Velocity Log Research Articles

Positioning Systems for Unmanned Underwater Vehicles: A Comprehensive Review

Positioning systems are integral to Unmanned Underwater Vehicle (UUV) operation, enabling precise navigation and control in complex underwater environments. This paper comprehensively reviews the key technologies employed for UUV positioning, including acoustic systems, inertial navigation, Doppler velocity logs, and GPS when near the surface. These systems are essential for seabed mapping, marine infrastructure inspection, and search and rescue operations. The review highlights recent technological advancements and examines the integration of these systems to enhance accuracy and operational efficiency. It also addresses ongoing challenges, such as communication constraints, environmental variability, and discrepancies between theoretical models and field applications. Future trends in positioning system development are discussed, with a focus on improving reliability and performance in diverse underwater conditions to support the expanding capabilities of UUVs across scientific, commercial, and rescue missions.

Study on the Robust Filter Method of SINS/DVL Integrated Navigation Systems in a Complex Underwater Environment

This paper proposes an improved adaptive filtering algorithm based on the Sage–Husa adaptive Kalman filtering algorithm to address the issue of measurement noise characteristics impacting the navigation accuracy in strapdown inertial navigation system (SINS)/Doppler Velocity Log (DVL) integrated navigation systems. Addressing the non-positive definite matrix problem prevalent in traditional adaptive filtering algorithms and aiming to enhance measurement noise estimation accuracy, this method incorporates upper and lower thresholds determined by a discrimination factor. In the presence of abnormal measurement data, these thresholds are utilized to adjust the covariance of the innovation, subsequently re-estimating the system’s measurement noise through a decision factor based on the innovation. Simulation and experiment results demonstrate that the proposed improved adaptive filtering algorithm outperforms the classical Kalman filter (KF) in terms of navigation accuracy and stability. Furthermore, the filtering performance surpasses that of the Sage–Husa algorithm. The simulation results in this paper show that the relative position positioning error of the improved method is reduced by 49.44% compared with the Sage–Husa filtering method.

Autonomous Underwater Vehicle Navigation Enhancement by Optimized Side-Scan Sonar Registration and Improved Post-Processing Model Based on Factor Graph Optimization

Autonomous Underwater Vehicles (AUVs) equipped with Side-Scan Sonar (SSS) play a critical role in seabed mapping, where precise navigation data are essential for mosaicking sonar images to delineate the seafloor’s topography and feature locations. However, the accuracy of AUV navigation, based on Strapdown Inertial Navigation System (SINS)/Doppler Velocity Log (DVL) systems, tends to degrade over long-term mapping, which compromises the quality of sonar image mosaics. This study addresses the challenge by introducing a post-processing navigation method for AUV SSS surveys, utilizing Factor Graph Optimization (FGO). Specifically, the method utilizes an improved Fourier-based image registration algorithm to generate more robust relative position measurements. Then, through the integration of these measurements with data from SINS, DVL, and surface Global Navigation Satellite System (GNSS) within the FGO framework, the approach notably enhances the accuracy of the complete trajectory for AUV missions. Finally, the proposed method has been validated through both the simulation and AUV marine experiments.

Global integrated navigation position correction algorithm and virtual polar region technology based on normal vector

To achieve the inherent uniformity of all-earth navigation for autonomous underwater vehicles (AUV), a global integrated navigation position correction algorithm based on the normal vector (n-vector) is proposed. First, a four-element vector comprising the non-singular n-vector and height represents the carrier’s position in the Earth-centered Earth-fixed (ECEF) frame. The integrated navigation systems are designed with the strapdown inertial navigation system (SINS), Doppler velocity log (DVL), and other equipment. Secondly, the reverse navigation algorithm in the ECEF mechanization is derived, and the results of forward and reverse navigation are fused to correct the AUV’s underwater position. Additionally, a virtual polar region technology based on the ECEF attitude, velocity, and height invariant method (E-AVHIM) is proposed to convert the actual test data obtained at low and middle latitudes into high latitudes for more convincing polar region algorithm verification. Simulations and lake trial demonstrated the excellence and efficiency of the proposed algorithm.

