Stochastic Signal Detection From A Saturated Noisy Observation And Its Application To Room Acoustics

In the measurement of actual phenomena, the observed data often suffer from loss or distortion due to the limited dynamic range of the measurement instruments. This paper describes a new method of dynamical state estimation for stochastic systems, in a practical case in which the observed data fluctuates within a finite amplitude domain owing to the dynamic range of the measurement instrument. The state estimation method proposed for use with such incomplete observation data (with information loss or distortion) is a theoretically based improvement of the wide sense digital filter, for situations in which the data is contaminated by an external noise of arbitrary distribution type. A recurrence type estimation algorithm is explicitly derived in series expansion form from the Bayesian viewpoint, with the aim of utilizing hierarchically the linear and non-linear correlation information between the observed value and the unknown state variable. The proposed estimation theory is experimentally confirmed by applying it to a problem of background noise correction in room acoustics.