Factorized Kalman Filtering

The paper deals with the Kalman filtering in the factorized form. The target application area is the urban traffic control, which main controlled variable – queue length, expressing the optimality of a traffic network most adequately, can not be directly observed and has to be estimated. Additional problem is that some state variables are of a discrete-valued nature. Thus, estimation of mixed-type data (continuous and discrete valued) models is highly desirable. A potential solution to this problem calls for a factorized version of the state-space model, which describes respective state factors individually. The present work considers the problem of the factorized filtering with Gaussian models and offers the solution, based on applying the L′DL decomposition of the covariance matrix. The result of such a filtering is the posterior state estimate with the mean value and the factorized matrix of covariance.