# Autonomous Underwater Vehicle Localization Using Sound Measurements of Passing Ships
## 1 Introduction
In [29], sensor fusion models that incorporate gyroscope, accelerometer and ultrasound sensors were presented. The robot pose can be estimated using the Extended Kalman Filter (EKF) to remove biases from IMU. In underwater environments, [PERSON] et al. [30] considered visual Simultaneous Localization and Mapping (SLAM) using a high frequency imaging sonar. [PERSON] et al. [31] described an experiment in which two methods (visual odometry and using a field of static nodes) of underwater robot localization were compared. Visual odometry or Visual SLAM are based on integrating perceived motion of the AUV. These methods are subject to long-term drift, and require occasional position fixes in order to maintain a low localization error. Moreover, Visual odometry or Visual SLAM require a high frequency imaging sonar, which consumes an AUV's power resource significantly. Thus, it is desirable to use a passive navigation solution for an AUV. Using a field of static nodes involves the creation of infrastructure which must be powered, but provides absolute position estimates. This paper considers an AUV, which can locate itself by integrating propeller and IMU (IMU-only localization) [26; 27]. Suppose that using the IMU-only localization, the AUV has been moving in underwater environments for a long time. This IMU-only localization is based on integrating perceived motion of the AUV. Thus, as the AUV stays longer in underwater environments, its localization error keeps growing. Recall that this paper presents the localization of an AUV in environments (such as harbors or ports) where there can be passing ships near the AUV. Thus, operation in the open sea is not within the scope of this paper. To fix long-term drift in the IMU-only localization, this paper proposes that the AUV localization utilizes the sound measurements of passing ships of which the trajectories are known a priori. These ships can be considered as \"a field of moving nodes\" to fix localization of the AUV. This paper handles the case where the target (passing ship in this paper) information is known, and the observer (AUV in this paper) trajectory is to be estimated using bearing measurements associated to the passing ships. Tracking a target using bearing-only measurements is termed the Bearing-Only Target Motion Analysis (BOTMA) problem [32; 33; 34; 35]. The observer maneuver is needed to observe the target state (position and velocity) in the BOTMA problem [36]. The proposed localization scheme can be considered as the reverse process of the BOTMA. In the considered localization problem, the AUV's velocity can be conjectured by integrating propeller and IMU [26; 27]. The error in this integration is modeled using a process noise. To solve the BOTMA problem, Range Parameterized EKF (RPEKF) was used to reduce the range estimation error [37; 38]. The EKF is suitable for real-time processing of nonlinear systems, since it is computationally efficient [34]. The RPEKF is composed of many independent EKFs, such that every EKF has a different initial range estimation. The combined target estimation is derived as a weighted sum of every EKF output. If the AUV cannot measure the sound of any ship, then it relies on locating itself by integrating propeller and IMU (IMU-only localization). We assume that the AUV has been moving in underwater environments using the IMU-only localization before time step 0. Note that the range between a ship and the AUV is not accessible at time step 0, due to long-term drift of the AUV. Thus, this paper modifies the RPEKF to decrease the range estimation error. Moreover, there may be a case where the long-term drift of the AUV is too severe. Assume that the AUV can access the approximate SL of a passing ship. Based on the SL, we can utilize an acoustic propagation model, which simulates the sound emanated from the ship. Environmental factors, such as underwater obstacles or topographical maps, can be taken into account in the modeling of an acoustic propagation model.