Fast recursive subspace adaptive ESPRIT algorithms

A class of fast recursive ESPRIT algorithms for adaptive (on-line) source localization based on subspace tracking and adaptive rank reduction is introduced. These adaptive ESPRIT algorithms can be used for on-line tracking of r maneuvering sources in space using the output of an N-element sensor array, where N>2r. The fastest of our algorithms requires only O(Nr)+O(r/sup 3/) complex arithmetic operations to update the estimated directions-of-arrival (DOAs) at each time instant. These highly efficient algorithms are more than only a concatenation of a subspace tracker and a conventional batch ESPRIT algorithm. A special QR-reduction to standard form is the key to the fast recursive algorithms. Detailed computer experiments substantiate the theoretical results.