B r o Okay L y n Do It Again

Sensors (Basel). 2022 Feb; 21(4): 1549.

Sensor Modeling for Underwater Localization Using a Particle Filter

David Herrero-Pérez

²Technical University of Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain

Enrico Meli, Bookish Editor

Received 2022 January 22; Accustomed 2022 Feb 16.

Abstruse

This newspaper presents a framework for processing, modeling, and fusing underwater sensor signals to provide a reliable perception for underwater localization in structured environments. Submerged sensory information is often affected by various sources of uncertainty that can deteriorate the positioning and tracking. By adopting uncertain modeling and multi-sensor fusion techniques, the framework can maintain a coherent representation of the environment, filtering outliers, inconsistencies in sequential observations, and useless information for positioning purposes. We evaluate the framework using cameras and range sensors for modeling uncertain features that stand for the environs around the vehicle. Nosotros locate the underwater vehicle using a Sequential Monte Carlo (SMC) method initialized from the GPS location obtained on the surface. The experimental results show that the framework provides a reliable environment representation during the underwater navigation to the localization system in existent-globe scenarios. Besides, they evaluate the improvement of localization compared to the position interpretation using reliable dead-reckoning systems.

Keywords: underwater vehicle frameworks, underwater localization, uncertainty modeling, multi-sensor fusion, navigation, sonar

1. Introduction

Present, underwater vehicles allow usa access to restricted areas and traditionally dangerous environments for human divers, such as deep seabed and under the ice. These vehicles can perform many tasks in a broad spectrum of applications, such as inspection, repair, and maintenance [1] in defense, oil and gas, and cable surveying, to name merely a few. Underwater vehicles incorporating a certain caste of autonomy normally rely on proprioceptive sensors [ii], such as an inertial navigation system (INS) integrated with Doppler velocity logs (DVLs) [iii]. This is because the submerged vehicle cannot notice the electromagnetic signals provided by the global navigation satellite organization (GNSS). Notwithstanding, these proprioceptive sensors suffer from drift and biases, leading to growing position uncertainty as the vehicle navigates. This fact makes unfeasible underwater dead-reckoning navigation. For this reason, several works in the literature combine the information of proprioceptive sensors to external positioning systems [4].

Acoustic positioning systems are the most used underwater external positioning approaches, from long baseline (LBL) [5,6,7] to sort baseline (SBL) [8] and ultrashort baseline (USBL) [ix,10]. However, these sensors endure from multipath Doppler effects and thermoclines, which induce acoustic reflection furnishings. These underwater localization systems also require the deployment of a network of ocean-floor mounted baseline transponders, often in the perimeter of the workplace area, for LBL or a support vessel with the transponders post-obit the vehicle for SBL and USBL. Nosotros tin also employ optical or sonar sensors to place specific landmarks in the environs and use them to locate the underwater vehicle using an a priori representation of the environs [11]. A meaning advantage of this approach is the cheap cost with a minimum modification of the workplace. The effectiveness of localization based on an a priori known representation of the environment depends on the wealth of useful information. We should bear in heed that optical and sonar sensors provide a short range of high-resolution uncertain sensing readings, mainly due to the different factors affecting their doubtfulness, such as multipath reflections and poor underwater visibility. Therefore, the modeling, processing, and fusing of underwater sensor readings are of paramount importance to build a reliable representation of the submarine environment. The reliability of such a perception is a primal for tracking and location purposes.

Tracking and localization methods aim to fuse uncertain position measurements to estimate the variable of involvement with different assumptions about the representation of the vehicle's location. The techniques based on variants of the Kalman filter and Sequential Monte Carlo (SMC) method are the virtually popular tracking and localization methods, respectively. The Kalman filter is a recursive country estimator of a detached-time controlled process governed by a linear stochastic differential equation. It is the minimum variance state reckoner for linear dynamic systems with Gaussian noise and the minimum variance linear state figurer for linear dynamic systems with non-Gaussian dissonance. Nosotros commonly use these methods for tracking the vehicle position in underwater scenarios. We tin can mention the Extended Kalman filter (EKF) [12,13,14] and the unscented Kalman filter (UKF) [nine,fifteen]. Yet, nosotros accept to remark that these techniques are suboptimal state estimators for a not-linear arrangement. Ane of the main advantages of such tracking techniques is that they represent the state and its uncertainty using a Gaussian distribution. This representation facilitates the efficient implementation of the filter with a reduced computational cost. However, they are non able to recover from divergences in the recursive interpretation procedure. The localization approaches based on the SMC method [16,17,xviii] are robust to uncertain and breathless data, assuasive recovery from divergences in the land interpretation process. Nevertheless, they suffer from astringent computational requirements. This fact is particularly for large and complex domains, where we require numerous samples to correspond complex stochastic distributions of the state-space model.

In this paper, nosotros present a framework for processing, modeling, and fusing underwater sensor signals to obtain a reliable representation of the submarine surround around the vehicle. We apply such perceptions for localization purposes during underwater navigation. We process the raw sensor readings to find the features surrounding the reference vehicle. This processing allows us to filter measures that do non match with features. We too incorporate doubt representation to the detected features. Nosotros use this information to fuse feature perceptions between them, which allows us to remove redundant information and maintain a coherent perception in sequent observations. The underline idea is to consider the dubiousness of the perception to propagate it to the localization method.

In item, we present the feature extraction from buffered data of underwater observations using optical and sonar sensors. We use a mechanism to verify these data by coherent consecutive and redundant perceptions. We update the uncertainty of such buffered perceptions induced by the movement of the vehicle and aging. Nosotros also remove the observations from the buffer by crumbling and disparity. We propagate the uncertainty of the sensor readings to the set of features surrounding the underwater vehicle. This set of features provides a coherent local representation of the environment. We also update and remove these features using the factors previously mentioned. The use of this local buffer representation allows us to filter out inconsistent exteroceptive sensory data. The reliability of this local representation is of paramount importance because incoherent perceptions can deteriorate the position estimations. We use the extracted features from noisy underwater sensors to feed the update phase of a particle filter localization method. We have to remark that nosotros can use the presented sensor modeling techniques with other localization approaches.

