Simulation Descriptions

 

Search and RescueDingy Rescue - Pollution - Historical


Search and Rescue Simulation:

This simulation demonstrates single object tracking using three different
particle filtering techniques.  We simulate a dinghy lost at sea.  The dinghy
(top-left frame) has a 7-dimensional state space: x- and y-location,
orientation, x- and y-velocities, change in orientation, and motion type.  The
motion type is a discrete variable taking values which represent a drifting,
rowing, or motorized motion type, and the dinghy switches between these motion
types as a Markov chain.

The observations (top-middle frame) which we get are similar to what we might
get when observing the ocean surface from above using an infrared camera.
Each pixel is corrupted by Gaussian noise, with a slightly higher mean
intensity of the pixel coincides with a dinghy's position.

At the bottom, we see the outputs of the three filters.  On the left is an
interacting particle filter, in the middle is a weighted particle filter, and
at the right is a branching particle filter.  In each frame is a red outline
showing the dinghy's true position, for comparison against the filter's
output.  We display the filter's guess by means of a box centred at the
filter's estimate for the dinghy's position and with a width twice the standard
deviation in position estimate.  Out of the centre of the box, we draw a line
indicating the filter's guess at the dinghy's orientation; the length of the
line indicates the filter's confidence at its guess.

Note that each filter operates in the full 7 dimensions of the dinghy's state.
However, we only display output related to three of the dimensions.

Dinghy Rescue Simulation:

This simulation demonstrates single object tracking using three different
particle filtering techniques.  We simulate a dinghy lost at sea.  The dinghy
(top-left frame) has a 7-dimensional state space: x- and y-location,
orientation, x- and y-velocities, change in orientation, and motion type.  The
motion type is a discrete variable taking values which represent a drifting,
rowing, or motorized motion type, and the dinghy switches between these motion
types as a Markov chain.

The observations (top-middle frame) which we get are similar to what we might
get when observing the ocean surface from above using an infrared camera.
Each pixel is corrupted by Gaussian noise, with a slightly higher mean
intensity of the pixel coincides with a dinghy's position.

At the bottom, we see the outputs of the three particle filters.  On the left
is static grid, in the middle is an adaptive grid, and at the right is a
refining grid.  In each frame is a red outline showing the dinghy's true
position, for comparison against the filter's output.  We display the filter's
guess by means of a box centred at the filter's estimate for the dinghy's
position and with a width twice the standard deviation in position estimate.
Out of the centre of the box, we draw a line indicating the filter's guess at
the dinghy's orientation; the length of the line indicates the filter's
confidence at its guess.

Note that each filter operates in the full 7 dimensions of the dinghy's state.
However, we only display output related to three of the dimensions.

Pollution Simulation:


In this simulation, we simulate pollution flowing through a water sheet.
A factory (lower-left corner) dumps random amounts of pollution at random
times, and the pollution diffuses, flows towards the right, and reacts.

At the bottom, we see the pollution levels as-is -- darker areas indicate more
pollution.  At the top, we see a ground-level view.  Our view of the pollution
is partially obscured by land, and at places where the pollution is visible,
the observed pollution level is noisy.

In this simulation, we do not perform any filtering.  Rather, it is meant to
show a possible application of filtering.  We may have well sites, or
measurement devices on the exposed water, to measure pollution levels and,
based on these measurements, we may attempt to determine the overall pollution
level of the water sheet.  Or, if we have multiple factories, we may wish to
determine which of the factories produces the most pollution, or the level of
pollution generated by each factory.

Historical Simulation:

The refining particle filter is able to filter the signal's historical path, in
addition to its current position.  In other words, based on the information
that we have at the current time, we can refine our estimate from a previous
time.

At left, we have the signal - a dinghy lost at sea.  It leaves behind a white
trail indicating its path since the beginning of the simulation.  The dinghy
(top-left frame) has a 7-dimensional state space: x- and y-location,
orientation, x- and y-velocities, change in orientation, and motion type.  The
motion type is a discrete variable taking values which represent a drifting,
rowing, or motorized motion type, and the dinghy switches between these motion
types as a Markov chain.

The observations (middle frame) which we get are similar to what we might get
when observing the ocean surface from above using an infrared camera.  Each
pixel is corrupted by Gaussian noise, with a slightly higher mean intensity of
the pixel coincides with a dinghy's position.

At right, we have the filter output.  The red outline and trail show the
dinghy's actual position and path for comparison with the filter output.  The
white box is centred at the filter's estimate and with width twice the standard
deviation in position estimate.  Out of the centre of the box, we draw a line
indicating the filter's guess at the dinghy's orientation; the length of the
line indicates the filter's confidence at its guess.  The green line represents
the filter's guess at the dinghy's path.