## 2 Navigation and Localization
### Acoustic Navigation
#### Acoustic Ranging  
In acoustic ranging positioning systems, AUVs are equipped with an acoustic transmitter that establishes communication with a set of hydrophones. Knowing the propagation velocity of sound in underwater, the distance between the AUV and hydrophones can be calculated through the propagation time of the acoustic signal. Then, a location for the AUV with respect to the set of hydrophones can be obtained by geometric methods. One of the differences between acoustic systems is the arrangement of the hydrophones. In LBL systems, hydrophones are fixed within a structure or any other known underwater point of reference--known as landmark--[15]. The length of the baseline can be up to hundreds of meters. In SBL and USBL systems, the hydrophones are placed on buoys or another vehicle at the surface, even on a second AUV. For SBL systems, baseline length is measured in meters and works by measuring a relative position between the reference sound source and the receiving array; meanwhile, baseline for USBL systems is in decimeters and the relative location from the hydrophone to the moving target is calculated by measuring the phase differences between acoustic elements [18]. In either arrangement, hydrophones are generally located by Global Navigation Satellite Systems. In Figure 6, all three configurations for acoustic localization systems are shown. Figure 6: Acoustic localization systems: (**a**) Long Baseline, (**b**) Short Baseline, (**c**) Ultra-Short Base Line. A schematic diagram of an SBL system is represented in Figure 7. Three hydrophones, represented by \(H1\), \(H2\), and \(H3\), are located at the points \(O\), \(N\), and \(M\), at the origin of the reference frame and along the \(x\) and \(y\) axes, respectively. The distance from the detected vehicle to the \(i\) hydrophone is called oblique distance, which is denoted by \(D_{i}\), with \(i\) = 1, 2, 3. The vehicle receives a signal from a hydrophone (\(H1\)) and sends a reply that is received by all the hydrophones (\(H1\), \(H2\), and \(H3\)); then, signal run time is measured. The propagation time of the acoustic signal from the transmitter in the vehicle to the hydrophone base (\(T_{i}\)) is used to obtain the oblique distance with the equation [18]:  
\[D_{i}=V\cdot T_{i}, \tag{2}\]  
where \(V\) is the nominal speed for underwater acoustic signals and is used as \(V\) = 1435 m/s. The location of the vehicle's transmitter--point \(P\)--with coordinates \(X_{p}\), \(Y_{p}\), and \(Z_{p}\), can be calculated using a traditional SBL model as follows:  
\[P=\left(X_{p},Y_{p},Z_{p}\right) \tag{3}\]  
\[X_{p}=\frac{D_{1}^{2}-\ D_{2}^{2}+N^{2}}{4N} \tag{4}\]  
\[Y_{p}=\frac{D_{1}^{2}-\ D_{3}^{2}+M^{2}}{4M} \tag{5}\]  
\[Z_{p}=\left\{\left[D_{1}^{2}-X_{p}^{2}+Y_{p}^{2}\right]^{\frac{1}{2}}+\left[D_ {2}^{2}-\left(X_{p}-N\right)^{2}+Y_{p}^{2}\right]^{\frac{1}{2}}-\left[D_{3}^{ 2}-X_{p}^{2}+\ \left(Y_{p}-M\right)^{2}\right]^{\frac{1}{2}}\right\}/\ 3 \tag{6}\]  
There exists an error between the measured position and the actual position of the transmitter. Among other factors, it is caused by not considering the variations of sound velocity produced by changes in the underwater environment conditions such as depth, temperature, density, and salinity. The accuracy of an acoustic positioning system will depend on different factors such as the distance and depth operational range, the number and availability of hydrophones, and the operational frequency. A few commercial baseline acoustic systems and accuracy specifications are shown in Table 2.  
Figure 7: Schematic diagram for Short Baseline (SBL) system. Although acoustic systems have been used in the past, they are still used as the main localization and navigation system for AUVs or teams of AUVs and Unmanned Surface Vehicles (USVs). [PERSON] et al. [47] worked on a filter for combining LBL and USBL systems to estimate position, linear velocity, and attitude of underwater vehicles.