## 3 Multi-Sensor-Based Remote Autonomous Navigation and Close-Range
### Remote Autonomous Navigation Based on LiDAR, Vision, and IMU Fusion
The loop closure detection technology of the RTAB-Map is detailed as follows:  
* Localization point acquisition: The RTAB-Map uses SURF to extract visual word features. The feature set of the image at time \(t\) is referred to as the image signature \(z_{t}\). The current localization point \(L_{t}\) is created using the signature \(z_{t}\) and time \(t\). * Localization point weight update: The similarity \(s\) between the current localization point \(L_{t}\) and the last localization point in short-term memory is computed by comparing the number of matching word pairs between signatures and the total number of words in the signatures. This similarity \(s\) is used to determine the new weight of the localization point \(L_{t}\). The formula for \(S(z_{t},z_{c})\) is: \[S(z_{t},z_{c})= \begin{cases}\frac{N_{p}}{N_{t}}&\text{if }N_{z_{t}}\geq N_{z}\\ \frac{N_{p}}{N_{z_{t}}}&\text{if }N_{z_{t}}<N_{z_{c}}\end{cases} \] (1) where \(N_{p}\) represents the number of matches and \(N_{z_{t}}\) and \(N_{z_{c}}\) denote the total number of words in signatures \(z_{t}\) and \(z_{c}\), respectively. * Bayesian filter update: The Bayesian filter calculates the likelihood of forming a loop between the current localization point \(L_{t}\) and points within the working memory (WM). \(S_{t}\) represents all loop closure hypotheses at time \(t\), where \(S_{t}=i\) indicates that \(L_{t}\) forms a loop closure with an already visited localization point. The posterior probability distribution \(p(S_{t}\mid L^{t})\) is computed as follows: \[p(S_{t}\mid L^{t})=\rho p(L_{t}\mid S_{t})\sum_{t=-1}^{t_{n}}p(S_{t}\mid S_{t- 1}=i)p(S_{t-1}=i\mid L^{(t-1)})\] (2) where \(\rho\) is a normalization factor, \(L^{t}\) is the sequence of localization points, and \(t_{n}\) represents the time index of the most recent localization point stored in WM. The observation function \(p\) and the likelihood function \(\gamma\) are used to differentiate the degree of similarity between \(L_{t}\) and \(S_{t}\). By comparing \(L_{t}\) with \(S_{t}=j\), the similarity \(s_{j}\) is obtained and compared with the standard deviation \(\sigma\). The calculation is as follows:  
\[p(L_{t}\mid S_{t}=j)=\gamma(S_{t}=j\mid L_{t})= \begin{cases}\frac{s_{j}-\sigma} {\mu}&\text{if }s_{j}\geq u+\sigma\\ 1&\text{if }s_{j}<u+\sigma\end{cases}  \tag{3}\]  
The probability of \(L_{t}\) being a new localization point \(S_{t}=-1\) is calculated as:  
\[p(L_{t}\mid S_{t}=-1)=\gamma(S_{t}=-1\mid L_{t})=\frac{\mu}{\sigma+1} \tag{4}\]where, if \(\gamma(S_{t}=-1\mid L_{t})\) is larger, \(L_{t}\) is more likely to be a new localization point. Loop closure hypothesis selection: When \(p(S_{t}=-1\mid L^{t})\) is below a set threshold, the loop closure hypothesis \(S_{t}=i\) with the highest probability in the transition model \(p(S_{t}\mid L^{t})\) is accepted. A loop closure link is established between the new and old localization points, and the weight of the localization points is updated. Localization point retrieval: To make full use of high-weight localization points, after a loop closure is detected, if the probability of forming a loop with adjacent localization points is highest, the localization point is moved from LTM back to WM. The words in the dictionary are updated for future loop closure detection. Localization point transfer: To meet the real-time requirements of the RTAB-Map, if the localization matching time exceeds a fixed maximum value \(T_{L}\), it indicates that these localization points are unlikely to form a loop closure. They are transferred from WM to LTM and will no longer participate in loop closure detection, reducing unnecessary time loss in localization.