小波变换与Kalman滤波在信号处理中的联合应用/the Combining Application of Wavelet Transform and Kalm

2018-11-29 03:36:46

signal 小波 processing time Kalman



通过测量或观测所获得信号或数据通常包含两个部分:其一是与所研究的对象存在直接或间接关系的有用部分,称为信息;另一部分是与所研究的对象无关的干挠部分,称为噪声。信号处理的目的就是最大限度去除或抑制与所研究对象无关的那部分干挠,突出或提取有用信息。
小波变换是一种用于信号处理的新方法,它的多分辨率特性使其在许多领域得到了应用。小波滤波就是利用信号和噪声在各尺度通下的小波变换系数有所不同的特点,来对它们进行分离,从而达到去噪的目的。通常含有噪声的信号经过小波变换,有用信息主要集中在低频部分,噪声则大部分包含在高频内,对这一部分采用适当的方法进行过滤,然后进行小波逆运算,重构信号,就可实现信号的降噪。
然而,小波变换很难信号实现的实时处理,Kalman滤波正好能弥补这一缺陷。当信号含有噪声时,Kalman滤波可以在最小均方误差条件下给出信号的最佳估计,而且是在时域中采用第推方式进行,因此速度快,便于实时处理。
由于风荷载是一种随机作用,结构在这种荷载的作用下,结构响应的统计参数不可能事先得到,而这种参数却是Kalman滤波的初始条件,也就不能实现真正的实时最佳估计。并且,在实际工程中,也不可能做到对每一个传来的数据进行实时处理,这期间有一个时间滞后的过程。根据这一特点, 本文综合利用了两种信号处理方法的优点,提出了基于小波变换的Kalman滤波方法。该方法既具有小波变换的多分辨率特性,又继承了的Kalman滤波方法的实时性,复合为一种“伪”实时滤波估计。最后,对Kalman滤波的发散问题进行了分析,并给出了相应的改进办法。
仿真算例结果证明了该方法实施的可能性和有效性。最后,针对此方法的实用性条件进行讨论,展望了其应用前景。



The signal/data obtained by measurement or observation usually contain two parts: one part is useful which has a direct or indirect relation to the research object, called information. And the other part is interferential has no relation to the research object, called noise. The purpose of signal processing is to suppress or get rid of the interferential part, and display or pick-up useful information.
Wavelet transform is a new method using in signal processing. The property of multi-resolution makes wavelet transform widely using in many fields. According to the difference of wavelet coefficients between information and noise transformed in different scale, they can be separated, and noise is got rid of. Usually, the signal containing noise is transformed using proper wavelet, and the majority of useful information is contained in the low frequency part, but noise mostly presents to the high frequency part. If proper processing method is used to the later part, and signal is de-noised by reconfiguration in using inverse wavelet transform.
But wavelet transform cannot be used in the real time signal processing. Kalman filtering just can fetch up the default, which can give the optimum estimation of signal under the condition of the minimum mean-square. And this method works in the time domain, the processing speed is fast, which make it be used in the real time signal processing.
Because the wind load is a random action, the statistical parameters of structural response under this load can hardly obtained beforehand. However these parameters is necessary to Klaman filtering as the preliminary condition. If not got, this signal processing cannot be called the genuine real time optimum estimation. According to the limit of real project, we cannot process each datum in real time, because signal transmission need some time, and there is a time lagging.
Considering this character, a new method of Kalman filtering based transform is given in this paper. This method has not only the property of multi-resolution of wavelet, but also the proper of real time processing of Kalman filtering. In fact this method is a pseudo real time processing.
In the end, the volatilization of Kalman filtering due to the measure data is discussed, and some corresponding methods are presented. And a simulant example shows that the filtering method is effective and feasible and effective. The application prospect of this method is prognosticated at the same time.