Unified Underwater Communication Positioning Navigation and Timing Network System Design and Application

Abstract

The dynamic and heterogeneous nature of marine environments, combined with severely constrained communication and energy resources, presents distinct challenges in constructing underwater Communication, Positioning, Navigation, and Timing (CPNT) systems compared to terrestrial Positioning, Navigation, and Timing (PNT) architecture. To address the inherent limitations of conventional decoupled CPNT systems – including high costs and low efficiency in communication and energy utilization – this study aims to propose a unified underwater CPNT ($U^{2}CPNT$) system that coordinates multi-modal data and resource allocation, thereby optimizing CPNT service performance in harsh underwater conditions. In this study, Cramér-Rao Lower Bound (CRLB) formalization is applied to theoretically analyze the feasibility of $U^{2}CPNT$ system, and the design of $U^{2}CPNT$ system is presented to realize the integrated design of CPNT. To validate the system performance, a real $U^{2}CPNT$ system was built and sea trials were conducted. With $U^{2}CPNT$ architecture, the integrated CPNT service can be provided, the positioning error is lower, the positioning continuity has improved by 7.68%, the velocity estimation error is less than 1 m/s, making $U^{2}CPNT$ a potential solution for underwater CPNT service.

1. Introduction

With the rapid expansion of human living spaces and the demand for natural resources, ocean exploration is receiving growing attention [1,2]. Various types of equipment have been created and applied, significantly expediting the resource development process and also driving progress in related research. CPNT technologies are among the most critical and indispensable technologies needed for maritime activities.

The development of Global Navigation Satellite System (GNSS), including Beidou (BD), Global Positioning System (GPS), GLONASS, and Galileo, provides robust support for CPNT services for activities conducted above the ocean surface. However, the communication medium applied for terrestrial PNT (Positioning Navigation and Timing) application is electromagnetic waves, which rapidly attenuate underwater because of the conductivity and dielectric loss of water. However, water can efficiently transmit mechanical vibration energy, making acoustic waves, a kind of mechanical energy, currently the only option for medium and long distance underwater communication method. Due to the scarcity of available communication and positioning resources [3,4], as well as the absence of a unified standard for CPNT systems, function and equipment are often designed separately, leading to a waste of system resources and low system effectiveness.

With the objective of building a unified underwater CPNT system, we investigate the essential conditions for the underwater CPNT service. Real-time precise positioning is the basis of underwater operation and navigation application, and the timing service is a crucial guarantee for underwater collaborative operations. Specifically, an underwater communication network with a long range and high data transmission rate can efficiently transmit information. However, the underwater environment is intricate and presents several unavoidable challenges.

• Since the magnetic wave, the main information carrier of the current PNT system, is unable to propagate far in water because of energy absorption, scattering, and seawater conductivity [5,6], the traditional PNT system cannot work properly underwater. In addition, as a new application field, more systematic research and implementation of the underwater PNT system are needed.
• Sound, a mechanical wave, has been demonstrated to be the sole medium capable of propagating over long distances underwater [7]. Several issues are associated with the acoustic channel, including restricted bandwidth, prolonged latency, dynamic time-space properties, and significant Doppler effect [4].
• Due to the low communication rate, the design of CPNT signals presents a considerable challenge to maximize the use of communication resources.
• Assessment and performance boundary analysis for integrated multifunction acoustic network systems lack systematic theoretical support.
• Given the high costs of sea trials, most analyses are simulation-based, which poses difficulties in accessing experimental data from actual sea trials.

Based on the practical need for an underwater CPNT system and the aforementioned challenges, it is worthwhile to delve deeper into investigating the feasibility of a practical and efficient underwater CPNT system. In this paper, we are dedicated to developing a $U^{2}CPNT$ framework to fully leverage the limited underwater communication and energy resources to support the development of the underwater CPNT system. Several original research studies have been conducted in this paper, which are outlined below.

• The design of the unified system architecture for the underwater CPNT system has been carried out.
• A CPNT network performance analysis model based on the Cramér–Rao bound was established.
• The improved performance of the $U^{2}CPNT$ network system in CPNT utilizing the model designed above has been illustrated.
• The results of theoretical analysis, simulation, and sea trials are compared, confirming their effectiveness.

Following the idea stated above, research studies are conducted in this paper, and several contributions have been made. First, we examine the current research status of underwater CPNT network systems and contrast it with terrestrial PNT systems. Subsequently, we construct the theoretical model for CPNT network performance using the Cramér–Rao bound. In addition, simulations have been carried out to demonstrate the performance enhancement achieved through the integrated design of the CPNT system. Finally, practical sea trial data have been utilized to validate the consistency between theoretical predictions and simulation results.

