Recursive estimation based on the equality-constrained optimization for intersection origin-destination matrices

A fast constrained recursive identification (CRI) algorithm is proposed to estimate intersection origin-destination (O-D) matrices dynamically. The basic idea of the CRI algorithm is to estimate intersection O-D matrices based on equality-constrained optimization and then to adjust them by Bell's correction (Bell, 1991a. The estimation of origin-destination matrices by constrained generalized least squares. Transporation Research 25B, 13-22; Bell, 1991b. The real-time estimation of origin-destination flows in the presence of platoon dispersion. Transportation Research 25B, 115-125.) for inequality constraints. Numerical results show that the accuracy of estimates by the CRI algorithm is fairly good--the solutions obtained by the CRI are optimal in majority of the cases, while the computational efforts are very limited--increment mainly lies on the evaluation of an inverse for an mxm matrix (m=4 for a typical intersection) compared with the ordinary recursive least squares method. These results mean that a properly designed recursive algorithm can indeed avoid iterative procedure in each time step to obtain highly accurate on-line estimates for intersection O-D matrices. Therefore, the CRI algorithm with its reasonable balance between accuracy and computational simplicity is very suitable for practical use.