Tensor-Structure Structured Least Squares (TS-SLS) to Improve the Performance of Multi-Dimensional Esprit-Type Algorithms

Multidimensional ESPRIT-type parameter estimation algorithms obtain their frequency estimates from the solution of sets of highly structured equations (the shift invariance equations). The structured least squares (SLS) algorithm is known as an efficient method to obtain these solutions since the inherent structure is explicitly taken into account. In this contribution we show that if the underlying R-dimensional signals are represented by tensors, this structure can be exploited even further. In addition to an improved signal subspace estimate, the SLS algorithm is modified to directly exploit the tensor structure of the signal subspace obtained through the higher order SVD. The resulting algorithm which we term tensor-structure SLS offers a superior performance compared to existing approaches in critical cases, e.g., if there are highly correlated sources or a small number of available snapshots.