基于QR分解的低复杂度RLS算法研究

摘要

为避免RLS算法在迭代过程中的数值发散现象，研究了复数域下基于QR分解的RLS估计算法，推导了基于Givens旋转的免开方、免除法的逆QR-RLS算法，通过变换可直接得到滤波系数更新所需增益向量，避免了QR-RLS算法的回代运算，同时消除了逆QR-RLS算法在每次迭代时的N次开方、2N次除法运算，有效降低了运算量。%To avoid the divergence problem encountering in RLS algorithm, the adaptive RLS filtering algorithm based on the QR decomposition over complex plane is analyzed. Then the Givens-based inverse QR-RLS algorithm, which wis a square-root-free and division-free scheme, is deduced in detail, which can overcome the divergence problem of RLS algorithm. Meanwhile, the square-root-free and division-free scheme can obtain the gain vector directly for coefficients-updated and save N square root and 2N division operations compared with inverse QR-RLS algorithm.