Nosotros organize the manuscript every bit follows. Section 2 describes the underwater platform used in this work. It details the sensory system incorporated into the vehicle and the description of the hardware architecture. We devote Section 3 to the processing and modeling of underwater sensor signals to provide a reliable representation during submarine navigation. This representation includes information about the uncertainty, which is updated using the factors that induce noise and imprecisions to such environs representation. We propagate such uncertain data to a recursive state reckoner. This fact allows united states of america to estimate both the location of the submerged vehicle and its uncertainty. Section 4 presents the modified sequential Monte Carlo (SMC) method equally a recursive computer to obtain the variable of interest. Section 5 shows the experimental results evaluating the proposed framework. We assess the processing, modeling, and sensor fusion of underwater sensor signals using the localization method. Finally, Section half dozen presents the conclusion and the hereafter works of the proposal.

2. Underwater Platform

Nosotros use the commercial platform Sibiu Pro underwater vehicle from Nido Robotics company incorporating new sensors and electronics for testing the developments presented in this work. The Sibiu Pro standard platform is a fully operational underwater vehicle operated with an umbilical cablevision. It is especially designed for the inspection and maintenance of submerged systems. The propulsion system uses a Thrust Vector Control (TVC) with three propellers that let the vehicle to movement/rotate in whatsoever direction combining them. It as well incorporates a 1080p camera with 1500 lumens lights to obtain a articulate prototype in depression-low-cal environments. Figure 1a shows the Sibiu Pro platform incorporating the sensory organisation used in this piece of work; the sonar scanner, the Doppler Velocity Logger (DVL), and the GPS.

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(a) Modified Sibiu Pro underwater vehicle from Nido Robotics visitor, and (b) hardware architecture and sensory organisation.

Figure 1b shows the hardware architecture and the sensory system incorporated into the platform to increase the functionalities. As proprioceptive sensors, we include a VectorNav VN-200 inertial navigation arrangement and a Nortek DVL-k. The former combines MEMS inertial sensors and a high-sensitivity GNSS receiver to estimate position, velocity, and orientation. Information technology too allows us to obtain the GPS location on the surface in UTM coordinates. The latter is an acoustic musical instrument that can estimate the velocity relative to the bottom or to the surface. The combination of both systems provides accurate dead-reckoning estimations obviating the GNSS receivers. As exteroceptive sensors, we include a Blue Robotics Ping sonar (Ping 360) and an 8-megapixels Sony IMX219 Raspberry photographic camera. The former is a mechanical scanning sonar providing underwater audio-visual imaging with 50 m range, 300 grand depth rating, and an open-source software interface using Ethernet. The latter replaces the camera of the Sibiu Pro platform with college specifications. We install the software that communicates with propulsion, lights, and sensors in a Raspberry Pi 3B, it using the interfaces indicated in Figure 1b. We currently perform the intensive ciphering in an external CPU that communicates with the Raspberry Pi using TCP/UDP protocols through the Ethernet of the umbilical cable.

three. Sensor Modeling

Nosotros present the processing and modeling of different underwater sensor signals to provide a reliable representation of the environment for underwater localization in structured environments. The information provided past these underwater sensors is oftentimes affected past diverse sources of uncertainty that can deteriorate the positioning and tracking. In item, we present the paradigm processing of artificial markers using an 8-megapixels Sony IMX219 Raspberry camera and the processing of the data provided by the mechanical sonar scanner Ping360 of Blue Robotics. The processing of the feature detection techniques aims to filter out noisy data and inconsistencies in sequential observations.

3.one. Visual Perception of Landmarks

We utilise a fiducial marker arrangement specially appropriated for localization in structured environments. In item, we distribute Aruco markers [19,20] along the structured environment to accept references during the navigation. The perception of such landmarks allows usa to improve the localization accuracy operating in the underwater environment. Following [xix], nosotros adopt the procedure for mark detection from grayscale images consisting of paradigm partition, contour extracting and filtering, marker code extraction, and mark identification. The prototype segmentation consists of the extraction of the most prominent contours in the grayscale paradigm. We use a local adaptive thresholding strategy based on the assay of neighboring pixels for their robustness to dissimilar lighting conditions. The contour extraction stage detects polygons with 4-vertices. We also discard four-vertex polygons contained in other quadrilateral features leaving merely the external ones. Then, the mark code extraction stage removes the perspective projection computing the homography matrix. We then tessellate the resulting pixels assigning zero or one value to each jail cell of a regular xi × 11 grid. Finally, the marker identification phase matches the tessellated paradigm with the dictionary of markers generated for the structured environment. We require four dissimilar identifiers for each Aruco marking generated (one for each possible rotation).

Although the concept of marker detection is unproblematic, there are several parameters to control the detection procedure. Besides, these parameters are strongly dependent on the image resolution. For these reasons, we have developed configuration tools to perform the calibration and configuration while the vehicle is operating underwater. Figure 2 shows an example of the vision processing for detecting the Aruco markers and the calibration tools used to facilitate the configuration. Figure 2a shows an image captured by the on-lath camera of the underwater vehicle operating in a swimming puddle with landmarks distributed throughout its walls. These landmarks consist of 11 × xi Aruco markers printed at 12 × 12 cm with a plastic moving-picture show roofing to make them waterproof. The prototype resolution is 480 × 360, which allows us to process xv frames per second from the figurer operating the vehicle. Figure 2b shows the interface for the on-line configuration of the parameters of the processing. This tool allows u.s. to modify the configuration of Aruco markers with wrong identification as the vehicle operates. The proper tunning of marker detection increases the robustness of the perception, which is of paramount importance because a lack of information technology could degrade the localization process.

