A Bayesian Filter for Sound Environment System with Quantized Observation<sup>*</sup>

Abstract

In the real sound environment, the observation data are usually contaminated by additional background noise of arbitrary distribution type. In order to estimate several evaluation quantities for specific signal based on the observed noisy data, it is fundamental to estimate the fluctuating wave form of the specific signal. On the other hand, the observation data are very often measured in a digital level form at discrete times. This is because some signal processing methods by utilizing a digital computer are indispensable for extracting exactly various kinds of statistical evaluation for the specific signal based on the quantized level data. In this study, a Bayesian filter matched to the complicated sound environment system is derived. First, in the real situation where the sound environment system is affected by background noise of arbitrary probability distribution, a stochastic system model with quantized observation is established. Next, two types of the recursive algorithm of Bayesian filter to estimate the unknown specific signal are theoretically proposed in the quantized level form. Finally, the effectiveness of the proposed theory is experimentally confirmed by applying it to the estimation problem of real sound environment.

State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

“…Furthermore, it is obvious that the proposed method in Sect. 4 is more useful than our previous method [11] and the extended Kalman filter. Furthermore, in the case of the quantized observation data with 2 dB, the estimate…”

“…For comparison, the estimation results calculated by using our previous method [11] and standard method are also shown in Figure 5 and Figure 6. Since Kalman's filtering theory has been widely used in the field of stochastic system, the extended Kalman filter [5] was also applied to the observation data as a trail by using observation model shown in Equation (15).…”

“…Especially, the experimental confirmation has been confined to only the numerical simulation and the application to real state estimation problems has seldom been carried out. From the above viewpoint, in our previous study, a state estimation algorithm has been derived by introducing a difference operation to the non-differentiable nonlinear function expressing the quantized observation [11].…”