一种三阶Volterra自适应滤波算法

An adaptive algorithm of third-order Volterra filter

采用更高阶Volterra滤波器更好地逼近非线性系统时,Volterra自适应滤波算法的计算复杂度呈幂级数增加。针对此问题,本文提出了一种在α稳定分布噪声背景下基于离散余弦变换(DCT)的三阶Volterra滤波算法。首先将Volterra滤波器的三次项权系数矩阵分解成一组二次项权系数矩阵;然后利用正交变换,将二次项权系数矩阵变换成对角矩阵,从而大大减少了权系数个数,有效降低了算法的计算复杂度;最后将Volterra自适应滤波器输出表示成线性滤波器输出形式,并由此得到权系数自适应调整算法。系统辨识的仿真结果表明,本算法在α稳定分布噪声背景下具有优越的性能。

As the orders of Volterra filter are enlarged to approach the nonlinear system better,the computational complexity of Volterra adaptive filtering algorithms increases by power series.An adaptive algorithm of third-order Volterra filter based on DCT in α-stable noise environment is proposed.First,the cubic term weighting coefficients matrixes are decomposed into a group of quadratic term weighting coefficients matrixes.Second,using orthogonal transformation,the quadratic term weighting coefficients matrixes are transformed into diagonal matrixes,so that not only the number of weighting coefficients is decreased greatly but also the computational complexity is effectively reduced.Lastly,the output of Volterra adaptive filter is expressed as the output of linear filter and the adaptive adjusting algorithm of weighting coefficients is proposed.Simulation results of system identification show that the new algorithm has better performance in α-stable noise environment.