LMS adaptive filtering_北京理工大学 统计信号处理

统计信号处理（全英文）

结课报告

题目：Least-Mean-Square Adaptive Filters

and i t’s Application

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任课教师：

Contents

1 Introduction (2)

2 Overview and Structure of Operation of LMS Algorithm (4)

2.1 Structure of Operation of LMS Algorithm (4)

2.2 Operation Procedures (5)

3 Derivation of LMS Algorithm (6)

3.1 The Idea of the Steepest-Descent Algorithm (6)

3.2 Least-Mean-Square Adaptation Algorithm (9)

3.3 Summary of the LMS Algorithm (11)

4 The application of the LMS Algorithm (12)

4.1 Instantaneous Frequency Measurement (12)

4.2 Adaptive Deconvolution for Processing of Time-Varying (14)

References (17)

1Introduction

Along with the rapid development of the mobile communications industry, the scope of application of adaptive filtering techniques is also growing. Early in the 1940s, it was established on the stationary random signal Wiener filtering theory. According to the statistical properties of the useful signal and interference noise (the autocorrelation function or power spectrum), the optimum filter with a linear minimum mean square error estimation criterion design, called Wiener filter. This filter can maximize filter out interference noise and extract useful signal. However, when the statistical characteristics of the input signal deviates from the design condition, it is not the best, which is limited in practical applications. By the early 1960s, due to the development of space technology, the emergence of Kalman filtering theory, namely the use of state-variable model of non-stationary random sequence of multi-input multi-output for optimal estimation. Now, the Kalman filter has been successfully applied to many areas, it both on the stationary and non-stationary random signal as a linear optimal filtering, but also for non-linear filtering. In essence, the Wiener filter is a special case of the Kalman filter.

In the design of the Kalman filter, you must know the state equation and measurement equation produces the input process of the system, which requires the prior knowledge of the statistical characteristics of the signal and noise, but in practice it is often difficult to predict the statistical properties, thus can’t achieving a good optimum filtering.

Widrow B Hoff and adaptive filter theory proposed in 1967, allows the parameters of the adaptive filter system automatically adjust to achieve the best condition, but also in the design, requiring little or no any information about the priori statistical knowledge of signal and noise. Implement such a filter is almost as simple as the Wiener filter, and the performance of the filter is almost as good as the Kalman filter. Thus, in recent decades, adaptive filtering theory and method has been developing rapidly.

Let’s talk about adaptive, In process and analysis, we according t o the characteristics of data to automatic adjust the method of processing data, processing