Fast and stable modification of the Gauss–Newton method for low‐rank signal estimation

The weighted nonlinear least-squares problem for low-rank signal estimation is considered. of constructing a numerical solution that stable and fast long time series addressed. A modified Gauss-Newton method, which can be implemented through the direct variable projection onto space signals, proposed. For weight matrix provides maximum likelihood estimator in presence autoregressive noise order $p$ computational cost iterations $O(N r^2 + N p^2 r \log N)$ as $N$ tends to infinity, where time-series length, $r$ rank approximating series. Moreover, proposed method applied data with missing values, without increasing cost. compared state-of-the-art methods based on approach terms floating-point stability