二阶Volterra变数据块长LMS算法

二阶Volterra数据块LMS算法利用当前时刻及其以前时刻更多输入信号和误差信号的信息提高了算法的收敛速度，但由于其固定数据块长取值的不同导致了算法的收敛速度和稳态误差此消彼长。针对这个问题，本文提出一种二阶Volterra变数据块长LMS算法，通过时刻改变输入信号数据块长度提高算法性能。本算法首先采用两个并行的二阶Volterra滤波器，其输入信号数据块长差值始终保持一个单位；然后将其各自的输出误差信号同时输入到数据块长判决器，通过判决器得到下一时刻各个滤波器输入信号的数据块长度；最后以第1个二阶Volterra滤波器的输出作为整个滤波系统的输出，从而改善了算法性能。将本算法应用于非线性系统辨识，计算机仿真结果表明，高斯噪声背景下本算法的收敛速度和稳态性能都得到了明显的提高。 

A Variable Data Block Length LMS Algorithm for Second-Order Volterra Filter

The data block LMS algorithm for second-order Volterra filter uses the present moment and its previous moment abundant information of input signals and error signals to increase the algorithm’s convergence speed. However, the fixed data block lengths which are different from each other, lead to a reciprocal relationship between the algorithm’s convergence speed and steady-state error. To solve the problem, a variable data block length LMS algorithm for second-order Volterra filter is proposed, which improves the algorithm’s performance by changing the input data block length at each moment. In this algorithm, firstly，two parallel second-order Volterra filters are used and the difference of their input data block lengths is one unit forever. Then, the two filters’ output error signals are put into a data block length decision device to adaptively adjust the two input data block lengths in next moment. Lastly, the output signal of the first second-order Volterra filter is taken as the output signal of the whole filtering system to improve the algorithm’s performance. This algorithm is applied to nonlinear system identification. The computer simulation results of nonlinear system identification show that both convergence speed and steady-state performance of the algorithm are significantly improved in Gaussian noise environment.