Algorithm for Real Time Correction of Stream Flow Concentration Based on Kalman Filter

Abstract

This paper develops an algorithm for real-time correction of stream flow concentration based on a Kalman filter to improve the performance of real-time forecasting of river discharge under circumstances in which the nonlinearity of stream flow concentration is significant. The Muskingum matrix equation expresses the system of stream flow concentration as a time-varying linear system and satisfies the state-space expression of the Kalman filter. Updating of the parameter matrices of the system impair the influence of the nonlinearity of stream flow concentration on the linear filtering. The advantage of the algorithm is that predictions of every subbasin can be corrected twice by getting “remote” and “local” correction values and can achieve rational updating. Furthermore, to prevent the occurrence of filter divergence and to reach better filtering accuracy, a new real-time statistical method is proposed to estimate the process noise covariance matrix and measurement noise covariance matrix. The algorithm proves reasonable and effective by its application in the example of the Three Gorges Basin.