一种快速递归全局最小二乘算法

A fast recursive global least squares algorithm

针对FIR系统输入和输出信号均被噪声干扰的情况,提出一种快速递归全局最小二乘(XS-RTLS)算法用于迭代计算全局最小二乘解,算法沿着输入数据的符号方向并采用著名的快速增益矢量,搜索约束瑞利商(c-RQ)的最小值得到系统参数估计。算法关于方向更新矢量的内积运算可通过加减运算实现,有效降低了计算复杂度;另外XS-RTLS算法没有进行相关矩阵求逆递归运算,因而具有长期稳定性,算法的全局收敛性通过Laslle不变性原理得到证明。最后通过仿真比较了XS-RTLS算法和递归最小二乘(RLS)算法在非时变系统和时变系统中的性能,验证了XS-RTLS算法的长期稳定性。

A fast recursive global least squares （XS-RGLS） algorithm is developed for iteratively computing the GLS solution for adaptive FIR filtering with input and output noises. The algorithm is obtained by searching the minimal point of c-RQ along input data sign vector and using the well-known fast gain vector. The number of multiplications required by XS-RGLS algorithm is reduced since all inner products with the update direction vector is computed with additions and subtractions. Moreover, the developed algorithm is independent of recursive computation of the inverse of the correlation matrix, thereby having good numerical stability. The global convergence of the new algorithm is studied by LaSalle＇s invariance principle. In time-invariant system and time-variant system, the performances of the relevant algorithms are compared via simulations, and the long-time numerical stability of the XS-RGLS algorithm is verified.