Navigation Sensors Research Articles

Automated Georectification, Mosaicking and 3D Point Cloud Generation Using UAV-Based Hyperspectral Imagery Observed by Line Scanner Imaging Sensors

Hyperspectral sensors mounted on unmanned aerial vehicles (UAV) offer the prospect of high-resolution multi-temporal spectral analysis for a range of remote-sensing applications. However, although accurate onboard navigation sensors track the moment-to-moment pose of the UAV in flight, geometric distortions are introduced into the scanned data sets. Consequently, considerable time-consuming (user/manual) post-processing rectification effort is generally required to retrieve geometrically accurate mosaics of the hyperspectral data cubes. Moreover, due to the line-scan nature of many hyperspectral sensors and their intrinsic inability to exploit structure from motion (SfM), only 2D mosaics are generally created. To address this, we propose a fast, automated and computationally robust georectification and mosaicking technique that generates 3D hyperspectral point clouds. The technique first morphologically and geometrically examines (and, if possible, repairs) poorly constructed individual hyperspectral cubes before aligning these cubes into swaths. The luminance of each individual cube is estimated and normalised, prior to being integrated into a swath of images. The hyperspectral swaths are co-registered to a targeted element of a luminance-normalised orthomosaic obtained using a standard red–green–blue (RGB) camera and SfM. To avoid computationally intensive image processing operations such as 2D convolutions, key elements of the orthomosaic are identified using pixel masks, pixel index manipulation and nearest neighbour searches. Maximally stable extremal regions (MSER) and speeded-up robust feature (SURF) extraction are then combined with maximum likelihood sample consensus (MLESAC) feature matching to generate the best geometric transformation model for each swath. This geometrically transforms and merges individual pushbroom scanlines into a single spatially continuous hyperspectral mosaic; and this georectified 2D hyperspectral mosaic is then converted into a 3D hyperspectral point cloud by aligning the hyperspectral mosaic with the RGB point cloud used to create the orthomosaic obtained using SfM. A high spatial accuracy is demonstrated. Hyperspectral mosaics with a 5 cm spatial resolution were mosaicked with root mean square positional accuracies of 0.42 m. The technique was tested on five scenes comprising two types of landscape. The entire process, which is coded in MATLAB, takes around twenty minutes to process data sets covering around 30 Ha at a 5 cm resolution on a laptop with 32 GB RAM and an Intel® Core i7-8850H CPU running at 2.60 GHz.

UV laser formation of complex topologies for sensitive elements of navigation sensors based on surface acoustic waves

A method utilizing a UV laser to form complex electrode structures on the surface of the sensitive element prototype for a solid-state gyroscope (SSG) based on surface acoustic waves (SAW) was tested. The prospects of using the method are demonstrated in terms of the flexibility of changing the topology, the speed of navigation sensors prototypes manufacturing, and reducing the cost. Methods for forming surface structures on piezoelectric materials using an IR and UV laser are compared. The parameters of laser formation of a surface pattern for configuring the topology of a sensitive element by evaporation of a thin-film coating 5000 nm and 200 nm thick deposited on lithium niobate substrates are determined. The amplitude-frequency characteristics of the manufactured samples of SAW-based SSG sensing elements are obtained. Additionally a finite-element modeling was performed to obtain theoretical prediction of dependencies of the sensing element characteristics on the thickness of the metallization forming the electrodes. It was found that when using a fiber UV laser with a wavelength of 355 nm, it is necessary to impose more stringent requirements on the quality of metallization and on the calculation of laser radiation regimes for processing coatings with a thickness of 200 nm. It is shown that when using a UV laser, it is possible to manufacture more compact sensitive elements of navigation sensors on surface acoustic waves than when using IR lasers.

Overview of Space-Capable Global Navigation Satellite Systems Receivers: Heritage, Status and the Trend towards Miniaturization.

