Approach method for an autonomous underwater vehicle based on mutual positioning with an unmanned aerial vehicle

Abstract

This paper proposes an approach method that enables an autonomous underwater vehicle (AUV) to accurately approach an unmanned aerial vehicle (UAV)-deployed station in the final stage of a mission. AUVs are increasingly used as fully autonomous underwater survey platforms, yet their operation is still constrained by the need for human or vessel support during deployment and recovery. To remove this constraint, the UAV deploys an underwater station that provides a positioning reference and acts as a recovery system. Using onboard acoustic positioning and communication devices, the AUV and the station mutually transmit signals, allowing the AUV to estimate its state relative to the station and guide its approach. Sea experiments evaluated the resulting approach accuracy relative to the station, showing that the AUV can converge to the station vicinity with the precision required for subsequent recovery. This study validates only the pre-recovery approach phase to the recovery station. Full docking and recovery are beyond the scope of this article. The proposed method provides fundamental technology for a reliable close-range approach, which is a key prerequisite for fully autonomous recovery without human or vessel assistance.

Introduction

As interest in sustainable ocean environmental management grows, unmanned aerial vehicles (UAVs) and autonomous underwater vehicles (AUVs) are increasingly utilized as key technological foundations in the fields of ocean research and environmental monitoring.

Several recent observation technology studies have pointed out that UAVs can play an important role in unmanned observation of marine regions.^1,2 Multicopter UAVs, in particular, are frequently used for environmental monitoring in coastal areas and coastal waters due to their ability to quickly capture images over a wide area, and are particularly effective in detecting floating debris and analyzing its spatiotemporal distribution. ³ Furthermore, review studies on risk assessment of contact between marine organisms and floating debris, as well as monitoring methods for coastal areas using UAVs, are progressing, demonstrating the expanding potential applications of these technologies.^4–7

On the other hand, AUVs are suitable for detailed data acquisition and long-term observation in underwater environments, and their use is advancing in scenarios where human operations are challenging, such as surveys in deep sea or shallow water, where the support vessel is difficult to access. One study has introduced filtering methods that combine inertial and acoustic data to achieve more reliable localization in large and deep-sea environments. ⁸ Another study has developed vision-based AUV systems that use computer vision and machine learning for coral reef inspection and geotagging, enabling efficient autonomous monitoring. ⁹

Traditionally, these unmanned vehicles were typically operated individually, but in recent years, coordinated control technology using multiple AUVs has gained attention, and research utilizing swarm robotics and autonomous navigation algorithms has become active. For example, proposals include relative navigation using acoustic communication between multiple AUVs, ¹⁰ obstacle avoidance control using reinforcement learning, ¹¹ control algorithms for stable formation navigation in dynamic environments, ¹² and area exploration based on swarm optimization. ¹³

This trend toward multi-vehicle coordination has further developed, and research is now expanding into cross-domain collaboration between different platforms (air, water, and underwater). By linking UAVs and AUVs, it is possible to divide roles, with UAVs performing wide-area exploration and communication relay, and AUVs performing detailed underwater observation.^14,15 Additionally, by adding unmanned surface vehicles (USVs) as relay nodes, multi-layer collaboration between UAVs, USVs, and AUVs has made it possible to autonomously execute complex missions.^16,17 There are also review papers on communication technologies using UAVs ¹⁸ and autonomous operation technologies for UAVs and AUVs. ¹⁹ The deployment of the AUV by the UAV has also been proposed. ²⁰

Furthermore, research is also progressing on aerial AUV deployment from UAVs as a physical deployment and recovery method, as well as on the evaluation of the impact of such deployment, ²¹ and a framework for aerial deployment of miniature AUVs has also been proposed. ²² Furthermore, hybrid unmanned aerial underwater vehicles capable of continuously moving between air and water (hybrid UAV/AUV) are also gaining attention, with research being conducted on their structural design, control methods, and medium transition technologies.^23–26

As a supporting technology for these collaborations, the construction of a highly reliable and efficient communication network is also important. Research is being conducted on hybrid communication configurations combining RF communication and optical wireless communication,^27,28 the design of an integrated communication protocol (IMC), ²⁹ communication framework design for UAV–USV formations, ³⁰ a review paper on communication technologies for underwater sensor networks, ³¹ and reviews UAV networks from a cyber-physical systems perspective, laying the groundwork for UAV network infrastructures. ³²

Additionally, as applications of unmanned vehicle groups to environmental tasks, methods for UAVs and USVs to collaborate in manipulating objects on the water surface ³³ and proposals for autonomous systems where a UAV and an AUV coordinate to assist in marine debris collection operations ³⁴ have been presented. Diverse application developments are progressing, including evaluations of USV development history and marine environmental monitoring by robotic swarms.^35,36

This study proposes an approach method of the AUV for cooperative survey with the UAV. The AUV is an underwater observation platform with a built-in energy source and a computer. This research project is developing a fully automated method to realize ocean surveys without human or ship support, in which a UAV transports and deploys the AUV to the target area and performs the entire process from survey and recovery to return to port (Figure 1). The elemental methods are (1) transport and deployment of the AUV to the target area by the UAV (Figure 1(A) and (B)), (2) ocean survey of the AUV based on the UAV (Figure 1(C)), and (3) recovery and return to the port (Figure 1(D) and (E)). Since the UAV can measure its position using the signals from the Global Navigation Satellite System (GNSS), the use of the UAV as a survey station makes it possible for the AUV to conduct surveys while also knowing its position using GNSS coordinates.

Figure 1.

The overall concept of the cooperative survey by a UAV and an AUV.

In particular, this study develops an approach method with accurate state estimation based on a UAV to recover an AUV (shown in Figure 1 with a red frame). This research establishes a fundamental technology for automating the recovery of the AUV, which has until now been carried out with the assistance of humans and vessels. Finally, the collaboration between the UAV and the AUV will make it possible to survey environments that are inaccessible to vessels.

The elemental methods of this research are (1) state estimation of an AUV based on a UAV and (2) an approach to a recovery station (Figure 2). The AUV performs relative positioning based on the recovery station deployed underwater from the UAV using the acoustic devices mounted on both the AUV and the recovery station. The AUV approaches the recovery station based on its relative positioning results. The recovery station is deployed by suspending it from the UAV using a single tether. Because wind, waves, and currents may cause a small horizontal offset from the UAV's vertical line, the proposed operation keeps the tether length as short as necessary to reduce the effective suspension length and minimize horizontal offset. This article assumes that the recovery station operates in the vicinity of the UAV's vertical line. The scope of this study is limited to the pre-recovery approach phase to the recovery station. Full docking and recovery are outside the scope of this article.

