Conjugate gradient eigenstructure tracking for adaptive spectral estimation

A conjugate gradient iteration is derived that converges to the set of r dominant/subdominant eigenpairs. This iteration is used to construct two eigenstructure tracking algorithms that track the r-dimensional dominant or subdominant subspaces of time-varying data or data-covariance matrices. The two eigenstructure tracking algorithms have update complexities O(m²r) and the other O(mr²), where m is the data dimension. The algorithms are customized to solve high resolution temporal and spatial frequency tracking problems. They are compared with existing techniques by tying into published simulation based performance tests. The algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost