Enabling Cooperative Autonomy in UUV Clusters: A Survey of Robust State Estimation and Information Fusion Techniques

Highlights

What are the main findings?

• Our quantitative analysis reveals a fundamental trade-off in cooperative navigation: batch optimization methods like FGO provide the highest accuracy at a significant computational cost, while robust filters like MCC-KF offer resilience to non-Gaussian noise with much greater efficiency but are prone to long-term drift.
• A critical review of intelligent strategies (e.g., DRL, Semantic Communication) and advanced navigation techniques shows that while conceptually powerful, their practical deployment is currently hindered by specific, unresolved challenges such as the sim-to-real gap, hyperparameter instability, and the lack of standardized underwater datasets.

What is the implication of the main finding?

• The key implication is that the optimal algorithm choice is a mission-specific engineering decision, not a one-size-fits-all solution; this paper provides the first data-driven framework (via our quantitative comparison) to guide researchers and engineers in making this critical trade-off between accuracy and resource constraints.
• This work implies that future research should prioritize the specific, practical bottlenecks identified in this review, and our data-driven roadmap provides concrete, actionable research questions to accelerate the transition of these advanced technologies from theory to robust, real-world application in autonomous underwater systems.

Abstract

Cooperative navigation is a fundamental enabling technology for unlocking the full potential of Unmanned Underwater Vehicle (UUV) clusters in GNSS-denied environments. However, the severe constraints of the underwater acoustic channel, such as high latency, low bandwidth, and non-Gaussian noise, pose significant challenges to designing robust and efficient state estimation and information fusion algorithms. While numerous surveys have cataloged the available techniques, they have remained largely descriptive, lacking a rigorous, quantitative comparison of their performance trade-offs under realistic conditions. This paper provides a comprehensive and critical review that moves beyond qualitative descriptions to establish a novel quantitative comparison framework. Through a standardized benchmark scenario, we provide the first data-driven, comparative analysis of key frontier algorithms—from recursive filters like the Maximum Correntropy Kalman Filter (MCC-KF) to batch optimization methods like Factor Graph Optimization (FGO)—evaluating them across critical metrics including accuracy, computational complexity, communication load, and robustness. Our results empirically reveal the fundamental performance gaps and trade-offs, offering actionable insights for system design. Furthermore, this paper provides in-depth technical analyses of advanced topics, including distributed fusion architectures, intelligent strategies like Deep Reinforcement Learning (DRL), and the unique challenges of navigating in extreme environments such as the polar regions. Finally, leveraging the insights derived from our quantitative analysis, we propose a structured, data-driven research roadmap to systematically guide future investigations in this critical domain.

1. Introduction

1.1. Critical Role of Sensor Fusion in Cooperative Navigation

Achieving robust autonomy and enabling complex cooperative behaviors in modern unmanned systems, from self-driving cars to UAV clusters, are primary research goals. In the most challenging operational domains—the underwater environment—these goals are pushed to their absolute limits by the underlying problem of robust state estimation for cooperative Unmanned Underwater Vehicle (UUV) clusters. While a single UUV is significantly limited in its operational efficiency, robustness, and data resolution for wide-area missions, a cooperative cluster of UUVs can overcome these inherent limitations [1]. However, the very foundation of this cooperation—the ability for vehicles to share sensor data and fuse it into a coherent navigational picture—is severely undermined by the underwater environment. As noted by Saeed et al. [2], the acoustic communication channels that UUVs rely on are not only prone to security threats like jamming and spoofing but are also fundamentally constrained by high latency, low bandwidth, and other non-ideal characteristics. Therefore, developing robust information fusion and state estimation algorithms that can function effectively despite these extreme sensor and communication challenges is not just a strategic need for advancing marine technology but a fundamental problem in the field of sensor fusion itself.

1.2. Motivation and Challenges

The primary motivation for this field stems from a paradigm shift from mono to cluster systems. To break through the bottleneck of monolithic systems, the research has shifted to clusters or swarms consisting of multiple UUVs [3], which brings revolutionary advantages, including mission sharing, enhanced distributed sensing, and improved navigation accuracy through mutual observation [4,5]. However, this cooperation is entirely dependent on overcoming the ubiquitous constraints of underwater acoustic channels, which is the core challenge of the entire field. The Underwater Acoustic Communication (UAC) channel suffers from severe physical limitations [6], including extreme propagation delays (acoustic waves propagate at about 1500 m/s), minimal bandwidth (typically a few kbps), and high sensitivity to multipath propagation and environmental noise.

Together, these characteristics lead to significant delays, packet loss, and frequent link interruptions [7], which constitute fundamental bottlenecks for cluster collaboration. As emphasized by the Office of Naval Research (ONR) [8], these constraints make traditional centralized fusion architectures impractical, creating an urgent need for robust, scalable, and delay-tolerant distributed methods [9]. Furthermore, the complex underwater environment results in sensor measurements with non-Gaussian, heavy-tailed noise, challenging traditional filtering algorithms based on the Gaussian assumption, highlighting that the core of the solution lies in distributed Cooperative Navigation (CN).

Figure 1 visually illustrates the system-level challenges faced by UUV clusters in collaborative navigation. As the only feasible means of underwater long-range communication, acoustic communication inherently suffers from high latency, low bandwidth, and high packet loss rates, which constitute fundamental bottlenecks for cluster collaboration. These unstable communication links not only cause delays and incomplete transmission of information between nodes but also render traditional centralized fusion architectures impractical. Additionally, the complex multipath effects and time-varying noise in the underwater environment directly result in sensor measurement data exhibiting non-Gaussian characteristics, further challenging traditional filtering algorithms based on the Gaussian assumption.

1.3. Overview of Algorithmic Approaches

The research community has dedicated considerable effort to overcoming these challenges, resulting in a rich and diverse landscape of state estimation and information fusion algorithms. These techniques span a wide spectrum, from adaptations of classical Bayesian filtering methods (e.g., Extended Kalman Filter, Unscented Kalman Filter) [10], to more advanced approaches based on robust statistics (e.g., M-estimation, MCC) [11], information theory, and graph-based optimization (e.g., Factor Graph Optimization) [12]. These methods are often integrated within various network architectures, ranging from centralized to fully decentralized schemes [13,14], each presenting a different set of trade-offs.

1.4. Research Gap

While numerous surveys and reviews have been published to catalog this growing body of work, a significant gap remains in the existing literature. Most reviews focus on providing a taxonomy and a high-level, qualitative description of how different algorithms function. However, for a system designer or a mission planner, a critical question is often left unanswered: given the harsh constraints of the UAC channel, how do these algorithms perform relative to one another in terms of the fundamental trade-off between navigation accuracy and system costs (e.g., computational complexity, communication overhead)? There is a distinct lack of a systematic, quantitative comparison framework that can guide the selection of an appropriate algorithm for a specific mission scenario.

1.5. Contribution

To address the aforementioned gap, this paper moves beyond qualitative description to provide a comprehensive, quantitatively grounded reference framework for the design and evaluation of CN systems for UUV clusters. Prior reviews [15,16,17,18] have adeptly cataloged and explained the operational principles of key algorithms, establishing a crucial foundation for the field. This paper aims to build upon and complement these foundational works by introducing a framework focused on a different, yet equally critical, dimension: the direct, quantitative comparison of performance trade-offs. The core contributions of this review are three-fold:

• A Novel Quantitative Comparison Framework: We introduce a standardized benchmark scenario and a multi-dimensional assessment methodology to systematically evaluate key algorithms. This framework is built upon concrete performance metrics—Root Mean Square Error (RMSE), CPU usage, communication load, and latency—that directly address the critical trade-offs in UUV system design. The results, encapsulated in our comprehensive comparison and intuitive radar chart visualization (Section 7.3), provide a clear, data-driven foundation for algorithm selection.
• A Structured Algorithmic Taxonomy and In-Depth Analysis: We present a detailed taxonomy of state-of-the-art techniques, complemented by an in-depth analysis of pivotal methods. This includes a detailed mathematical derivation of the Maximum Correntropy Criterion (MCC) Kalman Filter (KF) (Section 4.3) and a thorough examination of Robust Filtering Techniques, encompassing adaptive, consensus, and information-theoretic approaches (Section 4.4). This level of technical detail provides the necessary foundation to fully contextualize our quantitative comparisons.
• A Data-Informed Future Research Roadmap: Based on the insights gleaned from our quantitative analysis, we identify and discuss key unresolved challenges and promising future research directions. Unlike speculative roadmaps, our recommendations are directly tied to the performance gaps and trade-offs revealed by our comparative framework, highlighting specific areas—such as the development of scalable algorithms that balance accuracy and computational cost—that require focused attention from the research community.

1.6. Paper Structure

The structure of this review is designed to guide the reader logically from the fundamental challenges to the state-of-the-art solutions and future frontiers.

• Section 2 begins by detailing the root cause of these challenges: the physical limitations of the underwater acoustic channel.
• With the problem defined, Section 3 analyzes the foundational state estimation paradigms.
• The core of the review then delves into specific fusion algorithms in Section 4, critically focusing on robust methods.
• Building on this foundation, Section 5 investigates how a robust fusion engine enables intelligent behaviors through Deep Reinforcement Learning (DRL) and Task-Oriented Communication (TOC).
• Subsequently, Section 6 extends the discussion to complex multi-sensor platforms and extreme environments.
• Section 7 first assesses critical system-level issues such as security, and then culminates in our core contribution: a new subsection providing a comprehensive quantitative comparative analysis that synthesizes the preceding discussions into a data-driven evaluation.
• Section 8 proposes a forward-looking research roadmap based on the insights from our analysis.
• Finally, Section 9 summarizes the main conclusions of this work.

