## 1 Introduction
In these falling position control approaches, the ladle is moved in vertical and horizontal directions. However, the liquid can still spill from the pouring basin of the mold due to the splashing inside the ladle, which is caused by the movement of the ladle [25]. Therefore, the optimal positioning of the ladle which minimizes the amount of spilled liquid from the pouring basin of the mold was developed in [25; 26]. In these studies, a control system was constructed using the flow-rate feedforward control. Pouring precision can be degraded by disturbances that emerge from variable pouring conditions. To suppress the influence of such disturbances, flow-rate feedback control has to be established. However, it can be difficult to directly measure the flow rate of poured molten metal because sensors e.g., the flow meter, can be damaged by the high temperature of the molten metal. Therefore, to measure the pouring flow rate, the real-time flow-rate estimation approach using the Kalman filter (KF), specifically an extended Kalman filter (EKF), was developed in [27; 28]. However, this approach can only be applied to smooth shaped ladles, e.g., a fan-shaped ladle, due to the requirements of the Jacobian matrix used in the EKF. Nonetheless, ladles with complicated shapes for which it is difficult to derive a Jacobian matrix, have been used in practical settings. Thus, flow-rate estimation with an unscented Kalman filter (UKF), which does not require a Jacobian matrix, was proposed in [29]. Moreover, the flow-rate estimation method was integrated with the flow-rate feedback control system in [30]. However, it is difficult to implement and perform a real-time computation using an industrial controller, which has low computational power. To apply a real-time flow-rate estimation to an automatic pouring machine with a complicatedly shaped ladle, and implement the flow-rate estimation method in an industrial controller, the simplified flow-rate estimation method in which the steady-state KFs (SSKFs) and the EKF are decentralized to the motor systems and the pouring process, respectively, was proposed in our previous study [31]. The decentralization of Kalman filters (DKFs) were integrated with the flow-rate feedback control system in [32]. As a remaining issue, the appropriateness of the flow rate estimation method via DKFs as a real-time pouring flow-rate measurement in the automatic pouring machine must be verified. In [31], the effectiveness of the flow rate estimation by the DKFs was verified in the experiment with the ideal condition as the pouring process model in the DKFs is identified with the experimental pouring. However, some uncertainties in the model parameters identification with practical pouring can arise. It is especially difficult to identify the tilting angle of the ladle at the start of the liquid outflow, which can be influenced by the surface tension and density of the liquid in the ladle [32]. Moreover, in order to verify the effectiveness of the flow rate estimation, the true flow rate of the liquid outflow from the ladle in the experiment should be measured. It is, however, difficult to obtain the true flow rate of the liquid outflow. Therefore, in the current study, we verified the appropriateness of the flow-rate estimation method using DKFs by comparing it with two other existing real-time flow-rate estimations. We confirmed the noise levels and the estimation errors of the candidate real-time flow-rate estimations in the experiments with/without the error between the ideal and the actual tilting angle at the start of the liquid outflow. As evaluation of the estimation error, the estimated flow rates were compared with the simulated flow rate which represents faithfully the experimental pouring with the model of pouring process. In one of the compared methods, the flow rate was estimated by differentiating the weight of the outflow liquid measured by the load cell with respect to time [33]. In this approach, a low-pass filter was applied for reducing the noise of the measured data.