Companion webpage to G. Bustamante et al.' ICASSP'2016 submission
This page is structured into two parts.
Videos of Live experiments
The following videos show the real time behavior of the algorithm.
- On the TV screen, the red dot depicts the source. The KEMAR head
is depicted by a blue circle centered on the origin of the frame, and
the attached blue bar is oriented towards the boresight direction.
All these ground truth data are got from an Optitrack real time motion
- The audio-motor localization computes a Gaussian mixture
approximation of the head-to-source posterior pdf. The ellipsoids
drawn on the real time display are the 99%-probability
minimum-volume confidence sets associated to the hypotheses of this
posterior pdf. Their colors depict the posterior probability of the
associated hypothesis (red means high, blue means low, purple means
The following case studies have been tested.
- Open-loop uniform rotational movement of the head:
- Yet another open-loop uniform short rotational movement of the head:
- Open-loop uniform rectilinear translational movement of the head (up to little saturations of the neck velocity):
- Yet another open-loop uniform rectilinear translational movement of the head:
- Open-loop uniform nonholonomic circular movement of the head (its
relative angle w.r.t. the tangent vector of the trajectory is constant):
- Active motion as per ICASSP'2016 paper
- Sketch of the measure of information held in the posterior
pdf vs time index. Note that the applied velocities do not
have the same magnitudes over time in the three compared cases, so
that the rates of change of the relative plots may not be
meaningful. However, note that the information measure obtained by
the active motion strategy always decreases along time and reaches
the lowest steady state value.
Technical complements on the proof of the main result
The head-to-source situation at time
is characterized by the
posterior state pdf
approximated by the 2D
. This pdf can be
mapped into the 1D Gaussian approximation
of the predicted
, by using the unscented
transform. The aim is to maximize the variance
so as to
increase the entropy
. This involves the
composition of the several functions.
First the sigma-points
are computed from the
of the state vector at time
of the posterior
We consider that the random variable
undergoes a rigid motion defined by the translations
, and that the dynamic noise is neglected. Then
of the predicted state pdf
be obtained by applying the translation and rotation on each
Then each sigma-point
of the predicted
can be obtained from the
defined in () by:
are the components of each sigma point
is the Woodworth-Schlosberg formula for
interaural time difference approximation over a spherical head which
is used to guide the exploration of the space by the head.
function is used to retrieve the corresponding
azimuth of each sigma-point. Finally the mean
are computed using the unscented transform
formulae such as
are the classic
weights of the unscented transform.
can be defined as a function of the finite
translation and rotation
the maximium of this function is not analytically tractable. Its
is then computed so
as to point out the direction of its maximum, as follow:
The first order Taylor expansion of the functions
are composed around
translations and rotation
is the gradient operator.
is the Jacobian of
. Then the result of the
, is used to retrieve the
mean and the variance with () and ().
Finally, the first order Taylor expansion of
is obtained, highlighting the gradient
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