## 2 Navigation and Localization
### Sensor Fusion  
As established in Section 2.1, the main inconvenient of an INS is that the position and orientation accuracy drifts over time, so, to keep it under the limits expected for safe AUV navigation, the system must correct its error by comparing its position estimation with a fixed location measured from additional sensors--such as a GPS--periodically. To overcome this, the INS can be fused with other sensors. There are two main schemes for sensor fusion: loosely coupled (LC) and tightly coupled (TC). The basic difference is the data shared by the sensors. In an LC scheme, a solution for the position or orientation of the AUV is obtained for each sensor individually and then blended using a filter--such as a Kalman Filter (KF)--to obtain a more accurate and reliable solution. In a TC scheme, raw measurements of the sensors are processed directly on the filter to overcome problems as poor signal quality or limited coverage thanks to the filter's capabilities to predict the pose of the vehicle. In this case, a more robust filter is needed so variants of the KF are commonly used [86], such as an EKF or Unscented Kalman Filter (UKF). Filter selection is essential to get a better solution for the vehicle's pose and, besides the sensor fusion approach adopted, accuracy, numerical efficiency, and computational complexity must be considered. LC and TC schemes are represented in Figure 13 with velocity estimation from an INS and a Doppler Velocity Logger (DVL) as example. Most of the sensor fusion systems for AUV navigation are those of an INS aided by a DVL; typically, the fusion is under an LC scheme [87; 88; 89] with a linear filter. However, in cases where the DVL measurements are limited, an LC algorithm leaves the INS to work alone. This produces an accumulative error which gets bigger with time. Considering this, [PERSON] et al. [90] explored a TC scheme as an alternative. This approach includes depth updates given by a depth sensor among to raw measurements from the DVL to help the INS and avoid the drift caused by limited measurements on the LC approach. Different trajectories were simulated for an AUV including a straight line at a for 1,800 s with a constant velocity. For simulations, the update frequencies of the INS, DVL, and PS  
Figure 13: Loosely Coupled (LC) vs. Tightly Coupled (TC) sensor fusion schemes. were 200 Hz, 1 Hz, and 1 Hz, respectively. For \(x\), \(y\), and \(z\) axes, a gyro drift of 0.01\({}^{\circ}\)/h and a 100 \(\upmu\)g accelerometer bias were introduced as INS errors; 0.002 m/s as a constant DVL error, and 0.05 m as a constant PS error. The results showed a cumulative error of 1000 m at the end of the trajectory for the LC approach and only 10 m in the TC case. Same disadvantages of the LC fusion of an INS/DVL system was addressed by [PERSON] et al. [91]. In their work, they designed a navigation system based on a 150 Hz INS aided with a 1 Hz DVL, a 0.5 Hz magnetometer, and a 0.25 Hz PS under an Extended Loosely Coupled (ELC) approach within an EKF. They focused their work in exploring cases where only partial measurements of the DVL were available and used external information to complete the velocity calculation of the vehicle. To test their system, different trajectories of a vehicle were simulated. Results showed a better performance by the ELC scheme, with improvements up to 38% on Root-Mean-Square Errors when compared with the standalone INS and up to 12% compared with a TC scheme. Another approach is the fusion of INS with acoustic systems. In [92; 93], [PERSON] et al. investigated the use of an AUV positioning method based on a SINS and an LBL under a TC algorithm. Authors were looking to solve position error accumulation of AUVs. They compared the TC and LC approaches by simulating an AUV trajectory under different conditions, such as changing the number of hydrophones available.