Figure 2.

The elements of the proposed method.

The contributions of this study are summarized as follows:

This article proposes an AUV state-estimation method based on mutual UAV–AUV relative positioning, aiming to achieve the accuracy required for the pre-docking phase.

This article proposes an approach method that guides the AUV toward the recovery station based on the relative positioning.

Real sea experiments using a UAV and an AUV are conducted to validate the approach performance and to evaluate the state estimation accuracy against the accuracy requirement for the pre-docking phase toward automatic recovery.

Proposed method

State estimation based on mutual positioning

This study proposes an approach method for an AUV based on mutual positioning with a reference and recovery station deployed from a UAV (UAV-ST). In the previous study, only positioning information from an AUV was used, ³⁷ but by performing mutual positioning between an AUV and a UAV and aggregating the positioning information, accurate state estimation can be performed in real time. At the same time, an AUV approaches the UAV-ST in real time based on its own positioning results.

Figure 3 illustrates a concept of state estimation, assuming the AUV is equipped with minimal navigational sensors such as an acceleration sensor, an attitude sensor, a magnetometer, and a pressure sensor. Depth z can be directly measured by the pressure sensor, and roll angle $\theta$ and pitch angle $\varphi$ can be directly measured by the attitude sensor. Therefore, the state that the AUV should estimate is the horizontal position $(x,y)$ , yaw angle $\psi$ , and horizontal velocity $(v_x,v_y)$ . In this method, the AUV estimates the state by a particle filter, which is one of the stochastic state estimation methods. ³⁸ The ith particle of the AUV at time t is defined as follows:

$$\begin{array}{c}{\mathit{s}}_t^{\mathrm{A}i}={[x_t^{\mathrm{A}i}{y}_t^{\mathrm{A}i}{\psi }_t^{\mathrm{A}i}{v}_{x_t}^{\mathrm{A}i}{v}_{yt}^{\mathrm{A}i}]}^{\mathrm{T}}(i=1,\dots ,n)\end{array}$$

(1)

$n$ represents the number of particles. $(x_t^{\mathrm{A}}{y}_t^{\mathrm{A}}{\psi }_t^{\mathrm{A}})$ are defined in the world coordinate system, whereas $(v_{x_t}^{\mathrm{A}}{v}_{yt}^{\mathrm{A}})$ are in the AUV's coordinate system. AUV estimates the state transition from time t to $t+\mathrm{\Delta }t$ from measurements of acceleration ${\hat{\mathit{a}}}_t^{\mathrm{A}}$ and magnetic orientation ${\hat{\psi }}_t^{\mathrm{A}}$ . ³⁹

$$\begin{array}{c}{\mathit{v}}_{t+\mathrm{\Delta }t}^{\mathrm{A}i}={\mathit{v}}_t^{\mathrm{A}i}+{\mathit{a}}_t^{\mathrm{A}i}\mathrm{\Delta }t\end{array}$$

(2)

$$\begin{array}{c}{\mathit{v}}_t^{\mathrm{A}i}={[v_{x_t}^{\mathrm{A}i}{v}_{y_t}^{\mathrm{A}i}]}^{\mathrm{T}}\end{array}$$

(3)

$$\begin{array}{c}{\mathit{a}}_t^{\mathrm{A}i}={[a_{x_t}^{\mathrm{A}i}{a}_{y_t}^{\mathrm{A}i}]}^{\mathrm{T}}\end{array}$$

(4)

$$\begin{array}{c}{\mathit{x}}_{t+\mathrm{\Delta }t}^{\mathrm{A}i}={\mathit{x}}_t^{\mathrm{A}i}+\mathit{R}({\theta }_t^{\mathrm{A}},{\varphi }_t^{\mathrm{A}},{\psi }_t^{\mathrm{A}i}){\mathit{v}}_t^{\mathrm{A}i}\mathrm{\Delta }t\end{array}$$

(5)

$$\begin{array}{c}{\mathit{x}}_t^{\mathrm{A}i}={[x_t^{\mathrm{A}i}{y}_t^{\mathrm{A}i}]}^{\mathrm{T}}\end{array}$$

(6)

$$\begin{array}{c}{a}_{xt}^{\mathrm{A}i}\sim N({\hat{a}}_{x_t}^{\mathrm{A}},{({\sigma }_a)}^2)\end{array}$$

(7)

$$\begin{array}{c}{a}_{yt}^{\mathrm{A}i}\sim N({\hat{a}}_{y_t}^{\mathrm{A}},{({\sigma }_a)}^2)\end{array}$$

(8)

$$\begin{array}{c}{\psi }_t^{\mathrm{A}i}\sim N({\hat{\psi }}_t^{\mathrm{A}},{({\sigma }_{\psi })}^2)\end{array}$$

(9)

where $\mathit{R}$ is the rotation matrix. ${\sigma }_a$ and ${\sigma }_{\psi }$ are the standard deviations of the measured acceleration and magnetic orientation, respectively.

Figure 3.

State estimation based on mutual positioning.

The AUV corrects the state distribution based on mutual acoustic positioning by the UAV-ST deployed from the UAV. In this article, mutual positioning is defined as a bidirectional transmission and information-sharing scheme in which the AUV and the UAV-ST alternate acoustic transmissions. The UAV-ST obtains the relative positioning measurement and sends it to the AUV, and the AUV updates its state using both its own measurement and the measurement communicated from the UAV-ST, distinguishing the method from conventional transponder positioning.

Time interval of acoustic positioning is $\tau$ . Firstly, at time $t-\tau$ , the UAV-ST transmits an interrogation signal to the AUV, and the AUV responds. This allows the UAV-ST to obtain the relative distance ${\hat{r}}_{t-\tau }^{\mathrm{UA}}$ and relative direction ${\hat{\theta }}_{t-\tau }^{\mathrm{UA}}$ of the AUV. Next, at time t, the AUV transmits an interrogation signal to the UAV-ST, and the UAV-ST responds. The UAV-ST includes the ${\hat{r}}_{t-\tau }^{\mathrm{UA}}$ and ${\hat{\theta }}_{t-\tau }^{\mathrm{UA}}$ obtained at time $t-\tau$ , the positions ${\mathit{x}}_{t-\tau }^{\mathrm{U}}$ and ${\mathit{x}}_t^{\mathrm{U}}$ at times $t-\tau$ and t, and the azimuths ${\psi }_{t-\tau }^{\mathrm{U}}$ and ${\psi }_t^{\mathrm{U}}$ in the response signal. Based on the response signal, the AUV obtains the relative distance ${\hat{r}}_t^{\mathrm{AU}}$ and relative direction ${\hat{\theta }}_t^{\mathrm{AU}}$ to the UAV-ST. The AUV performs state estimation as follows based on the distance and direction information mutually measured with the UAV-ST at time t.

