# A Study of Multi-Step Sparse Vessel Trajectory Restoration Based on Feature Correlation
## 5 Experiment and Result Analysis
### Analysis of Model Features Selection Results  
To determine the input feature dimensions, this study extracts 397 vessel trajectory feature points and calculates the composite indicator of feature correlation. The results of its indicator calculation are shown in Table 3. According to Equation (9), the variables of longitude (LON) and latitude (LAT) are judged to be variables with an extremely high correlation with each other, indicating their importance in vessel trajectory restoration. The correlation of SOG and heading with the LAT and LON variables showed a high correlation, and heading showed a moderate correlation with LAT and LON, whereas the time variable showed a moderate correlation with LON and a low correlation with LAT. Based on the above findings, this study determined the variables with a composite indicator of higher than 0.4 as correlating with LAT and LON. Therefore, a total of five dimensions of LAT, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Abnormal** & **Abnormal** & **Abnormal** & **Summary** & **Percentage** \\
**Time** & **SOG** & **Position** & **Summary** & **Percentage** \\ \hline
3872 & 8 & 0 & 3880 & 2.769\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of abnormal and missing trajectory points. Figure 8: Preliminary restoration trajectory results. LON, SOG, COG, and heading were identified as the input features of the model, which can be expressed as \(X_{i}=\left\{\text{LAT}_{i},\text{LON}_{i},\text{COG}_{i},\text{SOG}_{i},\text{ Heading}_{i}\right\}\). In determining the model input feature step, this study adopted the traditional lag period method of the time series linear regression model. This method regards the latitude and longitude series as a spatio-temporal autocorrelation series, and the results of its latitude and longitude autocorrelation and partial autocorrelation calculation are shown in Figure 9. Through observation, it can be seen that the autocorrelation and partial autocorrelation coefficients of latitude and longitude show a trailing trend, and this trailing trend suggests that the traditional linear regression model may not be able to adequately capture the complex dependence structure in these series. Therefore, to further pinpoint the lagged values, this study uses the autoregressive moving average model (ARMA). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**LAT**} & \multicolumn{4}{c}{**LON**} \\ \cline{2-9}  & **PCC** & **SRCC** & **NMIE** & \(\rho\) & **PCC** & **SRCC** & **NMIE** & \(\rho\) \\ \hline Time & 0.056 & \(-\)0.032 & 0.992 & 0.360 & 0.470 & 0.146 & 1.000 & 0.539 \\ LAT & 1.000 & 1.000 & 1.000 & 1.000 & 0.808 & 0.882 & 0.992 & 0.894 \\ LON & 0.808 & 0.882 & 0.992 & 0.894 & 1.000 & 1.000 & 1.000 & 1.000 \\ COG & \(-\)0.702 & \(-\)0.694 & 0.868 & 0.755 & \(-\)0.787 & \(-\)0.689 & 0.877 & 0.784 \\ SOG & \(-\)0.529 & \(-\)0.625 & 0.614 & 0.589 & \(-\)0.526 & \(-\)0.493 & 0.622 & 0.547 \\ Heading & \(-\)0.741 & \(-\)0.776 & 0.629 & 0.715 & \(-\)0.788 & \(-\)0.717 & 0.635 & 0.713 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation results of latitude and longitude correlation indicators. Figure 9: Correlation coefficient values for latitude and longitude: (**a**) ACF of LAT; (**b**) PACF of LAT; (**c**) ACF of LON; (**d**) PACF of LON. Based on the correlation coefficient calculation for the latitude and longitude series, this study further calculates the ARMA model. To determine the optimal value of the input feature step, this study calculates based on the AIC and BIC information criteria, and its calculation results are shown in Figure 10. By comprehensively evaluating the judging values of the AIC and BIC information criteria this study found that the model reaches the optimum when the lag value is 10, indicating that each trajectory point has a strong correlation with the first 10 previous trajectory points.