低秩信号子空间：参数化、投影与信号估值
Low-rank signal subspace: parameterization, projection and signal estimation
摘要：
本文给出了低秩信号估值的加权非线性最小二乘问题的几个理论结果，该问题可以看作是一个Hankel结构的低秩逼近问题。本文给出了低秩时间序列广义线性递推关系（GLRR）子空间的参数化方法，并研究了它的性质。它示出了如何得到的结果有助于描述切面，证明最优化问题的功能和构造稳定的算法求解低秩逼近问题。对于后者，一个稳定的算法构造到子空间的时间序列，满足给定的GLRR的投影提出和证明。该算法是用于一个新的实现已知的高斯-牛顿法使用变量投影方法。从稳定性和计算成本两个方面进行了理论分析和算例比较。
英文摘要：
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 low-rank approximation problem. A parameterization of the subspace of low-rank time series connected with generalized linear recurrence relations (GLRRs) is described and its features are investigated. It is shown how the obtained results help to describe the tangent plane, prove optimization problem features and construct stable algorithms for solving low-rank approximation problems. For the latter, a stable algorithm for constructing the projection onto a subspace of time series that satisfy a given GLRR is proposed and justified. This algorithm is used for a new implementation of the known Gauss-Newton method using the variable projection approach. The comparison by stability and computational cost is performed theoretically and with the help of an example.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