The AUV's velocity at time $t-\tau$ is calculated from the AUV's position obtained from multiple positioning data as follows:

$$\begin{array}{c}{\hat{\mathit{x}}}_{t-\tau }^{\mathrm{A}}={\mathit{x}}_{t-\tau }^{\mathrm{U}}+{\hat{r}}_{t-\tau }^{\mathrm{UA}}\left[\begin{array}{c}\cos ({\psi }_{t-\tau }^{\mathrm{U}}+{\hat{\theta }}_{t-\tau }^{\mathrm{UA}})\\ \sin ({\psi }_{t-\tau }^{\mathrm{U}}+{\hat{\theta }}_{t-\tau }^{\mathrm{UA}})\end{array}\right]\end{array}$$

(10)

Since the measured position is subject to fluctuations caused by measurement noise, the following smoothing process is applied. The index set of samples within the most recent T seconds is defined as follows:

$$\begin{array}{c}{I}_{t-\tau }=\{i|t-\tau -T\le t_i\le t-\tau \}\end{array}$$

(11)

The smoothed position is then computed as the simple average over this time window.

$${\hat{\mathit{x}}}_{t-\tau }^{{\mathrm{A}}^{\mathrm{\prime }}}={\displaystyle \frac{1}{|I_{t-\tau }|}\sum _{i\in I_{t-\tau }}{\hat{\mathit{x}}}_{t_i}^{\mathrm{A}}}$$

(12)

Finally, the velocity is estimated from the smoothed positions as follows:

$$\begin{array}{c}{\hat{\mathit{v}}}_{t-\tau }^{\mathrm{\prime }}={\displaystyle \frac{{\hat{\mathit{x}}}_{t-\tau }^{{\mathrm{A}}^{\mathrm{\prime }}}-{\hat{\mathit{x}}}_{t-3\tau }^{{\mathrm{A}}^{\mathrm{\prime }}}}{2\tau }}\end{array}$$

(13)

$$\begin{array}{c}{\hat{\mathit{v}}}_{t-\tau }^{\mathrm{\prime }}={[{\hat{v}}_{x_{t-\tau }}^{\mathrm{\prime }}{\hat{v}}_{y_{t-\tau }}^{\mathrm{\prime }}]}^{\mathrm{T}}\end{array}$$

(14)

The velocity estimated here can be affected when the positioning results include large noise, for example, when outliers are present, which may cause deviations in the estimated value. Outliers are defined as abnormal acoustic positioning results that deviate markedly from the expected measurement behavior. They are assumed to originate from multipath due to reflections from the seafloor and the sea surface, as well as from failures in acoustic signal processing. To mitigate this effect, a velocity-based gating step is introduced. If the velocity is greater than or equal to $V_{\max }$ , it is set to $V_{\max }$ . If it is less than or equal to $-V_{\max }$ , it is set to $-V_{\max }$ . Otherwise, the value is left unchanged.

$${\hat{v}}_{x_{t-\tau }}^{\mathrm{c}}=\mathrm{clip}({\hat{v}}_{x_{t-\tau }}^{\mathrm{\prime }},-V_{\max },V_{\max })$$

(15)

$${\hat{v}}_{y_{t-\tau }}^{\mathrm{c}}=\mathrm{clip}({\hat{v}}_{y_{t-\tau }}^{\mathrm{\prime }},-V_{\max },V_{\max })$$

(16)

where $\mathrm{clip}(x,a,b)$ limits x to the interval $[a,b]$ by returning a if $x<a$ , b if $x>b$ , and x otherwise.

$$\begin{array}{c}{\hat{\mathit{v}}}_{t-\tau }^{\mathrm{c}}={[{\hat{v}}_{x_{t-\tau }}^{\mathrm{c}}{\hat{v}}_{y_{t-\tau }}^{\mathrm{c}}]}^{\mathrm{T}}\end{array}$$

(17)

$$\begin{array}{c}{\hat{\mathit{v}}}_{t-\tau }^{\mathrm{A}}=\mathit{R}(-{\theta }_{t-\tau }^{\mathrm{A}},-{\varphi }_{t-\tau }^{\mathrm{A}},-{\psi }_{t-\tau }^{\mathrm{A}}){\hat{\mathit{v}}}_{t-\tau }^{\mathrm{c}}\end{array}$$

(18)

$$\begin{array}{c}{\hat{\mathit{v}}}_{t-\tau }^{\mathrm{A}}={[{\hat{v}}_{x_{t-\tau }}^{\mathrm{A}}{\hat{v}}_{y_{t-\tau }}^{\mathrm{A}}]}^{\mathrm{T}}\end{array}$$

(19)

The AUV modifies the state distribution based on the above distance, direction, and velocity information. Derive the likelihood $L_{t-\tau }^{\mathrm{UA}i}$ for each particle of the AUV based on positioning measurements from the UAV-ST at time $t-\tau$ as follows.

$$\begin{array}{c}{L}_{t-\tau }^{\mathrm{UA}i}=L_{t-\tau }^{\mathrm{UA}r}({\mathit{s}}_{t-\tau }^i)\cdot L_{t-\tau }^{\mathrm{UA}\theta }({\mathit{s}}_{t-\tau }^i)\cdot L_{t-\tau }^{\mathrm{UA}vx}({\mathit{s}}_{t-\tau }^i)\cdot L_{t-\tau }^{\mathrm{UA}vy}({\mathit{s}}_{t-\tau }^i)\end{array}$$

(20)

$L_{t-\tau }^{\mathrm{UA}r}$ , $L_{t-\tau }^{\mathrm{UA}\theta }$ , $L_{t-\tau }^{\mathrm{UA}vx}$ , and $L_{t-\tau }^{\mathrm{UA}vy}$ denote the likelihood of the particle based on the distance, direction, and velocity measured by acoustic positioning from the UAV-ST, respectively; the likelihood is calculated based on the deviation between the measured and estimated values as follows:

$$\begin{array}{c}\mathrm{\Delta }{r}_{t-\tau }^{\mathrm{UA}i}=|\Vert {\mathit{x}}_{t-\tau }^{\mathrm{A}i}-{\mathit{x}}_{t-\tau }^{\mathrm{U}}\Vert -{\hat{r}}_{t-\tau }^{\mathrm{UA}}|\end{array}$$

