Itzik Klein

Gal Versano, Itzik Klein

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.

Shunit Truzman, Guy Revach, Nir Shlezinger et al. · eth-zurich

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 KFs performance. In this work, an outlier-insensitive KF is proposed, where robustness is achieved by modeling each potential outlier as a normally distributed random variable with unknown variance (NUV). The NUVs variances are 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 percentage less run-time. 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

Nadav Cohen, Itzik Klein

Inertial sensing is used in many applications and platforms, ranging from day-to-day devices such as smartphones to very complex ones such as autonomous vehicles. In recent years, the development of machine learning and deep learning techniques has increased significantly in the field of inertial sensing and sensor fusion. This is due to the development of efficient computing hardware and the accessibility of publicly available sensor data. These data-driven approaches mainly aim to empower model-based inertial sensing algorithms. To encourage further research in integrating deep learning with inertial navigation and fusion and to leverage their capabilities, this paper provides an in-depth review of deep learning methods for inertial sensing and sensor fusion. We discuss learning methods for calibration and denoising as well as approaches for improving pure inertial navigation and sensor fusion. The latter is done by learning some of the fusion filter parameters. The reviewed approaches are classified by the environment in which the vehicles operate: land, air, and sea. In addition, we analyze trends and future directions in deep learning-based navigation and provide statistical data on commonly used approaches.

Barak Or, Itzik Klein

The fusion between an inertial navigation system and global navigation satellite systems is regularly used in many platforms such as drones, land vehicles, and marine vessels. The fusion is commonly carried out in a model-based extended Kalman filter framework. One of the critical parameters of the filter is the process noise covariance. It is responsible for the real-time solution accuracy, as it considers both vehicle dynamics uncertainty and the inertial sensors quality. In most situations, the process noise is covariance assumed to be constant. Yet, due to vehicle dynamics and sensor measurement variations throughout the trajectory, the process noise covariance is subject to change. To cope with such situations, several adaptive model-based Kalman filters were suggested in the literature. In this paper, we propose a hybrid model and learning-based adaptive navigation filter. We rely on the model-based Kalman filter and design a deep neural network model to tune the momentary system noise covariance matrix, based only on the inertial sensor readings. Once the process noise covariance is learned, it is plugged into the well-established, model-based Kalman filter. After deriving the proposed hybrid framework, field experiment results using a quadrotor are presented and a comparison to model-based adaptive approaches is given. We show that the proposed method obtained an improvement of 25% in the position error. Furthermore, the proposed hybrid learning method can be used in any navigation filter and also in any relevant estimation problem.

Nadav Cohen, Itzik Klein

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 sensors 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 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.

Shlomi Amitai, Itzik Klein, Tali Treibitz

Depth estimation is critical for any robotic system. In the past years estimation of depth from monocular images have 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 on overcoming this. Moreover, underwater, there are more limitations for using high resolution depth sensors, this makes generating ground truth for learning methods another enormous obstacle. So far unsupervised methods that tried to solve this have achieved very limited success as they relied on domain transfer from dataset in air. We suggest training using subsequent frames self-supervised by a reprojection loss, as was demonstrated successfully above water. We suggest 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.

Shunit Truzman, Guy Revach, Nir Shlezinger et al.

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers in the observations, due to the sensitivity of its convex quadratic objective function. To mitigate such behavior, outlier detection algorithms can be applied. In this work, we propose a parameter-free algorithm which mitigates the harmful effect of outliers while requiring only a short iterative process of the standard update step of the KF. To that end, we model each potential outlier as a normal process with unknown variance and apply online estimation through either expectation maximization or alternating maximization algorithms. Simulations and field experiment evaluations demonstrate competitive performance of our method, showcasing its robustness to outliers in filtering scenarios compared to alternative algorithms.