The remainder of this paper is organized as follows. In Section 2, the related work of the CPNT system is investigated. In Section 3, the key challenges of the $U^{2}CPNT$ system are analyzed. Section 4 focuses on the overall design and systematic analysis of $U^{2}CPNT$. A case study is introduced in Section 5. Discussion and conclusions are discussed in the last two sections.

2. Related Work

The terrestrial PNT system predominantly uses GNSS, encompassing BDS, GPS, GLONASS, and GALILEO, to provide PNT services, as shown in Figure 1. Ground or aerial vehicles receive satellite messages that include information on time and satellite position. Then, vehicles can calculate their own position with more than four messages using the range measurement principle, allowing for the calibration of local time and the realization of navigation applications.

Within the NASA Moon-to-Mars (M2M) architecture, the sub-architecture for CPNT details the specific systems and infrastructure required to meet the M2M objectives [8]. The CPNT sub-architecture scales to support long-term science, exploration, and industrial needs. Although this is not a CPNT based on underwater acoustic networks, it also shows the importance of CPNT and has good results.

At first, communication [9], positioning [10], navigation [11], and timing [12] were studied separately. Later, PNT appeared, which considered positioning, navigation, and timing together. Giordano [13] studied the Lunar Pathfinder PNT experiment and the Moonlight Navigation Service, analyzing the future of lunar positioning, navigation, and timing technology.

However, PNT services rely on GNSS. When GNSS is interrupted, PNT services are not available. So, along came APNT. Distance measurement equipment (DME) is receiving renewed interest due to its ability to support future aviation navigation and surveillance needs. It is one of the main technologies that is being examined by the FAA Alternative Position Navigation and Timing (APNT) [14] program to support the need to provide an alternative to GNSS in a NextGen airspace. Lo [15] has been examining means to improve DME published accuracy, and examines two of the passive ranging systems being studied for APNT [16]. Han [17] investigates APNT solutions for aerial vehicles for which highly standardized PNT services are required to ensure secure and safe transportation, including solutions proposed by the FAA in North America.

However, currently CPNT services for deep-sea vehicles are provided by separate communication, positioning, and navigation systems, as well as separate synchronous clocks (atomic clocks). In this paper, a new design method and operating mode of CPNT [18] is proposed to overcome the inherent flaws of the current communication/positioning/navigation modes of deep-sea vehicles; meet the actual demands of deep-sea vehicles in real time; achieve high update rates, low power consumption, and high precision positioning and navigation; and be combined with current development trends.

In addition, underwater communication involves not only point-to-point communication, but also networking. Acoustic communication networking is a key technology. Its core technologies mainly include network topology design, efficient communication protocols [19], and energy management strategies [20]. Common underwater acoustic network topologies include chain, cluster, and cellular networks [21]. Traditional communication protocols often cannot be directly applied to underwater acoustic networks. Appropriate protocols need to be developed to enhance communication efficiency and reliability. Since underwater nodes have limited power and are difficult to recharge, effective energy management strategies are essential to prolong the network’s lifespan. Ref. [22] designed the UW-WiFi network architecture to solve the problem of underwater acoustic networking with limited coverage range and number of nodes. Ref. [23] developed an MAC protocol for this acoustic network to address the issue of various access requirements of different task nodes in channel resources. Ref. [24] designed an underwater distributed and adaptive resource management framework to maximizes network capacity by supporting an increased number of communications in the network. However, current network architectures, protocols, and resource management strategies are designed primarily for communication and networking purposes, lacking inherent support for PNT functionalities, and cannot be applied directly for the $U^{2}CPNT$ system.

Collectively, the previous work has catalyzed significant advances in underwater CPNT services. However, current underwater CPNT services are not integrated, which is quite inconsistent with the harsh underwater environment. We need a multipoint, long-term, wide range of CPNT services, and from the theory, model, simulation, sea trial and other aspects of systematic analysis. To solve this problem, we study $U^{2}CPNT$ with high maturity to achieve a unified underwater CPNT. In the next section, we will investigate the key technical challenges to facilitate better design of $U^{2}CPNT$ system.

3. Key Challenges

The underwater CPNT is a system that provides the PNT service on the backbone of the underwater network, thus the key technologies involved in underwater communication, networking, localization, and integrated design need to be developed. In this part, we will detail the challenges of each of the aforementioned technologies.

3.1. Underwater Communication

If we category the underwater communication method by potential transmission media, there are mainly four categories: underwater acoustic, optical, electromagnetic wave, and wired communication [25]. However, the underwater acoustic communication performance is quite different for radio communication, as described in

Table 1. Comparison of acoustic vs. radio communication in underwater environment.