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(a) Aruco marking with ID 2 detected by the on-lath photographic camera and (b) the on-line parameter configuration of maker recognition process with the (c) grayscale epitome, (d) binarized image, and (east) polygon extraction stage with marker identification.

Figure iic shows the grayscale prototype used for detecting the Aruco markers. Nosotros obtain the grayscale image using the algorithm indicated in the configuration tool shown in Figure twob. Figure twod shows the resulting grayscale paradigm binarization using the adaptive hateful thresholding technique indicated in the configuration tool. Nosotros configure the block size in pixels (Binariz. Block Size) to apply the adaptive thresholding. We can detect numerous polygons in the walls of the pond pool because they accept mosaic tiles. We only extract the polygons with an surface area higher than the parameter configured on-line. We indicate this parameter as (Min. Polygon Area) in the configuration tool. Another filter consists of but because quadrilateral polygons with border length higher than the parameter (Min. Quad Side) configured on-line. Figure 2e shows the polygon filtering and rejection, where the yellow foursquare indicates the area to remove the perspective projection computing the homography matrix. Nosotros depict the projected and binarized image in the upper left of the configuration tool of Effigy 2b, which is tessellated into a regular grid to compare information technology with the lexicon of Aruco markers. We then perform the matching with the possible patterns in the four possible orientations. In one case the landmark is detected, nosotros calculate the area in pixels squared of the perceived Aruco marker because we employ this magnitude to estimate the altitude to the perception.

The navigation system requires the distance estimation from the camera to the landmarks. The problem is non straightforward since the marker orientation can exist any, as seen from the robot photographic camera. Moreover, measuring the side of the detected polygon is not robust enough for distance triangulation. Lastly, but no less of import, the photographic camera lens distortion is quite appreciable, which is especially critical in non-centered perceptions. We solve these problems using a not-linear model to estimate the distance to the marker based on a measurable parameter of the detected Aruco model: the square root of the number of pixels contained in the polygon of the marker detection. A central issue is the calibration of the model. Nosotros proceed with a measurement process in which we measure out this size reference to the marker positioned at dissimilar known distances. Finally, we produce an interpolation function that provides a altitude interpretation from the computed size reference. This process performs quite well if the marker is in the center of the epitome. Otherwise, the distance is undervalued. We calibrate the altitude estimation using the following expression

$D i s t a n c e (10) = a_{1} 10^{b_{1}}, westward i t h \{\begin{matrix} a_{i} = 28.2239 \\ b_{ane} = - 0.903 \end{matrix}$

(i)

where x is the size reference obtained from the square root of the number of pixels contained in the polygon of the marker detection. We adjust $a_{1}$ and $b_{one}$ to obtain a coefficient of determination every bit shut equally possible to ane ( $R^{two} = i$ ) in the exponential fitting using least squares. Effigy 3a shows the setup for the distance calibration process. Figure 3b shows the distance scale using the non-linear interpolation role. We calibrate the uncertainty of distance estimation depending on the gradient of the altitude scale interpolation function. Nosotros can observe a steeper gradient with longer distance estimation.

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(a) Distance calibration of Aruco markers and (b) the distance calibration interpolation function.

Figure 4 summarizes the flowchart of the procedure for detecting the Aruco markers surrounding the underwater vehicle. The algorithm for detecting the landmarks operates with grayscale images. The first phase consists of the image binarization using an adaptive thresholding technique. We so excerpt the iv-vertices polygons filtering the ones that practice not satisfy some geometrical requirements. We detail the filtering criteria and the parameters for their configuration above. Nosotros remove the perspective project of the candidate 4-vertices polygons computing the homography matrix. We tessellate the resulting image using a regular grid to match such a resulting image and the reference Aruco markers in the possible orientations. Finally, we employ the square surface area in pixels of the perceived landmark to gauge the distance, whereas nosotros calculate the heading using the position of the detected marker in the paradigm. This processing provides us the fix of perceptions from each camera prototype.

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Flowchart of the procedure for detecting the Aruco markers surrounding the underwater vehicle.

3.2. Feature Extraction Using Sonar Scanner Readings

The information received from the mechanical scanning sonar is innate noisy because these agile acoustic devices estimate the distance using the time-of-flight principle. Echoes from sonar are affected by different sources of doubtfulness that tin can seriously degrade the distance estimation accuracy. Some examples are the broad opening angle of audio-visual signals presented past most sonar sensors and the multi-path reflections. One solution to filter out noisy distance estimation readings is to check the coherence of data received at dissimilar times. We deal with this problem past edifice the spatio-temporal relations between the sonar echoes. Maintaining the sonar buffer implies a series of operations:

Aging. We remove from the buffer those echoes that are older than a given amount of time. This filter is of paramount importance because the uncertainty of the local position of the sonar echoes grows unbounded with time.
Move. Whenever the vehicle moves, all the echoes stored in the buffer take to exist translated and rotated correspondingly. This update is key to maintaining a coherent representation of the environment.
Blanking. When a new scan is available, remove previous echoes that lie inside the scanning zone. The application of this filter is crucial for eliminating noise from the sonar buffer.

Figure 5a shows the underwater vehicle equipped with a mechanical scanning sonar at the summit operating at a circular swimming pool. Figure 5b depicts the spatio-temporal buffer of sonar echoes. The altitude estimation readings that lie along the dark-green thick radial line are incorporated into the buffer while the underwater vehicle moves, performing both translations and rotations. The rotation velocity is computed from the heading readings, while we estimate the translation velocity from the inertial and DVL sensors. Echoes with the most amplitude are represented in red, while others in different shades of yellowish. We tin find a static object shut to the robot, almost its left rear office, appears to move in the vehicle-centered coordinate space.

