target tracking (MTT) is one ofthe most important issues in the target trackingcommunity. Since target acceleration cannot bemeasured directly by existing sensors, MTT is ahybrid estimation problem [13]. Current MTTalgorithms mostly deal with the target motionuncertainty, including the decision-based single-modelmethod [2] and multiple-model method [4]. Themultiple-model method, although excellent in qualityand reliability, is computationally inefficient. In fact,in applications like guidance and navigation, theother method, the decision-based single-model oneis much more appealing due to its low computationalcomplexity. Given a timely maneuver detector, thedecision-based single-model method has been shownto achieve a tracking accuracy similar to that ofthe multiple-model method [5, 6], therefore is veryfavorable in resource-limited scenarios.According to the information employed in

the maneuver detector, current techniques can beclassified into three categories: innovation-based,image-based, and feature-based. The innovation-basedtechnique depends on the innovation information ofthe Kalman filter [13]. The formation of test statisticsis mostly based on the innovation or the inputestimation, which is also based on the innovation.The image-based technique exploits optical (e.g.,visible, infrared) image information to identifytarget orientation variations [7, 8]. The feature-basedtechnique utilizes motion feature information,especially radar target signatures, to detect the switchof the motion modes [5, 6, 913].Many researchers have focused on the

innovation-based technique so far, which has beensurveyed comprehensively in [1], [2]. Ru, et al.[3] have recently reviewed six traditional detectorsand proposed two novel detectors based on thesequential statistical test. They are all innovationbased. The comparison of their performance is alsopresented via simulation, which provides a guidelineto select the detector. However, it is difficult forthe innovation-based technique to achieve a shortdetection delay while maintaining high detectionprobabilities, due to the Q effect [1]. On the otherhand, in some performance-critical applications [14],the image-based and feature-based methods, exploitingmore information such as attitude and range rate, aremore attractive.Rich information from optical sensors can also

be exploited in maneuver detection [7, 8]. Sworder,et al. [7] propose an image-based maneuver detectionscheme by using pattern recognition to identifychanges in target orientation. Shetty, et al. [8] extractrepresentative features from the images for maneuverdetection, which avoids intensive image processing.The image-based technique greatly reduces detection

762 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 1 JANUARY 2012

delays at the cost of intensive image processing. Inaddition, optical sensors are susceptible to weatherconditions, therefore the image-based technique isonly suitable for short or medium range scenarios.Radar echoes not only carry the information

related to its motion state and shape which are usefulfor target tracking and recognition, but also conveyinformation related to its motion mode due to themodulation effects on electromagnetic scatteringcreated by target motion. In other words, a switch ofmotion modes always results in certain changes in theechoes. For instance, the attitude angle varies rapidlyduring the bank-to-turn (BTT) motion of a fixed-wingaircraft, leading to abrupt changes of target radar crosssection (RCS), glint, etc.In fact, the features extracted from radar echoes,

including range rate, glint, RCS, high resolutionDoppler profile (HRDP) and two-dimensionalrange-Doppler image, have been exploited formaneuver detection in the literature [5, 6, 913].Bizup, et al. [5] assume that the target performsa constant turn (CT) motion during the samplinginterval, and propose a maneuver detection methodbased on target centripetal acceleration which isestimated according to range rate measurements andtarget state estimates. Ru, et al. [6] make furtherimprovements by taking into account both tangentialand centripetal acceleration. However, they donot exploit the correlations within the range ratesequence. The estimated acceleration may sufferfrom underestimation. Apart from range rate, glintand RCS which are quite sensitive to target attitudeangle, are also exploited by researchers. For example,boresight error signal [9, 10] and echo amplitudefluctuations [11] are utilized for maneuver detectionsin recent studies. However, due to the complicatedrelationship among signatures, attitude angles andthe motion modes, it is difficult to analyticallycompute the probability distributions of the teststatistics for maneuvering or nonmaneuveringmotions. In fact, they are evaluated only throughsimulations. Target accelerated motions, especiallycentripetal accelerations, give rise to rapid attitudevariations. This is helpful to achieve high resolutionin cross-range and provides a feasible way todetect target maneuver using the HRDP. Fan[11] significantly improves maneuver detectionperformance by using pulsed Doppler (PD) radars.In two-dimensional range-Doppler images obtainedby high range resolution radars, the target is tilted inthe image because of maneuvers. Yang, et al. [12, 13]rigorously derive the relationship between the targetimage slope and the turn rate, but do not further applyit to maneuver detectors.In this paper we develop a novel turning maneuver

detector using the features extracted from theHRDP, by exploiting the considerable disparitiesof cross-range resolutions between maneuvering

