Inertial navigation systems (INS) are foundational to navigation in both manned and autonomous platforms, with overall performance critically dependent on accurate initial alignment. This process, typically performed while stationary, establishes a reference orientation for subsequent navigation. However, traditional gyrocompassing methods often fail with low-performance gyroscopes due to limited sensitivity to Earth’s rotation rate. To overcome these limitations, we present a deep learning-based framework that significantly improves heading estimation using mid-tier inertial sensors. By learning to model and correct sensor errors, our method enables accurate gyrocompassing without reliance on extended filtering or long stationary periods. Theoretical analysis and experimental validation reveal a tenfold reduction in waiting times and over 50% lower alignment errors, substantially narrowing the gap between consumer-grade and tactical-grade systems. This establishes a new lower error bound for affordable gyros and offers a practical path towards scalable, high-precision navigation.

Low-cost gyroscope calibration is essential for ensuring the accuracy and reliability of gyroscope measurements. Stationary calibration estimates the deterministic parts of measurement errors. To this end, a common practice is to average the gyroscope readings during a predefined period and estimate the gyroscope bias. Calibration duration plays a crucial role in performance, therefore, longer periods are preferred. However, some applications require quick startup times and calibration is therefore allowed only for a short time. In this work, we focus on reducing low-cost gyroscope calibration time using deep learning methods. We propose an end-to-end convolutional neural network for the application of gyroscope calibration. We explore the possibilities of using multiple real and virtual gyroscopes to improve the calibration performance of single gyroscopes. To train and validate our approach, we recorded a dataset consisting of 186.6 h of gyroscope readings, using 36 gyroscopes of four different brands. We also created a virtual dataset consisting of simulated gyroscope readings. The six datasets were used to evaluate our proposed approach. One of our key achievements in this work is reducing gyroscope calibration time by up to 89% using three low-cost gyroscopes. Our dataset is publicly available to allow reproducibility of our work and to increase research in the field.

Despite the crucial role of inertial measurements in motion tracking and navigation systems, the time-consuming and resource-intensive nature of collecting extensive inertial data has hindered the development of robust machine learning models in this field. In recent years, diffusion models have emerged as a revolutionary class of generative models, reshaping the landscape of artificial data generation. These models surpass generative adversarial networks and other state-of-the-art approaches to complex tasks. In this work, we propose diffusion-driven specific force-generated data for smartphone location recognition. We provide a comprehensive evaluation methodology by comparing synthetic and real recorded specific force data across multiple metrics. Our results demonstrate that our diffusion-based generative model successfully captures the distinctive characteristics of specific force signals across different smartphone placement conditions. Thus, by creating diverse, realistic synthetic data, we can reduce the burden of extensive data collection while providing high-quality training data for machine learning models.

The extended Kalman filter (EKF) is a widely adopted method for sensor fusion in navigation applications. A crucial aspect of the EKF is the online determination of the process noise covariance matrix reflecting the model uncertainty. While common EKF implementation assumes a constant process noise, in real-world scenarios, the process noise varies, leading to inaccuracies in the estimated state and potentially causing the filter to diverge. Model-based adaptive EKF methods were proposed and demonstrated performance improvements to cope with such situations, highlighting the need for a robust adaptive approach. In this paper, we derive an adaptive Kalman-informed transformer (A-KIT) designed to learn the varying process noise covariance online. Built upon the foundations of the EKF, A-KIT utilizes the well-known capabilities of set transformers, including inherent noise reduction and the ability to capture nonlinear behavior in the data. This approach is suitable for any application involving the EKF. In a case study, we demonstrate the effectiveness of A-KIT in nonlinear fusion between a Doppler velocity log and inertial sensors. This is accomplished using real data recorded from sensors mounted on an autonomous underwater vehicle operating in the Mediterranean Sea. We show that A-KIT outperforms the conventional EKF by more than 49.5% and model-based adaptive EKF by an average of 35.4% in terms of position accuracy. • A-KIT improves EKF accuracy by learning varying process noise online. • A-KIT uses set transformers for nonlinear behavior capture and noise reduction. • Demonstrated effectiveness with real AUV data from the Mediterranean Sea. • Achieves 49.5% better position accuracy over conventional EKF. • Outperforms model-based adaptive EKF by 35.4% in position accuracy.

Autonomous inspection tasks require path-planning algorithms to efficiently gather observations frompoints of interest(POIs). However, localization errors in urban environments introduce execution uncertainty, posing challenges to successfully completing such tasks. The existing inspection-planning algorithms do not explicitly address this uncertainty, which can hinder their performance. To overcome this, in this article, we introduceincremental random inspection-roadmap search (IRIS)-under uncertainty(IRIS-U$^{2}$), an inspection-planning algorithm that provides statistical assurances regarding coverage, path length, and collision probability. Our approach builds uponIRIS—our framework fordeterministic, highly efficient, and provably asymptotically optimal framework. This extension adapts IRIS to uncertain settings using a refined search procedure that estimates POI coverage probabilities through Monte Carlo (MC) sampling. We demonstrateIRIS-U$^{2}$through a case study on bridge inspections, achieving improved expected coverage, reduced collision probability, and increasingly precise statistical guarantees as MC samples grow. In addition, we explore bounded suboptimal solutions to reduce computation time while preserving statistical assurances.