Index	Acoustic Communication	Radio Wave Communication
Propagation Speed [31]	1500 m/s	3 × 108 m/s
Drawbacks [32]	Doppler, latency and shadow zones	High attenuation
Reliable Communication Distance [32]	Kilometers	Few meters
Energy Efficiency	low energy-efficiency (≈100 bits/Joule for several km) [33]	≈9850 bits/Joule for 10 m range [31]
Data Rate [32]	1.5 to 50 kbps (@0.5 km); 0.6 to 3.0 kbps (@28–120 km)	1 to 10 Mbps (@1–2 m); 50 to 100 bps (@200 m)
Bandwidth	100 kHz (<1 kHz for very long distance, >100 kHz for very short distance) [34]	3–30 MHz [35]

. Due to the high attenuation, the acoustic is the fundamental way of underwater long-range wireless communication [26,27]. For optical and magnetic induction, it is mainly used for short-range communication [28,29]. Although they suffer high attenuation and are sensitive to underwater environment, a significant bandwidth can be utilized compared to acoustic communication [30]. Ignoring the cost and effort for the deployment of an underwater cable, wired communication is the most stable way to provide high-speed communication.

To design and build an underwater CPNT system, medium and long distance wireless communication is the fundamental condition, which makes the acoustic wave the best choice. A higher data rate can ensure that sufficient effective information is transmitted, helping to increase positioning performance and service quality, which makes it an important point that should be considered in system design.

3.2. Localization

Localization is the key function of the CPNT system [36]. However, the most appropriate method for underwater application is acoustic localization considering the demand for long distance positioning [37,38,39]. For the localization service, it should be accurate, robust, and have an acceptable update frequency [40,41,42]. For traditional underwater localization, the system is designed only for localization, which contains little additional information. However, communication service can help transmit depth, velocity [43], attitude, and high precision time stamp, which will greatly improve positioning accuracy [44]. Based on the analysis above, the localization calculation should take advantage of as much information as possible.

3.3. Networking

In the context of the CPNT application, a flexible and reliable network architecture is needed that can ensure efficient end-to-end data delivery [45]. Tailed network protocols for underwater applications are essential for different functionalities under different topological structures. Following the classical terrestrial network architecture, we segment the network into layered structures. However, it is not suitable for underwater networking due to the instinctive difference between radio and acoustic communications [46]. A customized architecture is needed, and each layer’s protocols face unique challenges dictated by the specified requirements.

Efficiency in coordinating network nodes for channel occupancy and conflict avoidance is crucial for the MAC (Medium Access Control) layer due to the narrow band of acoustic channel [7]. At the network layer, it is crucial to consider the high delay dynamic topology [47], ensuring that the data can be transmitted to the destination node with minimal overhead. With respect to the transport layer, particular attention should be paid to rational congestion control and effective retransmission mechanisms [48]. For the application layer, it is important to balance efficiency, reliability, and energy consumption, while embracing cross-layer design and new technologies [49,50].

3.4. Integrated Design

The Underwater CPNT network aims to provide integrated CPNT services [51]. Among these functions, communication service is a prerequisite for positioning, navigation, and timing. The position service provides location information for underwater vehicles, the navigation service plans the route from the current location to the destination, and the timing is essential to maintain temporal and spatial consistency. The network is the basic support for the realization of a large-scale underwater CPNT service.

The aforementioned challenges reveal fundamental limitations in existing CPNT approaches. To overcome these barriers, such as software and hardware redundancy, as well as acoustic, electric, and magnetic incompatibility, which are mostly caused by separated design and implementation. We proposed an integrated design of the CPNT system, which can improve bandwidth usage efficiency and acoustic compatibility, reduce development cost, equipment size and power consumption.

4. Overall Design and System Analysis

This section is structured as three components: we begin by detailing the architectural blueprint of $U^{2}CPNT$; then the theoretical analysis will be performed to illustrate the advantages of $U^{2}CPNT$; finally, the implementation of hardware-software co-design will be introduced.

4.1. System Overall Design

The main idea is to use dive buoys, floating buoys, or unmanned boat platforms to establish an integrated underwater information tube, providing CPNT functions, combining acoustic communication with networking and positioning features, as shown in Figure 2.

There mainly exist two application modes for $U^{2}CPNT$ scenarios, cooperative mode and non-cooperative mode. For the cooperative mode, the underwater targets carry a beacon and work in coordination with the positioning system to achieve location by actively transmitting signals or responding to external signals. In non-cooperative mode, the underwater targets will be located mainly by passive acoustic detection. Due to the high accuracy, real-time performance, and reliability of cooperative positioning, its application demands in civilian fields have become increasingly widespread. In this study, we will focus on the cooperative mode; a detailed description is as follows.

