Two papers on consistent estimation of a route choice model and link speed using sparse GPS data

Global Positioning System and nomad devices are increasingly used to provide data from individuals in urban traffic networks. In these two papers we focus on consistent estimators of a route choice model and link speed. In many different applications, it is important to predict the continuation of an observed path, and also, given sparse data, predict where the individual (or vehicle) has been. Estimating the perceived cost functions is a difficult statistical estimation problem, for different reasons. First, the choice set is typically very large. Second, it may be important to take into account the correlation between the (generalized) costs of different routes, and thus allow for realistic substitution patterns. Third, due to technical or privacy considerations, the data may be temporally and spatially sparse, with only partially observed paths. Finally, the position of vehicles may have measurement errors. We address all these problems using an indirect inference (II) approach. We demonstrate the feasibility of the proposed estimator in a model with random link costs, allowing for a natural correlation structure across paths, where the full choice set is considered. In the second paper, we develop an estimator for the mean speed and travel time based on indirect inference when the data are spatially and temporally sparse. With sparse data, the full path of vehicles are not observed, which is typically addressed using map matching techniques. First, we show how speed can be estimated using an auxiliary model which includes map matching and a model of route choice. Next, we further develop the estimator and show how both speed and the route choice model can be jointly estimated by using iteration between an II estimator of speed and the II estimator of the route choice model (developed in Paper I). Monte Carlo evidence is provided which demonstrates that the estimator is able to accurately estimate both speed and parameters of the route choice model.QC 20130521