ROBUST ASR INSIDE A VEHICLE USING BLIND PROBABILISTIC BASED UNDER-DETERMINED CONVOLUTIVE MIXTURE SEPARATION TECHNIQUE - DSP for In-Vehicle and Mobile Systems - page 277

technique are compared. In section 5, we summarize and indicate future
direction of our research in this area.

2. UNDER-DETERMINED BLIND CONVOLUTIVE

MIXTURE SEPARATION

The method of blind source separation (BSS) attempts to estimate the
sources or inputs of a mixing system by observing the outputs of the system
without knowing how the sources were mixed together (no a priori
knowledge of the system) and what the sources are. The BSS is an important
problem and has many applications: e.g., interference free wireless
communication and robust automatic speech recognition in spoken dialogue
systems on mobile platforms. It is worth noting that in this chapter, the BSS
is applied within the framework of robust automatic speech recognition
problems. There are two cases (i) instantaneous mixture (IM) where the
mixing system has no memory and (ii) convolutive mixture where the length
of the filters that are used to represent a mixing system is greater than one.
Let N be the number of sensors used to observe the source signals and M be
the number of sources. Then the IM case can be written in matrix form as:

where x ( n ) is the mixed signal output matrix of size N x K, s ( n ) is the matrix
of source signals of size M x K, v ( n ) is the additive noise matrix of size N x K,
n = 1, 2.. .K are the time samples and a is the mixing matrix (mixing system)
of size N by M which is represented in terms of angles or directions of arrival
of source signals at the sensors i.e., a is a function of
The BSS is an easier problem to solve when N = M (finding a matrix);
several techniques have been developed. However, the BSS is a more
difficult problem to solve when N < M. In practice it is not possible to know
a priori how many sources are present (e.g., in the case of wireless
communication the sources correspond to the signals that get reflected from
various scatterers such as buildings and noise and in the case of spoken
dialogue systems they correspond to other speakers and noise) and they vary
dynamically as the environment changes and hence we will not know how
many sensors (e.g., antenna elements in the case of wireless communication
and microphones in the case of spoken dialogue system) to use so that it is
equal to the number of sources to observe the mixed signals. Therefore, BSS
when N < M has more practical applications and a more practical problem to
solve.