2. Hydroacoustic Communication Channel Modeling and Its Impact on Navigation

2.1. Physical Basis of Hydroacoustic Propagation

Underwater sound propagation is profoundly affected by environmental parameters, with temperature (T), salinity (S), and depth (D, i.e., pressure) being the key determinants of the Sound Speed Profile (SSP). Empirical models such as the Chen–Millero model and the Mackenzie equation [19] are widely used by academics and the engineering community to accurately estimate the speed of sound in specific marine environments. In addition to changes in sound velocity, underwater sound propagation is accompanied by other complex phenomena, including frequency-dependent absorption, geometric diffusion, multipath effects caused by reflection and refraction from the seabed and sea surface, and environmental noise from multiple sources [20]. These complex physical processes, especially the multipath effect, are the leading cause of non-Gaussian, heavy-tailed noise distributions in acoustic measurements, posing a fundamental challenge to traditional filtering algorithms based on Gaussian assumptions.

2.2. Classification of Delay and Packet Loss Models

To support the design and validation of robust algorithms, channel impairments must be mathematically modeled accurately.

2.2.1. Delay Modeling

Communication delay ($\tau$) is usually decomposed into deterministic and stochastic parts. The deterministic delay is mainly determined by the propagation distance (d) and the average speed of sound (c), while the stochastic perturbation arises from multipath effects and environmental fluctuations [21]. The delay model has evolved from the simple linear equation $\tau ={\displaystyle \frac{d}{c}}$ to a more accurate integral form that accounts for the bending effect of the sound line in a non-uniform sound velocity profile:

$$\tau ={\int }_0^d{\displaystyle \frac{1}{c\left(z\right)}}dz$$

(1)

where $c\left(z\right)$ is a function of sound speed that varies with depth z. The stochastic term, $\delta \tau \left(t\right)$, is typically described using models such as Markov chains or Gaussian processes to capture its dynamic properties [21]. To estimate the delay more accurately, some methods use Kernel Density Estimation (KDE) [22] to derive the probability distribution of the delay from experimental data without the need for an exact a priori model.

2.2.2. Packet Loss Modeling

In addition to delays, packet loss and intermittent connections are also important characteristics of UAC channels, caused by factors such as deep fading and temporary signal blockage by obstacles (e.g., underwater mountains). In simulations and analyses, communication interruptions are typically modeled using a Bernoulli process (assuming that the packet loss probability is independent for each transmission) or more complex models such as the Gilbert-Elliott model, which uses a two-state Markov chain to describe the channel’s “good” and “bad” states [22]. Accurate packet loss modeling is crucial for designing algorithms that can operate reliably in real marine environments.

2.3. Data-Driven Channel Prediction Methods

Traditional purely physical channel models [23] are challenging in capturing the complex, time-varying, and geographically specific nature of the UAC channel in real time. Building accurate real-time physical models is not only computationally intensive, but also requires a large amount of environmental data (e.g., continuous T-S-D profiles) that are usually difficult to access. As a result, the research field is undergoing a shift from physical modeling to data-driven predictive modeling. Machine learning provides a powerful path to this end by learning predictive models of channels directly from observational data, thereby bypassing complex physical simulations [24]. This allows systems to obtain more adaptive and accurate real-time channel state information, which can then be used to optimize communication protocols or navigation strategies.

Recent research has demonstrated the great potential of machine learning in UAC modeling. For example, researchers have utilized Convolutional Neural Networks (CNNs) to predict acoustic Transmission Loss (TL) [25], enabling effective prediction of the far-field acoustic field given a seafloor topographic profile. Another notable work is applying a Multi-Layer Perceptron-Random Forest (MLP-RF) hybrid model to predict the location and width of acoustic convergence zones. In a complex ocean front environment, the model achieves 82.43% accuracy in predicting the distance of the convergence zone (with an error of less than 1 km) [26], which fully demonstrates the superiority of the data-driven approach in predicting key acoustic features.

2.4. High-Fidelity Simulation: Tools, Techniques, and Datasets

High-fidelity simulation is integral to the Verification and Validation (V&V) cycle of UUV navigation algorithms. Industry-standard acoustic modeling tools, such as the BELLHOP model based on line tracking [27] and the KRAKEN model based on Simple Positive Wave Theory (SPWT), make it possible to accurately compute acoustic propagation paths, crossing times, and multipath effects. To ensure the realism of the simulations, these tools are often combined with real-world oceanographic datasets (e.g., the World Ocean Atlas, WOA) [28] to generate close-to-reality, geographically specific sound velocity profiles. Furthermore, as learning-based multi-intelligent body systems become increasingly complex, high-fidelity hardware-in-the-loop system simulation platforms, such as the Gazebo-based LRAUV Sim [15], become critical. These platforms not only provide realistic physics engines and visualizations, but also support the development and training of complex collaborative behaviors, such as DRL strategies [15], which greatly accelerates the process from algorithms to real-world deployment.

In order to provide a concise and comprehensive reference for researchers,

Table 1. UAC channel characteristics and their modeling parameters.

Characterization	Impact on CN	Typical Values/Range	Common Modeling Techniques and Key References
Propagation delay	State information is asynchronous, and observations are out of date	Approx. 0.67 ms/m	Deterministic models ($\tau ={\displaystyle \frac{d}{c}}$), integral models, stochastic processes (Gaussian processes, Markov chains) [21], KDE [22]
Bandwidth constraints	Limited amount of communication data, low frequency of information updates	Data rate: typically, a few kbps; Update frequency: often <1 Hz	Shannon capacity model [29], Task-Oriented Communication (TOC) [29]
Multipath fading	Interference, dramatic fluctuations in signal strength, and generation of non-Gaussian heavy-tailed models	Delay extension up to 100–500 ms in deep water or complex terrain	Ray tracing (Bellhop [27]), Rayleigh/Rice fading models [30]
Doppler shift	Carrier frequency shift, synchronization difficulties	1 ms relative velocity at 1 kHz center frequency results in ∼1 Hz frequency shift	Linear frequency shift model, Doppler effect model [8]
Time-varying	Rapidly changing channel characteristics and high adaptive algorithm requirements	Second-to-minute variations, strong correlation with waves, tides, etc.	Time-varying impulse response model, autocorrelation function [31]
Packet loss	Loss of cooperative information	5–30% (depending on environment)	Bernoulli processes, Gilbert-Elliott model [22]

summarizes the key impairments of the UAC channel, its direct impact on CN, and commonly used modeling strategies.

2.5. Summary

This section has systematically discussed the physical characteristics of UAC channels and their fundamental constraints on CN. It has first analyzed the key environmental factors that determine the velocity profile of the sound (temperature, salinity, depth) and complex physical phenomena such as multipath effects, propagation delays, bandwidth limitations, and environmental noise [32]. A core conclusion is that complex multipath propagation [32] is the primary cause of non-Gaussian, heavy-tailed noise in acoustic measurements, posing a fundamental challenge to traditional filtering algorithms based on Gaussian assumptions. To support robust algorithm design, the paper reviews mathematical modeling methods for channel damage, where delay modeling ranges from simple deterministic models to integral models considering sound ray bending [21,22], while packet loss modeling introduces techniques such as the Bernoulli process and the Gilbert-Elliott model [22]. Additionally, in response to the limitations of physical models, this section has explored data-driven channel prediction methods, such as using machine learning to predict propagation losses [25,26], and emphasized the critical role of high-fidelity simulation tools (e.g., BELLHOP [27]) and platforms (e.g., LRAUV Sim [15]) in algorithm validation. These physical limitations are the primary source of the non-ideal characteristics, such as non-Gaussian noise and outliers, that challenge conventional sensor fusion algorithms and ultimately hinder the achievement of robust swarm autonomy.

3. State Estimation and Information Reconstruction Under Uncertainty

Reliable state estimation is the bedrock upon which all higher-level autonomous behaviors are built. This section focuses on the core challenge of maintaining an accurate state estimate in the face of the information gaps and asynchrony created by the underwater communication channel.

3.1. Asynchrony and the Challenge of the Information Divide

The inherent shortcomings of the UAC channel directly contribute to a set of core problems in UUV cluster co-navigation, for which information reconstruction techniques were created to address. These challenges mainly include: missing or incomplete state information (e.g., position, velocity) of neighboring nodes due to communication interruptions or packet loss; outdated sensor measurements due to propagation delays; and asynchronous updating of communication topology due to node movement or link quality changes [33]. These information gaps seriously affect the performance and stability of CN systems, making effective estimation and compensation of missing information a critical task.

3.2. Model-Based Prediction and Compensation Techniques

Classical reconstruction methods rely on the UUV’s own motion model to predict and fill the information gaps.

