Principles of Modern Radar - Volume 2 1891121537

658 CHAPTER 14 Automatic Target Recognitionradar receivers typically use sophisticated beamforming to place nulls in the direction ofdirect path signals while optimizing gain towards the operational regions. This allowsthem to adequate detect and observe targets.The nature of passive radar measurements also complicates the observation and predictionof kinematic target features. While traditional radar systems excel at measuringthe range to the target, passive radar systems are best at measuring direction-of-arrival(DOA) and Doppler. Hence, translation into accurate state estimates in Cartesian coordinatesystems (often required to collect kinematic features) is a challenge. In practice,this is addressed through a combination of employing multiple receivers [117] and usingsophisticated signal processing and tracking algorithms [111].14.6.4 Step 4: Test the Feature SetOnce features have been observed, likelihood-based schemes [100–105] to compare themto a target library are common. For example, much of the literature in this area focuseson use of radar cross sections for classification of aircraft. In this case, the power at thepassive radar receiver is modeled asP RECEIVER =(√PTARGET + w R) 2+ w2I (14.16)where P TARGET is the real component of the received power due to the target and w is zeromeanadditive white Gaussian noise with real, w R , and imaginary, w I , parts [100–105].This leads to a Rician likelihood model, whose probability density function is given byp x (x) = x expσw2[ ( )]x 2 + s 2−2σ 2 wI 0( xsσ 2 w)(14.17)where x is the observed voltage at the receiver, s is the predicted voltage at the receiver forthe target from the library, σ 2 w is the noise power, and I 0 is the modified Bessel functionof the first kind [102]. If each of N MEAS measurements is assumed to be independent, theloglikelihood becomesln (p x (¯x)) =N∑MEASi=1( ) [xiln + lnσw2( )] ( )xi s i x2I 0 − i + si2σw2 2σw2(14.18)Since the first term in the loglikelihood equation does not vary with the elements in thetarget library, the score, S, used to identify the target can be reduced toN∑MEAS[ ( )] ( )xi s i x2S(¯x) = ln I 0 − i + si2 (14.19)σw2 2σw2i=1The target from the library resulting in the maximum score wins.14.7 HIGH-RESOLUTION RANGE PROFILESHigh-resolution range profiles (HRRPs) are based on returns from high-resolution radars(HRRs) or ultra-high-resolution radars. In this paradigm, the HRRP is the time domainresponse to interrogating the target with a set of high-range resolution pulses [76]. Thepulsewidths used to interrogate the target are selected to produce many returns, which dividetargets of interest into multiple returns, provide information about the target scatterers,and by extension, the target’s composition.