Enhancement of chaotic hydrological time series prediction with real-time noise reduction using Extended Kalman Filter

The Extended Kalman Filter (EKF), a popular nonlinear state estimation method from controls literature, was introduced as a real-time noise reduction method and its effectiveness was demonstrated on both synthetic chaotic time series and real river flow time series. EKF produced prediction improvement as high as 15%-40% on the benchmark time series with noise levels varying from 1% to 30%. Two river flow series, with low average flows, showed prediction improvement whereas three other flow series, with relatively large average flows, did not. Artificial Neural Network (ANN) models were used as the state-space models in EKF, and adopting them to time delays different from 1 unit was also demonstrated. The study demonstrated an 'indirect' validation method to verify the effectiveness of noise reduction when several interrelated time series were available; this was supported in observed discharge time series of the Ciliwung River in Jakarta, Indonesia.