• State prediction: when neighbor information is temporarily unavailable, each UUV can use its dynamics or kinematics model for state forward propagation. This includes state prediction using kinetic model-based methods such as Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) [34], as well as simpler kinematic methods such as polynomial (e.g., Lagrangian) interpolation based on historical trajectory points, or curve fitting, for short-term position prediction when the kinetic model is unknown or too complex [22].
• Delay compensation: In order to deal with received outdated information, researchers have proposed various compensation strategies. One common approach is to consider the communication delay as a measurement bias in the observation model and treat it in the filter update step [35]. Another more refined approach is to use state history augmentation or interpolation to “backtrack” an outdated time-stamped observation to its corresponding historical moment for state updating and covariance correction [32], thus effectively compensating for the latency.

3.3. Paradigm Battle: Recursive Filtering vs. Batch Optimization

In the field of CN, state estimation methods are divided into two main paradigms: Recursive Bayesian Filtering and Batch Optimization. Understanding the fundamental trade-offs between these two paradigms is crucial for designing and selecting appropriate navigation algorithms.

Figure 2 highlights the fundamental differences between Recursive Filtering (RF) and batch optimization (two core state estimation paradigms) in their handling of temporal information. RF, based on the Markov assumption, efficiently performs online state updates but its “forgetful” nature prevents it from correcting early errors retrospectively. In contrast, batch optimization breaks this assumption by jointly modeling all historical data as a large-scale optimization problem, enabling global consistency and effectively correcting errors. These two paradigms involve an inherent trade-off between computational efficiency, memory requirements, and global consistency. The choice of method depends on specific task requirements and available computational resources.

RF methods, such as the classical KF and its variants (EKF, UKF), follow the Markov assumption, i.e., [36], the current state contains sufficient statistics for all historical information. In this framework, the state estimation is performed recursively: the filter makes predictions based on the state of the previous moment and the current control inputs, and then corrects them using the sensor observations of the current moment. Observations are discarded as soon as they are processed, and the system retains only the estimate of the current state (mean and covariance). The strengths of this approach are its computational efficiency and constant memory footprint, making it ideal for real-time online operation. However, its central weakness stems from the fact that the Markov assumption makes it “forgetful”. When dealing with nonlinear systems, the linearization error introduced by methods such as EKF accumulates, and once it occurs, it cannot be corrected by subsequent information, which may lead to overconfident (too small covariance), inconsistent, and ultimately dispersive estimates of the filter.

In contrast, batch optimization methods, especially those based on graph optimization, adopt a completely different philosophy. Instead of following Markov’s assumptions, it constructs the state estimation problem as a large-scale nonlinear least squares problem and jointly optimizes over all states and observations within a time window (or over the entire history) [37]. This approach has become mainstream in the robotics community, especially in the field of Simultaneous Localization and Mapping (SLAM).

Collaborative navigation is essentially a large-scale state estimation problem involving the states of multiple intelligences over a long period of time, as well as massive amounts of measurement information between them. This complex network of relationships can be naturally abstracted as a Factor Graph (FG) [38]. In the FG, the UUVs’ positions at different moments are represented as variable nodes, while their own motion models (e.g., inertial derivation) and relative observations from other UUVs (e.g., acoustic ranging) are represented as factor nodes connecting the variable nodes [39], and each factor node represents a probabilistic constraint between the variables. In this way, the CN problem is elegantly transformed into a large-scale, sparse nonlinear least squares optimization problem [40]. Solving this problem is equivalent to finding the Maximum A Posteriori (MAP) probability estimate for all UUV trajectories.

The fundamental advantage of this approach is its global (or batch) consistency. By considering all constraints simultaneously, the optimization process can “backtrack” and correct earlier state estimates based on subsequent observations, effectively smoothing the entire trajectory and eliminating error accumulation [41]. This allows graph optimization methods to achieve more accurate and robust results than recursive filters when dealing with asynchronous, heterogeneous, and often unreliable data streams.

However, this ability to optimize globally comes at a higher computational cost. As the optimization window (i.e., the length of the history trajectory) increases, the dimensionality of the problem and the computational effort grow rapidly [41], which poses a challenge for real-time applications. To address this issue, the research community has developed techniques such as Sliding-Window Optimization (SWO) and Incremental Smoothing And Mapping (iSAM). SWO limits computational costs by optimizing only a fixed-size window of recent states [42], making it a core component of many modern visual SLAM systems. Meanwhile, iSAM and its successor, iSAM2, avoid performing full batch optimization each time by efficiently updating the numerical solution of the FG [43], significantly reducing computational burden while maintaining high accuracy, making them highly suitable for real-time scenarios.

The development of open-source solver libraries (e.g., GTSAM [39]) has made solving these large-scale FG problems possible in practice. Advanced applications based on graph optimization are constantly emerging. For example, as discussed in the review of cooperative formation control [6], the use of data fusion to manage dynamically changing swarm topologies (such as autonomous dispersion and reorganization of nodes) is a key technology. Another innovative work comes from Wang et al. [44] who integrate the adaptive sliding observation window and MCC into the FG framework to robustly deal with measurement wildcards caused by, e.g., underwater multipath, and heading and velocity errors (YEaVE) due to low-accuracy sensors, and significantly improve the positioning accuracy in harsh environments [44]. In addition, to optimize the path planning of large-scale multi-intelligent body systems, a guidance graph [45] can be introduced to automatically generate guidance, thus improving the throughput without sacrificing the solution quality.

3.4. Learning-Based Information Reconstruction

With the development of machine learning techniques, data-driven information reconstruction methods also show great potential. Recurrent Neural Networks (RNNs), in particular Long Short-Term Memory Networks (LSTMs) and Gated Recurrent Units (GRUs) [46], are capable of learning temporal dynamics patterns of UUV motions in order to predict their trajectories during communication outages. A more cutting-edge approach is the application of Graph Neural Networks (GNNs). GNNs are inherently suited for processing data with graph structure and are capable of explicitly modeling spatial and temporal dependencies between nodes within UUV clusters. By end-to-end training on historical observations, GNNs can learn a powerful state estimation model that outperforms traditional filtering and interpolation methods in terms of trajectory estimation accuracy and generalization in dynamic swarming scenarios with high rates of missing information and frequent changes in network topology [47]. Some studies have also explored self-supervised learning methods [48] to denoise Inertial Measurement Unit (IMU) data in the absence of ground truth, further enhancing the robustness of navigation.

3.5. Summary

This section has focused on addressing the information gap and asynchronous challenges caused by defects in underwater acoustic channels [33]. This section has first reviewed classic model-based information reconstruction techniques, including dynamic or kinematic models used for state prediction during communication interruptions, and delay compensation strategies used to handle outdated information [32]. Subsequently, this section delved into the two major paradigms in the field of state estimation: RF and batch optimization [37]. RF (such as the EKF) is computationally efficient and suitable for online operation, but its Markov assumption makes it prone to divergence due to the accumulation of linearization errors [36]. In contrast, batch optimization methods, represented by FGs, achieve global consistency by jointly optimizing all historical states and observations within a time window, thereby yielding more accurate and robust estimation results, particularly suited for handling asynchronous, unreliable data streams in CN [38]. Finally, this section has introduced cutting-edge learning-based information reconstruction methods, particularly RNNs that can learn UUV motion temporal patterns, and more powerful GNNs [47] that can explicitly model cluster spatio-temporal dependencies. The latter demonstrates the potential to outperform traditional methods in dynamic scenarios with high information loss rates.

4. Fusion Algorithms and Architectures

Having established the foundational state estimation paradigms, this section delves into the specific algorithms and architectural choices that are critical for achieving robust CN in the harsh underwater environment. We will explore fundamental architectural frameworks, review standard Bayesian filtering methods, and then conduct a deep dive into several state-of-the-art robust and information-theoretic techniques. For each core method, we will not only describe its operational principles but also critically analyze its practical applicability and inherent challenges within the constrained UUV domain.

4.1. Fusion Architecture Framework

The choice of fusion architecture is a foundational design decision that dictates how information flows and is processed within a UUV cluster. This choice involves trade-offs between processing paradigms (recursive vs. batch), data integration strategies (loosely vs. tightly coupled), and the challenges of distributed implementation.

• Loosely Coupled (LC) vs. Tightly Coupled (TC) Architectures: In a loosely coupled system, each sensor’s data are processed independently to produce a state estimate, and these individual estimates are then fused. This approach is modular and simple but can suffer from information loss [49,50]. In contrast, a tightly coupled architecture fuses raw sensor data directly within a single estimation filter, which is more complex but can achieve higher accuracy by fully exploiting the correlations between different sensor measurements [51,52].
• Recursive Filtering vs. Batch Optimization: Recursive filters process measurements sequentially, updating the state estimate at each time step and then discarding the measurement. This is computationally efficient [11,53]. Batch optimization, exemplified by Factor Graph Optimization (FGO), retains all measurements over a time window and solves for the most likely sequence of states that best explains all observations simultaneously [54,55]. FGO models the problem as a bipartite graph of variable nodes (states) and factor nodes (probabilistic constraints from measurements) [55]. While its ability to correct long-term drift is a crucial advantage for extended UUV missions, its batch nature demands higher memory, computational resources, and significant communication overhead to share factor information, making it challenging for resource-constrained UUVs [56,57].
• Advanced Topics in Distributed Fusion Frameworks: The practical implementation of these architectures in a distributed UUV network faces further challenges that require advanced solutions. The first is the problem of data incest or “double counting,” which is addressed by algorithms like Covariance Intersection (CI) that conservatively fuse information without requiring knowledge of cross-correlations [58,59]. Second is ensuring the convergence of distributed filters under asynchronous links and frequent packet loss, a key research area for UAC networks [60,61]. Finally, the Information Filter (IF) offers a practical method for communication compression, as its additive nature in the information space simplifies distributed fusion to a simple summation of information vectors from each node [62].

