# Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation) +
## 5 Indirectly Accounting for the ICT Measurements  
Recent literature addresses how to include ICT measures into the DODME problem to reduce the underdetermination of the underlying problem. A two-step ordinary least squares (OLS) OD estimation model is proposed in [23], incorporating the output from a Bayesian path reconstruction model that was developed to cope with an insufficient coverage rate of ICT data from license plate recognition and estimates both the dynamic OD demand and assignment matrix without the need for any historical matrix. Finally, refs. [13; 16] used the geopositioning data of probe vehicles from an ad hoc experiment that was designed by the authors to obtain an a priori dynamic origin-to-destination (OD) matrix and the reconstructed paths are included in the OD estimation process, and [17] used a data-analytics-based proprietary procedure to empirically estimate a dynamic assignment matrix. The linearization of the relationship between traffic counts and OD flows is the approach of most analytical models that are used to solve DODME [9]. This can be achieved by using the proportion of the OD demand flows that pass through the count location at a certain link. In these terms, the dynamic assignment matrix \(\mathbf{A}(\mathbf{X})=\left[a_{ijr}^{lt}\right]\) is the result of the mapping and \(a_{ijr}^{lt}\) represents the proportion of the OD flow that departs from origin \(i\) in period \(r\) and goes to destination \(j\) that crosses link \(l\in\hat{L}\subseteq L\) in period \(t\geq r\). These analytical approaches to the DODME problem show that all of them rely on the availability of the assignment matrix \(\mathbf{A}=\left[a_{ijr}^{lt}\right]\) for the various time intervals, which are calculated at the lower level of the bi-level problem using the dynamic traffic assignment at each time interval. The availability of the GPS-generated data enabled us to assume that, after suitable data processing to find the empirical paths and the inference of path choice proportions, it was possible to estimate a dynamic assignment matrix that relied on the information regarding traffic conditions. Since it would play a similar role to that of the analytical assignment matrix that is obtained by a DTA, it would, if appropriately processed [19], estimate a reliable assignment matrix from the available commercial data. The possibility of estimating an assignment matrix allows for reformulating the DODME by relating the estimated traffic counts with the OD flows using the estimated assignment matrix:  
\[y_{lt}=\sum_{(i,j)\in N}\sum_{r=1}^{t}\overline{a}_{ijr}^{lt}x_{ijr} \tag{11}\]  
where \(y_{lt}\) is the estimated flow in link \(l\) in period \(t\); \(x_{ijr}\) is the flow departing origin \(i\) with destination \(j\) in time interval \(t\in T\); and \(\overline{a}_{ijr}^{lt}\) is the estimated assignment matrix, which is the fraction of trips from origin \(i\) with destination \(j\) that depart from \(i\) in time interval \(r\) and reach link \(l\) at time \(t\), as estimated from the GPS traces. There are different approaches that are used to estimate the dynamic assignment matrix \(\vec{\pi}_{ijr}^{lt}\) from the GPS traces. In [13], it is implicitly considered that this estimate is directly provided by a counting process, assuming that the analyst has complete control over the raw data collected, whereas in other cases when such control is not available and the access to the preprocessed data is provided by commercial companies, some drawbacks appear, which are derived from privacy conditions. Reference [17] assumes that access to very large data sets (i.e., at least 6 months) and an undisclosed proprietary data analytics application was available to generate the estimated assignment matrix.