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(a) Underwater vehicle with mechanical scanning sonar at the meridian, (b) local buffer of data received from the sensor, and (c) local buffer subsequently the rotation and displacement of the underwater vehicle.

We can view the sonar buffer as a vehicle-centered consistent local map forth fourth dimension, at least upward to a certain degree depending on how the vehicle's velocity is measured or estimated. Nosotros can apply multiple feature extraction algorithms when a map is available. The next sections present the techniques adopted to perceive circumference arcs and line segments in structured environments. The perception of such features is useful for improving the accuracy of the navigation system.

three.2.1. Circular Model-Fitting

The recognition of circumference arcs is useful when the underwater vehicle operates in a structured environment with these features. We can mention round pond pools, fish farms, and tanks, to name but a few. The recognition of these features provides us information that allows us to locate the vehicle to the altitude estimated from the center of the circumference with a known location in the workplace. We can adopt different alternatives for the perception of circumference arcs [21] from the sonar scanner reading. We can mention algebraic-plumbing equipment methods and geometric-fitting techniques. The erstwhile is quite fast, but they lack robustness in the presence of outliers. The latter are iterative and tend to be robust in the presence of outliers. Since the sonar scanner readings tend to be quite noisy, algebraic plumbing fixtures techniques produce very few fittings, e'er when the robot is static, and thus nosotros conclude that geometric plumbing equipment methods seem more than appropriate for circumference arc extraction. Nosotros follow the circle-plumbing fixtures arroyo [22], which is detailed as follows.

Allow $P = {(10_{i}, y_{i})}_{i}$ be a prepare of points with a distribution approximately circular. We tin can use the following circle equation to model their position

where $(a, b)$ is the center of the circle andR its radius. Each point $(10_{i}, y_{i})$ in our prepare $P$ will approximately satisfy this equation. We tin rewrite this approximate equation factorizing in terms that contain the model parameters ${a, b, R}$ , and terms that incorporate the position of each betoken $(10_{i}, y_{i})$ every bit follows

$\begin{matrix} {(x_{i} - a)}^{two} + {(y_{i} - b)}^{2} & \approx R^{ii} \Rightarrow \\ \Rightarrow x_{i}^{2} + a^{2} - 2 a x_{i} + y_{i}^{2} + b^{2} - 2 b y_{i} & \approx R^{2} \Rightarrow \\ \Rightarrow (\begin{matrix} x_{i} & y_{i} & one \end{matrix}) (\begin{matrix} 2 a \\ 2 b \\ R^{2} - a^{two} - b^{ii} \end{matrix}) & \approx x_{i}^{2} + y_{i}^{two} . \end{matrix}$

(3)

We tin can then transform our model-plumbing equipment trouble into a linear least-squares trouble. Annotation that, since we have three unknown variables (a, b, and R), we need 3 (or more) $n_{e}$ equations to obtain a adamant (or overdetermined) system of linear equations; at least three points to decide the parameters of our model. So, edifice the matrices

$A = (\begin{matrix} x_{1} & y_{i} & 1 \\ {ten}_{2} & y_{two} & 1 \\ ⋮ & ⋮ & ⋮ \\ 10_{n_{e}} & y_{n_{east}} & 1 \end{matrix}),$

(iv)

$b = (\begin{matrix} 10_{1}^{2} + y_{1}^{2} \\ {ten}_{2}^{2} + y_{two}^{2} \\ ⋮ \\ x_{{due north}_{e}}^{2} + y_{{northward}_{eastward}}^{2} \end{matrix}),$

(5)

nosotros tin compute the matrix $X$ that minimizes the altitude ${∥ A Ten - b ∥}^{2}$ through

Finally, nosotros can obtain the model parameters using the following relations:

$a = \frac{X_{ane}}{2}, b = \frac{X_{2}}{2}, R = \sqrt{X_{3} + a^{two} + b^{2}},$

(7)

where { ${Ten}_{1}$ , $X_{2}$ , $X_{3}$ } is the solution of Equation (half dozen).

However, we frequently obtain measurements that do non fit with a distribution approximately circular. We should detect and filter out these measures to achieve a robust detection of circumference arcs in the structured surroundings. The random sample consensus (RANSAC) method [23] and its variants are central tools for outlier rejection. In particular, nosotros rely on the RANSAC variant maximum likelihood interpretation sample and consensus method MLESAC [24] to design the outlier rejection method in the circular model-plumbing fixtures approach. For this purpose, we define the cost role for the model parameters $a, b,$ and R as follows:

$\begin{matrix} e_{i} = | R - \sqrt{{(x_{i} - a)}^{ii} + {(y_{i} - b)}^{ii}} |, \end{matrix}$

(8)

$\begin{matrix} ρ (e_{i}) = \{\begin{matrix} e_{i} & if e_{i} < T, \\ T & if e_{i} \geq T, \end{matrix} \end{matrix}$

(9)

Algorithm 1 presents the circular model-fitting with outlier rejection. The algorithm requires the set of $P$ points received from the mechanical scanning sonar (Blue Robotics Ping 360), the threshold T used to compute the cost role, the probability of not finding a correct model, and the proportion of inliers in data. The output of the process is the best model parameters for $a, b,$ and R.

Figure half dozena shows an example of a fit to a circumvolve with noisy data using Algorithm ane. We stand for the ready of points P to fit using black crosses. The continuous green circumference is the target fit with the center at the green cross point. Nosotros show the best circle-fitting using three points with a red dotted circumvolve with the center at the reddish cross indicate. Finally, nosotros depict the best fit using all the inliers with a dashed blueish circumference with the center at the blue cross point. We tin discover that the all-time fit using all the inliers is closer to the target solution than the fit using 3 points. Figure half dozenb shows the resulting circumference using the mechanical scanning sonar readings while the underwater vehicle navigates in the swimming pool.