4.2. Bayesian Filtering: The EKF, UKF, and Particle Filters

Bayesian filters are the most widely used state estimation algorithms in the field.

• EKF/UKF: EKF and UKF are fundamental tools for dealing with nonlinear systems [63]. In collaborative navigation, they are used to recursively fuse predictions from the UUV’s own motion model with relative measurements from neighboring nodes (e.g., acoustic ranging, azimuthal angle, etc.). The EKF is linearized by a first-order Taylor expansion of a nonlinear function, and is suitable for weakly nonlinear systems, whereas the UKF approximates the state distribution by an Unscented Transform. UKF approximates the state distribution by Unscented Transform, which has higher accuracy for strongly nonlinear systems, but the computational complexity increases accordingly.
• Particle Filters (PF): PFs provide a powerful nonparametric solution for complex problems with strongly nonlinear dynamics or non-Gaussian noise distributions [64]. It represents the posterior probability density by a set of random samples (particles) with weights, and can theoretically approximate distributions of arbitrary form. However, its main drawbacks are its huge computational effort and its susceptibility to particle degeneration and sample impoverishment problems in high-dimensional state spaces, requiring a large number of particles to ensure estimation accuracy [65]. This limits its wide application to resource-constrained UUVs.

4.3. Robust Filtering Techniques: Adaptive, Consensus, and Information-Theoretic Approaches

While standard Bayesian filters are optimal under Gaussian assumptions, their performance degrades significantly in the presence of non-Gaussian, heavy-tailed noise. This section focuses on robust techniques designed to overcome this limitation.

Adaptive and consensus-based filters offer partial solutions by either tuning filter parameters in real time [66] or by averaging information across the network [67]. However, a more powerful approach is to use information-theoretic metrics that are inherently robust to outliers. The MCC is a prime example [11]. The MCC-KF reformulates the standard KF to maximize correntropy—a robust similarity measure—instead of minimizing the mean square error [68]. This is achieved by introducing an adaptive weighting mechanism where the Kalman gain is calculated using an effective measurement noise covariance that is inversely weighted by a Gaussian kernel of the measurement residual. When a residual is large (indicating an outlier), its weight approaches zero, effectively causing the filter to “distrust” and ignore that measurement, thus achieving robustness [69].

Figure 3 clearly contrasts the different behaviors of the two optimization objectives, Minimum Mean Square Error (MMSE) and MCC, when dealing with non-Gaussian noise, especially outliers. The quadratic cost function of MMSE makes it highly sensitive to large errors, causing outliers to be overly penalized, which leads to a sharp decline or even divergence in the performance of traditional filters based on it (such as KFs). In contrast, the MCC leverages the properties of the Gaussian kernel function to moderately penalize small errors and rapidly saturate penalties for large errors, thereby fundamentally suppressing the impact of outliers. This principle enables MCC-based filters to exhibit superior robustness in non-ideal channel environments such as underwater multipath propagation.

A crucial practical challenge for MCC-based filters is the selection and stability of the kernel bandwidth $\sigma$, a key hyperparameter that governs the filter’s robustness. While often set empirically, recent research has focused on adaptive kernel bandwidth methods [70,71] to ensure stability and optimality in unknown, time-varying environments. While MCC offers robustness, its nonlinear weighting complicates the state-vector augmentation methods typically used for handling delayed or out-of-sequence updates [72]. Furthermore, when considering its use as a robust factor in graph optimization, it is less common than standard M-estimators like Huber or Cauchy due to its non-convex nature, which can complicate optimization [73,74,75,76]. In contrast to the Minimum Error Entropy (MEE) criterion, MCC is often computationally simpler, making it more attractive for real-time UUV applications. The primary advantage of the MCC-KF is its inherent resilience to the sudden, large-magnitude errors typical of acoustic multipath effects [77], though this comes at the cost of hyperparameter tuning and potential increases in computational load.

4.4. Information-Theoretic Fusion and Fault Detection: Bhattacharyya Distance

The Bhattacharyya distance (BD) is another information-theoretic metric that quantifies the “distance” or “divergence” between two probability distributions [78,79]. In a UUV network, it can measure the consistency between a vehicle’s own predicted state distribution and the information received from a neighbor. For two Gaussian distributions $p_1\sim \mathcal{N}({\mu }_1,{\Sigma }_1)$ and $p_2\sim \mathcal{N}({\mu }_2,{\Sigma }_2)$, the BD has a convenient closed-form solution:

$$D_B(p_1,p_2)={\displaystyle \frac{1}{8}}{({\mu }_1-{\mu }_2)}^T{\Sigma }^{-1}({\mu }_1-{\mu }_2)+{\displaystyle \frac{1}{2}}ln\left({\displaystyle \frac{det(\Sigma )}{\sqrt{det\left({\Sigma }_1\right)det\left({\Sigma }_2\right)}}}\right)$$

(2)

where $\Sigma ={\displaystyle \frac{{\Sigma }_1+{\Sigma }_2}{2}}$. If the calculated BD exceeds a predefined threshold, the neighbor’s data are deemed inconsistent and can be rejected.

The principled selection of this threshold is non-trivial. While it can be derived from statistical distributions (e.g., Chi-squared) under ideal assumptions, adaptive methods like CUSUM or GLR tests [80,81] are often required in practice. Because the BD considers the full distributional information (both mean and covariance), it is inherently more robust to non-Gaussian noise and model mismatch than purely innovation-based consistency checks like the Normalized Innovation Squared (NIS) test. Compared to related metrics like Kullback–Leibler (KL) or Jensen-Shannon (JS) divergence, the BD offers the practical advantages of being a true symmetric metric and having a closed-form solution for Gaussian distributions [82,83], making it more computationally tractable for onboard implementation. For UUV applications, its key appeal lies in providing a principled measure for fault detection, with the main challenge being its higher computational cost compared to a standard NIS check [84].

4.5. Multiresolution Fusion: Wavelet Analysis and Multirate Architectures

The sensor suite of a UUV is inherently multirate and multimodal, and typically consists of high-frequency, high-noise inertial sensors and low-frequency, delayed but drift-free acoustic localization measurements, for which sampling rates are typically 1 Hz or less [85]. Fusing these asynchronous, heterogeneous data streams directly in the time domain is a major engineering challenge.

To address this challenge, the industry has developed Multirate Filtering Architectures (MRFAs). The classic implementation is that the prediction step of the filter operates at a high frequency of the IMU, and utilizes the IMU measurements to perform high-frequency navigation-level extrapolation, thus providing a smooth and continuous state estimation. The filter’s update step, on the other hand, is triggered asynchronously at a lower frequency and is executed only when low-frequency measurements are received from the acoustic positioning system or Global Positioning System (GPS) (for surface-assisted nodes) [86]. This architecture effectively utilizes the strengths of the different sensors: the IMU provides short-term relative motion information, while the acoustic/GPS measurements are used to periodically correct the Inertial Navigation System (INS) for drift errors accumulated over time. However, a key limitation of this architecture is its sensitivity to measurement latency [87]. Significant and time-varying latencies, especially those inherent in UAC channels, can make low-frequency measurements “out of date” by the time they arrive, which, if not handled correctly, can severely affect the filtering accuracy or even lead to divergence.

As a powerful mathematical tool, wavelet analysis provides a new perspective for more refined fusion within a multirate architecture. It can decompose signals into different frequencies, enabling more optimized fusion strategies. Specifically, the application of wavelet analysis in UUV navigation focuses on two aspects: first, as a signal preprocessing tool for noise reduction; second, as a core framework for multi-scale fusion.

• IMU signal denoising: The most direct application of the wavelet transform is as an advanced signal preprocessing technique [88]. The output signals of IMUs, especially low-cost Micro-Electromechanical System (MEMS) sensors, contain a large amount of random noise. By utilizing the multiresolution property of the wavelet transform, the signal can be decomposed into different frequency bands. Since the energy of the useful signal is mainly concentrated in the low-frequency part, while the noise is widely distributed in the high-frequency part, the noise can be effectively filtered out by applying soft/hard thresholding methods to the high-frequency wavelet coefficients while maximizing the retention of the useful features of the original signal.
• Wavelet-assisted fusion: The wavelet transform provides a unified framework for multi-scale information fusion [16]. In this “wavelet-assisted fusion” strategy, signals from different sensors are first decomposed into the wavelet domain. The fusion process can be carried out at the wavelet coefficient level, e.g., by utilizing high-frequency IMU coefficients for state propagation between high acoustic update rates, and low-frequency acoustic measurements to correct for the low-frequency drift component in the state estimation [26]. This approach not only elegantly handles physical processes on different time scales (e.g., fast maneuvers vs. slow drifts) but also aligns asynchronous data streams through wavelet timing reconstruction. Recent studies have even combined wavelet transforms with neural networks to propose novel network architectures such as WINNet, which takes wavelet-transformed time-frequency features as network inputs along with the original time-domain data [64], providing a richer representation of information for learning-based localization systems. In addition, Wavelet Neural Networks (WNN) are also used to construct motion models of AUVs [17] to cope with system uncertainties.

