This paper links multiple invariance sensor array processing (MI-SAP) to parallel factor (PARAFAC) analysis, which is a tool rooted in psychometrics and chemometrics. PARAFAC is a common name for low-rank decomposition of three- and higher way arrays. This link facilitates the derivation of powerful identifiability results for MI-SAP, shows that the uniqueness of single- and multiple-invariance ESPRIT stems from uniqueness of low-rank decomposition of three-way arrays, and allows tapping on the available expertise for fitting the PARAFAC model. The results are applicable to both data-domain and subspace MI-SAP formulations. The paper also includes a constructive uniqueness proof for a special PARAFAC model.
Bibliographical noteFunding Information:
Manuscript received January 21, 1999; revised March 27, 2000. Part of this paper was presented at the 32nd Asilomar Conference on Signals, Systems, and Computers, November 1-4, 1998, Monterey, CA. This work was supported by NSF CAREER CCR 9733540, NSF CCR 9805350, the Nordic Industry Foundation Project P93-149, and the F;TEK Foundation through Prof. L. Munck. The associate editor coordinating the review of this paper and approving it for publication was Dr. Alex B. Gershman.