In cooperative mode, the underwater target carries a beacon terminal, which is a cooperative target.

• During the positioning process, as the underwater targets pass through the deployment area, the subsurface buoys will receive beacon signals and transmit the signal to the surface control center. If the signal is received by more than four buoys with the same time label, the surface control center will be able to calculate the target’s position and transmit it to underwater vehicles;
• The positioning calculation can be performed on underwater targets if they possess the position information of the buoys;
• During the communication process, both upstream and downstream information flow through the link alongside with the positioning signal between the surface control center and underwater moving targets.

Following the analysis of $U^{2}CPNT$ scenarios, we propose the following definition, system composition, system function and other elements of $U^{2}CPNT$ system.

• Definition
  $U^{2}CPNT$ is an underwater network system that is able to provide an integrated CPNT service for underwater fixed or mobile nodes.
• System Composition
  A $U^{2}CPNT$ system consists of subsurface buoys (base station), moving targets (beacons), and a surface control center.
• System Functions
  A $U^{2}CPNT$ system possesses the following functions:
  • Providing information transmission service through underwater acoustic communication network;
  • Providing positioning and tracking service for underwater moving targets;
  • Providing position and time calibration service for underwater equipment.
• System Support
  To ensure the reliability and performance of the $U^{2}CPNT$ system, several supporting measures are needed:
  • Subsurface buoy position calibration during deployment and working phase;
  • Subsurface buoy status monitoring during whole system lifetime.

System Advantages

Compared with the traditional system, in which the communication and positioning function is designed and implemented separately, $U^{2}CPNT$ is a unified solution with networking as its core characteristics, where each layer is designed with the focus on serving CPNT as its characteristic.

Within this system design framework, the system is developed with a focus on the integration needs of communication, positioning, and networking software and hardware. The system offers several advantages: ease of maintenance, cost-effectiveness, robust scalability, extensive coverage, and high level of concealment.

4.2. Theoretical Analysis

4.2.1. Overview

The construction of a unified CPNT network framework enables the optimal utilization of software and hardware resources, thereby providing a comprehensive underwater CPNT service.

4.2.2. Theoretical Basis Derivation

To analyze feasibility of this approach. We define an overall gain function to conduction multi-objective optimization, using CRLB to construct a positioning accuracy optimization function composed of communication, timing, and some other factors. In addition to common influence factors such as positioning distance, beacon quantity, existence of communication, and timing, it can help reduce deviation to a certain degree.

Given that there exists 1 positioning beacon with its location $P={[x,y,z]}^T$, and N positioning base stations, whose location $r_i={[x_i,y_i,z_i]}^T$, with $i=1,2,\dots ,N$. If we know the arrival time $t_i$ and $t_j$ of the positioning signal $i_{th}$ and $j_{th}$, the arrival time difference can be calculated,

$${\Delta }_{i,j}=t_i-t_j={\displaystyle \frac{d_i-d_j}{v_s}},$$

(1)

$v_s$ is the propagation speed of sound in water, $d_i$ and $d_j$ is the distance between the beacon and the base stations, which can be represented by

$$d_i=\parallel P-r_i\parallel =\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2},$$

(2)

$\parallel ·\parallel$ represents Euclidean distance, with more than 3 distance between base stations and beacon, the location P of the beacon can be solved by algorithms such as non-linear least squares.

To analyze the influences of positioning accuracy, we define the utility function $U\left(P\right)=Tr\left(CRLB\right(P\left)\right)$, which is the mean square deviation of position estimation, to further explore how to minimize $U\left(P\right)$. And $CRLB\left(P\right)$ is the lower bound of Cramér-Rao, with $Tr\left(·\right)$ the trace. Assuming that the variance of measured noise is ${\sigma }^2$, and communication rate R, reliability $Rel$, communication distance D and time accuracy T will be taken into account.