Spaceborne Global Navigation Satellite Systems (GNSS) receivers have become ubiquitous sensors for spacecraft navigation, especially in Low Earth Orbits (LEOs), often also supporting science endeavors or as acting dedicated science payloads. Due to the large number of space-capable GNSS receiver models available, spacecraft designers, as well as scientists, may find it difficult to have or gain an overview of suitable state-of-the-art models for their purposes and constraints. Based on a literature review that included more than 90 different receiver models, this paper aims to provide an overview of space-capable GNSS receivers that have a heritage in space missions. It analyses trends from the collected data and provides an outlook on miniaturized GNSS receiver models, which have a high potential of being used in future space missions.

Design of a real-time orientation sensor based on atmospheric polarization light.

In recent years, biomimetic polarization navigation has become a research hotspot in navigation fields because of its autonomy and concealment. Existing point-source polarization navigation sensors mainly use a logarithmic amplifier as the arithmetic unit to obtain polarization information. However, these sensors suffer from zero drift and low detection accuracy, which limits their application range. To address the above issues, a polarization navigation sensor based on a differential amplifier is designed as the operational unit. Based on the change of the arithmetic unit of the polarization signal, the algorithm for calculating the heading angle of the sensor is improved. The results of the orientation experiments with the designed sensor in clear weather indicate that the orientation error is ±1.243∘, and the standard deviation is 0.351°. The polarization navigation sensor can extract polarized light information and calculate the heading without accumulation of errors over time accurately and achieves good real-time performance.

Pohang canal dataset: A multimodal maritime dataset for autonomous navigation in restricted waters

This paper presents a multimodal maritime dataset and the data collection procedure used to gather it, which aims to facilitate autonomous navigation in restricted water environments. The dataset comprises measurements obtained using various perception and navigation sensors, including a stereo camera, an infrared camera, an omnidirectional camera, three LiDARs, a marine radar, a global positioning system, and an attitude heading reference system. The data were collected along a 7.5-km-long route that includes a narrow canal, inner and outer ports, and near-coastal areas in Pohang, South Korea. The collection was conducted under diverse weather and visual conditions. The dataset and its detailed description are available for free download at https://sites.google.com/view/pohang-canal-dataset.

AI-Enabled Condition Monitoring Framework for Outdoor Mobile Robots Using 3D LiDAR Sensor

An automated condition monitoring (CM) framework is essential for outdoor mobile robots to trigger prompt maintenance and corrective actions based on the level of system deterioration and outdoor uneven terrain feature states. Vibration indicates system failures and terrain abnormalities in mobile robots; hence, five vibration threshold classes for CM in outdoor mobile robots were identified, considering both vibration source system deterioration and uneven terrain. This study proposes a novel CM approach for outdoor mobile robots using a 3D LiDAR, employed here instead of its usual use as a navigation sensor, by developing an algorithm to extract the vibration-indicated data based on the point cloud, assuring low computational costs without losing vibration characteristics. The algorithm computes cuboids for two prominent clusters in every point cloud frame and sets motion points at the corners and centroid of the cuboid. The three-dimensional vector displacement of these points over consecutive point cloud frames, which corresponds to the vibration-affected clusters, are compiled as vibration indication data for each threshold class. A simply structured 1D Convolutional Neural Network (1D CNN)-based vibration threshold prediction model is proposed for fast, accurate, and real-time application. Finally, a threshold class mapping framework is developed which fuses the predicted threshold classes on the 3D occupancy map of the workspace, generating a 3D CbM map in real time, fostering a Condition-based Maintenance (CbM) strategy. The offline evaluation test results show an average accuracy of vibration threshold classes of 89.6% and consistent accuracy during real-time field case studies of 89%. The test outcomes validate that the proposed 3D-LiDAR-based CM framework is suitable for outdoor mobile robots, assuring the robot’s health and operational safety.

