Abstract
This paper proposes the design method of the multiplicative Kalman filter and its application to the river flow prediction. The process representing the dynamics of the rainfall/runoff is assumed to be discrete-time and multiplicative with the lognormal noise. The adoption of the lognormal noise is motivated by the fact that the frequency distribution of the river flow around the moving average has the form of the lognormal distribution rather than the normal distribution.
This paper may be delineated as follows. The multiplicative model of the runoff is proposed and its interpretation is given. Secondly, the identification algorithm for the coefficients of the model is derived by the sequential least square method. Thirdly, the algorithm of the multiplicative Kalman filter with time-delay term is derived by the approach of the innovation process. Finally, the simulation studies are carried out by using real data of the Karasugawa River, Gunma and the result of the prediction is compared with that by the hydrological models.