• Communication Rate R
  Acoustic communication is the foundation for underwater positioning, and a higher communication rate allows more aided positioning information to be transmitted, such as the depth of the platform where the beacon is installed, speed, acceleration, attitude and some other parameters to help improve the accuracy of position estimation. Assuming that the higher the communication rate R, the lower the variance of measured noise ${\sigma }^2$ is:

  $${\sigma }^2\propto {\displaystyle \frac{1}{R}}$$

  (3)
• Reliability $Rel$
  Reliability will affect the packet loss rate and number of retransmissions, which will influence the effectiveness and accuracy of the measurement. Assuming that the higher the reliability, the lower the variance of measured noise ${\sigma }^2$ is:

  $${\sigma }^2\propto {\displaystyle \frac{1}{Rel}}$$

  (4)
• Communication Distance D
  As communication distance increases, signal attenuation and noise increase, and multi-path effect is more obvious, which will affect measurement accuracy. Assuming that the measurement noise is proportional to communication distance:

  $${\sigma }^2\propto D$$

  (5)
• Timing Accuracy T
  Timing service will directly affect the accuracy of measured time difference. And the higher the accuracy, the lower the variance of measured noise:

  $${\sigma }^2\propto T$$

  (6)
  According to the above analysis, the variance of measured noise can be represented as:

  $${\sigma }^2=\alpha {\displaystyle \frac{D}{R·Rel·T}}$$

  (7)
  $\alpha$ is the proportional coefficient.
  We utilize Fisher Information Matrix (FIM) to calculate CRLB, and elements of FIM of TDOA positioning system can be represented as:

  $${\left[\mathbf{I}\left(\mathbf{P}\right)\right]}_{mn}=\sum _{i<j}{\displaystyle \frac{1}{{\sigma }^2}}\left({\displaystyle \frac{\partial \Delta t_{ij}}{\partial p_m}}\right)\left({\displaystyle \frac{\partial \Delta t_{ij}}{\partial p_n}}\right)$$

  (8)
  With ${\sigma }^2$ substituted, we obtain

  $${\left[\mathbf{I}\left(\mathbf{P}\right)\right]}_{mn}=\sum _{i<j}{\displaystyle \frac{R·Rel·T}{\alpha D}}\left({\displaystyle \frac{\partial \Delta t_{ij}}{\partial p_m}}\right)\left({\displaystyle \frac{\partial \Delta t_{ij}}{\partial p_n}}\right)$$

  (9)

The above analysis, which is based on CRLB, provides a lower bound of the parameter estimation variance. We can see that along with an increase in communication rate, reliability, and timing accuracy, measured noise can be reduced. That means that combining additional information from other services will improve the performance of each service. In other words, by integrating CPNT with more information, positioning error can be reduced, and positioning and navigation performance will be further improved.

4.3. System Implementation

In this part, a guideline for the $U^{2}CPNT$ system will be introduced, including the design of the system framework, the design of the integrated signal, and the design of the integrated hardware.

4.3.1. System Framework Design

For cooperative positioning, the position calculation can be performed on underwater vehicles, as well as in the surface control center. If the calculation is carried out on underwater vehicles, additional hardware and software requirements are needed, such as the high-precision clock and dedicated calculation resources. Meanwhile, base stations will consume more energy due to the need for continuous signal transmission, which also exacerbates challenges in mitigating interference. In order to improve the system feasibility for all kinds of underwater platforms, reduce base station energy consumption, and acoustic interference, we put the position calculation system in the surface control center.

Basically, the $U^{2}CPNT$ system combines long baseline positioning and underwater acoustic communication principles by deploying five or more floating/submersible buoys or unmanned boat base stations, as shown in Figure 3, which is a minimum system. These stations, with known absolute positions obtained through the RTK Beidou/GPS systems for clock synchronization, receive periodic sound signals from acoustic beacons on underwater submersibles. By analyzing time variances and geographic data from base stations, the system accurately determines submersible positions and transmits this information to the surface/shore command center via wireless or mobile networks.

For large-area CPNT application, communication and networking are essential functions to ensure reliable information transmission. Acoustic beacons transmit submersible status data to buoy base stations, which relay the data to the command center. After calculating, the surface/shore-based command center interface shows the position, trajectory, depth, and status of underwater submersibles. The shore-based control center can also send control commands to UUVs. The system framework is shown Figure 4.

4.3.2. Integrated Signal Design

For the underwater CPNT system, each service is performed by acoustic communication. However, the separated realization, which is the current practice, will increase the strain on limited energy and communications resources. To conduct the integrated CPNT service, the key point is to implement the signal structure with the communication and positioning fusion design. With the positioning signal embedded, long baseline acoustic positioning technology can be enhanced. With the application of multi-user reliable transmission networking technology, the fusion of underwater acoustic communication, positioning, and networking can be achieved.

We take OFDM as the basic communication model, whose data rate is higher. Typically, a integrated $U^{2}CPNT$ signal structure is shown in Figure 5.

There are three components in the signal: dual-HFM, time slots, and CP/ZP-OFDM. Each part of the frame serves for positioning and communication, whose function is described in

Table 2. Function description of each part in signal frame.

