## Appendix A The Details about Estimation Methods
### UKF  
The details of UKF are shown in Table 2. The details of CKF are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Different Parts of Filter** & **Standard Kalman Filter** & **EKF** \\ \hline \multirow{6}{*}{System Model} & \(x(k+1)=A(k)x(k)+w(k)\) & \(x(k)=f(x(k-1)\), \(w(k-1))\) \\  & \(z(k)=C(k)x(k)+v(k)\) & \(z(k)=h(x(k)\), \(v(k))\) \\ \cline{1-1}  & \(E[w(k)w^{T}(j)]=Q(k)\delta(k-j)\) & \(E[w(k)w^{T}(j)]=Q(k)\delta(k-j)\) \\ \cline{1-1}  & \(E[v(k)v^{T}(j)]=R(k)\delta(k-j)\) & \(E[v(k)v^{T}(j)]=R(k)\delta(k-j)\) \\ \cline{1-1}  & \(E[w(k)v^{T}(j)]=0\) & \(E[w(k)v^{T}(j)]=0\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline \(\frac{\partial f}{\partial x}|_{\delta(k-1|k-1)}=F(k)\) \\ \cline{1-1}  & \(\frac{\partial f}{\partial w}|_{\delta(k-1|k-1)}=L(k)\) \\ \cline{1-1}  & \(\frac{\partial h}{\partial x}|_{\delta(k-1|k-1)}=H(k)\) \\ \cline{1-1}  & \(\frac{\partial h}{\partial x}|_{\delta(k-1|k-1)}=M(k)\) \\ \cline{1-1}  & \(\frac{\partial h}{\partial v}|_{\delta=t(k-1)}=M(k)\) \\ \hline \hline Prediction of the State & \(x(k(k-1)=A(k-1)(k-1|k-1)\) & \(x(k(k-1)=f(x(k-1|k-1),0)\) \\ \cline{1-1}  & \(\hat{x}(k|k)=\hat{x}(k(k-1)+K(k)(k-1))\) & \(\hat{x}(k)=\hat{x}(k(k-1)+K(k)(z(k)-\hat{h}(\hat{x}(k-1),0)\) \\ \cline{1-1}  & Filter gain & \(K(k)=P(k|k-1)C^{T}(k)(C(k)P(k|k-1)C^{T}(k)+R(k))^{-1}\) \\ \cline{1-1} Prediction of the Covariance & \(P(k|k-1)=A(k-1)P(k-1|k-1)A^{T}(k-1)+Q(k-1)\) & \(P(k|k-1)=F(k-1)P(k-1|k-1)F^{T}(k-1)+L(k-1)Q(k-1)L^{T}(k-1)\) \\ \cline{1-1}  & \(P(k|k)=(I-K(k)C(k))P(k|k-1)\) & \(P(k|k)=(I-K(k)H(k)P(k|k-1)\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The details of the Standard Kalman Filter and EKF.  
\begin{table}
**Different Parts of Filter** & **UKF** \\ \hline System Model & \(x(k)=f(x(k-1))+w(k-1)\) \\  & \(z(k)=h(x(k))+v(k)\) \\  & \(E[w(k)w^{T}(j)]=Q(k)\delta(k-j)\) \\  & \(E[v(k)v^{T}(j)]=R(k)\delta(k-j)\) \\  & \(E[w(k)v^{T}(j)]=0\) \\ \hline Prediction of the State & \(\hat{x}^{(0)}(k-1|k-1)=\hat{x}(k-1|k-1)\) \\  & \(\hat{x}^{(i)}(k-1|k-1)=\hat{x}(k-1|k-1)+\hat{x}^{(i)}\) \\  & where \\  & \(\hat{x}^{(i)}=\left(\sqrt{(n+k)P(k-1|k-1)}\right)_{i}^{T}\), \(i=1,\cdots,n\) \\  & \(\hat{x}^{(i)}=-\left(\sqrt{(n+k)P(k-1|k-1)}\right)_{i}^{T}\) \\  & \(i=n+1,\cdots,2n\) \\ Prediction of the State & and \\  & \(\hat{x}^{(i)}(k|k-1)=f(\hat{x}^{(i)}(k-1|k-1))\) \\  & \(\hat{x}(k|k-1)=\sum\limits_{i=0}^{2n}w^{(i)}\hat{x}^{(i)}(k|k-1)\) \\  & with \\  & \(w^{(0)}=\frac{k}{n+k}\) \\  & \(w^{(i)}=\frac{1}{2(n+k)}\), \(i=1,2\cdots 2n\) \\ \hline \hline \end{tabular} \
\begin{tabular}{c c} \hline \hline \(\hat{x}^{(0)}(k|k-1)=\hat{x}(k|k-1)\) \\  & \(\hat{x}^{(i)}(k|k-1)=\hat{x}(k|k-1)+\hat{x}^{(i)}\), \(i=1,\cdots,2n\) \\  & \(\hat{x}^{(i)}=\left(\sqrt{(n+k)P(k|k-1)}\right)_{i}^{T}\), \(i=1,\cdots,n\) \\ Updation of the State & \(\hat{x}^{(i)}=-\left(\sqrt{(n+k)P(k|k-1)}\right)_{i}^{T}\), \(i=n+1,\cdots,2n\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline \(\hat{x}^{(i)}(k|k-1)=h(\hat{x}^{(i)}(k|k-1))\) \\  & \(\hat{x}(k|k-1)=\sum\limits_{i=0}^{2n}w^{(i)}\hat{z}^{(i)}(k|k-1)\) \\  & \(\hat{x}(k|k)=\hat{x}(k|k-1)+K(k)\left(z(k)-\hat{z}(k|k-1)\right)\) \\ \hline \hline \(\hat{P}_{z}=\sum\limits_{i=0}^{2n}w^{(i)}\left(\hat{z}^{(i)}(k|k-1)-\hat{z}(k |k-1)\right)\) \\ Filter gain & \(\ast\left(z^{(i)}(k|k-1)-\hat{z}(k|k-1)\right)^{T}+R(k)\) \\  & \(P_{xz}=\sum\limits_{i=0}^{2n}w^{(i)}\left(\hat{x}^{(i)}(k|k-1)-\hat{x}(k|k-1) \right)\left(\hat{z}^{(i)}(k|k-1)-\hat{z}(k|k-1)\right)^{T}\) \\  & \(K(k)=P_{xz}P_{z}^{-1}\) \\ \hline Prediction of the Covariance & \(P(k|k-1)=\sum\limits_{i=0}^{2n}w^{(i)}\left(\hat{x}^{(i)}(k|k-1)-\hat{x}(k|k-1)\right)\) \\  & \(\ast\left(\hat{x}^{(i)}(k|k-1)-\hat{x}(k|k-1)\right)^{T}+Q(k-1)\) \\ \hline Updation of the Covariance & \(P(k+1|k+1)=P(k|k+1)-K(k)P_{z}K^{T}(k)\) \\ \hline \hline \end{tabular}
\end{table}
Table 10: The details of UKF.