A Generalized Approach to Direction Finding

Abstract

Assuming d sources and m sensors, a generalized formulation is proposed for the direction of arrival estimation problem. It is shown that several different techniques are special cases of the generalized approach. The techniques differ depending upon the manner in which either 1) the measured data is processed or 2) the angular information is extracted from the resulting equations. In the generalized formulation a matrix pencil M - λN is constructed. In general, the rank of the matrix pencil is d. However, for particular values of λ, the rank is decreased by 1. The values of λ for which this happens contain the information needed to estimate the angles of arrival. The pencil theorem establishes the relationship between these values of λ and some functional form f(ϕi) generated by the operators applied to the measurements.