(21)

$$\begin{array}{c}\mathrm{\Delta }{\theta }_{t-\tau }^{\mathrm{UA}i}=\left|\arg ({\mathit{x}}_{t-\tau }^{\mathrm{A}i}-{\mathit{x}}_{t-\tau }^{\mathrm{U}})-({\psi }_{t-\tau }^{\mathrm{U}}+{\hat{\theta }}_{t-\tau }^{\mathrm{UA}})\right|\end{array}$$

(22)

$$\begin{array}{c}{L}_{t-\tau }^{\mathrm{UA}r}({\mathit{s}}_{t-\tau }^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_r)}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{r}_{t-\tau }^{\mathrm{UA}i})}^2}{2{({\sigma }_r)}^2}}}\right)\right)\end{array}$$

(23)

$$\begin{array}{c}{L}_{t-\tau }^{\mathrm{UA}\theta }({\mathit{s}}_{t-\tau }^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_{\theta })}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{\theta }_{t-\tau }^{\mathrm{UA}i})}^2}{2{({\sigma }_{\theta })}^2}}}\right)\right)\end{array}$$

(24)

where ${\sigma }_r$ and ${\sigma }_{\theta }$ are the standard deviations of the distance and direction measurements, respectively. $k_r$ and $k_{\theta }$ are parameters for determining outliers. ⁴⁰ If they are determined to be outliers, the likelihood is set to 1.

$$\begin{array}{c}\mathrm{\Delta }{v}_{x_{t-\tau }}^{\mathrm{A}i}=|v_{x_{t-\tau }}^{\mathrm{A}i}-{\hat{v}}_{x_{t-\tau }}^{\mathrm{A}}|\end{array}$$

(25)

$$\begin{array}{c}\mathrm{\Delta }{v}_{y_{t-\tau }}^{\mathrm{A}i}=|v_{y_{t-\tau }}^{\mathrm{A}i}-{\hat{v}}_{y_{t-\tau }}^{\mathrm{A}}|\end{array}$$

(26)

$$\begin{array}{c}{L}_{t-\tau }^{\mathrm{UA}vx}({\mathit{s}}_{t-\tau }^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_v)}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{v}_{x_{t-\tau }}^{\mathrm{A}i})}^2}{2{({\sigma }_v)}^2}}}\right)\right)\end{array}$$

(27)

$$\begin{array}{c}{L}_{t-\tau }^{\mathrm{UA}vy}({\mathit{s}}_{t-\tau }^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_v)}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{v}_{y_{t-\tau }}^{\mathrm{A}i})}^2}{2{({\sigma }_v)}^2}}}\right)\right)\end{array}$$

(28)

where ${\sigma }_v$ is the standard deviation of the velocity calculation based on acoustic positioning. $k_v$ is a parameter used to determine outliers in the velocity calculation.

The state distribution is also corrected based on the likelihood $L_t^{\mathrm{AU}i}$ of each particle derived based on positioning measurements from the AUV at time t.

$$\begin{array}{c}{L}_t^{\mathrm{AU}i}=L_t^{\mathrm{AU}r}({\mathit{s}}_t^i)\cdot L_t^{\mathrm{AU}\theta }({\mathit{s}}_t^i)\end{array}$$

(29)

$$\begin{array}{c}\mathrm{\Delta }{r}_t^{\mathrm{AU}i}=|\Vert {\mathit{x}}_t^{\mathrm{U}}-{\mathit{x}}_t^{\mathrm{A}i}\Vert -{\hat{r}}_t^{\mathrm{AU}}|\end{array}$$

(30)

$$\begin{array}{c}\mathrm{\Delta }{\theta }_t^{\mathrm{AU}i}=\left|\arg ({\mathit{x}}_t^{\mathrm{U}}-{\mathit{x}}_t^{\mathrm{A}i})-({\psi }_t^{\mathrm{A}i}+{\hat{\theta }}_t^{\mathrm{AU}})\right|\end{array}$$

(31)

$$\begin{array}{c}{L}_t^{\mathrm{AU}r}({\mathit{s}}_t^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_r)}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{r}_t^{\mathrm{AU}i})}^2}{2{({\sigma }_r)}^2}}}\right)\right)\end{array}$$

(32)

$$\begin{array}{c}{L}_t^{\mathrm{AU}\theta }({\mathit{s}}_t^i)=max\left(1,\exp \left({\displaystyle \frac{{(k_{\theta })}^2}{2}+{\displaystyle \frac{-{(\mathrm{\Delta }{\theta }_t^{\mathrm{AU}i})}^2}{2{({\sigma }_{\theta })}^2}}}\right)\right)\end{array}$$

(33)

State initialization and correction

The UAV deploys the UAV-ST underwater, but the position of the AUV relative to it is unknown. Based on the relative distance ${\hat{r}}_t^{\mathrm{UA}}$ and relative azimuth ${\hat{\theta }}_t^{\mathrm{UA}}$ measured by the UAV-ST, the distribution of the estimated position is obtained. Using the UAV-ST as the origin, the distance and direction for each particle to generate the position of the AUV based on the positioning results are obtained as follows:

$$\begin{array}{c}{r}_t^{\mathrm{UA}i}\sim N({\hat{r}}_t^{\mathrm{UA}},{({\sigma }_r)}^2)\end{array}$$

(34)

$$\begin{array}{c}{\theta }_t^{\mathrm{UA}i}\sim N({\hat{\theta }}_t^{\mathrm{UA}},{({\sigma }_{\theta })}^2)\end{array}$$

(35)

There are n particles, and the estimated position of the particles are replaced using the following equation. The ratio of replaced particles to be set among the n particles is $\alpha$ .

$$\begin{array}{c}{x}_t^{\mathrm{A}i}=r_t^{\mathrm{UA}i}\cos ({\theta }_t^{\mathrm{UA}i})\end{array}$$

(36)

$$\begin{array}{c}{y}_t^{\mathrm{A}i}=r_t^{\mathrm{UA}i}\sin ({\theta }_t^{\mathrm{UA}i})\end{array}$$

(37)

$$\begin{array}{c}{\psi }_t^{\mathrm{A}i}\sim N({\hat{\psi }}_t^{\mathrm{A}},{({\sigma }_{\psi })}^2)\end{array}$$

(38)

$$\begin{array}{c}{v}_{x_t}^{\mathrm{A}i}\sim N({\hat{v}}_{x_t}^{\mathrm{A}},{({\sigma }_v)}^2)\end{array}$$

(39)

$$\begin{array}{c}{v}_{y_t}^{\mathrm{A}i}\sim N({\hat{v}}_{y_t}^{\mathrm{A}},{({\sigma }_v)}^2)\end{array}$$

(40)

This method can be used not only for initializing the position but also for correcting it when the position is lost. The particles are added constantly, so that the discrepancy between the estimation and the positioning result does not increase.