Maximum correntropy polynomial chaos Kalman filter for underwater navigation

This paper develops an underwater navigation solution that utilizes a strapdown inertial navigation system (SINS) and fuses a set of auxiliary sensors such as an acoustic positioning system, Doppler velocity log, depth meter, and magnetometer to accurately estimate an underwater vessel's position and orientation. The conventional integrated navigation system assumes Gaussian measurement noise, while in reality, the noises are non-Gaussian, particularly contaminated by heavy-tailed impulsive noises. To address this issue, and to fuse the system model with the acquired sensor measurements efficiently, we develop a square root polynomial chaos Kalman filter based on maximum correntropy criteria. The proposed method uses Hermite polynomial chaos expansion to tackle the nonlinearity, and it has the potential to estimate the states in a more accurate way in presence of a non-Gaussian measurement noise. The filter is initialized using acoustic beaconing to accurately locate the initial position of the vehicle. The computational complexity of the proposed filter is calculated in terms of flops count. The proposed method is compared with the existing maximum correntropy sigma point filters in terms of estimation accuracy and computational complexity. It is found from the simulation results that the proposed method is more accurate compared to the conventional deterministic sample point filters and Huber's M-estimator.

Object Weight and Hand Dominance Impact Kinematics in a Functional Reach-to-Drink Task in School-Aged Children.

This study evaluates the effects of object weight and hand dominance on the end-point kinematics of the hand-to-mouth (withdrawal) movement in a functional reach-to-drink task for typically developing school-aged children. Using 3D motion capture, speed (average velocity and peak velocity), straightness (ratio), and smoothness (number of velocity peaks and log dimensionless jerk) of hand movements were calculated for the withdrawal motion with three different bottle weights (empty, half-filled, and full). Average velocity (550.4 ± 142.0 versus 512.1 ± 145.6 mm/s) and peak velocity (916.3 ± 234 versus 842.7 ± 198.4 mm/s) were significantly higher with the empty versus half-filled bottle and with the non-dominant (average: 543.5 ± 145.2 mm/s; peak: 896.5 ± 207 mm/s) versus dominant (average: 525.2 ± 40.7 mm/s; peak: 864.2 ± 209.2 mm/s) hand. There were no differences in straightness or smoothness. These findings indicate that increasing weight in reach-to-drink task puts greater constraints on the task. The slower movements with the dominant hand might denote better precision control than the non-dominant hand. The quantitative motion capture results show average values for the kinematic variables for a functional reach-to-drink task in a typically developing population of school-aged children with changing weights of the bottles that are relevant to a real-life scenario. These results could inform the design of individualized therapeutic interventions to improve functional upper-extremity use in children with neurodevelopmental motor disorders.

An Integrated Navigation Method Aided by Position Correction Model and Velocity Model for AUVs.

When autonomous underwater vehicles (AUVs) perform underwater tasks, the absence of GPS position assistance can lead to a decrease in the accuracy of traditional navigation systems, such as the extended Kalman filter (EKF), due to the accumulation of errors. To enhance the navigation accuracy of AUVs in the absence of position assistance, this paper proposes an innovative navigation method that integrates a position correction model and a velocity model. Specifically, a velocity model is developed using a dynamic model and the Optimal Pruning Extreme Learning Machine (OP-ELM) method. This velocity model is trained online to provide velocity outputs during the intervals when the Doppler Velocity Log (DVL) is not updating, ensuring more consistent and reliable velocity estimation. Additionally, a position correction model (PCM) is constructed, based on a hybrid gated recurrent neural network (HGRNN). This model is specifically designed to correct the AUV's navigation position when GPS data are unavailable underwater. The HGRNN utilizes historical navigation data and patterns learned during training to predict and adjust the AUV's estimated position, thereby reducing the drift caused by the lack of real-time position updates. Experimental results demonstrate that the proposed VM-PCM-EKF algorithm can significantly improve the positioning accuracy of the navigation system, with a maximum accuracy improvement of 87.2% compared to conventional EKF algorithms. This method not only improves the reliability and accuracy of AUV missions but also opens up new possibilities for more complex and extended underwater operations.