Itzik Klein

The purpose of navigation is to determine the position, velocity, and orientation of manned and autonomous platforms, humans, and animals. Obtaining accurate navigation commonly requires fusion between several sensors, such as inertial sensors and global navigation satellite systems, in a model-based, nonlinear estimation framework. Recently, data-driven approaches applied in various fields show state-of-the-art performance, compared to model-based methods. In this paper we review multidisciplinary, data-driven based navigation algorithms developed and experimentally proven at the Autonomous Navigation and Sensor Fusion Lab (ANSFL) including algorithms suitable for human and animal applications, varied autonomous platforms, and multi-purpose navigation and fusion approaches

Nadav Cohen, Itzik Klein

Autonomous underwater vehicles (AUVs) are employed for marine applications and can operate in deep underwater environments beyond human reach. A standard solution for the autonomous navigation problem can be obtained by fusing the inertial navigation system and the Doppler velocity log sensor (DVL). The latter measures four beam velocities to estimate the vehicle's velocity vector. In real-world scenarios, the DVL may receive less than three beam velocities if the AUV operates in complex underwater environments. In such conditions, the vehicle's velocity vector could not be estimated leading to a navigation solution drift and in some situations the AUV is required to abort the mission and return to the surface. To circumvent such a situation, in this paper we propose a deep learning framework, LiBeamsNet, that utilizes the inertial data and the partial beam velocities to regress the missing beams in two missing beams scenarios. Once all the beams are obtained, the vehicle's velocity vector can be estimated. The approach performance was validated by sea experiments in the Mediterranean Sea. The results show up to 7.2% speed error in the vehicle's velocity vector estimation in a scenario that otherwise could not provide an estimate.

Daniel Engelsman, Itzik Klein

The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.

Nadav Cohen, Zeev Yampolsky, Itzik Klein

Autonomous underwater vehicles (AUVs) are regularly used for deep ocean applications. Commonly, the autonomous navigation task is carried out by a fusion between two sensors: the inertial navigation system and the Doppler velocity log (DVL). The DVL operates by transmitting four acoustic beams to the sea floor, and once reflected back, the AUV velocity vector can be estimated. However, in real-life scenarios, such as an uneven seabed, sea creatures blocking the DVL's view and, roll/pitch maneuvers, the acoustic beams' reflection is resulting in a scenario known as DVL outage. Consequently, a velocity update is not available to bind the inertial solution drift. To cope with such situations, in this paper, we leverage our BeamsNet framework and propose a Set-Transformer-based BeamsNet (ST-BeamsNet) that utilizes inertial data readings and previous DVL velocity measurements to regress the current AUV velocity in case of a complete DVL outage. The proposed approach was evaluated using data from experiments held in the Mediterranean Sea with the Snapir AUV and was compared to a moving average (MA) estimator. Our ST-BeamsNet estimated the AUV velocity vector with an 8.547% speed error, which is 26% better than the MA approach.

Eran Vertzberger, Itzik Klein

Attitude determination using the smartphone's inertial sensors poses a major challenge due to the sensor low-performance grade and variate nature of the walking pedestrian. In this paper, data-driven techniques are employed to address that challenge. To that end, a hybrid deep learning and model based solution for attitude estimation is proposed. Here, classical model based equations are applied to form an adaptive complementary filter structure. Instead of using constant or model based adaptive weights, the accelerometer weights in each axis are determined by a unique neural network. The performance of the proposed hybrid approach is evaluated relative to popular model based approaches using experimental data.

Barak Or, Itzik Klein

Autonomous underwater vehicles (AUV) are commonly used in many underwater applications. Usually, inertial sensors and Doppler velocity log readings are used in a nonlinear filter to estimate the AUV navigation solution. The process noise covariance matrix is tuned according to the inertial sensors' characteristics. This matrix greatly influences filter accuracy, robustness, and performance. A common practice is to assume that this matrix is fixed during the AUV operation. However, it varies over time as the amount of uncertainty is unknown. Therefore, adaptive tuning of this matrix can lead to a significant improvement in the filter performance. In this work, we propose a learning-based adaptive velocity-aided navigation filter. To that end, handcrafted features are generated and used to tune the momentary system noise covariance matrix. Once the process noise covariance is learned, it is fed into the model-based navigation filter. Simulation results show the benefits of our approach compared to other adaptive approaches.