Polarization Stability of Spun Fiber Resonator for Resonant Fiber Optic Gyro

As an important inertial navigation sensor, resonant fiber optic gyro (RFOG) has become a research hotspot in recent years due to its advantages of light weight and high stability. The optical effects in the fiber ring resonator(FRR), such as scattering effects, polarization mode crosstalk, etc., are the bottleneck restricting the development of RFOG, and they are also the key problems that researchers are trying to solve. Aiming at the problem of polarization noise, this paper conducts in-depth theoretical and experimental research on polarization stability using spun fiber resonator for the first time. Compared with a common polarization-maintaining fiber (PMF) resonator of the same length, the results show that the RFOG using the spun fiber resonator has improved temperature stability compared to the conventional resonator structure. This research provides a new idea for the polarization noise suppression method of RFOG, and lays an important foundation for the practical application of spun fiber in RFOG.

An embarrassingly simple approach for visual navigation of forest environments.

Navigation in forest environments is a challenging and open problem in the area of field robotics. Rovers in forest environments are required to infer the traversability of a priori unknown terrains, comprising a number of different types of compliant and rigid obstacles, under varying lighting and weather conditions. The challenges are further compounded for inexpensive small-sized (portable) rovers. While such rovers may be useful for collaboratively monitoring large tracts of forests as a swarm, with low environmental impact, their small-size affords them only a low viewpoint of their proximal terrain. Moreover, their limited view may frequently be partially occluded by compliant obstacles in close proximity such as shrubs and tall grass. Perhaps, consequently, most studies on off-road navigation typically use large-sized rovers equipped with expensive exteroceptive navigation sensors. We design a low-cost navigation system tailored for small-sized forest rovers. For navigation, a light-weight convolution neural network is used to predict depth images from RGB input images from a low-viewpoint monocular camera. Subsequently, a simple coarse-grained navigation algorithm aggregates the predicted depth information to steer our mobile platform towards open traversable areas in the forest while avoiding obstacles. In this study, the steering commands output from our navigation algorithm direct an operator pushing the mobile platform. Our navigation algorithm has been extensively tested in high-fidelity forest simulations and in field trials. Using no more than a 16 × 16 pixel depth prediction image from a 32 × 32 pixel RGB image, our algorithm running on a Raspberry Pi was able to successfully navigate a total of over 750 m of real-world forest terrain comprising shrubs, dense bushes, tall grass, fallen branches, fallen tree trunks, small ditches and mounds, and standing trees, under five different weather conditions and four different times of day. Furthermore, our algorithm exhibits robustness to changes in the mobile platform's camera pitch angle, motion blur, low lighting at dusk, and high-contrast lighting conditions.

Performance evaluation of coarse alignment methods for autonomous underwater vehicles in mooring conditions

The coarse alignment stage of inertial navigation systems (INS) is a step of paramount importance, specially for vehicles that employ the latter as a reference navigation solution, as is the case of autonomous underwater vehicles (AUVs). For such class of vehicles, the alignment has encumbrances that goes beyond those usually reported for terrestrial and aerial systems, as AUVs generally align at non benign environments (e.g., under swaying and mooring conditions) and have limited auxiliary navigation sensors. This work, hence, proposes a comparative analysis of the most representative coarse alignment methods applied to AUVs in mooring condition. The alignment approach herein explored, throughout its optimized and non-optimized versions, is the attitude decomposition-based initial alignment (ADIA) method, and the proposed comparison procedure tests different types of observation vectors resolved in the frames of interest. Experimental tests are conducted, which are based on kinematic data collected from an unmanned marine vehicle representing the typical swaying and attitude oscillations of AUVs in the mooring state, i.e., when subject to wave induced disturbances. Results lead to practical conclusions that can be applied to the AUV initial attitude estimation and are related to autonomy, accuracy and precision of the methods, as well as to their convergence rate and computational effort.