	Communication	Positioning
Dual-HFM	Signal Detection, Synchronization	Estimation of Signal Arrival Times
CP-OFDM	Delivery of Communication Aiding Information	Delivery of Positioning Aiding Information
ZP-OFDM	Carrying Communication Data Payloads	Carrying Node Position Information

.

From the point of view of system optimization, the advantages of integrating communication, positioning, and networking are capable of enhancing acoustic compatibility, reducing costs, minimizing size and power usage, increasing bandwidth efficiency, and strengthening information transmission and equipment control capabilities.

4.3.3. Integrated Hardware and Software Design

For an underwater system, communication and energy are two primary challenges. Separated hardware and software design will increase energy consumption, cause acoustic and electromagnetic interference, limiting global service quality. To solve this problem, an integrated design is essential, which means that the hardware has to satisfy each demand of CPNT.

With the integrated signal, the information needed for the CPNT service can be well transmitted. In this part, we discuss the integrated hardware and software design. Since the length of the integrated signal is longer than the positioning signal, the communication hardware can also be used for positioning. That means that common acoustic modem hardware can be reused for communication, positioning, and navigation. Meanwhile, considering the need for timing, a high-precision clock module is added and the entire architecture is shown in Figure 6.

It is important to conduct an integrated software design to realize the management and coordination of energy and communication resources. The $U^{2}CPNT$ software typically consists of the following components: user space and kernel space in the embedded Linux system, application modules, and functional modules in the DSP system. And data exchange between ARM and DSP processors is achieved through inter-core communication, as shown in Figure 7. This architecture enables coordinated hardware-software interaction between ARM and DSP while maintaining efficient power utilization and real-time communication, positioning, and networking capabilities.

4.3.4. Network Management

For a large-scale CPNT system, a network management system is essential. The acoustic channel is spatial-temporal varying, and the communication and energy resource are extremely limited. How to choose a reliable transmission protocol, determine the best route, mac protocol, and communication model according to the environment and system status is the key challenge in network design.

The terrestrial network framework follows the OSI architecture, which consists of 7 layers, providing a general principle for the current complex and extensive network system. For an underwater networking system, an agile and adaptive network protocol stack is a prerequisite for efficient networking. SeaLinx is a multi-instance and cross-layer optimization framework [46,52], as shown in Figure 8. In this framework, the core checks the communication and positioning requirements, the position of the nodes, power consumption, calculation, and storage load, and then selects the appropriate communication model and network protocol, which makes it an appropriate architecture for underwater large-scale networking applications. We designed the network management framework for $U^{2}CPNT$ based on this architecture.

In this section, we initially introduce the overall design and then perform the theoretical analysis to support the feasibility of $U^{2}CPNT$. With the system implementation introduced, the case study will be presented in the following section.

5. Case Study

In this section, we provide one case study of the CPNT system that is designed based on the principle proposed in the previous sections. Experiments are conducted for the system and the experience gained is documented.

5.1. Architecture and Implementation of the System

Based on the principle proposed, this system comprise three roles: User Equipment (UE), Base Station (BS) and Resolve Center (RC). Their relationship is depicted in Figure 9. The UE is carried by the underwater user node. Whenever UE has requirements for localization, communication, or timing service, it will establish a connection with BS. If the requirement is communication, the messages of UE will be processed and transmitted by BS under the control of the network protocol. And if the localization requirement is received, the surrounded BS will measure the arrival time of the signal, also known as TOA. These measurements will be used for the fusion in RC to resolve a position result for the user node. In other words, the functionality of RC may be assigned to a specific central BS or a shore-based center, according to the design of the system.

Based on the system architecture, a representative implementation of the proposed system is schematically illustrated in Figure 10. Now we detail the configuration of each component. As illustrated, BS can be deployed in two configurations: surface buoy or submerged buoy. The surface buoy configuration, unlike its submerged counterpart, integrates two additional devices: a GNSS receiver and a radio network interface. The GNSS receiver provides the position of the base station in real time, while the radio network module is dedicated to exchange messages between BS and shore-based center. However, in the submerged configuration, the GNSS receiver and radio network module are omitted due to the ineffective penetration of radio signals through water. UE integrete a pressure sensor in its configuration.This sensor provides depth measurements, allowing RC to transform the 3-dimensional positioning problem into 2-dimensional, thus simplifying the resolution process.

Given the above implementation, we will now provide the results of experiments conducted for the system in the following.

5.2. System Brief

The experiments were conducted in Dapeng Bay, Shenzhen, China, and the experimental configuration closely matched that described in [53].

