Information-Aided DVL Calibration

The Doppler velocity log (DVL) velocity measurements are critical to the accuracy of autonomous underwater vehicle (AUV) navigation solutions and, consequently, to mission success. To ensure accurate measurements, the DVL is commonly calibrated before mission start while the AUV sails on the water surface, receiving global navigation satellite system (GNSS) signals that provide accurate reference measurements. Conventionally, Kalman filter-based approaches are employed during calibration to estimate the scale factor and misalignment errors. However, in certain environments, GNSS signals may be unavailable, rendering conventional calibration impossible and forcing the use of uncalibrated DVL measurements, which degrades navigation performance. To address this limitation, this work proposes information-aided calibration (IAC) with two main contributions: first, improving the accuracy of conventional Kalman filter-based calibration in GNSS-enabled environments, and second, enabling GNSS-free DVL self-calibration. Using real-world AUV datasets, the proposed IAC models achieve up to a 20% average improvement in GNSS-enabled environments and up to a 35% improvement in velocity vector estimation during GNSS-free DVL self-calibration. Overall, the proposed approach improves navigation accuracy, reduces navigation drift, and consequently enhances mission reliability.

DVL-DeepONet: A Physics-Guided Operator Learning for Resilient Underwater Navigation

Autonomous Underwater Vehicles (AUVs) rely heavily on the fusion of inertial sensors and Doppler velocity logs (DVLs) for navigation. In standard autonomous navigation systems, the DVL measures four beam velocities, thereby enabling the estimation of the AUV velocity vector. However, during real-world missions, the DVL may receive noisy or incomplete beam measurements due to marine obstacles, seabed reflections, or environmental disturbances. Furthermore, some low-cost underwater platforms operate without inertial sensors to reduce system complexity and cost. In such cases, reliable estimation of the AUV velocity vector in real-world missing beam scenarios becomes challenging, leading to degraded navigation solutions. To circumvent these challenges and enable resilient underwater navigation, we propose DVL-DeepONet, a physics-guided deep neural operator framework along with three variants. The proposed models are designed to estimate DVL-based velocity information under multiple operational scenarios, including (i) noise-resilient estimation in coupled inertial/DVL measurements, (ii) DVL-only learning, and (iii) beam measurement recovery. By learning a nonlinear operator that maps temporal inertial/DVL observations directly to vehicle velocity while enforcing DVL measurement physics through a consistency constraint, the proposed approach enables robust velocity estimation even under degraded sensing conditions. The proposed framework is validated using real-world AUV experiments, comprising a cumulative path length of approximately 10,000 m. Experimental results demonstrate that the proposed DVL-DeepONet architectures outperform baseline model-based approaches and learning-based algorithms by 40%.

BLENDS: Bayesian Learning-Enhanced Deep Smoothing for GNSS-Denied Environments

Maintaining accurate navigation during GNSS outages remains a significant challenge for autonomous systems relying on low-cost inertial sensors. While classical smoothing methods, such as the two-filter smoother and Rauch-Tung-Striebel smoother, exploit measurements collected before and after an outage, their performance remains limited by the accuracy of conventional GNSS measurements. This paper presents Bayesian learning-enhanced navigation with deep smoothing (BLENDS), a transformer-based framework that augments Bayesian smoothing with learned covariance adaptation and state correction. The proposed method preserves the statistical foundations of Bayesian estimation while leveraging data-driven learning to improve navigation accuracy. Evaluations on the quadrotor dataset with GNSS outages demonstrate that BLENDS consistently outperforms both model-based smoothers, achieving up to 25.6% improvement in the position root mean square error while also reducing estimation uncertainty. Furthermore, BLENDS learns to compensate for the systematic bias between conventional GNSS positioning and RTK ground truth, enabling accuracy beyond that achievable with conventional GNSS measurements alone. The results demonstrate the potential of learning-enhanced Bayesian smoothing for resilient and high-accuracy navigation in GNSS-challenged environments.

Gauge Freedom Optimization for Truncation Error Reduction in Inertial Navigation

Numerical integration plays a central role in inertial navigation systems, where sensor measurements are propagated through time to obtain orientation, velocity, and position states. The accuracy of this propagation depends on the numerical integrator type, order and step-size. Prior work showed that for second-order systems with known forcing functions, the gauge freedom in the variation of parameters technique can be exploited to reduce truncation error without modifying the integrator. However, this approach requires analytical knowledge of the forcing function, limiting its applicability in real-world systems. To address this limitation we propose the u-space methodology, a novel state mapping that generalizes the gauge freedom to systems with unknown forcing functions. The optimal gauge is derived in closed form for second-order systems and in both closed and empirical form for first-order systems. The proposed approach was evaluated through Monte Carlo simulations across four forcing functions, five sensor grades, and four Adams-Bashforth orders, as well as on a real-world inertial navigation dataset. Results show consistent error reduction across all tested conditions, with the largest gains observed in the full inertial mechanization pipeline, making the approach applicable to high-grade inertial systems, where truncation error constitutes a larger share of the error budget, and to aided low-cost systems with high-rate updates, where propagation spans only short inter-update intervals.

