Where transport research and statistics meet....
Many tracking and tracing applications need to detect or he positions of the object being traced, based on observations that lack the accuracy to make this problem a trivial one.
The objective is to combine the constraints that the physical road network imposes and assumptions about minimum and maximum travel speeds. The combination of these should lead to a "good" estimation of a time-space trajectory for the object being traced.
For this purpose heuristic procedures have been proposed an implemented. These procedures usually do what is required, but the nature (or in fact definition) of heuristics is that one can not prove that they do their job in an optimal way.
Research done at TU Delft has shown that there is an elegant mathematical way to solve this problem. Physical constraints can be represented by a network graph and it can be shown that a Maximum Likelihood Problem Map Matching solution can be found by computing a shortest path over this graph.
The following notes show how.
Extended abstract submitted for the 15th International Symposium on Transportation and Traffic Theory (2001)
A Maximum Likelihood Map-Matching Algorithm, Research Note, 2001