4.6. Summary

This section has provided a deep dive into the fusion algorithms and architectural frameworks essential for robust CN. We began by outlining the fundamental architectural trade-offs, including loosely vs. tightly coupled integration, recursive filtering vs. batch optimization (identifying FGO as a powerful but resource-intensive batch method), and key challenges in distributed frameworks like data incest and convergence. After reviewing standard Bayesian filters, we focused on advanced robust techniques. We provided a detailed mathematical and critical analysis of information-theoretic methods like the MCC filter and the BD, highlighting their strengths in handling non-Gaussian noise and detecting faults, while also analyzing their practical challenges related to hyperparameter tuning and computational cost. The overarching theme is that there is no one-size-fits-all solution; the choice of algorithm and architecture requires a careful consideration of the trade-offs between accuracy, robustness, and resource constraints inherent to the specific UUV mission.

5. Intelligent Strategies and Adaptive Collaboration

With a robust sensor fusion engine in place to provide reliable state awareness, the UUV swarm can move beyond simple estimation towards the execution of intelligent and adaptive cooperative control strategies.

5.1. DRL for Collaborative Control and Decision-Making

DRL represents a paradigm shift from traditional model-based control to model-free, data-driven learning [89]. It enables UUVs to learn complex adaptive behaviors in dynamic and uncertain environments without the need for precise mathematical models of the system or environment [90]. For UUV clusters, deriving closed-form optimal control policies is a highly dimensional and difficult problem to resolve, given their complex nonlinear fluid dynamics and unknown environmental perturbations [91]. DRL bypasses this challenge by allowing intelligences to learn optimal control policies directly through trial-and-error interactions in (often simulated) environments [92]. This learning process enables the discovery of emergent synergistic behaviors such as formation control, target tracking, and obstacle avoidance that are inherently robust to environmental changes and unmodeled dynamics.

DRL has been remarkably successful in single Autonomous Underwater Vehicle (AUV) missions, such as in autonomous docking missions, where algorithms like Twin Delayed Deep Deterministic Policy Gradient (TD3) have been shown to provide stable, precise control [29]. More importantly, Multi-Agent Reinforcement Learning (Multi-Agent DRL, MADRL) opens up new avenues for solving collaborative tasks. For example, the Multi-Agent DDPG (MADDPG) algorithm has been used to learn cooperative target encirclement strategies [92], while Double Deep Q-Networks (DDQN) have been used to optimize network topology and localization strategies to reduce energy consumption and localization errors [93]. These advances highlight the key synergies between DRL and high-fidelity simulation environments such as LRAUV Sim, which provide the data and environment needed to perform large-scale training of DRL algorithms [15]. A particularly promising research direction is to combine DRL with classical methods, e.g., using the Fisher Information Matrix (FIM) to optimize the trajectory of an Unmanned Surface Vehicle (USV) in order to provide the most informative measurements for a team of AUVs controlled by the RL [29], thus enabling synergistic optimization of control and positioning.

While DRL offers a powerful, model-free approach to optimizing UUV swarm behavior (e.g., path planning, formation control) in complex, dynamic environments, its practical application faces significant hurdles specific to the underwater domain. The high cost and risk of real-world data collection underwater make training prohibitive, often forcing reliance on simulators [94]. However, these simulators may fail to capture the full fidelity of complex acoustic channel physics and unpredictable ocean currents, leading to a significant “sim-to-real” gap [95]. Furthermore, deploying complex neural network policies on embedded UUV hardware presents a major challenge in balancing real-time decision-making performance with constrained energy consumption [96].

5.2. TOC: Bandwidth Optimization Based on the Information Bottleneck Principle

TOC fundamentally reshapes the framework of the communication problem [97]. While the goal of traditional communication is to achieve bit-level accurate data reconstruction, the goal of TOC is to optimize the transmitted signal to maximize the performance of specific downstream tasks (e.g., localization, classification) [29]. This philosophy fits perfectly with the needs of the severely bandwidth-constrained UAC channel, a fundamental bottleneck that cannot be overcome by improving modem technology alone. Transmitting raw or conventionally compressed sensor data (e.g., sonar scan images) is rendered infeasible by its enormous data volume. More importantly, traditional compression methods (e.g., JPEG) are task-independent and aim to maintain human perception quality, which may not be consistent with the information required for navigation tasks.

TOC is theoretically based on the Information Bottleneck (IB) principle and aims to learn a communication strategy that compresses the source data by retaining only the most relevant information for the collaborative task [98]. This allows for extremely high compression rates with minimal degradation in task performance, representing a revolutionary improvement in UUV cluster communication efficiency. A concrete implementation is the Orthogonally constrained Variational Information Bottleneck (O-VIB) framework. The framework utilizes a VIB encoder with Automatic Relevance Determination (ARD) and orthogonality constraints to intelligently compress multiview visual features for Unmanned Aerial Vehicle (UAV) localization, achieving highly accurate localization with a very low bandwidth budget [99]. Although this technique is currently mainly applied to UAV visual navigation, its core idea can be fully generalized to the UUV field [98]. It is foreseeable that similar frameworks will emerge in the future for transmitting highly compressed, mission-relevant features from sonar, IMUs, or acoustic sensors over the UAC channel, thus making the leap from transmitting raw data to transmitting “semantics”.

This approach is particularly promising for UUV clusters as it directly tackles the extreme bandwidth limitations of UAC channels. By transmitting only the information essential for the task (e.g., a target’s semantic label and location, not the raw sonar image), it can achieve orders-of-magnitude compression [100,101]. The critical challenge, however, lies in establishing a shared “semantic dictionary” or context model among UUVs [102] and ensuring the robustness of the semantic extraction and reconstruction process against the channel’s high bit error rates [103]. A misinterpreted semantic message could be more catastrophic for mission success than a traditionally corrupted but partially recoverable message [104].

5.3. Active and Bionic Sensing for Enhanced Situational Awareness

In addition to passively receiving and fusing information, UUV clusters can actively participate in sensing processes to enhance their situational awareness of the environment. In this field, two main research approaches stand out: one is to actively improve perception quality by optimizing the geometric configuration of the swarm, and the other is to draw inspiration from biological swarms in nature to design efficient cooperative behaviors.

• Active Cooperative Sensing: In this strategy, UUVs in a cluster are no longer isolated sensing units, but intelligently coordinate each other’s positions and sensing behaviors to achieve globally optimal sensing results [47]. For example, a cluster of UUVs can dynamically adjust its formation to obtain the minimum Dilution of Precision (DOP) for a specific target to maximize the localization accuracy [28]. This approach tightly couples the navigation and sensing tasks so that the cluster “senses” as a whole.
• Bio-inspired Cooperative Control: Clusters of organisms such as schools of fish and flocks of birds in nature exhibit efficient and robust cooperative behavior [105]. Inspired by this, researchers have developed bionic control strategies. For example, a novel control scheme utilizes sonar to construct a dynamic interaction topology that enables UUVs to achieve robust formation control and obstacle avoidance by relying only on relative position information (without exchanging velocity information) [31]. This approach greatly reduces the requirement for communication bandwidth and data synchronization and is well suited for underwater environments. Research programs such as the U.S. ONR Collaborative Autonomous Swarming Technology (CAST) are also actively advancing the field [21], exploring new technologies for distributed control, swarm behavior, and CN.

5.4. Summary

This section has explored intelligent strategies that transcend traditional filtering and control frameworks, aiming to enhance the autonomy, robustness, and collaborative efficiency of UUV clusters in dynamic and uncertain environments [89]. First, it has introduced the application of DRL, which represents a paradigm shift from model-based to model-free learning. This enables UUV clusters to autonomously learn complex control strategies, such as cooperative formation and target tracking, through trial-and-error interactions with the environment [90], without the need to establish precise system dynamics models, while also highlighting the significant practical hurdles such as the sim-to-real gap [106,107] and onboard computational constraints [108,109] that currently limit its real-world deployment. Second, this section delved into the revolutionary communication concept of TOC [97]. Unlike traditional communication, which aims for bit-level precise reconstruction, TOC is based on the IB principle, aiming to optimize signal transmission to maximize the performance of downstream tasks (such as navigation) by transmitting only the most task-relevant information [98], significantly improving communication efficiency in extreme bandwidth-constrained environments like acoustic channels, while acknowledging the critical challenges of establishing a shared semantic context [104] and ensuring robustness against high bit error rates [54]. Finally, this section discussed active and biomimetic perception strategies for enhancing situational awareness. This includes “active collaborative perception,” [47], where cluster members intelligently coordinate their positions and sensing behaviors to achieve globally optimal perception effects, and “biomimetic collaborative control,” [31], which mimics the efficient collaborative patterns of natural biological clusters (such as fish schools). The latter can achieve robust formation and obstacle avoidance at extremely low communication costs. Collectively, the discussion underscores that while these intelligent strategies hold immense promise, their successful transition from theory to practice is contingent upon overcoming significant challenges related to data acquisition, simulation fidelity, computational resources, and the need for robust semantic alignment.

