Multilinear direction finding for sensor-array with multiple scales of invariance

International audienceIn this paper, we introduce a novel direction finding (DF) algorithm for a multi-scale sensor-array, that is, an array presenting multiple scales of spatial invariance. We show that the collected data can be represented as a Candecomp/Parafac (CP) model, for which we analyze the identifiability properties. A two-stage algorithm for direction-of-arrival (DOA) estimation with such an array is also proposed. This approach generalizes the results given in \cite{SidiSPT0800} to an array that presents an arbitrary number of spatial invariances. We illustrate, on two particular array geometries, that our method outperforms, in some difficult scenarios, the ESPRIT-based approach introduced Wong and Zoltowski in 1998, the ESPRIT-MUSIC of Zoltowski and Wong and the Tensor-ESPRIT. Moreover, we show that the single-snapshot case and the fully cross-correlated sources case can be handled by our method without any spatial smoothing procedure, provided that the array includes at least three scale-levels