Inferring origin-destination trip matrices with a decoupled GLS path flow estimator

Recently, path flow estimators (PFE) have been used for the estimation of origin-destination (O-D) matrices. This paper develops a formulation that incorporates a decoupled path flow estimator in a generalized least squares (GLS) framework. The approach seeks to solve a GLS problem that minimizes the sum of errors in traffic counts and O-D matrices based on an equilibrium assignment mapping derived exogenously from a K-shortest path ranking procedure. Solving the GLS-PFE inevitably involves non-invertible linear systems and non-negative constraints. A solution algorithm is designed to iteratively identify active constraints and solve linear systems by computing the pseudoinverse. A simplified version of this algorithm is further developed to improve its computational efficiency. The solution properties and computational efficiency of the two methods are tested and compared for small to mid-size networks. It is concluded that the simplified algorithm is efficient in solving the decoupled GLS-PFE problem for realistic size networks.