Daniel Engelsman, Yair Stolero, Itzik Klein

Inertial navigation systems (INS) are widely used in almost any operational environment, including aviation, marine, and land vehicles. Inertial measurements from accelerometers and gyroscopes allow the INS to estimate position, velocity, and orientation of its host vehicle. However, as inherent sensor measurement errors propagate into the state estimates, accuracy degrades over time. To mitigate the resulting drift in state estimates, different approaches of parametric and state estimation are proposed to compensate for undesirable errors, using frequency-domain filtering or external information fusion. Another approach uses multiple inertial sensors, a field with rapid growth potential and applications. The increased sampling of the observed phenomenon results in the improvement of several key factors such as signal accuracy, frequency resolution, noise rejection, and higher redundancy. This study offers an analysis tutorial of basic multiple inertial operation, with a new perspective on the error relationship to time, and number of sensors. To that end, a stationary and levelled sensors array is taken, and its robustness against the instrumental errors is analyzed. Subsequently, the hypothesized analytical model is compared with the experimental results, and the level of agreement between them is thoroughly discussed. Ultimately, our results showcase the vast potential of employing multiple sensors, as we observe improvements spanning from the signal level to the navigation states. This tutorial is suitable for both newcomers and people experienced with multiple inertial sensors.

Gal Versano, Itzik Klein

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.

Guy Damari, Zeev Yampolsky, Nadav Cohen et al.

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.

Daniel Engelsman, Itzik Klein

In underwater navigation, accurate heading information is crucial for accurately and continuously tracking trajectories, especially during extended missions beneath the waves. In order to determine the initial heading, a gyrocompassing procedure must be employed. As unmanned underwater vehicles (UUV) are susceptible to ocean currents and other disturbances, the model-based gyrocompassing procedure may experience degraded performance. To cope with such situations, this paper introduces a dedicated learning framework aimed at mitigating environmental effects and offering precise underwater gyrocompassing. Through the analysis of the dynamic UUV signature obtained from inertial measurements, our proposed framework learns to refine disturbed signals, enabling a focused examination of the earth's rotation rate vector. Leveraging recent machine learning advancements, empirical simulations assess the framework's adaptability to challenging underwater conditions. Ultimately, its contribution lies in providing a resilient gyrocompassing solution for UUVs.

Dusan Nemec, Gal Versano, Itai Savin et al.

Autonomous vehicles and wheeled robots are widely used in many applications in both indoor and outdoor settings. In practical situations with limited GNSS signals or degraded lighting conditions, the navigation solution may rely only on inertial sensors and as result drift in time due to errors in the inertial measurement. In this work, we propose WiCHINS, a wheeled and chassis inertial navigation system by combining wheel-mounted-inertial sensors with a chassis-mounted inertial sensor for accurate pure inertial navigation. To that end, we derive a three-stage framework, each with a dedicated extended Kalman filter. This framework utilizes the benefits of each location (wheel/body) during the estimation process. To evaluate our proposed approach, we employed a dataset with five inertial measurement units with a total recording time of 228.6 minutes. We compare our approach with four other inertial baselines and demonstrate an average position error of 11.4m, which is $2.4\%$ of the average traveled distance, using two wheels and one body inertial measurement units. As a consequence, our proposed method enables robust navigation in challenging environments and helps bridge the pure-inertial performance gap.

Daniel Engelsman, Itzik Klein

Autonomous systems across diverse domains have underscored the need for drift-resilient state estimation. Although satellite-based positioning and cameras are widely used, they often suffer from limited availability in many environments. As a result, positioning must rely solely on inertial sensors, leading to rapid accuracy degradation over time due to sensor biases and noise. To counteract this, alternative update sources-referred to as information aiding-serve as anchors of certainty. Among these, the zero-velocity update (ZUPT) is particularly effective in providing accurate corrections during stationary intervals, though it is restricted to surface-bound platforms. This work introduces a controlled ZUPT (C-ZUPT) approach for aerial navigation and control, independent of surface contact. By defining an uncertainty threshold, C-ZUPT identifies quasi-static equilibria to deliver precise velocity updates to the estimation filter. Extensive validation confirms that these opportunistic, high-quality updates significantly reduce inertial drift and control effort. As a result, C-ZUPT mitigates filter divergence and enhances navigation stability, enabling more energy-efficient hovering and substantially extending sustained flight-key advantages for resource-constrained aerial systems.