Approach method

The AUV obtains the distance ${\hat{r}}_t^{\mathrm{AU}}$ and the direction ${\hat{\theta }}_t^{\mathrm{AU}}$ to the UAV-ST. Since the AUV is assumed to be unable to obtain ground velocity, it approaches using force control based on positioning results. Commands are issued in the surge direction according to the target distance $r^{\mathrm{ref}}$ . Assuming that the steady-state value of the command is F, the surge force command value $F_{xt}^{\mathrm{ref}}$ is as follows:

$$\begin{array}{c}{F}_{xt}^{\mathrm{ref}}=\{\begin{array}{c}F,\mathrm{if}{\hat{r}}_t^{\mathrm{AU}}>r^{\mathrm{ref}}\\ 0,\mathrm{if}{\hat{r}}_t^{\mathrm{AU}}\le r^{\mathrm{ref}}\end{array}\end{array}$$

(41)

The AUV controls the yaw direction so that the direction ${\hat{\theta }}_t^{\mathrm{AU}}$ becomes 0. If the command value for yaw control is $T_{\psi t}^{\mathrm{ref}}$ , the following applies:

$$\begin{array}{c}{T}_{\psi t}^{\mathrm{ref}}=K_{\mathrm{P}}{\hat{\theta }}_t^{\mathrm{AU}}+K_{\mathrm{I}}\int {\hat{\theta }}_t^{\mathrm{AU}}\mathrm{d}t+K_{\mathrm{D}}{\displaystyle \frac{\mathrm{d}{\hat{\theta }}_t^{\mathrm{AU}}}{\mathrm{d}t}}\end{array}$$

(42)

$K_{\mathrm{P}}$ , $K_{\mathrm{I}}$ , and $K_{\mathrm{D}}$ are gains related to proportional, integral, and derivative PID control, respectively.

The AUV does not control itself using the estimated state. Instead, it approaches the UAV-ST by controlling surge force and yaw based on the distance and azimuth obtained from acoustic relative positioning. The acoustic positionings from the AUV are obtained every 2 $\tau$ , and the latest distance and azimuth are held as the control reference between updates, enabling a continuous reference between updates. Even when an update is missed, holding the latest measured distance and azimuth is a stability-prioritized strategy because it does not extrapolate the reference during the gap. In contrast, closing the loop through the estimated state would require prediction between sparse and intermittent acoustic updates. Without reliable high-rate velocity information and in the presence of disturbances and model errors, such prediction can drift and degrade robustness. Therefore, the measured distance and azimuth are used as the guidance reference. Once the UAV-ST becomes visually detectable, the AUV is intended to switch to vision-based positioning for higher-frequency localization.

Based on the above, the AUV approaches the target recovery device, the UAV-ST.

Implementation

The proposed method is implemented on a Blue AUV (Figure 4) and a UAV of PRODRONE Co., Ltd ⁴¹ (PRODRONE, Figure 5). The Blue AUV is a Blue ROV 2 sold by Blue Robotics ⁴² with an autonomous navigation program to enable autonomous operation. Blue AUV is equipped with an acceleration sensor, an attitude sensor, a magnetometer, a depth sensor, a camera, and an acoustic positioning and communication device. Tables 1 and 2 show the specifications of the Blue AUV and the UAV, respectively. Figure 6 shows the acoustic positioning system (UAV-ST) deployed from the UAV underwater. The dimensions of the UAV-ST are 0.4 × 0.2 × 0.2 m, which is the minimum size adopted because the primary focus is on a close-range approach rather than recovery in this study. Even if the frame were enlarged to a practical size for docking, such as 0.6 × 0.5 × 0.4 m, the additional mass would remain minor because a lightweight aluminum structure is used, and therefore, the increase would not hinder the UAV from transporting the UAV-ST. The UAV is also connected to the acoustic positioning system by a communication cable and can receive the system's depth, heading, and acoustic positioning results in real time.

Figure 4.

Blue AUV used in the sea trial.

Figure 5.

UAV used in the sea trial.

Figure 6.

Acoustic positioning system (UAV-ST).

Table 1.

Specifications of Blue AUV.

Size	0.45 m (L) × 0.33 m (W)× 0.25 m (H)
Weight	11 kg (in air), −0.5 kg (in water)
Max. depth	100 m
Endurance	4 h
Thrusters	200 W × 6
Sensors	Gyroscope Accelerometer Magnetometer Pressure sensor: Bar30 (Blue Robotics) Acoustic positioning and communication device: X150 USBL Beacon (Blueprint Subsea) Camera

Table 2.

Specifications of the UAV.

Size	2.181 m (L) × 2.398 m (W)× 0.676 m (H)
Weight	20.0 kg
Max. payload	20.0 kg
Endurance	33 min (no payload), 19 min (10 kg payload)

Experiments

A sea trial using a UAV and an AUV was conducted in Hiratsuka New Port, Japan, with the UAV-ST suspended from the UAV and operated under manual control. First, the UAV flew to the exploration area, and upon arrival at the target point, it stopped hovering and deployed the UAV-ST underwater. After UAV-ST was deployed underwater, the AUV began autonomous navigation with depth control at a depth of 1 m. The AUV and the UAV-ST alternately transmitted positioning signals at 6-second intervals to measure their relative positions ( $\tau$ ), and the AUV approached the UAV-ST based on its positioning results with the UAV-ST. The experiment procedure is shown in Figure 7. Figure 8 shows a map and an overview of the Hiratsuka Fishing Port, where the experiment was conducted. The X-axis is used for the north direction and the Y-axis for the east direction. Figure 9 shows a scene from the experiment.

Figure 7.

The procedure of the sea experiment.

Figure 8.

The map of Hiratsuka Fishing Port.

Figure 9.

The scene of the sea experiment.

The AUV's state was estimated through post-processing using the acoustic positioning and navigation sensor measurements acquired during the experiment. The parameters of the particle filter are shown in Table 3. The number of particles was set to 2000.

Table 3.

Parameters of the particle filter.