Classification and Analysis of Human Body Movement Characteristics Associated with Acrophobia Induced by Virtual Reality Scenes of Heights

Acrophobia (fear of heights), a prevalent psychological disorder, elicits profound fear and evokes a range of adverse physiological responses in individuals when exposed to heights, which will lead to a very dangerous state for people in actual heights. In this paper, we explore the behavioral influences in terms of movements in people confronted with virtual reality scenes of extreme heights and develop an acrophobia classification model based on human movement characteristics. To this end, we used wireless miniaturized inertial navigation sensors (WMINS) network to obtain the information of limb movements in the virtual environment. Based on these data, we constructed a series of data feature processing processes, proposed a system model for the classification of acrophobia and non-acrophobia based on human motion feature analysis, and realized the classification recognition of acrophobia and non-acrophobia through the designed integrated learning model. The final accuracy of acrophobia dichotomous classification based on limb motion information reached 94.64%, which has higher accuracy and efficiency compared with other existing research models. Overall, our study demonstrates a strong correlation between people’s mental state during fear of heights and their limb movements at that time.

Design Of Multi Sensor Quadcopter Navigation Data Acquisition For Early Fire Detection and Treatment

Recently, forest and land fires have become an event that has become a concern for the national and international community. This research creates a quadcopter as a tool for detecting forest and land fires. This system is an alternative tool for detecting forest and land fires that already exist. The advantage of this quadcopter is that it can collect data before the fire, during the fire, and after the fire. This quadcopter is designed and realized the developm­­­­­ent of an automatic navigation system for unmanned aircraft. This system is controlled by a microcontroller that processes IMU (Inertial Measurement Unit) sensor data in which there is a gyroscope and accelerometer, GPS, and magnetometer so that it can fly automatically. The purpose of this study is to acquire data on the navigation sensors used in the unmanned aerial vehicle (UAV) design, then the data from the navigation sensors will be combined using complement and median filters as position control input for the quadcopter. Based on this research, processing from sensor readings to sensor integration is able to produce better data, where the quadcopter's angle of view has an error percentage of 1.10° and 0.68°. This value is smaller than the percentage error of the magnetometer sensor alone or the IMU sensor alone which results in an error percentage of 1.18° and 0.76°.

INTEGRATION ANALYSIS OF DRONE MULTI SENSOR-GNSS-LIDAR-CAMERA FOR 3D MAPPING (CASE STUDY: PT GARAM, PAMEKASAN, MADURA)

Every year salt was carried out by PT Garam twice whereas the previous process used the method of terrestrial and manual calculations with sacks. Therefore, a map of salt production is needed using the Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU) sensor navigation system to increase the data's accuracy level. Unmanned Aerial Vehicle applications for the purpose of obtaining geometric documentation results and for capturing textures that characterize object structures. (Adamopoulos, 2020). LiDAR can classify based on the number of image acquisitions processed in the software, utilizing photogrammetric, and structural science principles from Motion technology. (Fernández, Hernandez et.al 2015) LiDAR Acquisition process that enables the creation of point clouds, three-dimensional models, and Digital Surface Models with high accuracy. (Barba, et al. 2019). A three-dimensional model makes it easy for users to choose a virtual position on the map, has good accuracy in interpreting the map, and displays a more real shape. LiDAR has a disadvantage in the form of coordinate data positions that have local references. (Cahyadi., et al. 2019). Unmanned Aerial Vehicle (UAV) technology has the advantage of efficiency in the cost and time of data collection. These researchers use multi-sensor technology GNSS, LiDAR, and Drones to map the stockpile of salt on open land and in warehouses. makes it easy to calculate the area of salt land and calculate the volume of salt production. This was done for PT GARAM to meet the community's needs and monitor the amount of salt production. This data can be used as a reference for digital asset inventory and the system can be applied to optimize the salt industry. The drones used in this study are the DJI Matrice 300 and the Low-Cost Drone Tarot Iron Man 650. Both types of drones are used to measure land and salt volume. The end product of the research is in the form of data generated in the form of a point cloud to calculate the salt stockpile volume and the elevation level of the salt land area

