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

In this paper, we introduce a novel direction-finding algorithm for a multiscale 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 model for which we analyze the identifiability properties. A two-stage algorithm for direction-of-arrival estimation with such an array is also proposed. This approach generalizes the results given in [1] 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 in [2], the ESPRIT-MUSIC of [3], and the tensor-ESPRIT of [4].