# An Adaptive Fast Incremental Smoothing Approach to INS/GPS/VO Factor Graph Inference
## 4 Discussion  
In summary, this paper proposes a factor-graph-based INS/GPS/VO integrated navigation method. Compared with traditional filtering-based (such as KF) integrated navigation methods, the factor-graph-based integrated navigation method can achieve plug-and-play functionality when facing asynchronous and delayed sensor measurements, and can handle multi-state correlated measurements such as VO, while also having high navigation accuracy. Sections 3.1 and 3.2 also verified this point. Therefore, when dealing with multi-state correlated measurements and facing asynchronous and delayed sensor measurements, using factor-graph-based integrated navigation methods has better accuracy and flexibility, and can achieve plug-and-play functionality. Although its computational complexity is higher than that of filter-based combined navigation methods, this aspect can optimize the algorithm to reduce its computational complexity. Furthermore, we also propose an adaptive fast incremental smoothing (AFIS) algorithm. Compared with existing factor graph  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Optimization**} & \multirow{2}{*}{**Batch-FG**} & \multirow{2}{*}{**IS-FG**} & \multirow{2}{*}{**AFIS-FG**} & \multicolumn{2}{c}{**FixLag-FG**} \\ \multicolumn{2}{c}{**Algorithm**} & & & & **(5)** \\ \hline Radial Error & Scenario 1 & 0.907 & 1.308 & 0.940 & 1.942 \\ (m) & Scenario 2 & 1.235 & 1.570 & 1.554 & 2.588 \\ \hline \end{tabular}
\end{table}
Table 2: RMSE statistical result of different algorithms in two different scenarios.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{2}{c}{**Optimization**} & \multirow{2}{*}{**Batch-FG**} & \multirow{2}{*}{**IS-FG**} & \multirow{2}{*}{**AFIS-FG**} & \multicolumn{2}{c}{**FixLag-FG**} \\ \multicolumn{2}{c}{**Algorithm**} & & & **(5)** \\ \hline \multirow{2}{*}{Time (s)} & Scenario 1 & 54.6 & 7.4 & 4.7 & 0.2665 \\  & Scenario 2 & 257.1 & 32.5 & 20.9 & 0.3971 \\ \hline \end{tabular}
\end{table}
Table 3: Total runtime statistical result of different algorithms in two different scenarios.  
optimization algorithms based on incremental smoothing (IS), the AFIS algorithm proposed in this paper can greatly improve the speed of factor graph optimization algorithms while maintaining comparable accuracy, which can better meet the real-time requirements of factor-graph-based integrated navigation methods. Simultaneously, the algorithm can be divided into two components: global optimization and local optimization. Local optimization pertains to optimizing newly added measurement-related partial state variables at each moment, whereas global optimization involves optimizing state variables continuously, which can be performed at regular intervals according to system requirements. Although the accuracy of global optimization at any given moment may not match that of traditional incremental smoothing methods, it is evident that this optimization mode offers greater flexibility. Section 3.3 also verified that the AFIS algorithm notably enhances computational speed while maintaining comparable accuracy to the IS algorithm.