Estimation of an origin/destination matrix: application to a ferry transport data

The estimation of the number of passengers with an identical journey is a common problem for public transport authorities. This problem is also known as the origin-destination estimation (OD) problem and it has been widely studied for the past 30 years. However, theory is missing when observations are not limited to the passenger counts but also include station surveys. Our aim is to provide a solid framework for the estimation of an OD matrix when only a portion of the journey counts are observable. Our method consists of a statistical estimation technique for OD matrix when we have the sum-of-row counts and survey-based observations. Our technique differs from the previous studies in that it does not need a prior OD matrix which can be hard to obtain. Instead, we model the passengers behavior through the survey data, and use the diagonalization of the partial OD matrix to reduce the space parameter and derive a consistent global OD matrix estimator. We demonstrate the robustness of our estimator and apply it to several examples showcasing the proposed models and approach. We highlight how other sources of data can be incorporated in the model such as explanatory variables, e.g. rainfall, indicator variables for major events, etc, and inference made in a principled, nonheuristic way.