Various type digital filters for an arbitrary sound environmental system with quantized observation mechanism and its application

The authors describe various state estimation methods of a quantized sound environmental system. The elimination of not only the usual background noise but also the quantization noise owing to digital observation is discussed. The methods include the traditional Kalman filter as a special case when Gaussian distribution is employed and where there is no level quantization. The level quantization mechanism is discussed from the statistical viewpoint and from the deterministic viewpoint. The methods presented can estimate any kind of statistic, including the lower and the higher order moments from the level quantized observation data. Not only the linear correlation but also the higher order nonlinear correlations between a state variable and a quantized observation are hierarchically used in the estimation algorithm. The quantized observation data are used in the linear and nonlinear forms. The effectiveness of the proposed methods was confirmed experimentally by applications to room acoustics data