Simulation Descriptions 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.