Manifold Ambiguities in Higher-Order Statistics-based Direction-Finding Systems

Abstract

Subspace-based direction-finding methods assume that all source’s manifold vectors
are linearly independent. However, when this condition is not satisfied, the estimation
methods will subsequently fail to identify the directions of the sources. This undesirable effect
is referred to as a manifold ambiguity. In this paper, the presence of manifold ambiguity
associated to a higher-order statistics-based array processing is investigated. By analyzing the
geometrical shape of the corresponding array manifold, a class of ambiguous sets based on a
uniform partition of the effective manifold curve can be found. A general procedure is
provided in order to model and categorize these ambiguities into the form of ambiguous
generator sets.