Hybrid Navigation Prototype for Small Aircraft Transportation Vehicles

The Small Aircraft Transportation (SAT) segment represented mainly by helicopters, piston fixed-wing aircraft, turboprop aircraft, and business jets requires a reliable source of navigation information with an appropriate price. This paper describes the research and development activity funded by Clean Sky 2 Cost Optimized Avionic Systems (COAST) development program targeting affordable hybrid navigation solutions. The affordability is driven by size, weight, and power consumption (SWAP) requirements. The desired level of accuracy, integrity, and availability is being achieved by a hybrid navigation solution based on GPS/INS fusion extended by other navigation sensors. The hybrid core of the systems uses GPS with SBAS augmentation to outperform standard tightly coupled GPS-based hybrid systems. The purpose of this article is to describe the current state, algorithmic structure, and hardware maturity of the navigation system prototype. The paper describes individual hardware components, points to the resulting prototype, and summarizes tests in a representative environment. The ultimate goal is to demonstrate the overall performance of the hybrid system based on a low-cost micro-electro-mechanical system (MEMS) Inertial Measurement Unit (IMU). The low-cost inertial sensor is one of the key components securing the affordability of the proposed system, so its testing plays important role. Another assumption considered in the system design was integration of standardly-used onboard sensors. For this purpose, the hardware prototype was tested in a demonstrative and outdoor environment. The results of this exercise are summarized in this paper.

UV-C Based Disinfectant Robot

Abstract: UVC (ultraviolet-C) light has been proven to kill various bacteria and viruses, including the COVID-19-producing virus, which has been discovered to be a powerful disinfectant. Manual UVC disinfection, on the other hand, can be tiresome, time-consuming, and hazardous for human operators. As our senior project, we developed a UVC-based disinfection robot to address these problems. Our robot has been designed to move and clean on its own in a variety of applications including hospitals, schools, and public places. Ultrasonic sensors for navigation and obstacle avoidance, a mobile platform, a UVC light source, and an Arduino microcontroller for communication and control comprise the robot.We conducted a microbiological test to gauge the robot's performance by comparing the number of microbe cells on a surface before and after UVC disinfection. Our findings demonstrated the robot's effectiveness as a disinfection tool by showing that bacterial colonies were reduced by 93.9%. By measuring UVC radiation levels at various angles and at various distances from the light source, we were also able to assess the safety of the robot. Our findings demonstrated that the robot complied with safety requirements for UVC radiation exposure to humans.

COLMAP-SLAM: A FRAMEWORK FOR VISUAL ODOMETRY

Abstract. SLAM technology is more and more integrated with other sensors for indoor and outdoor seamless navigation. This research topic is very active in particular on image matching with deep learning local features, keyframe selection approaches, or tests on new IMU and GNSS solutions. Integrating and testing new methodologies on other widely used SLAM implementations, such as ORB-SLAM, can be not a trivial task. Therefore, we propose an extension of COLMAP to be used in real-time as a feature-based Visual-SLAM that can be also coupled with other sensors. COLMAP has been chosen due to its modularity and the large community that assures the continuity of the repository. The paper presents a pipeline mainly thought for real-time evaluation of learning-based tie points and new SLAM features, that works with both monocular, stereo and multi-camera systems. It is also shown an example of keyframe selection algorithm based on deep learning local features, and a simple example of IMU integration. The code is available on the GitHub repository https://github.com/3DOM-FBK/COLMAP_SLAM.

RumexWeeds: A grassland dataset for agricultural robotics

AbstractComputer vision can lead toward more sustainable agricultural production by enabling robotic precision agriculture. Vision‐equipped robots are being deployed in the fields to take care of crops and control weeds. However, publicly available agricultural datasets containing both image data as well as data from navigational robot sensors are scarce. Our real‐world dataset RumexWeeds targets the detection of the grassland weeds: Rumex obtusifolius L. and Rumex crispus L. RumexWeeds includes whole image sequences instead of individual static images, which is rare for computer vision image datasets, yet crucial for robotic applications. It allows for more robust object detection, incorporating temporal aspects and considering different viewpoints of the same object. Furthermore, RumexWeeds includes data from additional navigational robot sensors—GNSS, IMU and odometry—which can increase robustness, when additionally fed to detection models. In total the dataset includes 5510 images with 15,519 manual bounding box annotations collected at three different farms and four different days in summer and autumn 2021. Additionally, RumexWeeds includes a subset of 340 ground truth pixels‐wise annotations. The dataset is publicly available at https://dtu-pas.github.io/RumexWeeds/. In this paper we also use RumexWeeds to provide baseline weed detection results considering a state‐of‐the‐art object detector; in this way we are elucidating interesting characteristics of the dataset.

