Rayleigh Estimates for High Resolution Direction Finding

Abstract

The problem of direction finding in sensor arrays lies with power detection and estimation procedures at the frequencies and angles of arrival previously steered by the array. Furthermore, because the received power at a given angle of arrival depends both on source features and the array factor, the power received by a degree of the angular bandwidth provides a better description of the source environment. This last point reduces the direction of arrival to a spectral estimation problem. This basic comments are introduced here in order to point out the three steps in a direction finding technique: the array weigths or spatial filtering to steer a given direction or angle of arrival, a power device to obtain the received power and finally, spectral estimate S(u) obtained by the quotient of the received power P(u) and the bandwidth of the spatial filter B(u),

$$ S(u) = \frac{{P(u)}}{{B(u)}}watts/gegree$$

(1)

being $u = {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k}}\bullet{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r}}$ where k is the wavenumber vector and r is the bector location in a 3-D space of each array element.