Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator

Methods commonly used for estimating origin-destination (O-D) matrices can be divided into three categories: direct sample estimation, model estimation and estimation from traffic counts. In this paper a generalized least squares estimator of the O-D matrix is proposed combining direct or model estimators with traffic counts via an assignment model. The presence of measurement errors and time variability in the observed flows is explicitly considered. A special case is also presented in which the flows are assumed to be deterministically known. For the proposed estimators, means and dispersion matrices are expressed in function of the possible bias in the direct or model estimators and assignment model misspecification. The variance of the O-D matrix obtained with the generalized least squares (GLS) estimators is proved to be lower than that obtained with direct or model estimators but, because of possible biases and misspecifications, it is suggested that their performances have to be compared by using risk or generalized mean square error criteria.