Reactive synthesis for relay-explorer consensus with intermittent communication

A distributed multi-agent system architecture is explored to reach approximate consensus with intermittent communication. The multi-agent system is cast as a relay-explorer problem, where a relay agent intermittently provides navigational feedback to multiple explorer agents that do not have on-board absolute navigational sensors in a pre-defined sub-region. Within each sub-region, there is one relay agent responsible for servicing the corresponding explorer agents, and the estimated trajectory of an explorer agent can cross the boundary and enter another sub-region. We develop a reactive synthesis approach to formulate the mission specifications, while the state–space system dynamics provide real-time information for state corrections. Specifically, we pre-synthesize a set of planning strategies corresponding to candidate instantiations (i.e., pre-specified representative information scenarios) to dynamically switch among the explorers, and the planning strategies enable transfer of the servicing responsibility between relay agents. To guarantee stability of the switching strategies and the approximate consensus of the explorer agents, we develop maximum dwell-time conditions using a Lyapunov-based analysis to allow the explorer agents to drift for a pre-defined period without requiring servicing from the relay agents. Finally, we include a simulation study to demonstrate the performance of the developed method.

The Use of Phyphox Application in Physics Experiments: A Literature Review

Nowadays, the most popular gadget owned by students is a smartphone. The sophistication of smartphones is not only used by students as a communication tool, but also internet browsing, reading e-books, and various other features that can facilitate student activities. In particular, smartphones create conditions for accessing educational programs, scientific materials, and mobile applications for field experiments. Many sensors are integrated in smartphones, thereby adding to the functionality of the smartphone itself. For example, basically every smartphone has an acceleration sensor that is used to determine orientation relative to the acceleration of gravity, a magnetometer to help GPS sensors for navigation, as well as a light sensor and a gyroscope to measure rotational speed. Pressure sensors are also available on some smartphones which can be used as indoor navigation. All of these sensors can be read with the appropriate application and can be used for smartphone-based school experiments, especially in Physics learning. Phyphox is one such sensor reading application that offers many features on it. This study provides reference for the Physics experiments innovation using Phyphox that can also help Physics educational practitioners and researchers to improve the scope and quality of Physics learning programs.

Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers' read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers' colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10-7 m s-2 and 10-5 m s-2 (in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is 10-5 rad s-1 and 5×10-4 rad s-1. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer, 5×10-11 m s-2, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around 10-10 rad s-1 at one second and 5×10-7 rad s-1 at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled.

Offshore towed-streamer positioning based on variance component estimation

In offshore towed-streamer seismic surveys, fusing observations from diverse navigation sensors to position streamers and hydrophones accurately is essential for high-quality seismic imaging and analysis. However, streamer positioning accuracy can be limited when nominal sensor precisions adopted in observation weighting become unrealistic in complex marine environments. This study used variance component estimation (VCE) to refine the weight determination of heteroscedastic observations involved in streamer positioning. First, a polynomial fitting model for streamer positioning was established. Subsequently, a simplified VCE method was presented in which the observations were classified based on both sensor type and distribution geometry. Finally, a six-streamer survey dataset acquired from the South China Sea was used to investigate the performance of the proposed method. A comparative analysis was performed between conventional empirical weighting methods and VCE methods implemented in various observation classification schemes. The experimental results verified the superiority of the stochastic model refinement in fully exploiting observations from multiple navigation sensors in offshore streamer positioning. Compared with the empirical weighting, VCE method reduced the mean standard deviation of the hydrophone positions by about 0.5 m.