低信噪比下的LMS自适应无偏时延估计

Bias-Free LMS Time Delay Estimation at Low Signal-to-Noise Ratio Levels

比较性研究了最小均方(LMS)时延估计器中有偏与无偏估计算法的时延估计性能,并基于Treichler的γ-LMS算法提出了一种改进的无偏估计方法.利用自适应滤波器中最佳逼近原理的几何解释来估计输入噪声的功率,迭代过程中逐步去除输入噪声的影响,使得最优维纳解的真实峰值得到增强,在低信噪比或复杂噪声环境下显著改善了自适应时延估计性能.该方法无需假设输入与输出噪声功率相等或功率比已知、有用信号应为白过程等限制条件,因此具有广泛的应用价值.仿真与实际数据处理都验证了该方法的有效性.

The performances of least mean square （LMS） time delay estimator （TDE） are analyzed using biased and unbiased estimation methods. Then a modified LMS method based on Treichler＇ s γ-LMS algorithm is developed for unbiased estimation in the presence of white input and output noises,in which the input noise variance is simply obtained by the Euclidean geometric interpretation of the best approximation in adaptive filters without any a priori knowledge of the interference. With this estimated variance,the proposed bias-free LMS-TDE can iteratively eliminate the input noise effects and actually enhance the true peak,thus it can reduce the probability of anomalous peak in noisy environments at lower signal-to-noise ratio （SNR） levels. It gets rid of the assumptions that the input and output noise powers am the same or their ratio is known, or the signals am all white processes. Simulations and real data application are both provided to validate its effectiveness.