Suitability of Correlation Arrays and Superresolution for Minehunting ...

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DSTO-TN-0443 4.3 Correlation of Targets Encouraged by this ‘near field’ finding, we now carry out a calculation for a sonar correlation array. The system considered is active and the targets are allowed to be in the near field. We derive an equation (for sonar) very similar to Equation (3.5) (for RA). 6 The need, raised in assumption 3a, for an extension from a 2-D to a 3-D image, is thus dealt with. Recall first that, for a monofrequency sonar system, in the far field, a simple relationship exists between the amplitude beam pattern B ( l, m) , or response when the array is steered to broadside, and the array grading function g ( x, y) ; this relationship is Equation (3.6), namely −1 B( l, m) = const. ∫∫ g( x, y) exp[ j2πλ ( lx + my) ] dxdy (4.1) = const. G( l λ , m λ) Here G( κ x , κ y ) is the inverse Fourier transform of g ( x, y) : G( κ x , κ y ) = ∫∫ g( x, y) exp[ j2π ( κ x x + κ y y) ]dxdy (4.2) Equation (4.1) gives the image of a point source or target; the response to many sources is given as a convolution involving (4.1). We now turn to an active sonar with pulse-echo determination of the range. (The system is no longer monofrequency.) We obtain the three-dimensional image of a collection of point targets. By definition, in (unweighted) delay-and-add beamforming, this image amplitude is obtained for a general scene simply by the formula B( r, l, m) = ∑ En[ ( r + r − rn ) c] (4.3) Here r = ( r , l, m) position of the n th element, and () t n , when expressed in essentially spherical coordinates, r n is the E n is the signal (voltage) received at that element at time t . For convenience we assume a point transmitter, located at the origin, and we assume the array to be unweighted [as in Blair and Anstee 2000]. For a point target j at r j , the full near-field treatment [Blair 2002] shows that, under conditions given in that report, the image amplitude is −1 −1 B1 ( r, l, m) = C∑ a j ξ [ 2c ( r − rj )] G1[ λc ( l − l j , m − m j )] (4.4) j where for the moment the two subscripts ‘1’ and the ∑ j operator are to be ignored. Here C is a real constant, a j (a real number) is the target strength of the scatterer j in 6 Actually, the generalisation of (3.5) to a collection of point targets, given by substituting (3.9) into (3.8). 10
DSTO-TN-0443 amplitude terms, the analytic signal ξ () t is the transmitted signal as a function of t , normalised so that ξ () 0 = 1, and λ c is the wavelength at the central frequency ν c of the signal ξ () t . ( ξ () t is taken to be a short pulse, but the theory is similar for a coded signal such as a chirp.) In (4.4), the subscript 1 has been added to B and G to signify that the relationship is written for subarray 1 of a correlation array. The analogous equation holds for subarray 2. For a collection of point scatterers, with j referring to the j th scatterer, B 1 is obtained by simply inserting the summation operation ∑ j in Equation (4.4). A condition on (4.4) is that the bandwidth ν ξ t satisfies ∆ ν
Page 1 and 2: Suitability of Correlation Arrays a
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Page 8 and 9: DSTO-TN-0443 even if the array leng
Page 10 and 11: DSTO-TN-0443 3. Correlation Telesco
Page 12 and 13: DSTO-TN-0443 ∗ ( u v) const. g (
Page 14 and 15: DSTO-TN-0443 3.4 Compound Grating A
Page 18 and 19: DSTO-TN-0443 It might be hoped that
Page 20 and 21: DSTO-TN-0443 to the synthetic appro
Page 22 and 23: DSTO-TN-0443 Superresolution (SR) t
Page 24 and 25: DSTO-TN-0443 weight’ in place of
Page 26 and 27: DSTO-TN-0443 squared. The multiplic
Page 28 and 29: DSTO-TN-0443 More detailed referenc
Page 30 and 31: DSTO-TN-0443 interpreted also as ma
Page 32 and 33: DSTO-TN-0443 MUSIC (Section 9.3), S
Page 34 and 35: DSTO-TN-0443 of the number of sourc
Page 36 and 37: DSTO-TN-0443 a few targets, randoml
Page 38 and 39: DSTO-TN-0443 The above work by SBF
Page 40 and 41: DSTO-TN-0443 The above theory is de
Page 42 and 43: DSTO-TN-0443 improvements obtained
Page 44 and 45: DSTO-TN-0443 as the FBLP method. On
Page 46 and 47: DSTO-TN-0443 Marple, S.L. (1987). D
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Page 52 and 53: DSTO-TN-0443 (B) is used. First, a
Page 54 and 55: DISTRIBUTION LIST Suitability of Co
Page 56 and 57: Engineering Societies Library, US M

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