${\sigma }_a$	$0.04\mathrm{m}/{\mathrm{s}}^2$
${\sigma }_{\psi }$	$8.0\circ$
${\sigma }_r$	$0.5\mathrm{m}$
${\sigma }_{\theta }$	$6.0\circ$
${\sigma }_v$	$0.005\mathrm{m}/\mathrm{s}$
$V_{\max }$	$0.25\mathrm{m}/\mathrm{s}$

Since the UAV-ST-referenced acoustic relative positioning is updated every 12 s, the update interval is relatively sparse. To limit the smoothing delay under such sparse updates, the moving-average window size is set to 2 samples for velocity estimation. This corresponds to a smoothing time parameter of $T=24.0$ s. Outlier gating is based on a maximum feasible velocity constraint derived from the AUV motion characteristics, and the bound is set to $V_{\max }=0.25$ m/s. Five trials were performed. The estimation performance of the proposed method is evaluated from the viewpoint of convergence using the station-referenced residuals between the AUV position acquired by the UAV-ST through acoustic relative positioning and the estimated AUV position. Non-divergence is judged when the station-referenced residual does not increase with time, eventually settles within a bounded range, and shows consistent behavior across repeated trials without large degradation.

Figure 10 shows the distances obtained by the UAV-ST and the AUV using acoustic positioning. The blue and light blue dots represent the distance acquired by the UAV-ST and the AUV, respectively. The distance decreases with time, indicating that the AUV is approaching the UAV-ST. Figure 11 shows the relative azimuth of the acoustic positioning system acquired by the AUV. After that, the AUV approaches while controlling its own azimuth in the direction of the acoustic arrival while keeping it within $\pm$ 50°. Finally, the AUV succeeded in approaching a distance of 6 m. Under the condition of a nominal 12 s acoustic update interval, consecutive positioning updates were successfully obtained with a 12 s spacing in 21 out of 23 intervals (91.3%). In the remaining two intervals, a consecutive update was missed, and the effective interval increased to 24 s (8.7%). For the 12 s intervals, the per-update range change $|\mathrm{\Delta }r|$ , computed from consecutive acoustic updates, had a median of 0.80 m with a standard deviation of 0.42 m. This indicates bounded range change between consecutive updates and supports stable approach behavior under the tested update condition. Although missed updates occurred only twice in this experiment, the impact of more frequent missed updates, which would make the held reference older, is left for future work.

Figure 10.

Distance measured by the UAV-ST and the AUV.

Figure 11.

Relative azimuth measured by the AUV.

Figures 12 to 14 show the results of one of five trials.

Figure 12.

Estimated trajectory of the AUV and the AUV's position measured by the UAV-ST.

Figure 13.

Standard deviations of X and Y positions of the AUV.

Figure 14.

Standard deviations of X and Y velocities of the AUV.

Figure 12 shows the estimated position of the AUV, which was estimated based on the relative positioning measurements acquired by the AUV and the UAV-ST through alternating acoustic positioning and the measurements of the AUV's onboard navigation sensors (acceleration sensor and magnetometer). The blue dots represent the estimated position, and the red dots represent the positioning results of the UAV-ST. The origin is the position of the UAV-ST, the X-axis represents the north direction, and the Y-axis represents the east direction. At the beginning, the AUV initializes its position at the origin, but it gradually corrects its position based on the mutual positioning results, and it navigates in the direction of the arrow to approach the UAV-ST.

Figures 13 and 14 show the standard deviation of the estimated positions and estimated velocities of the AUV. The standard deviations are gradually decreasing, and the estimation is converging.

Figure 15 shows the time series of the station-referenced residual between the AUV position acquired by the UAV-ST through acoustic relative positioning and the estimated AUV position at the time of acquisition. Box plots summarizing the five trials are also provided. The blue plots represent the residual in the X-direction, and the red plots represent the residual in the Y-direction. Initially, the residual is about 20 m. A transient spike is observed around 50 s, which is attributed to the filter initialization phase, where the initial uncertainty is large and several acoustic updates are required before the estimation stabilizes. The residual decreases over time and, in the terminal phase, settles to about 1–2 m in both the X and Y directions. In particular, the X-direction residual shows a small spread of at most 0.2 m with no noticeable temporal variation, while the Y-direction residual exhibits a larger but still limited spread of at most 1.0 m with only minor temporal variation. Since an independent absolute ground-truth reference was not available in the sea trials, the reported 1–2 m values are defined as station-referenced measurement–estimate residuals. They are used to evaluate convergence and repeatability rather than absolute positioning accuracy. Because the residual does not increase with time, eventually settles within a bounded range, and does not exhibit large degradation across trials, these results support that the estimation is non-divergent.

Figure 15.

Time series of the station-referenced residual between the estimated AUV position and the acoustic measurement.

Discussion

Robustness evaluation

This subsection evaluates the robustness of the proposed method against outliers of positioning measurements by varying the preprocessing window size and by examining the resulting changes in estimation and approach accuracy.

Since the UAV-ST-referenced acoustic relative positioning is updated every 12 s, moving-average smoothing is applied with window sizes of two and three samples to limit the smoothing delay under sparse updates. Accordingly, the smoothing time parameter is set to $T=24\mathrm{s}$ and $T=36\mathrm{s}$ , respectively. Outliers are also included in the measurement with a 5% occurrence probability to emulate outlier occurrence. If an outlier occurs, the following noise is added to ${\hat{r}}_t$ and ${\hat{\theta }}_t$ which indicate the distance and the azimuth measured by the AUV or the UAV-ST, respectively. The measurements ${\hat{r}}_{\mathrm{o},t}^{\mathrm{\prime }}$ and ${\hat{\theta }}_{o,t}^{{}^{\mathrm{\prime }}}$ used for the observations when the outlier occurs are computed as follows:

$$\begin{array}{c}{\hat{r}}_{\mathrm{o},t}^{\mathrm{\prime }}\sim N({\hat{r}}_t,{({\sigma }_{r,t}^{\mathrm{o}})}^2)\end{array}$$

(43)

$$\begin{array}{c}{\hat{\theta }}_{o,t}^{{}^{\mathrm{\prime }}}\sim N({\hat{\theta }}_t,{({\sigma }_{\theta ,t}^{\mathrm{o}})}^2)\end{array}$$

(44)

where ${\sigma }_{r,t}^{\mathrm{o}}$ and ${\sigma }_{\theta ,t}^{\mathrm{o}}$ are defined as the standard deviations of distance and azimuth measurements when the outlier occurs, respectively.

State estimation in the post-processing was conducted using the same data described in the Experiments section. Table 4 shows parameter settings for outlier measurements. The compared conditions were as follows. Five trials were performed under each condition.

Condition 1: No outliers, window size W = 2 (same condition in the Experiments section)

Condition 2: No outliers, window size W = 3

Condition 3: Outliers included, window size W = 2

Condition 4: Outliers included, window size W = 3

Table 4.

Parameter settings for outlier measurements.