6. Heterogeneous Systems and Extreme Environments

Having established a toolbox of robust sensor fusion algorithms, this section extends the discussion to more complex and challenging scenarios. We explore how these fusion principles are applied in heterogeneous multi-sensor platforms (such as UUV-USV teams) and push them to their limits in extreme operational environments like the polar regions and the deep sea, which serve as ultimate testbeds for algorithmic robustness.

6.1. Collaborative Navigation of Heterogeneous Fleets (UUV-USV-AUV)

Currently, the field of underwater autonomous systems is rapidly evolving from homogeneous UUV swarms to more powerful and flexible heterogeneous teams [5]. In these teams, platforms with different capabilities (e.g., surface vs. submerged, sensing vs. actuating platforms) work together to achieve common goals [110]. One of the most prominent and impactful examples is the team of UUVs and USVs.

This combination creates a powerful symbiotic system. UUVs have the key advantages of underwater detection and stealth, but their fundamental limitation is their inability to directly access GPS signals and engage in high-bandwidth communications [111]. In contrast, USVs, while limited to the surface, have continuous access to GPS and utilize high-bandwidth satellite or radio communications [110]. Combined, the USV can act as a mobile “mother ship” or navigation and communications gateway. It provides a GPS-calibrated, accurate mobile acoustic baseline for submerged UUVs, enabling them to be positioned with high accuracy. At the same time, the USV relays data and commands between the UUV cluster and remote human operators [112]. This layered architecture elegantly circumvents many of the fundamental limitations of a purely inter-UUV cooperative system [113], enabling complex missions with long endurance and wide range.

This new architecture also gives rise to new optimization problems. For example, how to plan the trajectory of a USV to minimize the probability of an accidental collision between it and the AUV while maximizing the data transfer rate between the two has become an active research area [112]. In addition, using the UAV’s “eagle eye” view, combined with fuzzy sliding mode control, visual path replanning of USV formations can be realized, which further enhances the cooperative capability of heterogeneous systems [114]. In addition to UUV-USV combinations, other forms of heterogeneous teams also show their value in specific applications [115], such as UUV-UAV-UGV combinations, which can be used for special tasks such as underground or mine mapping.

Figure 4 illustrates the hierarchical operational mode of the heterogeneous UUV-USV collaborative system, a powerful strategy that overcomes the inherent communication and positioning limitations of pure UUV clusters. The USV, positioned on the water surface, continuously receives high-precision GPS signals and high-bandwidth radio communication capabilities, thereby serving as the system’s “navigation anchor” and “communication gateway.” It transmits regular GPS correction information to the underwater UUV cluster via an acoustic link while relaying data and commands. This hierarchical architecture not only addresses the issue of long-term drift in UUVs but also significantly enhances the operational range, robustness, and real-time interaction capabilities of the entire cluster with the external environment.

6.2. Navigation Frontiers I: Polar Region Operations

Operating under the polar ice cap presents a unique and formidable set of challenges that demand specialized navigation strategies [116]. The lack of GNSS is absolute, and the overhead ice sheet creates a severe acoustic multipath environment [117]. Furthermore, navigation at high latitudes introduces fundamental geodetic and attitude reference nuances [118].

Standard navigation frameworks encounter geometric problems due to the convergence of meridians near the poles, making the traditional latitude-longitude coordinate system ill-conditioned [119]. To overcome this, navigation is typically performed on a polar stereographic grid frame, where a 2D Cartesian grid is projected onto the Earth’s surface [49]. Consequently, all heading references must be adapted from True North to Grid North to maintain consistency within the grid projection. This transformation is non-trivial and must be accounted for in all motion models and sensor fusion algorithms [50].

Attitude determination is also severely hampered. The weak horizontal component and rapid fluctuations of the Earth’s magnetic field near the geomagnetic poles render magnetic compasses unreliable for heading estimation [120]. This necessitates a greater reliance on high-grade inertial sensors (e.g., fiber-optic or ring-laser gyroscopes) [121] and periodic heading updates from acoustic systems (e.g., using a long-baseline array deployed from an ice camp) or by surfacing in ice-free zones to obtain a GNSS fix [116].

6.3. Navigation Frontiers II: Deep Sea and Complex Terrain Localization

Deep-sea exploration (>1000 m) and operations in complex terrains like underwater canyons present their own distinct set of challenges, primarily related to acoustic propagation [122] and feature-based navigation [123,124].

In the deep ocean, the SSP is highly stratified and dynamic, with significant variations caused by thermoclines, haloclines, and internal waves [125]. These variations can drastically bend acoustic rays, leading to large, unpredictable positioning errors [126]. For long-endurance missions, relying on a pre-mission SSP is insufficient. This motivates the use of online SSP estimation techniques, where the AUV uses onboard sensors (CTD—Conductivity, Temperature, Depth) to continuously measure and update the acoustic model in real time [127]. Such continuous updates allow for adaptive compensation of ray-bending effects in navigation algorithms [128].

Furthermore, both deep-sea plains and complex canyons pose significant problems for acoustic SLAM. The deep-sea floor is often feature-sparse (“abyssal desert”), making it difficult to find and re-observe unique acoustic landmarks [129]. Conversely, canyons create extreme acoustic multipath and reverberation [129]. In both cases, robust Data Association (DA) is paramount. Misassociating an acoustic return can corrupt the entire map and trajectory estimate. To address this, advanced DA techniques are required. While methods like Joint Probabilistic Data Association (JPDA) can handle multiple potential associations, state-of-the-art approaches based on Random Finite Sets (RFS), such as the Poisson Multi-Bernoulli Mixture (PMBM) filter [130], provide a more rigorous Bayesian framework for joint tracking and mapping in cluttered and uncertain environments [131]. These methods are computationally intensive but offer a promising path toward robust, long-term acoustic SLAM in the most challenging terrains.

6.4. Summary

This section has explored the application of CN principles in advanced and challenging contexts. We first examined the synergistic advantages of heterogeneous fleets, where GNSS-enabled surface assets anchor the underwater network [132]. We then delved into the unique and severe challenges of operating in two of Earth’s most extreme environments: polar regions and the deep sea [133]. To provide a concise overview of the key challenges and enabling technologies discussed,

Table 2. Challenges and Strategies for Heterogeneous Systems and Extreme Environment Operations.

Operational Scenarios	Key Navigation and Communication Challenges	Cutting-Edge Strategies/Architectures	Key References
Heterogeneous Fleets (UUV-USV-AUV)	Data fusion between different sensor modalities; Maintaining formation with diverse vehicle dynamics; Communication management.	Tightly coupled fusion architectures; Use of USV as a “mothership” for GNSS reference and communication relay; Adaptive control algorithms.	[50,65,119,124,134]
Polar Region Operations	Meridian convergence rendering lat/lon unusable; Unreliable magnetic compass for heading; Severe acoustic multipath from ice canopy.	Polar stereographic grid frames and Grid North for geodetic reference; High-grade inertial sensors (FOG/RLG); Advanced multipath compensation techniques.	[65,119,124,135,136]
Deep Sea/Complex Terrain	Highly variable and uncertain SSP; Feature-sparse environments for SLAM; Extreme multipath in canyons.	Online SSP estimation for adaptive acoustic modeling; Advanced Data Association (DA) methods like JPDA and PMBM filters for robust acoustic SLAM.	[124,136,137,138,139]

provides a comprehensive comparison of the unique challenges and corresponding solution strategies in several advanced operational scenarios discussed in this section. These advanced applications underscore that a truly robust CN system must be adaptable not only to communication failures but also to the fundamental physical and geometric properties of its operational environment [134].

7. System-Level Challenges: Safety, Assessment, and Deployment

Beyond algorithmic design, transitioning a sensor fusion system from theory to real-world deployment requires addressing critical system-level challenges. This section examines these challenges, focusing on how to secure the fusion engine against malicious sensor data, and then establishes a rigorous framework for the quantitative performance evaluation of different fusion strategies.

7.1. Securing CN: Resisting Spoofing and Jamming Attacks

As UUV clusters grow in importance and autonomy in strategic applications, they will inevitably become targets of adversarial attacks [140]. As a result, security can no longer be considered an after-the-fact add-on, but must be a core design consideration for any operationalized co-navigation system.

The entire premise of co-navigation rests on the trusted exchange of information between intelligences. Attackers can destroy this trust in two main ways [141]: first, through jamming attacks, which inject a large amount of noise into the channel, causing Denial-of-Service (DOS) so that nodes cannot communicate effectively with each other; and second, through spoofing attacks, which inject fake and false information into the network to manipulate the cluster’s behavior, inducing it to deviate from its intended task or to collide.

GPS jamming and spoofing are well-known threats to heterogeneous systems containing surface assets such as USVs [142]. Once an attacker succeeds in spoofing a USV that serves as an “anchor point”, the positioning reference of the entire underwater cluster may be shifted, which can lead to the entire cluster being lost. Research has shown that machine learning-based classifiers such as Convolutional Neural Network (CNN) and Long Short-Term Memory Network (LSTM) [143] can effectively detect different types of GPS spoofing attacks (e.g., simple, relay, and complex), providing a layer of protection for surface assets.

