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
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.