# Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle
## 1 Introduction  
Recently, significant progress has been achieved in unmanned underwater vehicles (UUVs) and related core technologies serving various purposes such as oceanographic data collection, exploration, reconnaissance, surveillance, and more. This progress has increased the demand for fundamental technological advancements in structural design, propulsion systems, control mechanisms, underwater docking, and underwater navigation technologies for these UUVs. Especially in underwater environments, the precise and rapid estimation of their state is crucial for mission execution and the subsequent analysis of acquired underwater data by unmanned underwater vehicles. Numerous methods exist to estimate the motion state of these vehicles, and research inspired by fish lateral line systems (LLSs) has developed actively. It is well known that fish can detect flow velocity and pressure in the surrounding flow field through the LLS. Inspired by the exceptional performance of the LLS in fish, there has been significant interest in research on artificial lateral line systems (ALLSs). [PERSON] et al. (2014) presented a data-driven methodology enabling the simultaneous recording of 3D pressure signals while in motion and examined flow features using a sensor array placed inside a fish-shaped head [1]. [PERSON] et al. (2014) introduced a strategy for an airfoil-shaped UUV to estimate flow properties using a bio-inspired, multi-modal artificial lateral line and demonstrate their use in feedback control. They showcased these strategies using a robotic prototype with a multi-modal artificial later line, highlighting distributed flow sensing and closed-loop control capabilities [2]. [PERSON] et al. (2016) carried out investigations using an artificial later line (ALL) array for estimating bulk flow velocity and angle, demonstrating its accuracy in measuring these parameters even in river conditions, with an average velocity estimation error of 14 cm/s [3]. [PERSON] et al. (2016)utilized an ALL for the precise evaluation of a swimming robot, proposing a nonlinear predictive model based on pressure analysis and motion kinematics data [4]. [PERSON] and [PERSON] (2016) introduced a sensor system that uses differential pressure sensors for precise measurements, demonstrating its ability to estimate hydrodynamic force and detect nearby walls by analyzing pressure distribution [5]. [PERSON] et al. (2017) investigated optimal 3D design strategies for dipole source characterization using ALLS. They proposed strategies to overcome design limitations, cooperatively explored ALL swarms, and analyzed the trade-offs between sensor quantity and characterization accuracy [6]. [PERSON] et al. (2018) focused on measuring the hydrodynamic pressure of a robotic fish during its movements near a straight wall and using the pressure data for feedback control of its motion [7]. [PERSON] et al. (2018) explored improving the ALLS in underwater technology using a cylindrical carrier. This study examined biomechanics, developed optimal sensor distribution, and validated the system through experiments, offering effective methods for flow velocity estimation and obstacle identification [8]. [PERSON] et al. (2018) examined the hydrodynamic features of the reverse KVS (Karman vortex street)-like vortex wake with an ALLS. Furthermore, they demonstrated the efficiency and viability of using an ALL for local sensing in nearby underwater robots [9]. [PERSON] et al. (2020) investigated the state estimation of a swimming robotic fish across various motions using a pressure variation (PV) model and regression analysis. Additionally, they proposed a trajectory estimation method and demonstrated it with minimal errors [10]. This paper proposes a pressure variation model (PVM) designed to predict the motion state, particularly the speed and direction, of underwater vehicles. Computational fluid dynamics (CFD), known for its precision and adaptability in simulating motion, is utilized to construct this model.