Fig. 1. Geometry of radar and target.

and nonmaneuvering motion modes. Due to theirwide applications in fire control, early warning, airsurveillance, etc., we consider the high pulse repetitionfrequency (PRF) PD radars in our study.At present, the HRDP has been comprehensively

applied in target detection, identification, multipletargets resolution, as well as in maneuver detection.Berizzi, et al. [15] propose several autofocusingalgorithms for the HRDP using the contrastoptimization approach. Xing, et al. [16] discuss thefactors affecting the Doppler resolution and proposea method to improve the HRDP resolution. Xia,et al. [17] address the problem of detection for dimtargets under a strong clutter background using theHRDP. Gao, et al. [18] show that the ERINT missileseeker can identify different parts of the target fromthe HRDP and provide information to the guidanceprocessor to determine where to hit the target. Jiang,et al. [19] introduce the approach to resolve themultiple targets using the HRDP. Fan [11] utilizesthe HRDP to detect target maneuver as previouslystated. However, the terminologies for the HRDP inthe above-mentioned literature are confusing. We referto it as the HRDP [20] in this paper.The rest of this paper is organized as follows.

Section II is a brief introduction to the preliminariesconcerning the HRDP, including its formulation,extraction requirements, and procedure. Section IIImakes an elaborate and systematic analysis of theturning maneuver detection principle, then the authorsdevelop a maneuver detector using the HRDP, andpropose two novel indices for performance evaluation.The simulation results are presented in Section IV.Finally, the conclusions are drawn in Section V.

II. HIGH RESOLUTION DOPPLER PROFILE

A. HRDP Formulation

To clarify the related terms, this subsectionformulates the HRDP. We only analyze thetwo-dimensional planar motion for simplicity. Threecoordinate systems (CSs), i.e., the target CS (oT-xy),the radar CS (oR-uv), and the reference CS (oT-u

0v0)are involved as shown in Fig. 1.The target range and azimuth at time t are assumed

to be Rt and 't, respectively. Thus, the reference CS

ZHU, ET AL.: TARGET TURNING MANEUVER DETECTION USING HIGH RESOLUTION DOPPLER PROFILE 763

has a translation (Rt cos't,Rt sin't) from the radar CS,and the target CS has a rotation t about the referenceCS. We assume that a reference scatterer P is locatedat [x,y]T in the target CS. Its coordinates in the radarCS are [ut,vt]

T and satisfy [21]

264utvt1

375=2641 0 Rt cos't0 1 Rt sin't0 0 1

375| {z }

T

T264 cost sint 0sint cost 00 0 1

375| {z }

R

264xy1

375

(1)

where T and R are the translation matrix and rotationmatrix, respectively. The instantaneous range from theorigin of the radar CS to the scatterer P then becomes

RP(t) = (u2t + v

2t )1=2: (2)

Assume that target size is much smaller than thetarget range, i.e., x Rt, y Rt. The target motioncan be decomposed into translational and rotationalmotions. Assuming that the target performs uniformrotational motion with a sufficiently small rotationangle during the coherent processing interval (CPI)t 2 [0,T] is reasonable. Thus, we can obtain

cos(t 0) 1sin(t 0) t 0 = !t

(3)

where 0 and t are the rotation angles at the onsettime of the CPI and time t, respectively, and ! is thetarget turn rate.Based on the above assumptions, substituting (1)

into (2), we obtain

RP(t) = Rt+[xcos('t 0)+ y sin('t 0)] [xsin('t 0)+ y cos('t 0)]!t: (4)

The radar carrier frequency is denoted as fc.Although PD radar is employed in this paper, notaffecting the correctness of the HRDP, we ignorethe envelope item of the echoes for simplicity.The baseband echo signal of the scatterer P can beexpressed as

sP(t) = (x,y)exp[j4fcRP(t)=c] (5)

where j is the unit of the imaginary number, and(x,y) is proportional to the reflectivity of thescatterer P(x,y). Equation (5) represents the echosignal of a single scatterer, and the entire target echosignal can be expressed as the combination of allscatterers echo signal, i.e.,

s(t) =Z Z

(x,y)exp[j4fcRP(t)=c]dxdy: (6)

Letr

l

=cos('t 0) sin('t 0)sin('t 0) cos('t 0)

x

y

(7)

where [r, l]T denote the coordinates of the scatterer Pin a new CS (oT-rl) obtained by rotating the target CSby the angle ('t 0), as shown in Fig. 1.By substituting (4) and (7) into (6), we obtain

s(t) =Z Z

(r, l)exp[j4fc(Rt+ r!lt)=c]drdl

= exp(j4fcRt=c)

