复指数信号模型非线性最小二乘解的几何结构及迭代算法

The Geometric Structure of Nonlinear Least Square Solution for Signal by Complex Exponents and Alternate Algorithm

本文给出了复指数信号模型非线性最小二乘解的几何结构 .从分析迭代算法的收敛性态入手得到解的几何结构 ,将有助于构造十分有效的迭代算法 .另外 ,本文在低信噪比 (10dB)及较小频率差 (0 0 2Hz)的情况下 。

The geometric structure of nonlinear least squares solution for signals by complex exponents is offered in this paper.Beginning with analysis for the convergent state of alternative algorithm solving two equations together contented by the model's nonlinear least squares solution,the recognition for geometric structure of nonlinear least squares solution is acquired.It would help to construct a fully effective algorithm and understanding for the solution's structure is deepened.The alternative algorithm presented by this paper is fully effective in higher SNR or when the difference of frequency in model is slightly increased.Nevertheless,the invalid convergence (large error) appears in the condition with lower SNR(10dB) and smaller difference of frequency (0 02 Hz),if the convergent control condition of alternative algorithm is only in accordance with varying quantity of least squares error.