In many actual applications of the adaptive filtering, input signals as well as output signals often contain observation noises. Hence, it is necessary to develop an adaptive filtering algorithm to such an errors-in-variables (EIV) model. One solution for identifying the EIV model is a total least squares (TLS) algorithm based on a singular value decomposition of an off-line processing. However, it has not been considered to identify the EIV IIR system using an adaptive TLS algorithm of which stability has been guaranteed during adaptation process. Hence we propose a normalized lattice IIR adaptive filtering algorithm for the TLS parameter estimation. We also show the effectiveness of the proposed algorithm under noisy circumstances through simulations.

This paper introduces some modelling methods of time-varying stochastic process and its linear/nonlinear adaptive identification. Time-varying models are often identified by using a least square criterion. However the criterion should assume a time invariant stochastic model and infinite observed data. In order to adjust these serious different assumptions, some windowing techniques are introduced. Although the windows are usually applied to a batch processing of parameter estimates, all adaptive methods should also consider them at difference point of view. In this paper, two typical windowing techniques are explained into adaptive processing. In addition to the use of windows, time-varying stochastic ARMA models are built with these criterions and windows. By using these criterions and models, this paper explains nonlinear parameter estimation and the property of estimation convergence. On these discussions, some approaches are introduced, i.e., sophisticated stochastic modelling and multi-rate processing.

In recent years, fractal processes have played important roles in various application fields. Since a 1/f process possesses the statistical self-similarity, it is considered sa a main part of fractal signal modeling. On the other hand, noise reduction is often needed in real-world signal processing. Hence, we propose an enhancement algorithm for 1/f signal disturbed by white noise. The algorithm is based on constrained minimization in a wavelet domain: the power of 1/f signal distortion in the wavelet domain is minimized under a constraint that the power of residual noise in the wavelet domain is smaller than a threshold level. We solve this constrained minimization problem using a Lagrangian equation. We also consider a setting method of the Lagrange multiplier in the proposed algorithm. In addition, we will confirm that the proposed algorithm with this Lagrange multiplier setting method obtains better enhancement results than the conventional algorithm through computer simulations.