Algorithm 1 Circular model-fitting with outlier rejection
Input:
`points`	▹ Set of points to be fitted
T	▹ Threshold used to compute the cost part
FAILURE_PROBABILITY	▹ Probability of non finding a correct model
INLIER_PROPORTION	▹ Proportion of inliers in data
Output:
$b east s t 2_a, b e due south t 2_b, b e southward t 2_R$	▹ Best model parameters constitute
Initialization
i: $b e s t_C \leftarrow 10^{12}$	▹ Initialize to a large number
ii: $N \leftarrow log (F A I L U R E_P R O B A B I L I T Y) / log (1 - I N L I E R_P R O P O R T I O N^{iii})$
Find model
3: for $i = ane$ to Northward practise
Find possible model
iv: Accept three points randomly
5: Build matrices $A$ and $b$ using equations (iv) and (five) and the 3 sampled points
half-dozen: Notice model parameters $a, b, R$ using equations (6) and (seven)
7: Compute the cost partC using equations (eight) to ()
If this possible model is meliorate than the previous ane, we continue it
viii:if ( $C < b e s t_C$ ) then
ix: $b east south t_C \leftarrow C$
10: $b east s t_a, b east s t_b, b e s t_R \leftarrow a, b, R$
11:end if
12: cease for
Refine the model using inliers
13: Select the points $(x_{i}, y_{i})$ such that $e_{i} < T$ using (8)
14: Build matrices $A$ and $b$ using equations (4) and (5) and the selected inliers
xv: Discover model parameters $b due east s t 2_a, b e south t ii_b, b eastward s t 2_R$ using equations (6) to (7)
16: return $b e south t 2_a, b e south t 2_b, b eastward due south t 2_R$

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(a) Example of circumvolve-plumbing fixtures using noisy data, and (b) the fitted circumference using data received from the mechanical scanning sonar in a swimming puddle with Algorithm 1.

three.2.2. Line Segment Model-Fitting

The perception of line segments in structured environments is a more complicated task than the circle fitting presented above. This fact is because we tin can obtain several features of this blazon from the sonar scanning sensor. We take to deal with the uncertainty of such perceptions to maintain a coherent representation of the surroundings surrounding the underwater vehicle. We adopt a fuzzy segment framework [25,26] to represent and bargain with the location uncertainty using line segments. These features include a representation of their uncertain location. The fuzzy segment framework represents the doubt using a fuzzy set up whose degree of membership reflects how much the location could be occupied. This fuzzy segment framework provides ability tools, based on similarity estimation of fuzzy logic [27], to match the caste of similarity of information expressed as fuzzy segments. We use such tools to fuse and manage formally the uncertainty of the observations represented by fuzzy sets [28].

Allow a line segment S be divers equally a tuple as

$Southward = {θ, ρ, (x_{i}, y_{i}), (10_{j}, y_{j}), one thousand},$

(xi)

where $θ$ and $ρ$ are the parameters of the line equation $x c o s (θ) + y s i due north (θ) = ρ$ obtained past plumbing equipment m collinear range sensor observations, and $(10_{i}, y_{i})$ and $(10_{j}, y_{j})$ are the end-points of the line segment calculated as the project of the sensor observations on the fitted line using the k collinear sensor observations.

We need to extract the fix of chiliad collinear sensor scanner readings to perform the eigenvector line plumbing fixtures mentioned in a higher place. Nosotros take adopted an optimized algorithm that only dissever sets from consecutive reading. The chief reason is the performance constraints of our application. In particular, we utilize the Iterative End Point Fit (IEPF) algorithm [29,30], which requires the initial definition of the minimum number of points $k_{thou i due north}$ of a gear up of collinear observations and the maximum altitude $ρ_{yard a ten}$ of the scatter sensor readings to the fitted line segment. We have to remark that this algorithm requires a ready of ordered observations. For a prepare s of continuous sensor scanner readings, the algorithm is as follows:

Initialization. We initialize the algorithm with a set south containing all the ordered observations.
Step 1. If the set southward is equanimous of more than $k_{m i n}$ observations, draw a line segment betwixt the beginning and last information (end-points), otherwise turn down the ready southward.
Pace 2. Find the indicate P with maximum distance $ρ_{P}$ to the fitted line segment between the end-points.
Footstep three. If $ρ_{P} \geq ρ_{chiliad a ten}$ splits the ready s at P into two subsets ${southward}_{1}$ and ${southward}_{2}$ and goes to Step 1 for both subsets. Otherwise, the fix s is a candidate to exist a line segment.
Stopping criteria. Nosotros finalize the search when all the subsets are a candidate to be a line segment satisfying the condition $ρ_{P} \leq ρ_{m a x}$ or are rejected because they have fewer than ${grand}_{m i northward}$ observations.

Effigy vii shows an example of the Iterative End Point Fit recursive (IEPF) method. We can observe that the algorithm operates with a set southward of k continuous sensor scanner readings. The initial step consists of drawing a line segment (represented as a red dotted line) betwixt the finish-points of the initial set southward. Since there are numerous sensor readings further away from the conviction interval defined past the $ρ_{yard a x}$ parameter (represented as a blueish dotted line), the initial gear up is divided by the signal P at the furthest distance $ρ_{P}$ from the line segment between end-points (cherry-red dotted line) into 2 subsets. If all the sensor readings of the corresponding set (with more than ${chiliad}_{m i n}$ observations) are within the conviction interval, we consider such a ready of sensor readings as a candidate to be fitted every bit a line segment. We repeat this procedure until in that location is not any set candidate to form a line segment. We have to remark that this arroyo does not provide a set of line segments but groups of sensor readings candidate to be fitted as line-segments.

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Iterative Cease Bespeak Fit (IEPF) algorithm: (a) initial splitting process considering k points, (b,c) recursive split, and (d) stopping criterion.

