Example of trilateration on the output areas of Sheffield
In the last post, we looked at methods to find the optimum landmark. In this post we look at how to find one’s location given a set of landmarks.
Previously I’ve naively found the probability of each location on a grid, given the reported distances to the landmarks, then sampled from this grid to find the probability for each output area.
In this notebook we approach the problem differently, and look for the probability of the set of distances to the landmarks given the output area. By swapping the order, we are able to use the node in the Bayesian network.
Read more (ipynb)
Combining two estimated distances to find your location.
Trilateration is like triangulation, but uses the distances to landmarks, rather than their angles, to determine one’s location. GPS is probably the most common example of trilateration in use at the moment.
In our problem we have a set of landmarks. We know the distance (with some uncertainty) to one, and we want to know which of the remaining landmarks we should select next to maximise the amount of information we gain about our location.
For our particular example, we ask people to estimate the distance of various landmarks from their house.
We look at how to find a good landmark quickly, by using Bayes’ rule to rearrange the expression for the entropy in the probability distribution.