基于时变哈密顿矩阵的标准系统自适应滤波
综合数学
2026-03-12 v1
摘要
在许多实际应用中，信号和环境是时变的，这使得固定滤波器不可靠。自适应滤波则实时更新，以抑制噪声、跟踪非平稳信号并识别未知系统。本文基于具有时变对称半正定哈密顿矩阵的标准系统，提出一种自适应滤波框架。该方法采用梯度导数方案调整哈密顿矩阵，以最小化系统输出与参考信号之间的平方误差。我们通过Lyapunov分析建立了理论稳定性保证，确保系统轨迹有界且误差信号收敛，前提是满足适当假设。此外，我们 presented numerical integration schemes preserving the underlying Hamiltonian structure and projective techniques to maintain positive semidefiniteness of the Hamiltonian matrix. extensive simulations on synthetic nonstationary signals illustrate the effectiveness and robustness of the proposed adaptive filter.
关键词
引用
@article{arxiv.2603.10096,
title = {Adaptive Filtering via Canonical Systems with Time-Varying Hamiltonians},
author = {Keshav Raj Acharya and Pitambar Acharya},
journal= {arXiv preprint arXiv:2603.10096},
year = {2026}
}