Spherical subspace tracking: analysis, convergence and detection schemes

Some of the properties and applications of spherical subspace updating are described. A proof of convergence for the two-level spherical update is briefly summarized and discussed. Square root (SVD) versions of the spherical update are developed, and multilevel updates are introduced. A minimum description length (MDL) detection scheme is developed based on a four-level spherical update. The four-level MDL detection performance is virtually identical with the performance of full eigenstructure based MDL. However, the four-level spherical update is noniterative and much less complex than full eigen updating, i.e., O(nr) versus O(n³), where n is the data dimension and r is the size of the dominant (signal) subspace