Convergence Analysis of Smooth Variable Structure Filter for River Flow and Stage Estimation using Lagrangian Sensors

State estimation of river system includes the flow and stage estimation and used in the estimation of the final sensor's velocity which is proportional to the river velocity. The estimation process includes the system model and measurements. The measurements can be carried out using Eulerian sensor or Lagrangian sensor. The Lagrangian sensor is considered in this research since it able to observe the overall system compared to the Eulerian sensor that perform measurement in fixed position. Besides that, the estimation can be carried out using DA method such as Extended Kalman Filter (EKF) and Particle Filter (PF). The Smooth Variable Structure Filter (SVSF) is introduced to give better response in terms of error reduction by having convergence rate and the smoothing boundary layer width. The convergence analysis of SVSF shows the effectiveness of the proposed method in terms of mathematical representation. The simulation results proved the SVSF have better response compared to the forward simulation, EKF and PF. This shown by 25.6% for RMSE, 25.92% for SD, 15.34% for MAE and the computational time is reduced by 95.51 % if compared with PF.