Estimators
Suppose we are tracking a person who is walking across the view of a video camera. At each frame we make a determination of the location of this person. This could be done any number of ways, as we have seen, but in each case we find ourselves with an estimate of the position of the person at each frame. This estimation is not likely to be extremely accurate. The reasons for this are many. They may include inaccuracies in the sensor, approximations in earlier processing stages, issues arising from occlusion or shadows, or the apparent changing of shape when a person is walking due to their legs and arms swinging as they move. Whatever the source, we expect that these measurements will vary, perhaps somewhat randomly, about the "actual" values that might be received from an idealized sensor. We can think of all these inaccuracies, taken together, as simply adding noise to our tracking process.
We'd like to have the capability of estimating the motion of this person in a way that makes maximal use of the measurements we've made. Thus, the cumulative effect of our many measurements could allow us to detect the part of the person's observed trajectory that does not arise from noise. The key additional ingredient is a model for the person's motion. For example, we might model the person's motion with the following statement: "A person enters the frame at one side and walks across the frame at constant velocity." Given this model, we can ask not only where the person is but ...
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