## KALMAN FILTERING APPROACH FOR ‘PREDICTIVE TRAFFIC MODELLING’

### Authors

Shaleen Srivastava, Jacobs UK Limited

### Description

KALMAN FILTERING APPROACH FOR ‘PREDICTIVE TRAFFIC MODELLING’

### Abstract

Accurate and reliable information about the current traffic state is a fundamental requirement for a ‘Predictive Transport Model'. Traffic information usually is derived from ground measurement techniques. Measurement accuracy is generally considered to be the "degree of accordance with reality". A "lack of accordance with reality" can occur in several distinct ways with quite different consequences in a predictive or tactical or an operational model. Most of the tools used for the traffic state measurement and estimation for real-time predictions in a predictive model are designed to work well with normally distributed estimation errors. However, many traffic state estimation errors occurring in the context of real-time traffic predictions are not normally distributed and can have severe consequences if not handled appropriately.

There is also a possibility of occurrence of 'systematic errors' in the data which is processed to create volumetric and speed trajectories for clusters analysis. For example, UTC loops may be subject to phantom detections and missed detections that can cause cumulative systematic errors in measurement of traffic state (both volumetric and speed data). False alarms can be produced by automatic incident detection systems using conservation of vehicles (or simulation) if there is a discrepancy in counts at successive detectors. Hence, these errors severely limit the effectiveness of a real time predictive model. This problem has led to a situation that traffic simulation based predictive models are perceived as being unreliable, i.e., requiring too much calibration effort in order to work properly. However, the real problem is not calibration as much as error handling and there are numerous evidences from recent studies that can prove this fact. Its very much like a conventional traffic model in which a ‘garbage in’ is a ‘garbage out’.

We can call an input data stream reliable only if the frequency of inaccuracies occurring in the data is low. Unfortunately, this desired low frequency of errors is not easily achieved. These inaccuracies and errors as a result are passed on to the real-time traffic prediction simulation and hence make the traffic predictions itself as unreliable. Hence, in order to prevent a degradation of the accuracy of the traffic predictions, an ‘artificial intelligence’ system should be implemented to filter the traffic data accurately in order to estimate the accurate traffic state in real time for traffic predictions. One of the solutions is to use traffic data fusion process by applying calibrated Kalman Filtering approach to increase the effective reliability of the system and thus improve the accuracy of the resulting traffic information. The Kalman Filtering approach to data fusion allows the system to estimate the traffic flow on the network based on the current and future traffic state estimation.

The idea of using Kalman Filter is to exploit redundancy in the information obtained from the traffic simulation. Use of an appropriate traffic simulation model of the traffic state can identify certain circumstances that are highly unlikely. In this approach, a prior information about the dynamics of traffic patterns and route selection behaviour are included in system. An extended Kalman filter is used to estimate the state of the traffic simulation model (i.e., the space-discrete traffic density and mean speed profiles) based on the traffic measurements. The model equation and the measurement equations contain stochastic noise processes, which in the absence of error are rather well described by normal distribution. The accuracy of the traffic simulation and the different traffic flow measurements are specified by the covariances of the stochastic noise processes. Therefore, every measurement consists of a mean value and a variance in the probability model of Kalman Filter specifies the accuracy of traffic predictions. The Kalman Filtering process thus increase the redundancy in the traffic flow estimation and therefore improve the accuracy of traffic flow predictions in a predictive traffic model.

#### Publisher

Association for European Transport