Nadav Cohen, Itzik Klein

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.

Yair Stolero, Itzik Klein

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 hours 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.

Guy Damari, Itzik Klein

Autonomous underwater vehicles rely on precise navigation systems that combine the inertial navigation system and the Doppler velocity log for successful missions in challenging environments where satellite navigation is unavailable. The effectiveness of this integration critically depends on accurate alignment between the sensor reference frames. Standard model-based alignment methods between these sensor systems suffer from lengthy convergence times, dependence on prescribed motion patterns, and reliance on external aiding sensors, significantly limiting operational flexibility. To address these limitations, this paper presents ResAlignNet, a data-driven approach using the 1D ResNet-18 architecture that transforms the alignment problem into deep neural network optimization, operating as an in-situ solution that requires only sensors on board without external positioning aids or complex vehicle maneuvers, while achieving rapid convergence in seconds. Additionally, the approach demonstrates the learning capabilities of Sim2Real transfer, enabling training in synthetic data while deploying in operational sensor measurements. Experimental validation using the Snapir autonomous underwater vehicle demonstrates that ResAlignNet achieves alignment accuracy within 0.8° using only 25 seconds of data collection, representing a 65\% reduction in convergence time compared to standard velocity-based methods. The trajectory-independent solution eliminates motion pattern requirements and enables immediate vehicle deployment without lengthy pre-mission procedures, advancing underwater navigation capabilities through robust sensor-agnostic alignment that scales across different operational scenarios and sensor specifications.

Gal Versano, Itzik Klein

Modern autonomous navigation for unmanned ground vehicles relies on different estimators to fuse inertial sensors and GNSS measurements. However, the constant noise covariance matrices often struggle to account for dynamic real-world conditions. In this work we propose a hybrid estimation framework that bridges classical state estimation foundations with modern deep learning approaches. Instead of altering the fundamental unscented Kalman filter equations, a dedicated deep neural network is developed to predict the process and measurement noise uncertainty directly from raw inertial and GNSS measurements. We present a sim2real approach, with training performed only on simulative data. In this manner, we offer perfect ground truth data and relieves the burden of extensive data recordings. To evaluate our proposed approach and examine its generalization capabilities, we employed a 160-minutes test set from three datasets each with different types of vehicles (off-road vehicle, passenger car, and mobile robot), inertial sensors, road surface, and environmental conditions. We demonstrate across the three datasets a position improvement of $12.7\%$ compared to the adaptive model-based approach. Thus, offering a scalable and a more robust solution for unmanned ground vehicles navigation tasks.

Barak Diker, Itzik Klein

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.

Nadav Cohen, Itzik Klein

Autonomous Underwater Vehicles (AUVs) commonly utilize an inertial navigation system (INS) and a Doppler velocity log (DVL) for underwater navigation. To that end, their measurements are integrated through a nonlinear filter such as the extended Kalman filter (EKF). The DVL velocity vector estimate depends on retrieving reflections from the seabed, ensuring that at least three out of its four transmitted acoustic beams return successfully. When fewer than three beams are obtained, the DVL cannot provide a velocity update to bind the navigation solution drift. To cope with this challenge, in this paper, we propose a hybrid neural coupled (HNC) approach for seamless AUV navigation in situations of limited DVL measurements. First, we drive an approach to regress two or three missing DVL beams. Then, those beams, together with the measured beams, are incorporated into the EKF. We examined INS/DVL fusion both in loosely and tightly coupled approaches. Our method was trained and evaluated on recorded data from AUV experiments conducted in the Mediterranean Sea on two different occasions. The results illustrate that our proposed method outperforms the baseline loosely and tightly coupled model-based approaches by an average of 96.15%. It also demonstrates superior performance compared to a model-based beam estimator by an average of 12.41% in terms of velocity accuracy for scenarios involving two or three missing beams. Therefore, we demonstrate that our approach offers seamless AUV navigation in situations of limited beam measurements.

Zeev Yampolsky, Yair Stolero, Nitzan Pri-Hadash et al.

