## 7 Experimental Verifications
In this study, \(q_{simn}=2.0\times 10^{-4}\) and \(q_{sim0}=q_{simN}=0.0\) were given. Table 3 presents the results of mTV. As seen from the comparison with TV and mTV, the evaluation values by mTVs are smaller than those by TVs because mTVs can suppress the influence of the set-points changes. Therefore, we can compare clearly the amounts of the noises by mTVs. In the evaluations by IAEs to the condition with +3 deg error between the ideal and the actual tilting angle at the start of the liquid outflow, IAE of DKFs with the covariance of process noise in Equation (46) was slightly smaller than that in Equation (37). Thus, the estimation accuracy of the flow rate by DKFs can be improved by increasing the covariance of process noise in the liquid height on the pouring mouth. However, the amount of noise in the estimated flow rate was increased by increasing the covariance of process noise in the liquid height on the pouring mouth as shown in the evaluation by mTVs. In the application of DKFs in the flow-rate control, the covariance of process noise in the liquid height on the pouring mouth should be increased while evaluating the noise in the estimated flow rate. Both the IAE and the TV of DKFs were the smallest in the estimation methods performed in this study because the noise in the estimated flow rate by DKFs could be suppressed. However, IAE of DKFs was increased with increasing the error between the ideal and the actual tilting angle at the start of the liquid outflow. Therefore, we consider the present flow-rate estimation by DKFs to be appropriate for estimating the flow rate in a pouring motion with small disturbances. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Estimation Method**} & **Tilting Angle Error at Start** & **Tilting Angle Error at Start** \\  & **to Liquid Outflow +0 deg** & **to Liquid Outflow +3 deg** \\ \hline DKFs with Covariance of Process Noise in Equation (37) & \(4.277\times 10^{-5}\) & \(2.005\times 10^{-4}\) \\ DKFs with Covariance of Process Noise in Equation (46) & \(6.236\times 10^{-5}\) & \(1.909\times 10^{-4}\) \\ Differentiating Load Cell Data & \(2.431\times 10^{-3}\) & \(2.518\times 10^{-3}\) \\ Visible Camera & \(1.420\times 10^{-3}\) & \(1.568\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Integral absolute errors (IAEs) between estimated flow rates and simulated flow rates. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Estimation Method**} & **Tilting Angle Error at Start** & **Tilting Angle Error at Start** \\  & **to Liquid Outflow +0 deg** & **to Liquid Outflow +3 deg** \\ \hline DKFs with Covariance of Process Noise in Equation (37) & \(4.855\times 10^{-4}\) & \(4.746\times 10^{-4}\) \\ DKFs with Covariance of Process Noise in Equation (46) & \(8.628\times 10^{-4}\) & \(8.357\times 10^{-4}\) \\ Differentiating Load Cell Data & \(1.443\times 10^{-1}\) & \(1.486\times 10^{-1}\) \\ Visible Camera & \(3.861\times 10^{-2}\) & \(4.006\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total variations (TVs) of estimated flow rates. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Estimation Method**} & **Tilting Angle Error at Start** & **Tilting Angle Error at Start** \\  & **to Liquid Outflow +0 deg** & **to Liquid Outflow +3 deg** \\ \hline DKFs with Covariance of Process Noise in Equation (37) & \(8.549\times 10^{-5}\) & \(7.460\times 10^{-5}\) \\ DKFs with Covariance of Process Noise in Equation (46) & \(4.628\times 10^{-4}\) & \(4.357\times 10^{-4}\) \\ Differentiating Load Cell Data & \(1.439\times 10^{-1}\) & \(1.482\times 10^{-1}\) \\ Visible Camera & \(3.821\times 10^{-2}\) & \(3.966\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Modified total variations (mTVs) of estimated flow rates.