Tensor Extended Kalman Filter and Its Application to Traffic Prediction

Traffic prediction is a very important mechanism in intelligent transportation systems for applications including routing planning and traffic control. In order to infer multifarious traffic information, one/two-relational traffic data in the vector/matrix form need to be expanded to multi-relational traffic data in an arbitrary tensor form. However, none of the existing approaches is capable of performing traffic prediction by characterizing and tracking the inherent nonlinear dynamics which are often encountered in realistic time-series analysis. Although the extended Kalman filter (EKF) has been proven to be quite promising in inferring nonlinear dynamics from time series, but the current EKF approach still suffers, unfortunately, from a serious drawback that state variables have to be represented in vector form. In fact, the characteristics of multi-relational states in practice can never been manifested accurately in practice and the performance of an EKF would be greatly restricted thereby. In this work, we introduce a new tensor extended Kalman filter (TEKF) approach to accommodate arbitrary input, output, and state variables all in arbitrary tensor forms. We also propose a new tensor-based expectation-maximization (EM) algorithm to estimate the nonlinear state-transition and observation-model mappings. The computational and memory complexities of the proposed TEKF approach are also studied in this paper. Finally, numerical experiments are conducted to evaluate the traffic prediction performance of the proposed new TEKF approach over the simulated and realworld traffic datasets in comparison with three other existing deep-learning prediction methods.