An inertial navigation system (INS) utilizes three orthogonal accelerometers and gyroscopes to determine platform position, velocity, and orientation. There are countless applications for INS, including robotics, autonomous platforms, and the internet of things. Recent research explores the integration of data-driven methods with INS, highlighting significant innovations, improving accuracy and efficiency. Despite the growing interest in this field and the availability of INS datasets, no datasets are available for gyro-free INS (GFINS) and multiple inertial measurement unit (MIMU) architectures. To fill this gap and to stimulate further research in this field, we designed and recorded GFINS and MIMU datasets using 54 inertial sensors grouped in nine inertial measurement units. These sensors can be used to define and evaluate different types of MIMU and GFINS architectures. The inertial sensors were arranged in three different sensor configurations and mounted on a mobile robot and a passenger car. In total, the dataset contains 35 hours of inertial data and corresponding ground truth trajectories. The data and code are freely accessible through our GitHub repository.

Zeev Yampolsky, Itzik Klein

Autonomous underwater vehicles (AUVs) are underwater robotic platforms used in a variety of applications. An AUV's navigation solution relies heavily on the fusion of inertial sensors and Doppler velocity logs (DVL), where the latter delivers accurate velocity updates. To ensure accurate navigation, a DVL calibration is undertaken before the mission begins to estimate its error terms. During calibration, the AUV follows a complex trajectory and employs nonlinear estimation filters to estimate error terms. In this paper, we introduce DCNet, a data-driven framework that utilizes a two-dimensional convolution kernel in an innovative way. Using DCNet and our proposed DVL error model, we offer a rapid calibration procedure. This can be applied to a trajectory with a nearly constant velocity. To train and test our proposed approach a dataset of 276 minutes long with real DVL recorded measurements was used. We demonstrated an average improvement of 70% in accuracy and 80% improvement in calibration time, compared to the baseline approach, with a low-performance DVL. As a result of those improvements, an AUV employing a low-cost DVL, can achieve higher accuracy, shorter calibration time, and apply a simple nearly constant velocity calibration trajectory. Our results also open up new applications for marine robotics utilizing low-cost, high-accurate DVLs.

Zeev Yampolsky, Itzik Klein

Autonomous underwater vehicles (AUVs) are used in a wide range of underwater applications, ranging from seafloor mapping to industrial operations. While underwater, the AUV navigation solution commonly relies on the fusion between inertial sensors and Doppler velocity logs (DVL). To achieve accurate DVL measurements a calibration procedure should be conducted before the mission begins. Model-based calibration approaches include filtering approaches utilizing global navigation satellite system signals. In this paper, we propose an end-to-end deep-learning framework for the calibration procedure. Using stimulative data, we show that our proposed approach outperforms model-based approaches by 35% in accuracy and 80% in the required calibration time.

Zeev Yampolsky, Felipe O. Silva, Adriano Frutuoso et al.

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.

Arup Kumar Sahoo, Itzik Klein

A fundamental requirement for full autonomy in mobile robots is accurate navigation even in situations where satellite navigation or cameras are unavailable. In such practical situations, relying only on inertial sensors will result in navigation solution drift due to the sensors' inherent noise and error terms. One of the emerging solutions to mitigate drift is to maneuver the robot in a snake-like slithering motion to increase the inertial signal-to-noise ratio, allowing the regression of the mobile robot position. In this work, we propose MoRPI-PINN as a physics-informed neural network framework for accurate inertial-based mobile robot navigation. By embedding physical laws and constraints into the training process, MoRPI-PINN is capable of providing an accurate and robust navigation solution. Using real-world experiments, we show accuracy improvements of over 85% compared to other approaches. MoRPI-PINN is a lightweight approach that can be implemented even on edge devices and used in any typical mobile robot application.

