LMS自适应无偏估计修正方法

Modified Bias-Free Estimation Method Using LMS Adaptive Algorithm

系统分析了LMS算法有偏估计的来源及其影响,并基于Treichler的γ-LMS算法提出了一种改进的无偏估计方法。根据自适应滤波器的最佳逼近原理和各信号矢量的几何关系,利用传统LMS算法获得的信息来估计输入噪声的功率,再通过γ-LMS算法在迭代过程中逐步修正维纳解,去除输入噪声的影响从而得到系统参数的真实估计。该方法无需假设输入与输出噪声功率相等或功率比已知、有用信号是白过程等限制条件。仿真与实际数据处理都验证了该方法的有效性,特别是将其应用于实际管道泄漏检测的被动时延估计系统中,在低信噪比或复杂噪声环境下LMS自适应算法的估计性能得到了改善。

A modified LMS algorithm is developed for the unbiased estimation based on Treichler γ-LMS algorithm. By the best approximation and the geometric interpretation of signal vectors in adaptive filters, the input noise variance is obtained with the information obtained from the traditional LMS algorithm. Then, based on γ-LMS algorithm, it can iteratively eliminate the input noise effects to obtain the bias in the Wiener solution and the true system coefficients. The proposed bias-free LMS algorithm need not to assume that the input and output noise powers are the same or their ratio is known, or the signals are all white processes. Simulations and experimental data validate the effectiveness of the method. In particular, the real pipe leakage detection is used in a passive time delay estimation system, the performance of the LMS algorithm can be improved in lower signal-noise-ratio （SNR） or more complicated environments.