To reduce the cost of sea trials, instead of using equipment such as AUVs or ROVs as UE, an alternative approach was adopted: A beacon was mounted on a steel rod, which was fixed on the port side of a boat and lowered to a fixed depth of 3 m, as illustrated in Figure 11a,b. The beacon was towed to move as the boat maneuvered. Furthermore, a GNSS receiver was installed at the top of the rod above the water surface to obtain the true geodetic coordinates and velocity of the beacon, serving as a benchmark to validate the performance of the positioning and velocity measurement.

During the sea trials, four BSs were deployed in a rectangular configuration, as illustrated in Figure 12, with their precise coordinates annotated in the figure. Upon commencement of the experiment, the beacon-towed boat followed a random-walk trajectory, the details of which were recorded via an onboard GNSS receiver and are presented in Figure 12b.

For joint communication and localization, OFDM was adopted as the signal frame of the physical layer, the structure of which is illustrated in Figure 13. The dual-HFM are dedicated for signal detection and sychronization, the CP-OFDM block acts as the preamble which facilitates the parameters estimation and contains information both for decoding, and the ZP-OFDM blocks contain user messages. In the above text, we provide a description related to communication. In terms of localization, along with the dual-HFM detection process, the TOA could be estimated simultaneously. The TOA measurements will then be transmitted to RC, and the localization algorithm will produce a result with these measurements as input. For clarity, the specific algorithmic procedures are omitted here. Readers could refer to the work by Liu et al. for further details [53].

Other details of the experiments are listed

Table 3. Signal parameters.

Parameter	Value
Carrier frequency	24 kHz
Bandwidth	6 kHz
Sampling rate	96 kHz
$D_H$	37 ms
$G_H$	5.3 ms
$D_C$	290.6 ms
$D_Z$	170.6 ms
$G_Z$	150 ms
(CP-/ZP-OFDM) Number of sub-carriers	1024/1024
(CP-/ZP-OFDM) Number of data-carriers	224/672
(CP-/ZP-OFDM) Number of pilots	672/256
(CP-/ZP-OFDM) Number of null sub-carriers	128/96

. The depth of the water in the testing area was approximately 10 m. Based on the output of the sound velocity profile, the variation in the sound speed from the surface to the seabed was limited; thus, an effective sound speed of 1530.37 m/s was selected and provided as input to the method.

5.3. Experiment Results

5.3.1. Time Synchronization

For underwater systems, the timing source is usually a crystal oscillator, which has low accuracy and tends to drift over time. However, it is important to maintain the precise reference time for underwater CPNT service. In this part, we simulate the time synchronization using Matlab and assess the performance of localization with and without time service to investigate the influence of the timing service. We evaluated the localization error with varying levels of timing accuracy.

Figure 14 and Figure 15 present the localization results under timing error standard deviations of ${\sigma }_t$ = 1 × 10⁻³ and ${\sigma }_t$ = 1 × 10⁻⁴, respectively. The corresponding statistical analysis is provided in

Table 4. Statisitcs for localization results.

${\mathit{\sigma }}_{\mathit{t}}$	Mean (w/o Skew)	Variance (w/o Skew)	Mean (with Skew)	Variance (with Skew)
1 × 10−3	2.361	0.490	2.764	1.671
1 × 10−4	2.361	0.490	2.362	0.501

. As evidenced by the tabulated and graphical results, the mean and variance of localization errors exhibit systematic differences between time-synchronized and non-synchronized cases across varying ${\sigma }_t$ levels. While these discrepancies become less pronounced at lower timing error magnitudes (${\sigma }_t$ = 1 × 10⁻⁴), the statistical analysis still reveals measurable performance gaps.

Since the positioning method we adopted is TDOA, it is reasonable that it is not sensitive to the base station time. However, time synchronization services consistently improve the localization accuracy, even under different timing uncertainty conditions, and we can see that with less clock skew from the positioning result, the estimated trajectory will be more precise and the localization error will be significantly lower.

5.3.2. Depth Information Transmission

Positioning is inherently a 3-dimensional problem, but is often simplified to a 2-dimensional solution for underwater positioning in practice. In the experiment, we investigate the benefit brought about by depth information, supported by a communication service.

With depth information, the positioning problem can be reduced to 2D calculation, and detailed work can be referred in [53]. In addition, it’s useful to increase the positioning continuity. For traditional TDOA positioning, 4 or more beacons are needed. When the number of beacon information received is less than 3, the beacon location can not be calculated. With depth information, the position can still be resolved. During this experiment, 729 positioning points are obtained, and among which 52 points are calculated by 3 points, improving the positioning continuity by 7.68%. The detailed information is shown in

Table 5. Positioning Continuity with Depth.