Yair Stolero, Itzik Klein

Autonomous underwater vehicles (AUVs) are essential for various applications, including oceanographic surveys, underwater mapping, and infrastructure inspections. Accurate and robust navigation are critical to completing these tasks. To this end, a Doppler velocity log (DVL) and inertial sensors are fused together. Recently, a model-based approach demonstrated the ability to extract the vehicle acceleration vector from DVL velocity measurements. Motivated by this advancement, in this paper we present an end-to-end deep learning approach to estimate the AUV acceleration vector based on past DVL velocity measurements. Based on recorded data from sea experiments, we demonstrate that the proposed method improves acceleration vector estimation by more than 65% compared to the model-based approach by using data-driven techniques. As a result of our data-driven approach, we can enhance navigation accuracy and reliability in AUV applications, contributing to more efficient and effective underwater missions through improved accuracy and reliability.

Zeev Yampolsky, Ofir Kruzel, Victoria Khalfin Fekson et al.

Inertial sensors are crucial for recognizing pedestrian activity. Recent advances in deep learning have greatly improved inertial sensing performance and robustness. Different domains and platforms use deep-learning techniques to enhance network performance, but there is no common benchmark. The latter is crucial for fair comparison and evaluation within a standardized framework. The aim of this paper is to fill this gap by defining and analyzing ten data-driven techniques for improving neural inertial classification networks. In order to accomplish this, we focused on three aspects of neural networks: network architecture, data augmentation, and data preprocessing. The experiments were conducted across four datasets collected from 78 participants. In total, over 936 minutes of inertial data sampled between 50-200Hz were analyzed. Data augmentation through rotation and multi-head architecture consistently yields the most significant improvements. Additionally, this study outlines benchmarking strategies for enhancing neural inertial classification networks.

Nadav Cohen, Itzik Klein

Autonomous underwater vehicles are specialized platforms engineered for deep underwater operations. Critical to their functionality is autonomous navigation, typically relying on an inertial navigation system and a Doppler velocity log. In real-world scenarios, incomplete Doppler velocity log measurements occur, resulting in positioning errors and mission aborts. To cope with such situations, a model and learning approaches were derived. This paper presents a comparative analysis of two cutting-edge deep learning methodologies, namely LiBeamsNet and MissBeamNet, alongside a model-based average estimator. These approaches are evaluated for their efficacy in regressing missing Doppler velocity log beams when two beams are unavailable. In our study, we used data recorded by a DVL mounted on an autonomous underwater vehicle operated in the Mediterranean Sea. We found that both deep learning architectures outperformed model-based approaches by over 16% in velocity prediction accuracy.

Gal Versano. Itai Savin, Itzik Klein

Modern canine applications span medical and service roles, while robotic legged dogs serve as autonomous platforms for high-risk industrial inspection, disaster response, and search and rescue operations. For both, accurate positioning remains a significant challenge due to the cumulative drift inherent in inertial sensing. To bridge this gap, we propose three algorithms for accurate positioning using only inertial sensors, collectively referred to as dog dead reckoning (DDR). To evaluate our approaches, we designed DogMotion, a wearable unit for canine data recording. Using DogMotion, we recorded a dataset of 13 minutes. Additionally, we utilized a robotic legged dog dataset with a duration of 116 minutes. Across the two distinct datasets we demonstrate that our neural-aided methods consistently outperform model-based approaches, achieving an absolute distance error of less than 10\%. Consequently, we provide a lightweight and low-cost positioning solution for both biological and legged robotic dogs. To support reproducibility, our codebase and associated datasets have been made publicly available.

Michal Levin, Itzik Klein

Low-cost micro-electromechanical accelerometers are widely used in navigation, robotics, and consumer devices for motion sensing and position estimation. However, their performance is often degraded by bias errors. To eliminate deterministic bias terms a calibration procedure is applied under stationary conditions. It requires accelerom- eter leveling or complex orientation-dependent calibration procedures. To overcome those requirements, in this paper we present a model-free learning-based calibration method that estimates accelerometer bias under stationary conditions, without requiring knowledge of the sensor orientation and without the need to rotate the sensors. The proposed approach provides a fast, practical, and scalable solution suitable for rapid field deployment. Experimental validation on a 13.39-hour dataset collected from six accelerometers shows that the proposed method consistently achieves error levels more than 52% lower than traditional techniques. On a broader scale, this work contributes to the advancement of accurate calibration methods in orientation-free scenarios. As a consequence, it improves the reliability of low-cost inertial sensors in diverse scientific and industrial applications and eliminates the need for leveled calibration.

