2007 IEEE International Conference on Signal Processing and Communications (ICSPC 2007), 24-27 November 2007, Dubai, United Arab Emirates
TRACKING MANEUVERING SOURCES IN ICA
S.A. Banani 1, MA. Masnadi-Shirazi 2, A. Masnadi-Shirazi3
IDept of Electrical Engineering, Shiraz University, Shiraz, Iran
2Dept of Electrical Engineering, Shiraz University, Shiraz, Iran
3Dept of Electrical Engineering, University of California, San Diego, USA
ABSTRACT
The problem addressed in this work is to separate the
signals of moving sources with independent component
analysis (ICA) and tracking the kinematics (position,
velocity, acceleration) of each individual source in the
working space using Particle filters. To identify the
unpredictable movement of the speaker over time, the
new proposed state switching scheme handles the
uncertainty of the speakerzs motion by incorporating
multiple motion models in the tracking process instead of
using the conventional IMM algorithm. The algorithm
performance has been verified by illustrating some
simulation results.
Index Terms- ICA; Particle filter; Source
separation; tracking; positioning
1. INTRODUCTION
The problem of tracking sources in reverberating
environments is relevant in several applications,
including seismology, sonar and speech. Localizing and
tracking multiple speakers talking in the same room can
be used, for example, to automatically steer camera
sensors in video-conferencing applications.
Several works with deferent strategies have been
done in the field of tracking and source separation. Some
works like [1] focuses on TRINICON algorithm in the
noise free environment. But in real life, there is always
some kind of noise present in the observations. Noise can
correspond to the actual physical noise in measuring
devices or accuracies of the model used.
In [2] an algorithm based on IMM-PDA filters has
been proposed. Each of the speakers, state equation
describing their movement and the observation equation
has been assumed to be a linear function of the state.
However, any of the equations may be a nonlinear
function of the states. In such a case, using Kalman filters
are not suggested. Furthermore, when there are severe
nonlinearities in either of the state or observation
equations, extended Kalman filters falls beneath its
suboptimal performance. In this cases, using Particle
filters as nonlinear state estimators are more suitable.
In this work we will present a novel, general
framework that can deal with both cases, that is, dealing
with the nonlinearities of the state and observation
equations for tracking the sources and separating the
voices of multiple, possibly moving, speakers in the
noisy environment. In order to be able to cover the
unpredictable movement of the speaker over time, the
new proposed state inference scheme, handles the
uncertainty of the speakerzs motion by incorporating
multiple motion models in the tracking process.
2. PROBLEM DESCTRIPTON
2.1. ICA Model
In the standard noisy ICA, the noise is assumed to be
additive. This is a rather realistic assumption used in
factor analysis and signal processing, and allows for a
simple formulation of the noisy model. Thus, the noisy
ICA model can be expressed as
Ok = Aksk + Wk (1)
where the vector Sk is the vector of independent sources
and 0k iS the observation vector in each iteration and Wk is
the vector of additive noise that in general can have any
non-Gaussian distribution.
Assume that we have L independent source
components and M observations at each iteration. The
indices k shows that in each iteration, the mixing matrix
A is changing due to the movement of sources or
possibly non-stationary environment of the work space.
As the elements of matrix A, i.e.
aij,
are some
parameters that depend on the distances between the
microphones and the sources, we may write any desirable
nonlinear relation between
a,
and the distances. Thus
we may write
a,j
=
fij (rij),
i =
1,2,..., M
j
=
1,2,...,I L (2)
where is the distance between source j and
microphone i.
Note that in general,
r,
depends on x, y and z which
are the related distances in three dimensions of working
space. For example if source i is located in the origin, i.e.
(0, 0, 0),
We may write
1-4244-1236-6/07/$25.00
©
2007 IEEE
991