Y. Y. Tang et al. (Eds.): WAA 2001, LNCS 2251, pp. 305-313, 2001.  Springer-Verlag Berlin Heidelberg 2001 Multiscale Kalman Filtering of Fractal Signals Using Wavelet Transform * Juan Zhao 1 , Hong Ma 1 , Zhi-sheng You 2 , and Michio Umeda 3 1 Dept of Mathematics, Sichuan University Chengdu 610064,China 2 Dept of Computer Science, Sichuan University Chengdu 610064,China 3 Dept of Information Engineering, Osaka Electro-Communication University Osaka, Japan Abstract. A filter bank design based on orthonormal wavelets and equipped with a multiscale Kalman filter was recently proposed for signal restoration of fractal signals corrupted by external noise. In this paper, we give the corresponding parameters of the dynamic system and more accurate estimation. Comparisons between Wiener and Kalman filters are given. Typical computer simulation results demonstrate its feasibility and effectiveness. 1 Introduction The family of 1/f stochastic processes constitutes an important class of models for different signal processing applications. Examples are geophysical and economic time series, biological and speech signals, noise in electronic devices, burst errors in communications, and recently, traffic in computer networks[4]. A typical model for these processes is the fractional Brownian motion (fBm), which is a Gaussian zero- mean nonstationary stochastic process ) (t B H indexed by a parameter 0<H<1 and has two important characteristics: • non-stationary variations; • self-similarity. Recently, wavelet theory is a powerful method based on time-scale considerations, as an adequate tool for analyzing this type of processes, which could really provide a research method for every aspect of fractal signals processing. Many methods for estimating 1/f-type fractal signals embedded in noise have been proposed in order to conquer the traditional lacks, such as wavelet maximum likelihood ratio estimating method proposed by G.W.Worell and A.V.Oppenleim [7], multi-scale Wiener filters and Kalman filters considering the system influence proposed by B.S.Chen etrc.[1],[2] and multi-scale Wiener filters [4]and Kalman * Supported by the NNSF of China(No.60074017 and No.69732010).