${\sigma }_{r,t}^{\mathrm{o}}$	$5.0\mathrm{m}$
${\sigma }_{\theta ,t}^{\mathrm{o}}$	$5.0\circ$

The time-series station-referenced residual between the estimated AUV position and the acoustic measurement is shown in Figure 15 for Condition 1 and in Figure 16 for Conditions 2 to 4. In Figure 16, the top, middle, and bottom panels correspond to Conditions 2 to 4, respectively. When the window size was 2, the residual did not increase even when outliers occurred; instead, it remained stable and converged. In contrast, when the window size was 3, there was a period during which the residual slightly increased, but it eventually converged to 1–2 m. This is because the UAV-ST-referenced acoustic positioning is updated at 12-second intervals, and increasing the window size gradually introduces a delay in smoothing, which can lead to estimation errors.

Figure 16.

Time series comparison of the station-referenced residual between the estimated AUV position and the acoustic measurement under different preprocessing conditions. The top, middle, and bottom panels correspond to Conditions 2, 3, and 4, respectively.

Scalability evaluation

This subsection investigates scalability to longer-range and deeper-water scenarios by introducing range-dependent degradations in acoustic measurements and analyzing how the approach performance changes under these conditions.

The sea trials in this study were conducted in shallow water (approximately 1 m depth) over a short range of 25 m. In such environments, acoustic measurements can be affected by strong multipath from surface and bottom reflections, leading to large errors and intermittent observations. In deeper-water and longer-range operations, the propagation conditions change, and additional factors may become dominant, such as depth-dependent sound-speed structure, higher attenuation, and increased intermittency. To discuss scalability beyond the tested range, an additional analysis introduces range-dependent degradations associated with reduced SNR (signal-to-noise ratio), namely increased measurement error, decreased positioning success rate, and an increased outlier rate. These degradations are modeled as an approximation using first-order (linear) functions of range to represent monotonic deterioration trends, rather than a physics-accurate propagation model or a precise extrapolation.

Let ${\hat{r}}_t$ and ${\hat{\theta }}_t$ denote the distance and azimuth measured by the AUV or the UAV-ST. The parameters $r^{\mathrm{near}}$ and $r^{\mathrm{far}}$ define the valid distance interval. For any ${\hat{r}}_t\in [r^{\mathrm{near}},r^{\mathrm{far}}]$ , the normalized distance $u({\hat{r}}_t)$ is introduced.

$$u({\hat{r}}_t)={\displaystyle \frac{{\hat{r}}_t-r^{\mathrm{near}}}{r^{\mathrm{far}}-r^{\mathrm{near}}}(r^{\mathrm{near}}\le {\hat{r}}_t\le r^{\mathrm{far}})}$$

(45)

The success probability $p_t$ is defined by normalized distance $u({\hat{r}}_t)$ , where $p^{\mathrm{near}}$ and $p^{\mathrm{far}}$ is the success probability at ${\hat{r}}_t$ = $r^{\mathrm{near}}$ and ${\hat{r}}_t=r^{\mathrm{far}}$ , respectively.

$$p_t=p^{\mathrm{near}}+(p^{\mathrm{far}}-p^{\mathrm{near}})u({\hat{r}}_t)$$

(46)

The outlier occurrence probability $p_{\mathrm{o},t}$ , the standard deviation for distance measurement ${\sigma }_{r,t}^{\mathrm{\prime }}$ , and the standard deviation for azimuth measurement ${\sigma }_{\theta ,t}^{\mathrm{\prime }}$ can be computed in the same manner.

$$p_{\mathrm{o},t}=p_{\mathrm{o}}^{\mathrm{near}}+(p_{\mathrm{o}}^{\mathrm{far}}-p_{\mathrm{o}}^{\mathrm{near}})u({\hat{r}}_t)$$

(47)

$${\sigma }_{r,t}^{\mathrm{\prime }}={\sigma }_r^{\mathrm{near}}+({\sigma }_r^{\mathrm{far}}-{\sigma }_r^{\mathrm{near}})u({\hat{r}}_t)$$

(48)

$${\sigma }_{\theta ,t}^{\mathrm{\prime }}={\sigma }_{\theta }^{\mathrm{near}}+({\sigma }_{\theta }^{\mathrm{far}}-{\sigma }_{\theta }^{\mathrm{near}})u({\hat{r}}_t)$$

(49)

The measurements ${\hat{r}}_t^{\mathrm{\prime }}$ and ${\hat{\theta }}_t^{{}^{\mathrm{\prime }}}$ used for the observations are computed as follows based on these standard deviations ${\sigma }_{r,t}^{\mathrm{\prime }}$ and ${\sigma }_{\theta ,t}^{\mathrm{\prime }}$ , respectively.

$$\begin{array}{c}{\hat{r}}_t^{\mathrm{\prime }}\sim N({\hat{r}}_t,{({\sigma }_{r,t}^{\mathrm{\prime }})}^2)\end{array}$$

(50)

$$\begin{array}{c}{\hat{\theta }}_t^{{}^{\mathrm{\prime }}}\sim N({\hat{\theta }}_t,{({\sigma }_{\theta ,t}^{\mathrm{\prime }})}^2)\end{array}$$

(51)

The positioning measurements used for the observations when the outlier occurs are computed in the same way as the Robustness evaluation subsection. Table 5 shows parameter settings for the distance-based measurement model. Parameter settings for outlier measurements are the same as those in Table 4. The moving-average parameter T for the velocity was set to 24.0 s.

Table 5.

Parameter settings for the distance-based measurement model.

$r^{\mathrm{near}}$	$5.0\mathrm{m}$
$r^{\mathrm{far}}$	$25.0\mathrm{m}$
$p^{\mathrm{near}}$	$0.98$
$p^{\mathrm{far}}$	$0.55$
$p_{\mathrm{o}}^{\mathrm{near}}$	$0.002$
$p_{\mathrm{o}}^{\mathrm{far}}$	$0.05$
${\sigma }_r^{\mathrm{near}}$	$0.2\mathrm{m}$
${\sigma }_r^{\mathrm{far}}$	$1.5\mathrm{m}$
${\sigma }_{\theta }^{\mathrm{near}}$	$1.0\circ$
${\sigma }_{\theta }^{\mathrm{far}}$	$6.0\circ$

State estimation in the post-processing was conducted using the same data described in the Experiments section. Five trials were performed.

Figure 17 shows the time-series station-referenced residual in simulation using the distance-based measurement model. Because positioning failures, measurement errors, and disturbances are more pronounced at long range, the residual is large immediately after the start, and the variability across trials is also large. However, the positioning results become more stable over time, and accordingly, the estimation results also stabilize; the final residual in the vicinity of the UAV-ST converges to 1–2 m. This indicates that even when approaching from a long distance, the estimation gradually converges, enabling the AUV to approach the vicinity of the UAV-ST with stable accuracy. Validation in real-world deep-water and long-range conditions is left for future work.

