一种新的变步长LMS自适应滤波算法研究及其应用

A new variable step LMS algorithm and its application

变步长LMS自适应滤波算法克服了传统自适应滤波算法的不足,通过构造合适的变步长因子,在提高收敛速度的同时保证了较小的稳态误差,在实际中得到了广泛应用。为进一步改善算法性能,首先对传统的和现有改进的变步长LMS算法机理进行了深入分析,在此基础上,提出了一种新的变步长LMS自适应滤波算法。该算法通过建立一个新的步长因子与误差的非线性函数模型,使得算法在不失精度的情况下,具有较快的收敛速度。论文对新算法的机理进行了较为详尽的阐述,对算法中关键参数的选取对滤波性能的影响进行了深入分析,并给出了算法中关键参数的自适应确定方法。仿真实验表明,相对于其他自适应滤波算法,该算法在收敛速度方面有了很大的提高。将新算法应用于对实际龙口水位监测数据的滤波中,取得了良好效果。

By constructing an appropriate variable step length factor, the variable step least mean square （LMS） adaptive filtering algo- rithm is presented to overcome the inadequate of the traditional LMS adaptive filtering algorithm, and the small steady-state error is main- tained while the convergence rate is improved, which is used in practice. To further improve the algorithm performance, a new variable step LMS algorithm is proposed based on the thorough analysis of the traditional algorithm and the existing improved algorithm. The new algo- rithm exhibits faster convergence speed under the condition of the guaranteed precision by establishing a new non-linear functional model between the step size and error. The principle of the proposed algorithm is illustrated, and the influences of key parameters on the perform- ance of the filter are further analyzed as well. Simulation results show that the algorithm can improve the rate of convergence compared with other adaptive filtering algorithms. The new algorithm is applied in water level data filtering at the closure gap, and good results are achieved.