Algorithm 1: Filtering process.
Step 1.	Model the augmented form of the state equation based on (8)–(16)
Step 2.	Realize the linearization process of the nonlinear system to obtain $A^{(l)}({\widehat{u}}^{(1)}(\tau |\tau ))$ and linear equation based on (35)–(38)
Step 3.	Calculate state prediction value $\widehat{U}(\tau +1|\tau )$ according to (18)
Step 4.	Calculate the error of the state prediction $\tilde{U}(\tau +1|\tau )$ according to (19)
Step 5.	Determine the covariance matrix of the state prediction error $P(\tau +1|\tau )$ with (20)
Step 6.	Compute the forecast and prediction error of system measurement $\widehat{z}(\tau +1|\tau )$ and $\tilde{z}(\tau +1|\tau )$ with (21) and (22)
Step 7.	Solve for Kalman gain matrix $K(\tau +1)$ based on (24)–(28)
Step 8.	Calculate the state estimate $\widehat{U}(\tau +1|\tau +1)$ at $\tau +1$ using (23)
Step 9.	Update the estimated error covariance matrix by (28)–(30)
Step 10.	Set $\tau =\tau +1$ and go to Step 2.