标题： 约束最小二乘法在扩展复数因子分析中的应用 显示英文标题

标题： Constrained Least Squares for Extended Complex Factor Analysis

摘要： 对于未知色噪声的子空间估计，因子分析（FA）是替代流行的特征值分解（EVD）的一个很好的选择。在因子分析中寻找未知参数可以通过求解非线性最小二乘问题来实现。对于这类优化问题，高斯-牛顿（GN）算法是一种强大且简单的方法。GN算法中最昂贵的部分是在每次迭代中通过求解方程组来找到下降方向。本文我们证明了对于FA，这些方程组中涉及的矩阵可以以封闭形式对角化，并且可以以计算高效的方式找到解。我们展示了如何在不实际构造这些矩阵的情况下更新未知参数。通过数值模拟研究了该算法的收敛性能。 显示英文摘要

摘要： For subspace estimation with an unknown colored noise, Factor Analysis (FA) is a good candidate for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in factor analysis can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.