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 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 m × m 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.