hal-00722262
https://enpc.hal.science/hal-00722262
doi:10.1007/s10479-010-0784-0
[ENPC] Ecole des Ponts ParisTech
[UNIV-MLV] Université de Marne la Vallée
[PARISTECH] ParisTech
[ENPC-LVMT] Laboratoire Ville, Mobilité, Transport
[IFSTTAR] Ifsttar
[UNIV-EIFFEL] Université Gustave Eiffel
[IFSTTAR-UNIVEIFFEL] Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux
[UPEM-UNIVEIFFEL] Université Paris-Est Marne-la-Vallée
Optimal linear estimator of origin-destination flows with redundant data
Meunier, Frédéric
[INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO]
ART
Laplacian of graph
Linear estimator
Minimal variance
Multiflow
OD matrix
Suppose given a network endowed with a multiflow. We want to estimate some quantities connected with this multiflow, for instance the value of an s-t flow for one of the sources-sinks pairs s-t, but only measures on some arcs are available, at least on one s-t cocycle (set of arcs having exactly one endpoint in a subset X of vertices with saX and ta parts per thousand X). These measures, supposed to be unbiased, are random variables whose variances are known. How can we combine them optimally in order to get the best estimator of the value of the s-t flow? This question arises in practical situations when the OD matrix of a transportation network must be estimated. We will give a complete answer for the case when we deal with linear combinations, not only for the value of an s-t flow but also for any quantity depending linearly from the multiflow. Interestingly, we will see that the Laplacian matrix of the network plays a central role.
2010
en
Annals of Operations Research
Springer Verlag