A time-varying Newton algorithm for adaptive subspace tracking

As an application of such techniques we develop new algorithms for computing the principal and minor subspace of a time-varying family of symmetric matrices. Using a convenient local parameterization of the Grassmann manifold, we derive simple expressions for the subspace tracking schemes. Key benefits of the algorithms are (a) the reduced complexity aspects due to efficient parameterizations of the Grassmannian and (b) their guaranteed accuracy during all iterates. Numerical simulations illustrate the feasibility of the approach.