Gershy Ben-Arie, Daniel Engelsman, Rotem Dror et al.

An accurate initial heading angle is essential for efficient and safe navigation across diverse domains. Unlike magnetometers, gyroscopes can provide accurate heading reference independent of the magnetic disturbances in a process known as gyrocompassing. Yet, accurate and timely gyrocompassing, using low-cost gyroscopes, remains a significant challenge in scenarios where external navigation aids are unavailable. Such challenges are commonly addressed in real-world applications such as autonomous vehicles, where size, weight, and power limitations restrict sensor quality, and noisy measurements severely degrade gyrocompassing performance. To cope with this challenge, we propose a novel diffusion denoiser-aided gyrocompass approach. It integrates a diffusion-based denoising framework with an enhanced learning-based heading estimation model. The diffusion denoiser processes raw inertial sensor signals before input to the deep learning model, resulting in accurate gyrocompassing. Experiments using both simulated and real sensor data demonstrate that our proposed approach improves gyrocompassing accuracy by 26% compared to model-based gyrocompassing and by 15% compared to other learning-driven approaches. This advancement holds particular significance for ensuring accurate and robust navigation in autonomous platforms that incorporate low-cost gyroscopes within their navigation systems.

Netta Palez, Léonie Straß, Sebastian Meller et al.

Canine gait analysis using wearable inertial sensors is gaining attention in veterinary clinical settings, as it provides valuable insights into a range of mobility impairments. Neurological and orthopedic conditions cannot always be easily distinguished even by experienced clinicians. The current study explored and developed a deep learning approach using inertial sensor readings to assess whether neurological and orthopedic gait could facilitate gait analysis. Our investigation focused on optimizing both performance and generalizability in distinguishing between these gait abnormalities. Variations in sensor configurations, assessment protocols, and enhancements to deep learning model architectures were further suggested. Using a dataset of 29 dogs, our proposed approach achieved 96% accuracy in the multiclass classification task (healthy/orthopedic/neurological) and 82% accuracy in the binary classification task (healthy/non-healthy) when generalizing to unseen dogs. Our results demonstrate the potential of inertial-based deep learning models to serve as a practical and objective diagnostic and clinical aid to differentiate gait assessment in orthopedic and neurological conditions.

Noa Cohen, Rotem Dror, Itzik Klein

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.

Gal Versano, Itzik Klein

Autonomous mobile robots are widely used for navigation, transportation, and inspection tasks indoors and outdoors. In practical situations of limited satellite signals or poor lighting conditions, navigation depends only on inertial sensors. In such cases, the navigation solution rapidly drifts due to inertial measurement errors. In this work, we propose WMINet a wheel-mounted inertial deep learning approach to estimate the mobile robot's position based only on its inertial sensors. To that end, we merge two common practical methods to reduce inertial drift: a wheel-mounted approach and driving the mobile robot in periodic trajectories. Additionally, we enforce a wheelbase constraint to further improve positioning performance. To evaluate our proposed approach we recorded using the Rosbot-XL a wheel-mounted initial dataset totaling 190 minutes, which is made publicly available. Our approach demonstrated a 66\% improvement over state-of-the-art approaches. As a consequence, our approach enables navigation in challenging environments and bridges the pure inertial gap. This enables seamless robot navigation using only inertial sensors for short periods.

Nadav Cohen, Itzik Klein

Accurate underwater navigation is a challenging task due to the absence of global navigation satellite system signals and the reliance on inertial navigation systems that suffer from drift over time. Doppler velocity logs (DVLs) are typically used to mitigate this drift through velocity measurements, which are commonly estimated using a parameter estimation approach such as least squares (LS). However, LS works under the assumption of ideal conditions and does not account for sensor biases, leading to suboptimal performance. This paper proposes a data-driven alternative based on multi-output Gaussian process regression (MOGPR) to improve DVL velocity estimation. MOGPR provides velocity estimates and associated measurement covariances, enabling an adaptive integration within an error-state Extended Kalman Filter (EKF). We evaluate our proposed approach using real-world AUV data and compare it against LS and a state-of-the-art deep learning model, BeamsNet. Results demonstrate that MOGPR reduces velocity estimation errors by approximately 20% while simultaneously enhancing overall navigation accuracy, particularly in the orientation states. Additionally, the incorporation of uncertainty estimates from MOGPR enables an adaptive EKF framework, improving navigation robustness in dynamic underwater environments.

