Proceedings with Extended Abstracts (single PDF file) - Radio ...

STANDARD DEVIATIONS OF CORRELATION LENGTHSIN SPACED ANTENNA OBSERVATIONS USING THE MU RADARG. Hassenpflug † M. Yamamoto S. FukaoRadio Science Center for Space and Atmosphere, Kyoto University,Gokasho, Uji 611-0011, Japan. † Mailto: gernot@kurasc.kyoto-u.ac.jpIntroductionExpressions for anisotropic correlation scales returned from Bragg scatterers and receivedby receivers in spaced antenna (SA) configuration are given by Holloway et al. [1997a].We obtain expressions for standard deviation (SD) of correlation lengths of anisotropiccorrelation ellipses (see Figure 1(a)). Variance of zero-lag cross correlation coefficients isrequired: we use the expression given in Awe [1964], as well as an expressions based onZhang et al. [2003]. Theoretical SD are compared with experimental SD, and show goodagreement. Theoretical expressions can be used to predict expected SD, and to designSA configurations for minimum SD within radar limitations.Theoretical ExpressionsExpressions in Holloway et al. [1997a] hold for case of receiver antenna phase centersequidistant from transmitter antenna phase center. Using variance of cross correlationcoefficients c ij (τ) in Awe [1964], and a new expression for the variance based on Zhanget al. [2003],Var [c ij (0)] = 1 (1 + 2c22M ij (0) − 4c 2 ij(0) exp ( )τp 2 /4τc2 + c2ij (0)c 2 ij(τ p ) ) (1)Iwe obtain by the standard theory of error propagation SD of the ground diffractionpattern scales (ξ x ′, ξ y ′), refractive index perturbation correlation lengths (ρ x ′, ρ y ′), andorientation of the correlation ellipse bearing from north ψ N . Variance given by Awe[1964] is slightly greater than that given by Eqn. 1, as seen in Figure 1(b). τ p is peakcross-correlation lag, τ c is square root of the second central moment of the correlationfunction. M I = T/( √ πτ c ) as defined in Zhang et al. [2003]. Expressions for variance ofξ x ′ and ξ y ′ depend on baseline lengths B ij :Var [ξ x ′] =( ξ3x ′2) 2·3(i≠j)∑i,j=1( 1B 2 ij( ) ξ3 3(i≠j) (Var [ξ y ′] = y ′ ∑ 12·2i,j=1Bij2) 2F 2ij(ξ x ′) Var [c ij]c 2 ij) 2F 2ij(ξ y ′) Var [c ij]c 2 ijwhere F 12 , F 13 , F 23 are parameters related to the SA geometry:(2)(3)156F 12 (ξ x ′) = (1 − cos 2ψ N) cot α 13 cot α 23 + (1 + cos 2ψ N ) − sin 2ψ N (cot α 13 + cot α 23 )sin 2 α 12 (cot α 13 − cot α 12 ) (cot α 23 − cot α 12 )