Cs4758 Kalman HMM Examples
Cs4758 Kalman HMM Examples
Cs4758 Kalman HMM Examples
and
Localiza/on
Kalman
Filters
and
HMMs
CS
4758
Ashutosh
Saxena
Cornell
University
Applica/on
Examples.
Tracking
in
1D.
Tracking
in
2D
(visual
tracking).
Localiza/on
in
2D.
Tracking
Visual Tracking
Localiza/on in 2D
Learning Algorithms.
Representa/on.
Model.
Inference.
Learning.
Others:
Dataset.
Details:
Features,
etc.
TRACKING IN 1D
Wrong
model?
Say
the
dam
in
the
lake
was
lling
up
at
a
constant
rate.
And
we
use
the
same
model?
How
to
x
this?
The
following
two
assump/ons
could
be
causing
this:
The
model
we
have
chosen.
The
parameters
of
our
model.
q = .01
q = 0.1
q = 1
Filling Model.
TRACKING IN 2D
Visual
Tracking
in
2D
Problem:
Find
out
a
given
object
in
every
frame.
Features
Detector
(logis/c
classier,
SVM)
Probability
of
being
person
(0,1).
Representa9on:
y={0,1}
Does
the
rectangle
at
(x,y,len,width)
contains
a
person.
Model:
Use
logis/c
classier
or
SVM,
which
has
parameters
w.
(Cost
func/on?)
Learning
algorithm:
Gradient
descent.
(Or
use
exis/ng
code.)
Inference
algorithm:
wT(x)
>
0
Which
side
of
separa/ng
hyperplane
does
it
lie.
Other
details:
Which
features
to
use,
dataset,
etc.
Why Tracking?
Model: ?
ROBOT LOCALIZATION
Problem
Sensor:
laser
scans.
Given
a
2D
map.
Simpler
Problem
Sensor:
presence/absence
of
well
in
each
direc/on.
Given
a
2D
map.
Representa/on
Kalman
Filters?
How
to
interpret
map
boundaries?
HMM?
2D
Localiza/on:
Model
{N,
M,
aij,
bi(j),
i}
N
=
M
=
No
knowledge
about
robot
state
in
the
beginning:
i
=
Sensors
make
never
more
than
one
mistake:
bi(j)
=
25%
robot
moves
in
each
direc=on:
aij
=
t=1
t = 2
t = 3
t = 4
t = 5
Inference: HMM
HMM
Representa/on:
state,
observa/on.
Model
Inference
Learning:
?
EM
algorithm
(use
exis/ng
HMM
toolboxes.)
PARTICLE FILTER