Nosotros represent the doubtfulness on the location of the line segment S using the trapezoidal fuzzy prepare $t_{ρ}$ . This prepare represents the doubt in the $ρ$ parameter. Different factors tin can bear upon the location uncertainty of the $ρ$ parameter, such as the line segment plumbing equipment from scattering sonar scanner readings, the aging of the fuzzy segment edifice, and the motion of the underwater vehicle, to proper name but a few. Assuming the independence of all these factors, nosotros can ascertain the trapezoidal fuzzy set $t_{ρ}$ in the $Ω$ domain equally the addition of the representation of all the sources of uncertainty that affect the $ρ$ parameter as

$t p_{ρ} = t p_{ρ}^{one} \oplus t p_{ρ}^{2} \oplus . . . \oplus t p_{ρ}^{n} = (- ρ_{0}, - ρ_{ane}, ρ_{1}, ρ_{0}),$

(12)

where $t p_{ρ}^{i}$ with $i = ane, \dots, north$ are the trapezoidal fuzzy sets representing the i factors that influence the $ρ$ parameter, ⊕ is the bounded sum operator, ( $- ρ_{0}$ , $ρ_{0}$ ) is the $α$ -cut in the fuzzy membership $μ = 0$ , and ( $- ρ_{one}$ , $ρ_{1}$ ) is the $α$ -cut in fuzzy membership $μ = 1$ . These $α$ -cuts define the regions within fuzzy segments are considered within the degree of similarity $α$ . We tin can use this criterion to address matching problems taking into account the location incertitude. Effigy viii shows the scatter points fitted to a fuzzy segment with the trapezoidal fuzzy fix $t p_{ρ}$ , divers every bit an ordered tuple $(- ρ_{0}, - ρ_{1}, ρ_{i}, ρ_{0})$ , including the different factors affecting the location dubiousness.

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Besprinkle of points and fuzzy segment representing its uncertainty with a trapezoidal fuzzy prepare.

Thus, we define a fuzzy segment as a line segment S including its associated location uncertainty represented every bit a trapezoidal fuzzy set $t_{ρ}$ every bit

$F S = {θ, ρ, t p_{ρ}, (x_{i}, y_{i}), (x_{j}, y_{j}), k},$

(13)

where $t p_{ρ}$ is the trapezoidal fuzzy set representing the uncertainty in $ρ$ . We build this fuzzy ready from the sonar scanner readings candidate to be fitted equally a line segment. In detail, nosotros assign the interval with confidence level $0.68$ to the $α$ -cut in $μ = 1$ , and the interval with a conviction level of $0.95$ to the $α$ -cut in $μ = 0$ . These intervals are the values of one and two standard deviations for a Gaussian distribution of the observations. The conviction interval for the Gaussian distribution with known variance is given by $ρ \pm | t_{k - 1; one - \frac{α}{ii}} | \cdot σ_{ρ}$ , where $t_{one thousand - 1; one - \frac{α}{2}}$ is the value of a t-pupil distribution with $g - one$ degrees of freedom with probability $\frac{α}{2}$ and $σ_{ρ}$ is the standard deviation of the fitted $ρ$ parameter. Thus, the fuzzy set that represents the uncertainty of the fitted line is given past

$t p_{ρ} = (- | t_{0.025} | \cdot σ_{ρ}, - | t_{0.xvi} | \cdot σ_{ρ}, | t_{0.16} | \cdot σ_{ρ}, | t_{0.025} | \cdot σ_{ρ}) .$

(14)

We tin calculate the dubiety in the $θ$ parameter of the line equation $x c o south (θ) + y southward i n (θ) = ρ$ obtained past fitting one thousand collinear range sensor observations as

$t p_{θ} = (θ - a t a n (\frac{2 ρ_{0}}{l}), θ - a t a north (\frac{ii ρ_{1}}{50}), θ + a t a n (\frac{2 ρ_{i}}{l}), θ + a t a due north (\frac{2 ρ_{0}}{l})),$

(xv)

where l is line segment length.

We can maintain a coherent representation surrounding the underwater vehicle with the fuzzy segments using a similar arroyo to the Spatio-temporal relations betwixt the different sonar echoes presented above. We can update the location and uncertainty of such features using the time elapsed from their generation. We tin besides update their position using the motion interpretation of the underwater vehicle. The divisional sum operator ⊕ allows us to fuse the dubiety of the fuzzy segment $t p_{ρ}$ with the motion estimation and the elapsed time from the generation of the features representing the globe around the vehicle.

We can also fuse the detection of new features to the local perception representing the environment surrounding the underwater vehicle using the caste of similarity between fuzzy segments. We merge like features by detecting their collinearity and fusing their dubiousness. 2 segments $F S_{a}$ and $F {South}_{b}$ are considered collinear if they satisfy

$\begin{matrix} f (t p_{θ_{a}}, t p_{θ_{b}}) \geq 0.5 \land f (t p_{ρ_{a}}, t p_{ρ_{b}}) \geq 0.five, \end{matrix}$

(sixteen)

where $f (x, y)$ function is the matching degree between two trapezoidal fuzzy sets divers in the same universe $Ω$ every bit follows

$f (x, y) = \frac{(A_{x} + A_{y}) \cdot A_{x y}}{ii \cdot A_{x} \cdot A_{y}},$

(17)

where $A_{x}$ and $A_{y}$ announce the expanse enclosed by the fuzzy sets ten and y, respectively, and $A_{10 y}$ denotes the surface area of the intersection of x and y.

