A Markov Chain Monte Carlo-Based Origin Destination Matrix Estimator that is Robust to Imperfect Intelligent Transportation Systems Data

Abstract

A method for estimating the Origin Destination (OD) split proportion matrix based on the observed traffic volume count data such as those from Intelligent Transportation System (ITS) is presented in this article. The nature of the ITS data, which frequently contains erroneous observations or missing values, requires that the procedure (1) is resistant to outlying errors, (2) can cope with missing values, and (3) can yield uncertainty estimates so that the reliability of the OD estimator can be assessed. The main goal of this article is to develop a robust estimation procedure that can handle both outliers and missing values and provide the interval estimates for the OD split proportion matrix. To accommodate outlying observations, a heavy-tailed error distribution (i.e., the t-distribution with low degrees of freedom) is assumed as opposed to assuming a Gaussian error distribution. Because the problem is intractable using traditional analytical techniques, a modern statistical computational technique, known as the Markov Chain Monte Carlo (MCMC) method, is employed. By using the MCMC method, the estimation of the split proportion matrix, interval estimation, and imputation of missing values can be done simultaneously. The main advantages of the new method are that (1) an extra step to identify outliers in data cleaning can be avoided, and (2) that partial observations (e.g., an observation containing missing values only at a few destinations) can be saved and utilized for OD estimation. In effect, the new OD estimation process effectively uses all ITS data in the OD estimation process. In addition, the method can provide statistically valid uncertainty estimates (interval estimates) for the estimated OD matrix even when there are outliers and/or missing values. The use of interval estimates in ITS applications has been limited in practice. However, using reasonable upper and lower bound estimates, rather than the mean estimate, will give more flexibility to ITS operators. The new MCMC method for OD estimation is evaluated using simulated data and observed ITS data from a test bed in San Antonio, Texas, that has been instrumented with inductance loops.