A damping method of grid strapdown inertial navigation system for polar region

Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.

P-Wave Velocity Log Simulation for Petroelastic Inversion Using Gardner’s Equation, Neural Networks And Ensemble Methods Based on Trees: A Case Study of the Santos Basin, Brazil

One of the main tools for reservoir characterization is analyzing well-log data. The importance of such methods stems from petrophysical properties estimation, such as porosity, which is very important to the oil and gas industry. In scenarios where data is hard to collect, data loss and technical failures during the acquisition impose an extra challenge. Thus mathematical and petrophysical models are good candidates to fill information gaps in the well-log dataset. In such a way, the rock’s petroelastic and petrophysical properties can be successfully estimated. Several studies correlate the velocity of compressional waves (VP) to other basic well data. In this study, we used the Gardner equation and Machine Learning methods such as Neural Networks, Random Forest and Gradient Boosting regressions to generate VPlogs. We used real-world data acquired from twenty wells of the pre-salt formation from Santos Basin in Brazil to train and test the Machine Learning methods and evaluated the data estimated by those models using statistical metrics. We calculated the acoustic impedance from the estimated logs and used it to create a prior model for a petroelastic inversion, which allowed us to estimate the natural logarithm of the acoustic impedance for a seismic volume. The Machine Learning methods presented lesser errors between estimated and measured velocities when compared to Gardner’s equation.

An Invariant Filtering Method Based on Frame Transformed for Underwater INS/DVL/PS Navigation

Underwater vehicles heavily depend on the integration of inertial navigation with Doppler Velocity Log (DVL) for fusion-based localization. Given the constraints imposed by sensor costs, ensuring the optimization ability and robustness of fusion algorithms is of paramount importance. While filtering-based techniques such as Extended Kalman Filter (EKF) offer mature solutions to nonlinear problems, their reliance on linearization approximation may compromise final accuracy. Recently, Invariant EKF (IEKF) methods based on the concept of smooth manifolds have emerged to address this limitation. However, the optimization by matrix Lie groups must satisfy the “group affine” property to ensure state independence, which constrains the applicability of IEKF to high-precision positioning of underwater multi-sensor fusion. In this study, an alternative state-independent underwater fusion invariant filtering approach based on a two-frame group utilizing DVL, Inertial Measurement Unit (IMU), and Earth-Centered Earth-Fixed (ECEF) configuration is proposed. This methodology circumvents the necessity for group affine in the presence of biases. We account for inertial biases and DVL pole-arm effects, achieving convergence in an imperfect IEKF by either fixed observation or body observation information. Through simulations and real datasets that are time-synchronized, we demonstrate the effectiveness and robustness of the proposed algorithm.

Robust adaptive non‐linear alignment algorithm for SINS/DVL integrated navigation system based on variational Bayesian

AbstractThe problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Mitigation method of acoustic doppler velocity measurement bias

A Doppler velocity log (DVL) is used to estimate ship’s velocity by processing seafloor echo. The velocity measurement bias (i.e., long term accuracy) is often regarded as an important technical specification to quantify the accuracy of DVL. The bias describes the accuracy of the instrument after averaging over a sufficiently long time, such that the velocity variance approaches zero. The goal of this paper is to obtain an effective method to mitigate the bias in velocity measurement based on analyzing the DVL seafloor echo characteristics. First, a DVL bottom echo model is constructed based on highlight model, which can focus on the statistical characteristics of the echo waveform information. Then the algorithm for retrieving the echo highlight information is presented. The parameters of the highlight model based on experimental data of DVL echo are analyzed. The intrinsic connection between the highlight model and the point-based scattering model is discussed. Finally, the method of velocity measurement to mitigate the bias according to the relationship between the statistical characteristics of the highlights and bias is put forward. Simulation results show that the proposed method significantly mitigates the bias.