We combine new fuzzy segment perceptions with the ones contained in the buffer representing the environment around the underwater vehicle that satisfies the collinear status (xvi). This procedure allows us to enrich the local representation and remove redundant data, which reduces the doubt of erstwhile and imprecise feature representations. The combined fuzzy segment $F S_{r}$ from two collinear ones is calculated by

$F S_{r} = {θ_{r}, ρ_{r}, t p_{ρ_{r}}, (x_{i r}, y_{i r}), (x_{j r}, y_{j r}), k_{a} + k_{b}},$

(18)

where ( $x_{i r}$ , $y_{i r}$ ) and ( $x_{j r}$ , $y_{j r}$ ) are the cease-signal perpendicular projections of ( $10_{i a}$ , $y_{i a}$ ), ( $x_{j a}$ , $y_{j a}$ ), ( $x_{i b}$ , $y_{i b}$ ), and ( $x_{j b}$ , $y_{j b}$ ) on the line with ( $θ_{r}$ , $ρ_{r}$ ) parameters calculated as

$\begin{matrix} θ_{r} & = & \frac{{chiliad}_{a} θ_{a} + k_{b} θ_{b}}{{yard}_{a} + {grand}_{b}}, \\ ρ_{r} & = & \frac{k_{a} ρ_{a} + 1000_{b} ρ_{b}}{k_{a} + k_{b}}, \\ t p_{ρ_{r}} & = & (2 - f (t p_{ρ_{a}}, t p_{ρ_{b}})) \frac{k_{a} t p_{ρ_{a}} \oplus {yard}_{b} t p_{ρ_{b}}}{k_{a} + k_{b}}, \end{matrix}$

where $t p_{ρ_{r}}$ is the trapezoidal fuzzy set representing the uncertainty of the fusedfuzzy segment.

Figure 9a shows an example of the buffer data using the range observations from the mechanical sonar scanner sensor. We extract the fix of candidate points to be considered a line segment using the IEPF method. We fit these candidates to form a line using an eigenvector line fitting method. We represent these line segments using light-green lines. Effigy 9b depicts the local representation of the surround around the vehicle using fuzzy segments. We tin can observe that such features include the location uncertainty using the corresponding trapezoidal fuzzy set $t p_{ρ}$ . This local representation using fuzzy segments allows us to add and remove perceptions using a formal model, maintaining a coherent representation around the vehicle.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g009.jpg

(a) Local buffer of sonar scanner information with line segment fitting and (b) fuzzy segment representation effectually the underwater vehicle.

Figure 10 shows the flowchart of the process for building and maintaining a local representation of the environment using fuzzy segments. Nosotros group the sonar scanner readings into n sets with ${k_{1}, \dots, {grand}_{n}}$ observations using the IEPF method described in a higher place. We and so fit such groups of consecutive sensor readings using some eigenvector line fitting method to obtain the set of line segments ${S_{1}, \dots, S_{n}}$ . We utilize the conviction interval of the line-plumbing equipment algorithm to build the trapezoidal fuzzy sets ${t p_{ρ 1}, \dots, t p_{ρ northward}}$ representing the uncertainty of the fuzzy segment with (fourteen). Once we accept calculated the prepare of n fuzzy segments detected from the observations, they are fused with the set of yard fuzzy segments representing the environment around the underwater vehicle using the (16) criteria, or they are incorporated into such a representation. We update periodically the prepare of fuzzy segments ${Fifty F {Southward}_{1}, \dots, L F S_{m}}$ representing the local surround around the vehicle introducing the different sources of dubiety affecting them. We model the doubt of the vehicle motion and the crumbling of the representation using trapezoidal fuzzy sets. We incorporate these sources of doubt into the fuzzy segment representation using the bounded sum operator of (12). We as well remove these uncertain features when the surface area enclosed past the trapezoidal fuzzy gear up $t p_{ρ}$ of the fuzzy segment is higher than a prescribed threshold.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g010.jpg

Flowchart of the procedure for building the fuzzy segment representation surrounding the underwater vehicle.

iv. Particle Filter

We item the flowchart of the navigation organization in Figure 11. The localization system makes use of the GPS location provided by the Vectornav VN-200 navigation system. This device combines an inertial solid-land microelectromechanical organization (MEMS) with a high-sensitivity GNSS receiver using Kalman filtering algorithms to guess the position, velocity, and orientation. While the vehicle is on the surface, the navigation system makes utilise of the GPS. When the vehicle detects that it dives, by using the barometer of the standard Sibiu Pro platform, the last known and high-quality GPS position (using the HDOP Horizontal Dilution of Precision) is stored as a reference. The GNSS receiver yet provides locations at depression depths, but the position estimation degrades severely. Thus, nosotros ignore GPS information when the barometer depth is higher than a threshold $t h r$ , for example, 30 centimeters for the standard Sibiu Pro platform. We initialize the structured representation of the environment where the vehicle operates using a reference to the UTM (Universal Transverse Mercator) location where the vehicle submerged. From here on, the underwater localization method works in local metric coordinates. Nosotros convert these local estimations to global positions using the reference UTM position and the local coordinates. Nosotros can then convert the resulting UTM positions to latitude/longitude coordinates for visualization purposes. When the vehicle emerges again, we switch to GPS positions.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g011.jpg

Flowchart of the navigation system.

When the vehicle is operating submerged, we employ a particle filter or Sequential Monte Carlo (SMC) method to fuse the proprioceptive and exteroceptive sensory information to gauge the location. SMC method estimates a variable of involvement, typically with non-Gaussian and potentially multi-modal Probability Density Function (PDF) [31], in dynamical systems with fractional observations and random perturbations, both in the measurements and in the dynamical organization. The technique uses a set of particles (also called samples), with a likelihood weight representing the probability of that particle beingness sampled from the PDF, to represent the stochastic distributions of the state-space model and the noisy and partial observations. We tin obtain an gauge of the variable of interest past the weighted sum of all the samples. The particle filter is recursive in nature operating in two phases: prediction and update. The former modifies the particles according to the acting model (prediction stage) and also incorporates random noise on the variable of interest. The latter re-evaluate the weight of samples $w_{i}$ using the sensory information available (update stage). We evaluate the particles periodically to remove particles with small weights. These samples accept a low probability of being a sample from the PDF. This process is called resampling. Resampling techniques aim to avoid weight disparity, and thus the particles with negligible weight are replaced by new particles in the proximity of samples with college weights.

