TY - UNPB

T1 - Modified Gauss-Newton method in low-rank signal estimation

AU - Zvonarev, N.

AU - Golyandina, N.

PY - 2018/3/4

Y1 - 2018/3/4

N2 - The paper is devoted to the solution of a weighted non-linear least-squares problem for low-rank signal estimation, which is related Hankel structured low-rank approximation problems. The solution is constructed by a modified weighted Gauss-Newton method. The advantage of the suggested method is the possibility of its stable and fast implementation. The method is compared with a known method, which uses the variable-projection approach, by stability, accuracy and computational cost. For the weighting matrix, which corresponds to autoregressive processes of order $p$, the computational cost is $O(N r^2 + N p^2 + r N \log N)$, where $N$ is the time series length, $r$ is the rank of approximating time series. For the proof of the suggested method, useful properties of the space of series of rank $r$ are studied.

AB - The paper is devoted to the solution of a weighted non-linear least-squares problem for low-rank signal estimation, which is related Hankel structured low-rank approximation problems. The solution is constructed by a modified weighted Gauss-Newton method. The advantage of the suggested method is the possibility of its stable and fast implementation. The method is compared with a known method, which uses the variable-projection approach, by stability, accuracy and computational cost. For the weighting matrix, which corresponds to autoregressive processes of order $p$, the computational cost is $O(N r^2 + N p^2 + r N \log N)$, where $N$ is the time series length, $r$ is the rank of approximating time series. For the proof of the suggested method, useful properties of the space of series of rank $r$ are studied.

KW - math.NA

KW - 15B99, 15B05, 37M10, 41A29, 49M15, 65F30, 65K05, 65Y20, 68W25, 93E24

KW - linear recurrence relation

KW - Hankel structured low-rank approximation

KW - signal estimation

KW - Gauss-Newton optimization

KW - variable projection

M3 - Preprint

BT - Modified Gauss-Newton method in low-rank signal estimation

ER -