The estimation of Origin-Destination matrices by constrained Generalised Least Squares

The Generalised Least Squares (GLS) approach to the estimation of Origin-Destination matrices permits the combination of survey and traffic count data in a way that allows for the relative accuracy of the two data sources. However, the procedure may result in estimates that infringe non-negativity or other constraints on the fitted values. A simple algorithm to solve the solutions are derived for the variances and covariances of the fitted values both with and without active constraints. It is demonstrated that the imposition of inequality constraints can improve the accuracy of those fitted values directly and indirectly affected them, by reducing their sensitivity to error in the inputs.