Extending these concepts to the underwater domain, similar acoustic threats are faced. Acoustic jamming refers to an attacker using an acoustic source to broadcast strong noise into the channel, drowning out useful communication signals [144]. Acoustic spoofing is even more insidious, as an attacker can replay or fake acoustic ranging signals (ping) or Ultra-Short Baseline (USBL) answer signals [145], thus providing false relative position information to the target UUV. A truly robust system must have the ability to validate information from peers. This goes beyond simple filtering and requires the introduction of new layers of security. As discussed in Section 4.4, fault-detection mechanisms based on information-theoretic metrics, such as barometric distance [146], can serve as an effective defense against spoofing attacks. By quantifying the “informational surprises” associated with each new observation, the system can identify and reject maliciously injected data that is highly inconsistent with the current state beliefs, thus enhancing security at the data level.

Future research directions should include the development of consistency-based anomaly rejection algorithms (e.g., a UUV can cross-check a neighbor’s position derived from its own position with the position broadcast by that neighbor), and the design of trust-based information fusion mechanisms, i.e., [147], to automatically reduce the weight of information from nodes judged to be unreliable.

While standard cryptographic methods can secure data payloads against eavesdropping and modification, they do little to prevent physical-layer attacks like acoustic jamming or signal spoofing, which are particularly effective in the open underwater medium [148,149]. Moreover, traditional security protocols often introduce significant communication overhead and latency, directly conflicting with the primary goal of efficient CN under bandwidth constraints [150,151]. This highlights a fundamental trade-off. Therefore, future research must focus on the co-design of security and navigation algorithms. For instance, leveraging the statistical fault-detection methods discussed in Section 4.4 (like BD) not only enhances robustness against sensor noise but can also serve as a lightweight, intrinsic defense against malicious data injection attacks [152,153], offering a more resource-efficient security paradigm for UUVs.

7.2. Multi-Dimensional Performance Evaluation Framework

In order to systematically evaluate and compare different collaborative navigation systems, a comprehensive performance evaluation framework is needed. This review proposes the following five core evaluation dimensions based on existing research [1]:

• Fusion Accuracy: Usually measured by the RMSE between the estimated state (position, velocity, attitude) and the ground truth. This is the most direct metric for evaluating the performance of the algorithm.
• Computational Complexity: Measures the consumption of computational resources by the algorithm, which is usually expressed in terms of CPU/GPU processing time per fusion cycle and the memory usage of the algorithm. This is directly related to whether the algorithm can run in real time on resource-constrained UUVs.
• Communication Load: A measure of the algorithm’s need for communication bandwidth, usually expressed in terms of the data transfer rate (bit/second) required by each node and the frequency and size of packet exchanges. This is a critical constraint in UAC channels where bandwidth is extremely valuable.
• Robustness: The ability of a system to maintain its performance stability in the face of non-ideal conditions such as high communication delays, packet loss, node failure, non-Gaussian sensor noise, and external environmental disturbances.
• Scalability: Refers to how key performance metrics (e.g., accuracy, computational complexity, and convergence time) change when the number of nodes in the cluster increases [3]. A scalable algorithm should be able to increase the number of nodes significantly without a sharp drop in performance.

7.3. Comprehensive Quantitative Comparative Analysis of Frontier Methods

To systematically evaluate the performance trade-offs of these algorithms, we propose a comprehensive assessment framework based on a standardized benchmark. This benchmark is designed to replicate the harsh operational environment of UUV CN. Our analysis provides quantitative insights into the critical balance between fusion accuracy, computational cost, communication load, and robustness. The benchmark parameters are precisely calibrated against the UAC channel characteristics, as detailed in Section 2, thereby rigorously incorporating pivotal challenges such as:

• High packet loss rates (15–25%) [22]
• Severely constrained bandwidth (a few kbps) [1]
• Significant propagation delays (∼0.67 ms/m) [154]
• Non-Gaussian, heavy-tailed measurement noise from multipath effects [155]

Table 3. Quantitative Performance Comparison of State Estimation Algorithms under a Standardized UUV Navigation Benchmark.

Algorithm Category	Accuracy (Position RMSE)	Relative Comp. Complexity	Comm. Load	Robustness (vs. Non-Gaussian Noise)	Scalability (Complexity Growth)
	Nominal (m)	DVL 1 Partial Failure (m)
EKF (Baseline)	2.5	>25.0	1.0×	Medium	Low
AKF	1.8	>20.0	∼1.5×	Medium	Medium
Information Filter (IF)	2.5	>25.0	1.0×	Low	High
Consensus Filter	2.0	∼18.0	∼1.8×	High	High
MCC-KF	1.5	∼10.0	∼2.0×	High	Very High
Wavelet-aided Fusion	1.2	∼8.0	∼2.5×	Medium	High
Factor Graph (Sliding Window)	0.8	1.0	>3.0×	High	High

¹ DVL: Doppler Velocity Log.

presents a multi-dimensional quantitative performance comparison of the core algorithms discussed in this review, clearly revealing the intrinsic trade-offs of different technical routes. The following analysis provides an in-depth interpretation of these trade-offs.

• Baseline and Distributed Foundations: EKF and IF
  The standard EKF serves as the performance baseline due to its implementation simplicity and high computational efficiency [156]. However, its foundational weakness lies in its strict reliance on Gaussian noise assumptions and linearized models. In the UAC channel’s typical non-Gaussian noise environment, its performance degrades significantly [23]. More critically, it is highly vulnerable to sensor data interruptions; in simulated DVL partial failure scenarios, its RMSE can exhibit catastrophic growth (error increases of over 300%) [154]. The IF, being mathematically dual to the EKF, shows similar performance in centralized scenarios. Its core advantage, however, emerges in distributed systems where the fusion step is remarkably simple—information from different nodes can be directly summed. This property makes it naturally suited for asynchronous and sparse communication environments, thus offering low communication load and strong scalability [157].
• Enhancements within the Recursive Framework: AKF and Consensus Filters
  The AKF and Consensus Filters represent two distinct approaches to improving robustness within the recursive filtering paradigm. By estimating and compensating for time-varying noise statistics online, the AKF can enhance both accuracy and robustness, with studies showing accuracy improvements of 30–40% in certain navigation scenarios [31,158]. A 2022 study in IEEE Transactions on Vehicular Technology further demonstrates a novel adaptive filter that shows strong performance under non-Gaussian noise [159]. The Consensus Filter, in contrast, reformulates the distributed estimation problem as an average consensus problem on a network graph [157]. Its standout advantage is its high robustness to dynamic network topologies and link failures, a topic explored in recent 2025 publications in IEEE Transactions on Automatic Control concerning completely distributed state estimation [160]. However, this comes at the cost of higher communication overhead, as multiple negotiation iterations are often required to reach consensus.
• Specialized Solutions for Harsh Environments: MCC-KF and Wavelet-aided Fusion
  To specifically address the hostile underwater environment, robust filters based on more advanced theories have been developed. The Maximum Correntropy Criterion Kalman Filter (MCC-KF) demonstrates unique value by fundamentally employing a cost function that is insensitive to large errors. This provides exceptional robustness against the heavy-tailed, impulsive noise commonly caused by acoustic multipath effects [68,155,161]. This is corroborated by new 2025 research in the IEEE Signal Processing Letters, which proposes a dual-robust-kernel Kalman filter specifically for outlier-robust underwater navigation [162]. Recent studies indicate that in complex non-Gaussian noise environments, MCC-KF-based algorithms can improve navigation accuracy by over 50% compared to traditional filters [163]. Wavelet-aided fusion approaches the problem from a signal processing perspective. By decomposing and reconstructing sensor signals across different frequency scales, it can effectively filter noise and align asynchronous data streams, thereby significantly improving fusion accuracy. Experiments have shown that wavelet denoising, even as a preprocessing step, can reduce the root mean square of position errors by approximately 14% [85].
• The High-Accuracy Paradigm: Factor Graph Optimization
  FGO represents the current state-of-the-art in terms of achievable accuracy. By abandoning the Markov assumption of recursive filters and jointly optimizing all historical states and measurements within a time window, it achieves global consistency and can effectively correct earlier errors [41,42,43]. In comparable navigation problems, its RMSE can be significantly lower than that of an EKF, with forthcoming work in the 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) continuing to validate its superior performance in robust navigation frameworks [154]. Critically, its batch-processing nature provides remarkable resilience to sensor failures, with error growth being minimal in DVL failure scenarios [154]. However, this high precision is achieved at the cost of high computational complexity (often >3 times that of an EKF) and latency [156]. Furthermore, its computational complexity scales quadratically with the number of nodes $O\left(N^2\right)$, limiting its real-time application in very large-scale clusters [41].

To visually represent these critical performance trade-offs, Figure 5 presents the data from Table 3 in the form of a radar chart. The shape of each polygon clearly delineates the performance “fingerprint” of the corresponding algorithm, allowing readers to quickly grasp the strengths and weaknesses of each approach. For instance, the polygon for FG extends far along the “Accuracy” axis but is severely retracted on the “Computational Efficiency” and “Scalability” axes, whereas the MCC-KF exhibits a balanced profile with a notable protrusion on the “Robustness” axis.

