无需离散化即可精准估计线性调频信号参数，突破传统方法的基失配瓶颈。
Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization
- 通过约束二维原子范数最小化实现连续参数直接估计
- 数值实验表明可实现啁啾参数的精确恢复
- 适合信号处理与雷达领域需要高精度参数估计的研究者
本文研究从线性调频信号混合中估计啁啾参数的基本问题。与以往通过离散化参数空间再估计的方法不同，我们提出一种无网格方法，将逆问题重构为结构化测量下的约束二维原子范数最小化。该重构使连续参数可直接估计，避免了基失配问题。采用近似半定规划（SDP）求解所提出的凸优化问题，并构造对偶多项式以验证原子分解的最优性。数值仿真表明，所提原子范数最小化方法可实现啁啾参数的精确恢复。
原文摘要 · Abstract (English)
This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the chirp parameters, we propose a gridless approach by reformulating the inverse problem as a constrained two-dimensional atomic norm minimization from structured measurements. This reformulation enables the direct estimation of continuous-valued parameters without discretization, thereby resolving the issue of basis mismatch. An approximate semidefinite programming (SDP) is employed to solve the proposed convex program. Additionally, a dual polynomial is constructed to certify the optimality of the atomic decomposition. Numerical simulations demonstrate that exact recovery of chirp parameters is achievable using the proposed atomic norm minimization.
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