Z Z

(r, l)exp(j4fcr=c)drexp(j4fc!lt=c)dl:

(8)We denote the first layer integral as l, i.e.,

l =Z(r, l)exp(j4fcr=c)dr (9)

where l is the combined total reflectivity of thescatterers whose cross-ranges are the same l. Ifwe compensate for the phase item induced by thetarget translation in (8) and multiply it by the itemexp(j4fcRt=c), we obtain

s0(t) =Zl exp

j22!

lt

dl (10)

where is the wavelength.By applying the inverse Fourier transform (IFT)

to s0(t), we obtain the target reflectivity along thecross-range l, which is known as the HRDP. Inpractice, the target turn rate is not known, and scalingthe HRDP is impossible. The abscissa withoutscaling is the cross-range l multiplied by the scalingfactor 2!=, i.e., Doppler shift. This is one of thereasons why we call it the HRDP rather than the highresolution cross-range profile.

B. Resolution, CPI, CIA, and Sampling Rate

REMARK 1 (Resolution) If the CPI is T, theresolution of the HRDP is

l =

2!T=

2 (11)where = !T is the rotation angle during the CPI,which is also the attitude angle variation within theCPI, i.e., coherent integration angle (CIA).

The derivation of Remark 1 is straightforwardaccording to the properties of the IFT. Thus, weomit it here. Note that (11) is consistent with thecross-range resolution of the inverse synthetic apertureradar (ISAR).From (11), the longer the CPI, the greater the

CIA and the higher the resolution of the HRDP.However, the resolution of the HRDP does notincrease with the CIA without limitation because ofthe small rotation angle assumption and the Dopplermigration effect. The HRDP distorts with a longCPI. Fortunately, achieving a perfectly undistortedHRDP is not necessary for the maneuver detector.

764 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 1 JANUARY 2012

The only one necessity is that the resolution of theHRDP should be less than the target cross-range sizeL so that the maneuver detector can distinguish thealternative hypothesis from the null hypothesis (seeSection IIIA). Thus, the lower bounds for profiling onthe CPI or the CIA can be obtained.

REMARK 2 (CPI or CIA) The lower bounds forprofiling on the CPI or the CIA are

T > =2!L

> =2L: (12)

In practice a digital signal processing system isemployed. The echo signal s0(t) is discretized, andthe inverse discrete Fourier transform (IDFT) isapplied. According to the properties of the IDFT, thelower bounds on the sampling rate can be obtained toachieve the unaliased HRDP.

REMARK 3 (Sampling Rate) The lower bounds onthe sampling rate to achieve the unaliased HRDP are

fs 2!L=: (13)From (13), the minimum sampling rate depends on

the target turn rate and the target cross-range size, andcan be determined according to prior knowledge.

C. HRDP Extraction Procedure

Xing, et al. [16] propose a method to improve theHRDP resolution. The translational motion is firstcompensated, and the instantaneous Doppler shiftsof the scatterers along the cross-range are estimatedusing the superresolution algorithm RELAX. Thus,the resolution of the regenerated HRDP improvessignificantly. However, the HRDP resolution requiredfor the maneuver detector to be much lower than thatof any other applications. Therefore, we only performthe translational motion compensation and omit themore sophisticated processing in this paper.As previously stated, the phase item for the

translational motion compensation is exp(j4fcRt=c).It is reasonable to assume that the target performsnearly constant radial accelerated motion during theCPI. Denoting the radial velocity and accelerationby Vr and ar, respectively, the phase item can bewritten as

T = exp[j4fc(R0 +Vrt+ 12art2)=c]: (14)Equation (14) consists of three terms. The first

term is a constant and has no contribution to theHRDP. The second term is the linear term, whichinduces a shift of the HRDP but does not distort itsshape. The third term is the quadratic term, whichresults in the expansion of the HRDP and must becompensated. In this paper, the linear term is alsocompensated for the sake of the feature extractionprocessing.

Fig. 2. HRDP extraction procedure.