Daniel Engelsman, Itzik Klein

Linear quadratic Gaussian (LQG) control is a well-established method for optimal control through state estimation, particularly in stabilizing an inverted pendulum on a cart. In standard laboratory setups, sensor redundancy enables direct measurement of configuration variables using displacement sensors and rotary encoders. However, in outdoor environments, dynamically stable mobile platforms-such as Segways, hoverboards, and bipedal robots-often have limited sensor availability, restricting state estimation primarily to attitude stabilization. Since the tilt angle cannot be directly measured, it is typically estimated through sensor fusion, increasing reliance on inertial sensors and necessitating a lightweight, self-contained perception module. Prior research has not incorporated accelerometer data into the LQG framework for stabilizing pendulum-like systems, as jerk states are not explicitly modeled in the Newton-Euler formalism. In this paper, we address this gap by leveraging local differential flatness to incorporate higher-order dynamics into the system model. This refinement enhances state estimation, enabling a more robust LQG controller that predicts accelerations for dynamically stable mobile platforms.

Zeev Yampolsky, Itzik Klein

Gyroscopes are inertial sensors that measure the angular velocity of the platforms to which they are attached. To estimate the gyroscope deterministic error terms prior mission start, a calibration procedure is performed. When considering low-cost gyroscopes, the calibration requires a turntable as the gyros are incapable of sensing the Earth turn rate. In this paper, we propose a data-driven framework to estimate the scale factor and bias of a gyroscope. To train and validate our approach, a dataset of 56 minutes was recorded using a turntable. We demonstrated that our proposed approach outperforms the model-based approach, in terms of accuracy and convergence time. Specifically, we improved the scale factor and bias estimation by an average of 72% during six seconds of calibration time, demonstrating an average of 75% calibration time improvement. That is, instead of minutes, our approach requires only several seconds for the calibration.

Aleksei Zakharchenko, Sharon Farber, Itzik Klein

Inertial sensors are widely used in a variety of applications. A common task is orientation estimation. To tackle such a task, attitude and heading reference system algorithms are applied. Relying on the gyroscope readings, the accelerometer measurements are used to update the attitude angles, and magnetometer measurements are utilized to update the heading angle. In indoor environments, magnetometers suffer from interference that degrades their performance resulting in poor heading angle estimation. Therefore, applications that estimate the heading angle of moving objects, such as walking pedestrians, closets, and refrigerators, are prone to error. To circumvent such situations, we propose DoorINet, an end-to-end deep-learning framework to calculate the heading angle from door-mounted, low-cost inertial sensors without using magnetometers. To evaluate our approach, we record a unique dataset containing 391 minutes of accelerometer and gyroscope measurements and corresponding ground-truth heading angle. We show that our proposed approach outperforms commonly used, model based approaches and data-driven methods.

Nadav Cohen, Itzik Klein

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.

Itzik Klein, Guy Revach, Nir Shlezinger et al.

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 pro-vides a more accurate error estimation.

Vitaly Shalumov, Itzik Klein

In target tracking, the estimation of an unknown weaving target frequency is crucial for improving the miss distance. The estimation process is commonly carried out in a Kalman framework. The objective of this paper is to examine the potential of using neural networks in target tracking applications. To that end, we propose estimating the weaving frequency using deep neural networks, instead of classical Kalman framework based estimation. Particularly, we focus on the case where a set of possible constant target frequencies is known. Several neural network architectures, requiring low computational resources were designed to estimate the unknown frequency out of the known set of frequencies. The proposed approach performance is compared with the multiple model adaptive estimation algorithm. Simulation results show that in the examined scenarios, deep neural network outperforms multiple model adaptive estimation in terms of accuracy and the amount of required measurements to convergence.