Maximum likelihood estimation of an origin-destination matrix from a partial registration plate survey

Previous techniques for analysing partial registration plate data are firstly reviewed. These generally fall into one of two broad categories: statistically based methods for single origin, single destination problems; and simple-minded, deterministic approaches using vehicle passage time data (i.e., the times at which vehicles pass the observation points), for surveys with multiple origins and destinations. The present paper addresses the problem of finding a maximum likelihood estimator (MLE) of an origin-destination matrix and of journey time statistics--when passage time data are available, in the multiple origin/destination case. These estimators possess the well-known large sample properties of asymptotic unbiasedness, normality, and efficiency. The proposed approach also has the advantage over the deterministic methods (used in most existing registration plate matching packages) of simultaneously analysing all possible matches between all origins and destinations, rather than considering them in some arbitrary, priority order. Since the MLEs cannot be obtained analytically, alternative numerical techniques for determining them are evaluated, with respect to their convergence properties and computational efficiency. The most appropriate of these (based on a general-purpose statistical algorithm for "missing data" problems) is described in greater detail, including issues relevant to its computer implementation. Selected results from a more comprehensive simulation study are used to illustrate the performance of the maximum likelihood approach. In the (limited) results reported, the MLEs are seen to have considerably smaller mean square errors than the deterministic methods mentioned above, but are only marginally superior to the estimators produced by an efficient heuristic technique proposed previously by the author. Further empirical work would, however, be required to establish that the patterns observed in these simulations are examples of more general phenomena. Finally, possible extensions to the method and future research directions are discussed.