The Kalman filter (KF) is a widely-used algorithm for tracking the latent state of a dynamical system from noisy observations. For systems that are well-described by linear Gaussian state space models, the KF minimizes the mean-squared error (MSE). However, in practice, observations are corrupted by outliers, severely impairing the KF’s performance. In this work, an outlier-insensitive KF (OIKF) is proposed, where robustness is achieved by modeling a potential outlier as a normally distributed random variable with unknown variance (NUV). The NUV’s variance is estimated online, using both expectation-maximization (EM) and alternating maximization (AM). The former was previously proposed for the task of smoothing with outliers and was adapted here to filtering, while both EM and AM obtained the same performance and outperformed the other algorithms, the AM approach is less complex and thus requires 40% less runtime. Our empirical study demonstrates that the MSE of our proposed outlier-insensitive KF outperforms previously proposed algorithms, and that for data clean of outliers, it reverts to the classic KF, i.e., MSE optimality is preserved.

Depth estimation is critical for any robotic system. In the past years, the estimation of depth from monocular images has shown great improvement. However, in the underwater environment results are still lagging behind due to appearance changes caused by the medium. So far little effort has been invested in overcoming this. Moreover, underwater, there are more limitations to using high-resolution depth sensors, which is a serious obstacle to generating ground truth. So far unsupervised methods that tried to solve this have achieved limited success as they relied on domain transfer from a dataset in the air. We suggest network training using subsequent frames, self-supervised by a reprojection loss, as was demonstrated successfully above water. We propose several additions to the self-supervised framework to cope with the underwater environment and achieve state-of-the-art results on a challenging forward-looking underwater dataset.

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the underlying statistics; however, deep learning based tracking systems struggle to reliably characterize uncertainty. In this paper, we investigate the ability of KalmanNet, a recently proposed; hybrid; model-based; deep state tracking algorithm, to estimate an uncertainty measure. By exploiting the interpretable nature of KalmanNet, we show that the error covariance matrix can be computed based on its internal features, as an uncertainty measure. We demonstrate that when the system dynamics are known, KalmanNet—which learns its mapping from data without access to the statistics—provides uncertainty similar to that provided by the KF; and while in the presence of evolution model-mismatch, KalmanNet provides a more accurate error estimation.

Autonomous underwater vehicles (AUV) perform various applications such as seafloor mapping and underwater structure health monitoring. Commonly, an inertial navigation system aided by a Doppler velocity log (DVL) is used to provide the vehicle’s navigation solution. In such fusion, the DVL provides the velocity vector of the AUV, which determines the navigation solution’s accuracy and helps estimate the navigation states. This paper proposes BeamsNet, an end-to-end deep learning framework to regress the estimated DVL velocity vector that improves the accuracy of the velocity vector estimate, and could replace the model-based approach. Two versions of BeamsNet, differing in their input to the network, are suggested. The first uses the current DVL beam measurements and inertial sensor data, while the other utilizes only DVL data, taking the current and past DVL measurements for the regression process. Both simulation and sea experiments were made to validate the proposed learning approach relative to the model-based approach. Sea experiments were made with the Snapir AUV in the Mediterranean Sea, collecting approximately four and a half hours of DVL and inertial sensor data. Our results show that the proposed approach achieved an improvement of more than 60% in estimating the DVL velocity vector.

Accurate attitude and heading is required for many applications. For pedestrian navigation, the major challenge is to cope with linear accelerations and magnetic disturbances. To that end, a data driven adaptive complementary filter for attitude and heading estimation is proposed. The accelerometers and magnetometers weights in each axis are adjusted according to optimized gain maps. The proposed approach is compared to commonly used algorithms using experimental data representing commonly used smartphone dynamics. Results show the contribution of the proposed approach to the attitude accuracy.

One of the common ways to perform indoor localization for pedestrians is to employ the smartphone's inertial sensors, in a process known as pedestrian dead reckoning (PDR). Estimation of the pedestrian's heading is a crucial step in PDR algorithms, since it is a key factor in the positioning accuracy. In this paper, rather than assuming the smartphone to be fixed in a certain orientation on the pedestrian, we focus on estimating the vertical direction within the sensor frame of an unconstrained device. To that end, we establish a framework for gravity direction estimation and highlight the important role it has for solving the heading in the horizontal plane. By employing only accelerometers and gyroscopes, we derive, present and compare different approaches both for estimating the gravity direction and for computing the heading angle. The results are demonstrated and analyzed using data recorded from field experiments.