Low-rank signal subspace: parameterization, projection and signal estimation

The paper contains several theoretical results related to the weighted nonlinear least-squares problem for low-rank signal estimation, which can be considered as a Hankel structured approximation problem. A parameterization of subspace time series connected with generalized linear recurrence relations (GLRRs) is described and its features are investigated. It shown how obtained help describe tangent plane, prove optimization construct stable algorithms solving problems. For latter, algorithm constructing projection onto that satisfy given GLRR proposed justified. This used new implementation known Gauss-Newton method using variable approach. comparison by stability computational cost performed theoretically an example.