ABSTRACT
Parallel Factor (PARAFAC) analysis is a common name for what could be concisely described as the theory and methods for low-rank decomposition of multidimensional data arrays. Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) is a well-known landmark in the area of high-resolution array processing. This chapter is devoted to the problem of high-resolution localization and tracking of multiple Frequency-Hopped (FH) signals. It presents two basic approaches. One relies on hop detection preprocessing to isolate hop-free subsets of the temporal data. The second approach tackles the joint problem of multiuser hop timing and angle-carrier estimation, using a combination of dynamic programming and multidimensional harmonic retrieval. The chapter reviews some fundamentals on rank and low-rank decomposition of matrices and higher-way arrays. It reviews basic PARAFAC identifiability results followed by a brief account of the general principle behind the workhorse algorithm for fitting low-rank decomposition models in higher dimensions.
