Research output: Contribution to journal › Article › peer-review
The weighted nonlinear least-squares problem for low-rank signal estimation is considered. The problem of constructing a numerical solution that is stable and fast for long time series is addressed. A modified weighted Gauss–Newton method, which can be implemented through the direct variable projection onto a space of low-rank signals, is proposed. For a weight matrix that provides the maximum likelihood estimator of the signal in the presence of autoregressive noise of order p the computational cost of iterations is (Formula presented.) as N tends to infinity, where N is the time-series length, r is the rank of the approximating time series. Moreover, the proposed method can be applied to data with missing values, without increasing the computational cost. The method is compared with state-of-the-art methods based on the variable projection approach in terms of floating-point numerical stability and computational cost.
Original language | English |
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Article number | e2428 |
Journal | Numerical Linear Algebra with Applications |
Volume | 29 |
Issue number | 4 |
Early online date | 20 Dec 2021 |
DOIs | |
State | Published - Aug 2022 |
ID: 93205595