Parallel factor analysis in sensor array processing

This paper links multiple invariance sensor array processing (MI-SAP) to pa rallel factor (PARAFAC) analysis, which is a tool rooted in psychometrics a nd chemometrics. PARAFAC is a common name for low-rank decomposition of thr ee- and higher way arrays. This link facilitates the derivation of powerful identifiability results for MI-SAP, shows that the uniqueness of single- a nd multiple-invariance ESPRIT stems from uniqueness-of low-rank decompositi on of three-way arrays, and allows tapping on the available expertise for f itting the PARAFAC model. The results are applicable to both data-domain an d subspace MI-SAP formulations. The paper also includes a constructive uniq ueness proof for a special PARAFAC model.