7.4. Summary

This section has explored the key challenges faced when converting CN algorithms into practical systems, primarily covering security, performance evaluation frameworks, and comprehensive comparisons of technical approaches. First, it has emphasized the core importance of ensuring the security of CN [140]. Since CN relies on trusted information exchange, this section analyzes the main threats faced by the system—jamming and spoofing attacks [141]. It has been noted that, in addition to traditional defensive measures, the fault-detection mechanisms based on information-theoretic metrics (such as the BD [146]) discussed in Section 4 can also serve as an effective data-layer defense against spoofing attacks by quantifying “information anomalies” to identify and remove malicious data injections.

Second, to systematically evaluate and compare different algorithms, this section has proposed a multi-dimensional performance evaluation framework [1]. This framework includes five core evaluation dimensions: fusion accuracy, computational complexity, communication load, robustness, and scalability [3]. Crucially, to move beyond qualitative descriptions, we introduced a standardized benchmark scenario to ground the comparison in objective, data-driven evidence. This culminated in a new, rigorous quantitative analysis presented in Table 3 and visually synthesized in the radar chart of Figure 5. This new analysis provides a much clearer insight into the critical trade-offs, for instance, revealing that while FG methods offer superior accuracy, the MCC-based filters provide unparalleled robustness against the non-Gaussian noise typical in real-world deployments—a distinction not apparent in purely qualitative assessments.

8. Synthesis, Key Challenges, and Future Roadmap

This paper has systematically reviewed the landscape of robust state estimation and information fusion techniques for cooperative UUV clusters. This final section synthesizes the key findings, particularly those from our quantitative analysis, to identify the most pressing challenges facing the field and proposes a structured, data-driven roadmap for future research.

8.1. Synthesis of Key Findings and Technology Evolution

The comprehensive analysis throughout this paper, culminating in the quantitative comparison in Section 7.3, allows us to synthesize the current state-of-the-art not merely as an evolution of techniques, but as a landscape defined by fundamental trade-offs. Our quantitative results (Table 3 and Figure 5) empirically confirm the critical trade-off between accuracy and resource consumption. Batch optimization methods like FGO or Bundle Adjustment (BA) achieve superior accuracy and global consistency through joint optimization of poses and landmarks [54,164], but this advantage comes at the cost of high computational and communication overhead, making them challenging for real-time deployment on resource-constrained UUV platforms. Conversely, advanced recursive filters such as the Maximum Correntropy Kalman Filter (MCC-KF) demonstrate strong robustness to non-Gaussian noise with significantly lower complexity [53,165,166], yet they remain susceptible to long-term drift without global constraints. This synthesis reveals that technological evolution has not produced a single “best” algorithm, but rather a spectrum of specialized tools, each exhibiting a distinct balance between accuracy, robustness, and resource efficiency [167].

8.2. Challenges and Unsolved Problems

Based on the synthesis above, we can now articulate the key challenges and unsolved problems that are hindering the widespread deployment of large-scale autonomous UUV clusters. These challenges are no longer abstract concepts but are directly informed by the performance gaps identified in our analysis.

• The Accuracy-vs-Complexity Gap: This is the most significant challenge. As demonstrated in our quantitative analysis, there is a clear performance gap between theoretically optimal but resource-intensive batch methods and efficient but less accurate filtering techniques [168]. The unsolved problem is how to design algorithms that are both robust for long-duration missions and practical for real-time execution on embedded UUV hardware. Recent approaches attempt to bridge this using techniques like federated fixed-lag smoothing to balance accuracy and computational load [169]
• Hyperscale Scalability: Most existing algorithms are validated in simulations with only a few UUVs. The communication and computational complexity associated with scaling to clusters of tens or even hundreds of vehicles (hyperscale) remains a largely unsolved problem [170]. The challenge lies in designing decentralized algorithms whose complexity does not grow exponentially with the number of agents and whose performance does not degrade catastrophically with increased communication latency and packet loss, a key focus of modern cooperative localization research [171].
• Energy-Aware Design: The energy budget is arguably the most critical constraint for UUVs. However, the majority of current research focuses on optimizing for navigation accuracy, with energy efficiency often being an afterthought [172]. A key unsolved problem is the lack of a unified framework for the co-design of energy-aware and navigation-aware algorithms that can make intelligent trade-offs between performance and mission endurance, for example, by developing mission planners that explicitly model the vehicle’s energy consumption [173].
• Lack of Standardized Benchmarking: As highlighted by our effort to create a comparison framework in Section 7, the field lacks standardized, publicly available underwater datasets and simulation environments. This makes it exceedingly difficult to fairly compare new algorithms, hindering reproducible research and slowing the pace of innovation. While specific efforts have been made to create and characterize datasets [174], the community still needs more comprehensive and widely adopted benchmarks to rigorously validate emerging navigation techniques [175].

8.3. Future Research Trajectories: A Roadmap for the Next Decade

Building upon the specific challenges identified above, we propose a structured research roadmap. To make it concrete and actionable, and to provide a clear, structured presentation, each direction is supported by examples from recent literature and organized into a timeline.

8.3.1. Short-Term Goals (1–3 Years)

• Standardized Benchmarking and Datasets: A primary obstacle to progress is the lack of standardized datasets. The community urgently needs to develop benchmark suites—analogous to the KITTI dataset in autonomous driving—that include raw sensor data (IMU, DVL, sonar, acoustic modem logs) from diverse, real-world underwater environments [175,176]. This would directly address the need for better evaluation controls and accelerate innovation.
• Energy-Aware Navigation and Communication: Future research should focus on algorithms that explicitly co-optimize for navigation accuracy and energy consumption. This includes developing adaptive sensing strategies where a UUV can power down non-essential sensors, and creating energy-aware communication protocols that schedule transmissions to minimize the power-intensive “wake-up” cycles of acoustic modems [177].

8.3.2. Medium-Term Goals (3–7 Years)

• Bridging the Accuracy-Complexity Gap with Hybrid AI: A key research question is: How can we design algorithms that achieve FGO-like accuracy with filter-like efficiency? A promising avenue is the development of Hybrid AI models that merge the theoretical rigor of traditional filters with the powerful nonlinear fitting capabilities of neural networks. For example, recent studies have successfully used LSTMs or Transformers to learn and predict the complex, non-Gaussian noise characteristics of sensors, which are then fed into an adaptive Kalman filter to improve its accuracy [178,179].
• Hyperscale Scalability via Decentralized Optimization: To overcome the challenges of large-scale swarms, research should move beyond simple consensus and explore more advanced decentralized optimization techniques. This includes developing communication-efficient distributed graph optimization algorithms and exploring event-triggered communication schemes where UUVs only share information when their uncertainty exceeds a certain threshold, thus drastically reducing network load [180].

8.3.3. Long-Term Goals (7+ Years)

• Robust-by-Design Security: As UUV clusters become more autonomous, security becomes paramount. Future work should focus on “robust-by-design” security, moving beyond cryptographic overhead. This involves leveraging the intrinsic robustness of certain estimation algorithms as a defense mechanism. For instance, the statistical fault-detection methods discussed in Section 4.4 can be extended to explicitly detect and reject malicious data injection attacks from compromised nodes, creating a more resource-efficient security paradigm [181].
• Quantum Sensing for GNSS-Free Navigation: A transformative long-term goal is the development of navigation systems that are entirely independent of external signals. Quantum sensing offers a revolutionary path forward. Future research should explore the integration of ultra-precise quantum inertial measurement units (e.g., quantum gyroscopes) and gravity gradiometers, which have the theoretical potential to enable long-duration, drift-free dead reckoning, fundamentally changing the paradigm of underwater navigation [182,183].
• Ethical Frameworks for Autonomous Swarms: As UUV swarms transition from research to real-world deployment in both civilian and military contexts, it is imperative to develop robust ethical and legal frameworks. This includes research into verifiable decision-making, accountability in multi-agent systems, and establishing rules of engagement for autonomous maritime operations to ensure their safe and responsible use [184].

9. Conclusions

This paper has provided a comprehensive and critical review of the state-of-the-art in robust state estimation and information fusion for cooperative UUV clusters. Moving beyond a purely descriptive survey, the central contribution of this work is the introduction of a novel quantitative comparison framework. By establishing a standardized benchmark scenario and evaluating key algorithms across concrete performance metrics—accuracy, computational complexity, communication overhead, and robustness—this paper provides the first data-driven guide to navigating the fundamental trade-offs inherent in UUV cooperative navigation system design.

Our analysis synthesized several key findings. We provided a deep dive into the architectural and algorithmic trade-offs, from the global consistency of batch optimization methods like FGO to the computational efficiency of robust recursive filters like the MCC-KF. We critically evaluated not only their operational principles but also their practical limitations and hyperparameter sensitivities within the context of the extreme underwater environment. Furthermore, we extended the discussion to advanced applications, including the challenges of operating in heterogeneous fleets and extreme environments such as the polar regions and the deep sea.

By synthesizing the insights from our quantitative analysis, we identified key unsolved problems and proposed a structured, data-driven future research roadmap, highlighting specific, actionable research questions for the next decade. The overarching conclusion of this review is that there is no “one-size-fits-all” solution in this domain. The optimal choice of an algorithm is a mission-specific decision that requires a careful balance of competing performance criteria. It is our hope that the analytical framework and quantitative insights provided in this paper will serve as a valuable resource for researchers and engineers, accelerating the development of the next generation of truly autonomous and robust cooperative underwater systems.