Point Process Estimations Derived from Statistical Description of Vehicular Headways
This thesis applies recent developments of the martingale approach to point processes to obtain a recursive nonlinear filter in the context of urban traffic. Beginning with a review of the statistical description of vehicular headways, a convex probability density of headways is proposed. Techniques are then discussed to determine the four parameters necessary to specify this density. Subsequently, a complete description of the interarrival times is given which incorporates the entire past statistics of an observed counting process and leads to the derivation of its local description. The results are then utilized to formulate and solve the disorder problem for the switch rate point process involved. The utility of these results to traffic estimation/detection problems is discussed and a series of evaluations are performed.