Figure 17.

Time series of the station-referenced residual between the estimated AUV position and the acoustic measurement in simulation using the distance-based measurement model.

Transition evaluation

This subsection evaluates the feasibility of transitioning from acoustic guidance to vision-based guidance in the pre-recovery phase by assessing whether the achieved terminal accuracy satisfies the visual acquisition conditions near the UAV-ST.

In this study, the approach performance in the pre-docking phase is evaluated using acoustic relative positioning. In the subsequent phase, a staged guidance scheme is planned, where the acoustic approach is followed by vision-based docking using optical markers. Moreover, prior work using the same AUV platform has demonstrated successful optical-marker docking to a hovering-type AUV underwater. ⁴³ Therefore, the key focus of this study is to guide the AUV into the vicinity of the UAV-ST and satisfy the marker acquisition conditions required for vision-based docking, after which the established optical-marker docking method can be applied.

Even if the UAV-ST is horizontally offset from the UAV nadir due to tether motion, the approach objective in this study is defined with respect to the UAV-ST itself. Therefore, a static offset from the UAV does not directly degrade the ability of the AUV to approach the UAV-ST. The relevant concern is time-varying tether motion, which can introduce additional geometric uncertainty in acoustic relative measurements. Although tether motion was not directly measured in the present trials, a design-oriented bound can be discussed.

For docking operations, maintaining the tether inclination within ${\theta }_{\max }=10\circ$ is considered a practical requirement. Methods to ensure $\theta <10\circ$ under wind and wave disturbances are left for future work. Assuming a representative tether length of $L=3$ m, the horizontal displacement is bounded by ${\delta }_{\max }=L\sin {\theta }_{\max }\approx 0.52$ m. For visual acquisition with a horizontal field of view of $80\circ$ , the lateral half-width at distance R is $w(R)=R\tan 40\circ$ . Thus, ${\delta }_{\max }$ remains small relative to the field-of-view margin. For example, $w(5\mathrm{m})\approx 4.2$ m.

A feasibility-based acquisition rate is evaluated using the distribution of terminal residuals and the camera field-of-view geometry. A trial is counted as visually acquirable at a distance R when $e+{\delta }_{\max }<w(R)$ , where $e=\sqrt{\mathrm{\Delta }{x}^2+\mathrm{\Delta }{y}^2}$ . Using the five-trial terminal residual examples, the fraction satisfying the condition is 5/5 at $R=5$ m, 4/5 at $R=4$ m, and 3/5 at $R=3$ m. These results quantitatively indicate that transitioning at 4 to 5 m provides sufficient geometric margin for visual acquisition. Since visibility can still be affected by turbidity and lighting, the vision detection and operational refinement are stated as future work.

Comparison with prior studies

This subsection compares the performance of the proposed method with prior work using the same evaluation metrics.

For performance comparison, several previous studies are referenced. Using the acoustic virtual long baseline (LBL) method, the AUV's positioning accuracy has been reported to be within 2 m, demonstrating consistently high performance. ⁴⁴ In addition, a representative DVL/INS-based approach can exhibit a final error on the order of several meters relative to the recovery station due to drift accumulation. ⁴⁵ Thus, its performance is primarily characterized by long-term drift rather than instantaneous accuracy. On the other hand, the proposed method aims to suppress the terminal station-referenced residual by positioning based on the recovery station, and achieves a terminal residual on the order of 1–2 m even without onboard INS/DVL, relying only on lower-accuracy navigation sensors. This comparison is made in terms of the final residual relative to the station and is not intended as a direct comparison of instantaneous positioning error.

Electromagnetic (EM)-guidance docking with sub-decimeter accuracy has also been reported, but this is achieved in the close-range final stage using a dedicated EM docking station with large coils. ⁴⁶ Accordingly, it is not directly comparable to the 1–2 m accuracy reported here, which corresponds to an acoustic-based approach. The proposed approach targets robust mid- to long-range guidance with minimal additional hardware, where performance is constrained by acoustic propagation effects such as multipath and sound-speed variability. For the close-range final docking stage, the system is intended to transition to a vision-based approach using an optical marker to obtain higher precision. As described above, the achieved final accuracy indicates that the AUV can be guided into the near-field region where optical localization becomes feasible, enabling a transition from an acoustic-based approach to vision-based docking.

Because prior studies differ in sensors, ranges, and ground-truth availability, an additional controlled quantitative comparison is provided by reprocessing the same sea-trial log under a conventional one-sided positioning configuration that uses only the AUV-side positioning updates. To emulate this configuration, state re-estimation was performed using only the AUV-side positioning measurements. To reduce the effect of filter initialization, the UAV-ST-side measurements were used only for the first three measurements and were disabled thereafter. Figure 18 shows the time series of the station-referenced residual between the estimated AUV position and the acoustic measurement for one-sided positioning. As a result, the median terminal residual exceeded 10 m, indicating that reaching the station vicinity is difficult under one-sided positioning. In addition, the feasibility of transitioning to vision-based localization at $R=5$ m was evaluated using the field-of-view condition together with the terminal residual distribution, and no successful cases were obtained in five trials. Because the UAV-ST-side updates provide information useful for velocity inference in addition to relative position, exploiting mutual positioning information stabilizes the estimation and improves approach performance. These results quantitatively demonstrate the benefit of mutual positioning. Based on these results, the proposed method using mutual positioning yields a terminal station-referenced residual that remains approximately within the 1–2 m, whereas one-sided positioning results in a terminal residual exceeding 10 m. The box plots also show different distributions, confirming that the proposed method substantially reduces the residual.

Figure 18.

Time series of the station-referenced residual between the estimated AUV position and the acoustic measurement for one-sided positioning.

Conclusion

This study developed an approach method that enables an AUV to autonomously approach a UAV-deployed recovery station (UAV-ST) in real sea environments. After the UAV deployed the UAV-ST, the AUV navigated autonomously and successfully approached the UAV-ST using acoustic positioning updates. In post-processing, the AUV's state was estimated from measurements of the acoustic positioning and onboard sensors. The station-referenced measurement–estimate residual was shown to remain within 1–2 m in the vicinity of the UAV-ST. In addition, scalability was examined through a simulation that introduced distance-dependent positioning success rates and measurement noises as a first-order (linear) approximation model. The results indicate that the proposed approach remains feasible under degraded measurement conditions. This study validates the pre-recovery approach phase. Future work will build on this approach to develop a docking method that enables fully automatic AUV recovery by the UAV.