Wheel-Mounted/GNSS Fusion with AI-Aided Position Updates

Accurate and robust localization remains a fundamental challenge for autonomous ground vehicles. In this work, we propose a hybrid neural inertial navigation framework that integrates a wheel-mounted inertial sensors, enforced periodic trajectories, and a simple, efficient neural network capable of regressing vehicle displacement with GNSS position updates in an error-state extended Kalman filter. The periodic trajectories increase the inertial signal-to-noise ratio, allowing the network to use only inertial readings to estimate displacement. The approach is validated through real-world experiments using multiple wheel-mounted inertial sensors. Experimental results demonstrate that the proposed method achieves a significant improvement in positioning accuracy, reducing the position root mean squared error by approximately 46 % compared to standard wheel-mounted inertial sensor fusion with GNSS updates.

Enhanced INS/GNSS State Estimation using GNSS-Based Acceleration Measurements

Accurate and reliable navigation is essential for autonomous ground vehicle operations. Standard INS/GNSS fusion relies on GNSS position updates, which provide limited observability of orientation and inertial sensor error states, particularly during low-dynamic motion. In this work, we propose utilizing past GNSS measurements alongside a motion model to extract meaningful vehicle acceleration information. This acceleration measurement is then integrated into the INS/GNSS filter to improve its robustness and accuracy. The proposed approach is evaluated on two real-world unmanned ground vehicle datasets collected from different mobile platforms and inertial sensor grades. Results demonstrate consistent positioning accuracy improvements relative to the standard position-aided filter, with mean position root mean square error improvements of 11.40 % and 20.74 % on the two datasets, respectively.

AI-Aided Advancements in Autonomous Underwater Vehicle Navigation

Autonomous underwater vehicles (AUVs) have become indispensable for deep-sea exploration, spanning critical scientific research and commercial applications. The rapid attenuation of electromagnetic waves renders satellite radio signals unavailable, while the dynamic unpredictability of the marine environment presents formidable navigation challenges. This chapter explores recent advancements in AI-aided AUV positioning, specifically focusing on advanced sensor fusion architectures that integrate inertial navigation systems with Doppler velocity logs and cameras. Beyond traditional model-based filtering, we examine the transformative emergence of AI-driven learning approaches in enhancing inertial dead-reckoning tasks and adaptive fusion algorithms. By addressing these recent milestones, this chapter provides a comprehensive roadmap for achieving the high-precision navigation essential for autonomous underwater missions.

Multi-Scaled Unscented Kalman Filter

The unscented Kalman filter (UKF) is a commonly used algorithm capable of estimating the states of nonlinear dynamic systems. It carefully chooses a set of sample points, called sigma points that capture the nonlinear system states posterior mean and covariance. The filter is based on the scaled unscented transform, where the scaling parameters impact the spreading of the sigma points, determining the estimated model capturing. In its current form, the UKF employs a single set of scaling parameters shared by all sigma points. Because states in multi-dimensional models often exhibit substantially different behaviors, this imposes a critical limitation: the standard UKF parameters cannot be tuned to extend the spread for one dimension while reducing it for another. To bridge this gap, we propose the multi-scaled UKF to enable spreading differently per state, while maintaining the key properties of the sigma points and UKF. A rigorous mathematical foundation is provided, introducing a novel theoretical approach to multi-scaling. The benefits of this approach are demonstrated through two distinct nonlinear dynamic systems. Consequently, our multi-scaled UKF captures the nonlinear behavior of multi-dimensional states more effectively, leading to improved estimation accuracy.

Neural-Assisted in-Motion Self-Heading Alignment

Autonomous platforms operating in the oceans require accurate navigation to successfully complete their mission. In this regard, the initial heading estimation accuracy and the time required to achieve it play a critical role. The initial heading is traditionally estimated by model-based approaches employing orientation decomposition. However, methods such as the dual vector decomposition and optimized attitude decomposition achieve satisfactory heading accuracy only after long alignment times. To allow rapid and accurate initial heading estimation, we propose an end-to-end, model-free, neural-assisted framework using the same inputs as the model-based approaches. Our proposed approach was trained and evaluated on real-world dataset captured by an autonomous surface vehicle. Our approach shows a significant accuracy improvement over the model-based approaches achieving an average absolute error improvement of 53%. Additionally, our proposed approach was able to reduce the alignment time by up to 67%. Thus, by employing our proposed approach, the reduction in alignment time and improved accuracy allow for a shorter deployment time of an autonomous platform and increased navigation accuracy during the mission.

Bayesian Learning-Enhanced Navigation with Deep Smoothing for Inertial-Aided Navigation

Accurate post-processing navigation is essential for applications such as survey and mapping, where the full measurement history can be exploited to refine past state estimates. Fixed-interval smoothing algorithms represent the theoretically optimal solution under Gaussian assumptions. However, loosely coupled INS/GNSS systems fundamentally inherit the systematic position bias of raw GNSS measurements, leaving a persistent accuracy gap that model-based smoothers cannot resolve. To address this limitation, we propose BLENDS, which integrates Bayesian learning with deep smoothing to enhance navigation performance. BLENDS is a a data-driven post-processing framework that augments the classical two-filter smoother with a transformer-based neural network. It learns to modify the filter covariance matrices and apply an additive correction to the smoothed error-state directly within the Bayesian framework. A novel Bayesian-consistent loss jointly supervises the smoothed mean and covariance, enforcing minimum-variance estimates while maintaining statistical consistency. BLENDS is evaluated on two real-world datasets spanning a mobile robot and a quadrotor. Across all unseen test trajectories, BLENDS achieves horizontal position improvements of up to 63% over the baseline forward EKF.