# Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation) +
## 1 Introduction  
The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling, namely, in traffic management and information systems, especially in urban areas and in real-time applications, stimulate the research interest in dynamic traffic models. The main components of the core engine of these systems use a dynamic origin-to-destination (OD) matrix that describes the time dependencies of travel patterns in urban scenarios as the main input. This is a relevant reason for drawing the continuous attention of researchers to the dynamic origin-destination matrix estimation (DODME) problem, as a quick look at recent publications shows [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. Additionally, the complexity of the problem, its underdetermination, and the many alternatives that it offers make it an appealing research topic. Furthermore, the availability of new traffic measurements due to the pervasive penetration of ICT measurements offers new paths to explore [12, 13, 14, 15, 16, 17, 18, 19]. The objective of this study was to provide an insight into what can be achieved when, in addition to link flow counts, travel times that come from treated GPS traces are directly or indirectly considered in the formulation of a DODME. A rough classification of the approaches that are taken in these studies could be as follows:  
* Analytical approaches that are supported by hypotheses on the relationships between the observed link flows on subsets of links of a road network that is equipped with sensors, and the assignment matrices that are used in the estimation of the corresponding link flows. Assignment matrices that are provided by a traffic assignment method, usually a dynamic traffic assignment (DTA), in those approaches aim at estimating discretized time-dependent origin-to-destination (OD) matrices. * Similar hypotheses exist that instead resort either to a derivative-free optimization or methods that numerically approximate the calculation of the derivatives because the assignment matrix is usually generated by a DTA whose network loading is based on traffic simulation, i.e., a mesoscopic approach, and therefore the result is not analytical and, consequently, the resulting relationships cannot be differentiated. Although a variety of derivative-free methods were used in the past, in recent years, despite some inconveniences, most researchers tend to use the stochastic perturbation stochastic approximation (SPSA) [20] or variants of it within a computational framework of simulation-based optimization [21]. * Data-driven problem reformulations that are based on approaches that calculate the key components of the modeling approach from the empirical measurements from ICT applications. However, leaving aside some attempts to include other data sources in the formulation of the OD estimation, i.e., Bluetooth travel times between pairs of suitably located antennas [14; 15; 18; 22], most of the references rely on the observed link flow counts and a historical origin-to-destination (OD) matrix as the information to solve the problem. There are alternative approaches in the literature that are based on license plate recognition data collection applications [23]. These approaches were not considered in this study since it was focused on GPS tracking. Newly published papers considered sensitivity analysis of misfunctioning sensors on the static OD flow estimation [24]. A Bayesian method to synthesize multiple sources of data to estimate a dynamic OD matrix was proposed by [25], including the use of travel times on partial paths as we do, and [26] proposed a three-dimensional (3D) convolution-based deep neural network using automatic identification from LPR and partial paths.