In order to guarantee that the expansion of thecompensated HRDP is less than one Doppler cell, theacceleration estimation precision ar must satisfy

jarj< =2T2: (15)From (15), if the CPI T is long enough, the

requirements for the acceleration estimation accuracywill be critical. For example, if = 3 cm and T =100 ms, then jarj< 1:5 m=s2. Berizzi, et al. [15]propose several autofocusing algorithms based onthe optimization of the contrast functions, resultingin an accurate estimated acceleration. We performthe acceleration compensation using one of theiralgorithms, where the standard amplitude contrastfunction C2 is used. The range rate Vr can be estimatedimmediately after the acceleration compensation.In many applications, the high PRF PD radar

is commonly used to obtain high resolution in thefrequency domain. The first step of the HRDPextraction procedure is to locate the peak or centerof every pulse return, and the complex amplitudeis calculated by interpolation. Thus, the resultingsampling rate is equal to the PRF, which is usuallymuch greater than the required sampling rate forprofiling in (13). Therefore, the motion compensationstep can be followed by decimation. Clearly,performing the antialias filtering before decimationis necessary. The HRDP extraction procedure isillustrated in Fig. 2.

III. TURNING MANEUVER DETECTION

A. Turning Maneuver Detection Principle

As previously stated, the attitude angle usuallyvaries rapidly as the target performs a turningmaneuver. The attitude angle also varies as the targetperforms the nonradial straight motion with a constantvelocity. However, the attitude rates are quite differentbetween nonmaneuvering and maneuvering motions.The target velocity is assumed to be along the x-axisin the target CS as shown in Fig. 1. We drop the timesubscript t for brevity. The target attitude angle is

= +' : (16)The target tangential and centripetal accelerations

are denoted as at and ac, respectively. According tothe target motion equations, we have

_V = at_ = ac=V:

(17)

ZHU, ET AL.: TARGET TURNING MANEUVER DETECTION USING HIGH RESOLUTION DOPPLER PROFILE 765

The nonmaneuvering target has a constant velocity.The attitude rate and its derivative can thus beexpressed as

!n = _ = _'=V sinR

n = _!n =V2 sin2R2

(18)

where the subscript n denotes nonmaneuvering. Thederivation of (18) uses the equation _R =Vcos,where _R is the target radial velocity or range rate andis also denoted as Vr.When the target maneuvers, the attitude rate and

its derivative can be expressed as

!m = _ = _' _ = V sinR acV

m = _!m =V2 sin2R2

+at sinR

+acatV2

_acV

(19)

where the subscript m denotes maneuvering.Therefore, the CIA can be approximated as

i !iT+ 12iT2, i=m,n: (20)The form of (19) is very complicated, therefore it

is inconvenient to compare it with (18) immediately.We consider the following two special cases.1) at = 0, and ac = constant c1, i.e., the target

performs the CT motion. From (19) we obtain

!m1 =V sinR

acV

m1 =V2 sin2R2

:

(21)

The target is usually far from the radar, andVsin=R ac=V holds. From (21), the targetattitude rate !m1 differs greatly from that under thenonmaneuvering motion, and thus the CIAs alsodiffer. This is the basis of turning maneuver detectionin the paper.2) ac = 0, at = constant c2, i.e., the target performs

the constant acceleration (CA) motion. From (19) wethen obtain

!m2 =VsinR

m2 =V2 sin2R2

+at sinR

:

(22)

By comparing (22) with (18), the attitude ratesare equal, i.e., !m2 = !n, and their derivatives areslightly different. m2 has an additional term at sin=Rcompared with n. If the target is far from the radar,the term is small enough to be ignored. Therefore,the CIA is slightly different from that under thenonmaneuvering motion. This brings difficulties tothe maneuver detector. In this paper we focus on themaneuver detection in the presence of centripetalacceleration, i.e., turning maneuver detection. This

is one of the current hot topics in the maneuverdetection not only because the turning maneuver isthe frequent motion mode that the targets, especiallymilitary targets, perform during a combat but alsobecause it has great influence on the target trackingperformance [3, 5, 911].The attitude rates of the nonmaneuvering and

turning maneuvering motions are quite different basedon the previous analysis. According to Remark 2,a minimum CIA is required to obtain the targetHRDP. Consequently, the CPI can be appropriatelydetermined, so that the CIA is smaller than theminimum required when the target performs anonmaneuvering motion, and that the CIA meetsthe profiling requirements when the target performsa turning maneuvering motion. Hence it is unableto distinguish scatterers from target HRDP, andthe target behaves as a point target under thenonmaneuvering situation. On the contrary, under theturning maneuvering situation it is able to distinguishmultiple scatterers from the target HRDP, and thetarget behaves as an extended target. This is theprinciple of turning maneuver detection using theHRDP. Thus, the resolution of the HRDP requiredby the detector is fairly low. We need not identify thedifferent parts of the target from the HRDP exactly.The slightly distorted HRDP is also acceptable.Therefore, the CPI T is the key parameter, and it

must satisfy

n