Traffic state estimation is a challenging task due to the collection of sparse and noisy measurements from specific points of the traffic network. The emergence of Connected and Automated Vehicles (CAVs) provides new capabilities for traffic state estimation using extended floating car data such as position, speed and spacing information. In this work we propose a Bayesian Traffic State Estimation (BTSE) methodology for estimating the traffic density based on extended floating car data. BTSE utilizes the Bayesian paradigm to express any prior information to derive probability distributions of the traffic density of different road segments of the traffic network. Two variations of the BTSE methodology are developed to handle the offline and online estimation problem. The BTSE methodology is evaluated both using realistic SUMO microsimulations for M25 Highway, London, U.K., and a real-life vehicle-trajectory dataset from German highways, extracted from videos recorded by drones. The efficiency and accuracy of the BTSE methodology is compared to an existing methodology in the literature. We present results for the estimation performance of the methods showing that the Bayesian methodology consistently results in lower mean absolute percentage error than the compared literature method. The BTSE methodology yields high-quality estimation results even for a low penetration rate of CAVs (e.g. 5%).
One of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We focus on Shannon information gain, one of the most widely used utilities when the experimental goal is parameter inference. We compare the performance of various methods for approximating expected Shannon information gain in common nonlinear models from the statistics literature, with a particular emphasis on Laplace importance sampling (LIS) and approximate Laplace importance sampling (ALIS), a new method that aims to reduce the computational cost of LIS. Specifically, in order to centre the importance distributions LIS requires computation of the posterior mode for each of a large number of simulated possibilities for the response vector. ALIS substantially reduces the amount of numerical optimization that is required, in some cases eliminating all optimization, by centering the importance distributions on the data-generating parameter values wherever possible. Both methods are thoroughly compared with existing approximations including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation. It is found that LIS and ALIS both give an efficient trade-off between mean squared error and computational cost for utility estimation, and ALIS can be up to 70% cheaper than LIS. Usually ALIS gives an approximation that is cheaper but less accurate than LIS, while still being efficient, giving a useful addition to the suite of efficient methods. However, we observed one case where ALIS is both cheaper and more accurate. In addition, for the first time we show that LIS and ALIS yield superior designs to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization.
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