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A methodology is developed to estimate a route-level probability OD flow matrix for a time-of-day period that takes advantage of the increasing availability of large quantities of boarding and alighting data collected via Automatic Passenger Counter (APC) technologies. Unlike previous transit OD estimation approaches, the problem formulation considers the distribution, rather than only the means, of the APC data. A Heuristic Expectation Maximization (HEM) algorithm is developed to provide an approximate solution to the estimation formulation while achieving computational feasibility for applications to realistically long bus routes.The performance of the HEM algorithm is evaluated numerically and empirically by comparing OD flow estimates to estimates produced by three other methods: the Expectation Maximization (EM) method, the Iterative Proportion Fitting (IPF) method and a Conditional Maximization (CM) method. The EM method provides a solution to the formulation, but it is computationally prohibitive for practical use. The IPF method represents traditional methods, where only the means of the APC data are considered. The CM method is developed in this study as another computationally feasible method that considers the distribution of APC data, but it is seen to extract information on the probability OD flows less efficiently than the HEM method.The numerical study demonstrates that the HEM algorithm provides a good approximation to the solution produced by the EM algorithm. In addition, the numerical and empirical studies demonstrate that the HEM algorithm produces more accurate estimates than the IPF and CM methods when large quantities of APC data are available. Moreover, the numerical and empirical studies quantify the effects of three pertinent factors on the accuracy of OD flow estimates: the number of bus trips with APC data, the sample size of an OD flow survey used with APC data to estimate OD flows, and the magnitude of measurement errors in APC counts. The HEM algorithm does not work particularly well when only a few bus trips have APC data. However, the improvement in the quality of the estimates produced with increased quantities of APC data when using the HEM method is greater than when using the CM method and is much greater than when using the IPF method. The numerical studies further demonstrate that the HEM method outperforms the IPF and CM methods if the number of bus trips with APC counts is larger than a certain threshold. This threshold increases with the sample size of an OD flow onboard survey if such a survey is used in the estimation. The threshold also increases with increasing magnitude of measurement errors in APC counts. Nevertheless, the threshold is relatively small compared to what can be feasibly collected from APC-equipped buses.Additional properties of probability OD flow estimation using the HEM algorithm are also investigated, such as convergence of the algorithm, sensitivity of OD estimates to the underlying OD structure and the distributional assumptions, and performance of OD estimation under congested conditions on buses due to bus bunching and high demand.