Filtro de Kalman, espaço de Hilbert definido por Kernels reprodutivos, não linear,não estacionário, eco acústico

Abstract

Acoustic echo is a phenomenon caused by the reflection of sound when it is perceived by its emission source with some delay. It appears in full duplex communication systems in a detrimental manner to the interaction between the speakers, reducing the intelligibility of exchanged information. Because it is a very unpleasant effect, acoustic echo attenuation or canceling procedures, if possible, become necessary procedures to mitigate such phenomenon. Several techniques have been reported in the literature in order to cancel acoustic echo, which includes the application of structures based on adaptive filtering. Typically, strategies where the adaptive filtering is used, it is assumed that the path traveled by the acoustic echo can be modeled as a linear time-invariant system. However, because the elements that form such a path, such as amplifiers and speakers, present non-linear characteristics, linear models fail to adequately represent the whole path traveled by the acoustic echo. In recent approaches it has been assumed that the echo response should obey non-linear and non-stationary models, whereas in acoustic environments the signal to be modeled can be modified by the movement of people and objects. Thus, the appropriate response representation model becomes essential for satisfactory adaptive system’s performance on echo identification and cancellation. This work aims to propose a new technique in the nonlinear and time variant estimation from the application of the Kalman filtering theory, which presents a good answer in the identification of non-stationary systems, in a Hilbert Space defined by Reproductive Kernel, where linearity can be treated linearly, using as an example of application the cancellation of acoustic echo