一种优化的自适应总体最小二乘系统辨识算法

对于监督信号和训练信号都含有噪声的系统辨识问题,如果采用经典的最小均方和迭代最小二乘算法进行估计,会带来较大的误差,而直接求解又会有较大的计算量,不利于在线计算.将权向量的求解转化为增广输入向量自相关矩阵瑞利商的受限最佳化问题,对增广输入向量进行遮代估计,同时建立了步长因子和误差信号问的函数关系,这个函数关系是建立在代价函数相对于步长梯度的基础上,而不是基于经验公式.所提算法结构简单,具有更好的稳健性,仿真表明这种算法相对于同类总体最小二乘算法和其他自适应算法有更快的收敛速度和更高的收敛精度.

Novel Variable Step-Size Adaptive TLS Algorithm

In the application of system identification in which the supervising signal and the training signal are both noisy, the typical adaptive algorithms such as least mean square(LMS) algorithm and recursive least square(RLS) algorithm will get an inaccurate estimate, and direct computing the matrix equation will get large burden of computation going against on-line implementation. The weight vector can be obtained by the constrained optimization of the rayleigh quotient of auto-correlation matrix of the input vector augmented. By constructing a function relationship between the step-size parameter and the error signal which is based on the gradient of the cost function and step size factor other than the experiential formula, the proposed algorithm has good robust performance. This algorithm has a simple structure, and simulations show that the algorithm proposed provides faster convergence rate and less misadjustment at steady-state than other TLS algorithms and adaptive algorithms.