Total Points	3 Points Positioning	4 Points Positioning	Continuity Enhancement
729	677	52	7.68%

.

5.3.3. Velocity Estimation

Positioning and velocity are two important parameters for the navigation application. Positioning accuracy has been discussed, and velocity estimation will be investigated in this part. We take the calculated velocity and analyze the angle error and magnitude error. To better illustrate the results, reduce the noise and smooth out abrupt changes in the signal, we applied a smoothing filter (Savitzky-Golay), and the results are shown in Figure 16.

From the figures, we can clearly see that the magnitude error is less than 1 m/s, which is sufficiently accurate. Meanwhile, the maximum value of angle error is not more than 30 degrees. It is reasonable since no additional angle measurement method has been implemented. However, the results show the navigation capability of our system.

6. Discussion

From the above results, the conclusion can be reached that, with this unified architecture, hardware and software design, the system can provide integrated CPNT service.

This paper presents a theoretical and experimental study of the integrated underwater CPNT system, and the concept of $U^{2}CPNT$. In general, the concept $U^{2}CPNT$ provides a general solution for CPNT service in an underwater environment. This scope of this contribution was to introduce the Cramér–Rao bound method to analyze the advantage of integrated CPNT system.

We concluded the content and created a table to better compare our results with those of previous studies in

Table 6. Comparison with relative studies.

	Communication	Positioning	Navigation	Timing	Networking	System Implementation
$U^{2}CPNT$	✓	✓	✓	✓	✓	✓
Underwater acoustic sensor networks [9]	✓	✓				✓
Underwater localization [10]		✓				✓
Subsea navigation technologies [11]			✓			✓
Underwater timing techniques [12]				✓		✓
PNT and Moonlight navigation [13]		✓	✓	✓		✓
APNT [14,15,16,17]		✓	✓	✓		✓
Integration of CPNT for deep-sea vehicles [18]	✓	✓	✓	✓
Adaptive Pipeline MAC Protocol [19]	✓				✓	✓
An on-demand scheduling-based MAC protocol [23]	✓				✓	✓

. It should be noted that the underwater CPNT system is quite different from the terrestrial PNT system because of the difference between the sound wave and the magnetic wave. We must also realize the importance of communication, networking, and resource management, as communication and energy resources are so precious to the underwater system.

However, one limitation of these methods is that the theoretical analysis is qualitative demonstration. Despite its preliminary character, this study can clearly indicate that this $U^{2}CPNT$ will improve the performance of separated CPNT service according sea trial results.

One important future direction of $U^{2}CPNT$ research is investigate deeply the influence factors of each service to strengthen the theoretical analysis. Another one is to study the different deployment strategies according different nodes characteristics and task demands.

The architecture design and sea trial results will hopefully serve as useful feedback information for improvements for underwater CPNT research work.

7. Conclusions

In this paper, we investigate the design and application of underwater CPNT by constructing a $U^{2}CPNT$ network system to address the challenges caused by the harsh underwater environment. We designed the architecture $U^{2}CPNT$, conducted theoretical analysis, constructed a real system and carried out sea trials, demonstrating the advantages and promising potentials of the $U^{2}CPNT$ system.

• The theoretical analysis based on the Cramér-Rao bound illustrates the feasibility of the unified architecture, demonstrating that, along with an increase in communication rate, reliability, and timing accuracy, measured noise can be reduced.
• The integrated design combines the CPNT service together, while it can effectively reduce hardware and software redundancy. A real system was constructed and the results of the sea trial indicate that the implemented system can provide an integrated CPNT service under the designed $U^{2}CPNT$ framework.
• We investigate the key performance parameters of positioning and navigation. We evaluated the localization error under two distinct timing drift conditions, with variance 1.671 when ${\sigma }_d$ equals to 1 × 10⁻³ and variance 0.501 for 1 × 10⁻⁴ respectively. The results reveal that larger localization errors are primarily induced by more significant timing errors. We take the depth information transmission as an application of communication, and realize the calculation of position with 3 beacons, improving the positioning continuity by 7.68%. For velocity estimation, which is an important parameter in navigation service, the velocity estimation error is less than 1 m/s, with angle error less than 30°, proving the navigation capability of our system.

This study demonstrates that the proposed $U^{2}CPNT$ architecture establishes a scalable framework for integrated underwater CPNT services. Although our results validate the core design principles, further research on different CPNT models and algorithms can be carried out. Meanwhile, it was observed that the appropriate design of the signal structure and the intelligent deployment algorithm are also important for the system performance and further optimization of the system, which can be valuable work in the future.