Geometrical determination of ambiguities in bearing estimation for sparse linear arrays

The aim of this paper is to study the presence of manifold ambiguities [1], [2] in linear arrays. We propose a general framework for the analysis and so we obtain a generalisation of results given in recent publications [3], [4] for an}· rank ambiguities. We present a geometrical construction able to determine all the ambiguous directions which can appear for a given linear array. This is a geometrical approach closely connected to [4]. The method allows determination of any rank ambiguities and for each ambiguous direction set the rank of ambiguity is determined. The search is exhaustive. Application of the method requires no assumption for the linear array and is easy to implement. We apply the method to the search of ambiguities for sparse linear arrays, in particular minimum redundant and non redundant arrays [5], [6], [7]. We show how an ambiguous generator set can be associated to each intersensor distance if the intersensor distances (lags) are all multiples of the half wavelength.