Example of Flow Forecasting with Kalman Filter

Abstract

Problems of filter design arise in applications of the Kalman Filter to ARMAX models used in flow forecasting. In this paper, two issues often raised by forecasters are addressed. First, the formulation of ARMAX flow models into state‐space framework is discussed. The recommended formulation is to write the ARMAX model as the observation equation in the Kalman Filter. The model coefficients are then the state variables and are updated continually by the algorithm. Second, a procedure that allows specification of time‐invariant noise covariances is presented. It involves transforming the raw flow data prior to application of the Kalman algorithm. The concepts are illustrated in an example of flow forecasting on the Fraser River in British Columbia, Canada. The performance of two forecasting schemes based on the same flow model are compared; one uses untransformed flow data, the other uses transformed flow as observations.