AN APPLICATION OF A NEURAL-KALMAN FILTER FOR DYNAMIC ESTIMATION OF O-D TRAVEL TIME AND FLOW WITH THE DIFFERENT NUMBER OF TRAFFIC DETECTORS

The authors have been engaged in developing a new paradigm for estimating dynamic O-D travel time and flow on a freeway corridor. The fundamental framework is to 1) develop a Neural-Kalman filter (NKF) method, which is a new algorithm by integrating artificial neural network (ANN) model into a Kalman filter, 2) introduce a macroscopic model for predicting traffic states in advance and 3) estimate dynamic O-D travel time and flow simultaneously within one process. The NKF method was originally proposed by Nakatsuji et. al.1)2), and was modified in steps by Suzuki and Nakatsuji 3)4)5) to estimate O-D travel time and flow on a freeway: A basic concept of the new model was briefly described in Suzuki and Nakatsuji 3)5). They presented how to formulate the Kalman filter to consider the influence of traffic situations for arbitrary number of time steps as long as necessary 3)5). This development enabled the NKF to be applied for the dynamic estimations of O-D travel time and flow on long freeways. The integration of ANN models into a Kalman filter was found effective in describing the non-linear features of dynamic O-D travel time and flow 3)5). An advance prediction of traffic states by the macroscopic traffic flow model contributed in improving the estimation precision 4)5). The parameters of a macroscopic model were independently optimized for each road link of the expressway to improve an estimation precision3), and a sigmoid function of ANN model was also modified to improve the training performance 4). Some numerical analyses were carried out using simulated traffic data on the expressways in Bangkok Metropolis, Thailand 3)4)5). In this way, the first and second objectives of the framework mentioned above have been almost realized and examined through some numerical analyses using traffic data simulated by a microscopic traffic simulation package, FRESIM 6). However, the last objective still remains unresolved. The problem that lies in the third topic is the interaction between O-D travel time and flow. The interaction has not been considered in previous studies of dynamic O-D flow estimations, for instance, at an isolated intersection 7) 8) on a small freeway 9) and O-D travel time estimations 2) 10) 11). On the other hand, some researchers have used travel time information for dynamic O-D flow estimations on a long freeway. Ashok and Ben-Akiva 12) applied a Kalman filter to estimate O-D flows from link traffic counts on a long freeway corridor. Travel time of specific O-D pairs was used for the estimations, assuming that the travel time was constant during the whole simulation period. This assumption is not realistic for an actual freeway because travel time varies with traffic situations. Chang and Wu 13) investigated the influence of O-D travel time in O-D flows on a freeway. In order to avoid complexity in the formulation of Kalman filter and to reduce computational burden, they took into account the O-D travel time only for two time steps immediately before. Another Kalman filter approach was proposed by Madant et al.14) to estimate O-D flows considering dynamic changes in travel time. However, the approach has no feedback process from O-D flows to travel time because a traffic simulator independently calculated the travel time without considering dynamic changes of O-D flows. In this way, the O-D travel time has been solely treated as implicit variable and not been directly used in O-D flow estimations. Moreover, there has been no feedback process considered from O-D flow to travel time even though travel time varies over time according to O-D flows. Consequently, no model is successful yet in estimating both O-D travel time and flow simultaneously encompassing mutual interactions. In addition, this new method is featured as an indirect estimation method based on a feedback technique. It estimates O-D travel time and flow in real time while measuring traffic variables, such as link traffic volumes, spot speeds and off-ramp volumes. It uses as much information as possible about traffic state available through traffic detectors to estimate O-D travel time and flow accurately. Hence, it is anticipated that the estimation precision will improve by installing more traffic detectors. Different from other western countries, traffic detectors are densely installed and well maintained in Japan. The traffic data measured are reliable enough for such a. feedback method to have a potential of providing satisfactory estimation precision. Still there are many issues to be addressed before practical application, nevertheless it is interesting to evaluate issues such as the relationship between installing more traffic detectors to the improvement in estimation precision. That is, the questions whether installation of more traffic detectors can improve the precision in the estimation of O-D travel time and flow , how many detectors should be installed to satisfy the estimation precision required, and so on, are relevant.