Sparus Docking Station: A current aware docking station system for a non‐holonomic AUV

AbstractThis paper presents the design and development of a funnel‐shaped Sparus Docking Station intended for the non‐holonomic torpedo‐shaped Sparus II Autonomous Underwater Vehicle. The Sparus Docking Station is equipped with sensors and batteries, allowing for a stand‐alone long‐term deployment of the vehicle. An inverted Ultra Short Base‐Line system is used to locate the Docking Station as well as to provide long‐term drift‐less vehicle navigation. The Sparus Docking Station is able to observe the ocean currents using a Doppler Velocity Log, being motorized to allow its self‐alignment with the current. Moreover, a docking algorithm accounting for the current is used to guide the robot during the docking maneuver. The paper reports consecutive successful experimental results of the docking maneuver in sea trials in two different countries.

Autonomous underwater vehicle link alignment control in unknown environments using reinforcement learning

AbstractHigh‐speed underwater wireless optical communication holds immense promise in ocean monitoring and surveys, providing crucial support for the real‐time sharing of observational data collected by autonomous underwater vehicles (AUVs). However, due to inaccurate target information and external interference in unknown environments, link alignment is challenging and needs to be addressed. In response to these challenges, we propose a reinforcement learning‐based alignment method to control the AUV to establish an optical link and maintain alignment. Our alignment control system utilizes a combination of sensors, including a depth sensor, Doppler velocity log (DVL), gyroscope, ultra‐short baseline device, and acoustic modem. These sensors are used in conjunction with a particle filter to observe the environment and estimate the AUV's state accurately. The soft actor‐critic algorithm is used to train a reinforcement learning‐based controller in a simulated environment to reduce pointing errors and energy consumption in alignment. After experimental validation in simulation, we deployed the controller on an actual AUV called Tri‐TON. In experiments at sea, Tri‐TON maintained the link and angular pointing errors within 1 m and , respectively. Experimental results demonstrate that the proposed alignment control method can establish underwater optical communication between AUV fleets, thus improving the efficiency of marine surveys.

Investigation of the subsurface structure at the target site in Kumamoto, Japan, and the distributed data of the blind prediction exercise: report for the experiments for the 6th international symposium on effects of surface geology on seismic motion

This technical report explains details on the results of the investigation to build a subsurface structural model and a selection of earthquake data at the target site of the blind prediction exercise for “The 6th International Association of Seismology and Physics of the Earth’s Interior/International Association of Earthquake Engineering International Symposium on the Effect of Surface Geology on Seismic Motion (ESG6).” The selection process of the target site in the Kumamoto Plain, Japan, in ESG6 was explained with a historical review of the blind prediction tests in the previous ESG conferences. We have collected existing subsurface structural and earthquake data and conducted geophysical and geotechnical surveys in and around the target site to generate important velocity structure and the earthquake data used in the blind test. Microtremor data were obtained in triangular arrays ranging in side lengths from 1 to 962 m, and active surface wave data were derived along a 36-m line at the site. These data were provided for the prediction of a subsurface structural model in the first step of the blind prediction exercise. We also conducted a velocity logging in a borehole to a bottom depth of 39 m at the site and laboratory tests of soil samples from the borehole. We constructed a velocity profile of the shallow and deep sedimentary layers from a combination of the geophysical and geotechnical data at the site, and validated it by comparing the characteristics of the ground motion data from the moderate event. This “preferred velocity model” was provided as a standard model to the participants in the second and third steps of the blind prediction test to predict the earthquake ground motions of a moderate event and the mainshock of the 2016 Kumamoto earthquake.Graphical

Correction of velocity estimation bias caused by phase‐shift beamforming in acoustic Doppler velocity logs

AbstractThe performance of Doppler velocity logs (DVLs) in terms of velocity estimate error is directly linked to the geometry of the beam and the pulse transmitted. Beyond a specific transmitted bandwidth, the phase‐shift beamformer can introduce significant errors in velocity estimation. To delineate the operating mechanism of phase‐shift errors within a phased array of acoustic DVLs, the correlation between bottom echo and velocity distribution, in conjunction with the power‐weighted function, was initially examined predicated on spectral estimation theory. Subsequently, numerical and analytical models of the Gaussian‐shaped Doppler spectrum were formulated. The models are employed to evaluate the velocity estimation inaccuracies attributed to phase shifts in extant DVLs, and the comparative results with field experiments corroborate the model's efficacy in forecasting errors. The theoretical findings evaluate the performance limitations of the current phased array transducer design and provide insights for developing new designs. Pool experimental results show that this design effectively reduces the velocity estimation error caused by phase shift under static conditions and in the presence of Doppler frequencies to a level of almost complete elimination of the error compared to conventional configurations.

Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory.

This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (SE(3)) and 3-sphere space (S3) are used to express the pose (position and attitude) and misalignment, respectively. SE(3) contains position and attitude transformation matrices, and S3 comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved.

Optimizing AUV Navigation Using Factor Graphs with Side-Scan Sonar Integration

For seabed mapping, the prevalence of autonomous underwater vehicles (AUVs) employing side-scan sonar (SSS) necessitates robust navigation solutions. However, the positioning errors of traditional strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) systems accumulated significantly, further exacerbated by DVL’s susceptibility to failure in complex underwater conditions. This research proposes an integrated navigation approach that utilizes factor graph optimization (FGO) along with an improved pre-integration technique integrating SSS-derived position measurements. Firstly, the reliability of SSS image registration in the presence of strong noise and feature-poor environments is improved by replacing the feature-based methods with a Fourier-based method. Moreover, the high-precision inertial measurement unit (IMU) pre-integration method could correct the heading errors of SINS significantly by considering the Earth’s rotation. Finally, the AUV’s marine experimental results demonstrated that the proposed integration method not only offers improved SSS image registration and corrects initial heading discrepancies but also delivers greater system stability, particularly in instances of DVL data loss.

A water track laser Doppler velocimeter for use in underwater navigation

Doppler velocity log (DVL) is usually employed to suppress the divergency of the Strapdown Inertial Navigation System (SINS) in underwater navigation, which is not concealable due to high transmittance for acoustic wave in the water. To conduct underwater navigation task with high concealment, a differential laser Doppler velocimeter (LDV) working at water track mode is integrated with SINS in this paper. The developed LDV measures the advance velocity of the underwater carrier with respect to the surrounding water in underwater navigation scenario with advantages of high concealment, high real-time performance, high update rate, light weight, and small dimension. A dynamic river test was conducted to validate the underwater navigation performance of SINS/LDV integrated system. The experimental results show that during the voyage of 4493s and 5271.8 m, the maximum horizontal positioning errors of the proposed SINS/LDV integrated underwater navigation system is 27.8 m and the relative position error is less than 0.6% with respect to total distance. Therefore, the water track LDV is practical to aid SINS in underwater navigation environment.

2D Near‐Surface Full‐Waveform Tomography Reveals Bedrock Controls on Critical Zone Architecture

AbstractFor decades, seismic imaging methods have been used to study the critical zone, Earth's thin, life‐supporting skin. The vast majority of critical zone seismic studies use traveltime tomography, which poorly resolves heterogeneity at many scales relevant to near‐surface processes, therefore limiting progress in critical zone science. Full‐waveform tomography can overcome this limitation by leveraging more seismic data and enhancing the resolution of geophysical imaging. In this study, we apply 2D full‐waveform tomography to match the phases of observed seismograms and elucidate previously undetected heterogeneity in the critical zone at a well‐studied catchment in the Laramie Range, Wyoming. In contrast to traveltime tomograms from the same data set, our results show variations in depth to bedrock ranging from 5 to 60 m over lateral scales of just tens of meters and image steep low‐velocity anomalies suggesting hydrologic pathways into the deep critical zone. Our results also show that areas with thick fractured bedrock layers correspond to zones of slightly lower velocities in the deep bedrock, while zones of high bedrock velocity correspond to sharp vertical transitions from bedrock to saprolite. By corroborating these findings with borehole imagery, we hypothesize that lateral changes in bedrock fracture density majorly impact critical zone architecture. Borehole data also show that our full‐waveform tomography results agree significantly better with velocity logs than previously published traveltime tomography models. Full‐waveform tomography thus appears unprecedentedly capable of imaging the spatially complex porosity structure crucial to critical zone hydrology and processes.