Algorithm 1: Set-membership estimation framework for USV steering motion

Input Data: Initial motion state $S_0$, initial motion estimation ${\widehat{S}}_0$, initial ellipsoid        parameters $P_0$, total simulation time $o_{max}$, rudder angle $u_0$, the upper and        lower limits of quantification $\pm \varpi$. Output: Estimation value ${\widehat{S}}_i$$(i\in [1,o_{\max }])$ of motion state. Generate $S_0$, ${\widehat{S}}_0$, $P_0$, $o_{max}$, $u_0$, $\pm \varpi$;        for $o=1:o_{max}$    step 1: Generate process noise $W_o$;    step 2: Generate measurement noise $V_o$;    step 3: Calculate real motion state $S_o$ and its measurement $Z_o$;    step 4: Select the length of a binary bit string $p_o$;    step 5: Perform the binary coding for $Z_o$, which includes quantization,        encoding, transmission and decoding;    step 6: Calculate decoded measurement ${\overrightarrow{Z}}_o$;    step 7: Acquire the optimal estimator gain $K_o$ by solving optimization        problem Corollary 1 subjected to LMIs (25);    step 8: Calculate the estimation value ${\widehat{S}}_{o+1}$ based on ${\widehat{S}}_o$, $K_o$, and ${\overrightarrow{Z}}_o$.   end