Let $x^{k} = {[p^{k}, θ^{thou}]}^{T}$ exist the state-space at the time k of the submerged underwater vehicle, where $p^{g}$ = ( ${ten}^{k}$ , $y^{k}$ ) is the 2D location and $θ^{k}$ is the vehicle'south orientation. We correspond the 2D location $p^{grand}$ uncertainty of each particle by a 2D Gaussian part, whose distribution follows a multivariate normal distribution $ϕ (p^{k}) \sim N_{ii} (p^{1000}, σ)$ with $σ$ the correlation coefficient between ( $x^{grand}$ , $y^{k}$ ) variables. This representation allows us to model the location uncertainty of the perceptions and and so merges it with the set of particles representing the probability density role of the variable of interest [32]. It besides allows u.s.a. to evaluate the probability of the particles representing the PDF, which is used to reject them at the resampling stage.

Thus, we stand for the location of the underwater vehicle (variable of interest) as a set of n particles ${southward}_{i}^{chiliad} = [x_{i}^{k}; w_{i}^{k}; ϕ_{i}^{chiliad} : i = 1, \dots, due north]$ , where: the index i denotes the sample (copies of the variable of involvement), the weight ${westward}_{i}$ defines the contribution of the particle i to the overall estimate of the variable of involvement, and the density function $ϕ_{i}$ represents the 2D location dubiousness ( $x^{chiliad}$ , $y^{one thousand}$ ) of each particle i to the interpretation of the location dubiousness. Algorithm 2 presents a pseudo-code of the recursive estimation procedure of the country-space using the particle filter. When the vehicle submerges, nosotros set up the time pace grand to zero and initialize the set ${south}^{chiliad}$ of n particles considering the last location p and uncertainty provided past the Vectornav VN-200 navigation system using the GNSS receiver and the inertial navigation organization (INS). In particular, we initialize the location uncertainty with correlation coefficient $σ$ to all the samples, which are randomly distributed around the position estimation p of GPS depending on the accurateness of such an interpretation.

So, the localization algorithm estimates the variable of interest $10^{k}$ recursively past the prediction and update stages. The former incorporates the move estimation $α$ , provided past the INS and DVL devices, to all the particles representing the location conventionalities. Nosotros too include a certain degree of random noise configured by a normal distribution with variance $α_{u}$ to spread the particles. The spreading of particles contributes to a amend representation of the vehicle belief since the resampling duplicates samples with high weight. The latter updates the weights $w^{k}$ of the ready of particles $s_{i}^{k}$ representing the vehicle belief by the product of the 2D Gaussian distribution of the features detected $γ$ and the $ϕ^{k}$ distribution of each sample. We obtain such a weight from the resulting likelihood of the production operation between two 2D Gaussians representing the location uncertainty. This arroyo allows us to merge the uncertainty of both sources: the sample and the perceived characteristic. The outcome of the production functioning betwixt ii Gaussian distributions has a low likelihood for distributions representing different locations. Since these samples with depression weight have a low probability of being a sample from the vehicle belief, we remove them from duplicating samples with high weight. These redundant particles take a different location when nosotros use the random dissonance of the prediction stage. There are dissimilar criteria to perform the resampling [33], we adopt the effective number of particles (ENP) every bit defined in Algorithm 2. When this number is lower than the product $β \cdot n$ , with $β$ tuned for the particular awarding and north the number of samples, we perform the resampling of the fix of particles. We draw the flowchart of all these steps in Effigy 11. Finally, the particle filter approach allows us to estimate a position $x^{k}$ and its location uncertainty $σ^{k}$ from the vehicle conventionalities by the weighted boilerplate of the samples and the correlation coefficient, respectively.

Algorithm ii: Particle filtering for localization.
Initialization
i: $p_{i}^{0} \leftarrow N_{2} (p, σ) {i = 1, \dots, due north}$	▹ Randomly initialization of particles from location p
ii: $ϕ_{i}^{0} \leftarrow {Northward}_{2} (p_{i}^{0}, σ) {i = 1, \dots, n}$	▹ Initialization of distribution from the position $p_{i}^{0}$
3: $s_{i}^{0} \leftarrow [x_{i}^{0}; {due west}_{i}^{0}; ϕ_{i}^{0} : i = 1, \dots, n]$	▹ Initialization of samples inside the uncertain location
Recursive loop for localization
4: while true do
five: thou++
half-dozen: ENP = $\frac{one}{\sum_{i = 1}^{n} fifty o g^{2} (w_{i}^{k})}$	▹ Effective number of particles
vii:if ENP < $β \cdot n$ then	▹ Condition of particle population depletion ( $0 \leq β \leq 1$ )
8: $s^{m}$	← Resampling( ${west}^{k}$ )
9:finish if
10:Prediction stage
11: $10^{k + ane}$ ← $h (x^{k}, α)$	▹ Include action $α$ (dead-reckoning displacements)
12: $10^{k + ane}$ ← ${ten}^{m + ane}$ + $α$ · $N (0, α_{u})$	▹ Include ramdom noise to the variable of interest
13:Update stage
14: $w^{yard + ane}$ = $w^{grand} \cdot m (γ, x_{j}^{yard})$	▹ Update with sensing $γ$
15: Normalization of the weights
16:for j← 1 to due north do
17: $w_{j}^{k + 1}$ = $\frac{{westward}_{j}^{thou + one}}{\sum_{i = 1}^{due north} {west}_{i}^{thousand + 1}}$
18:end for
19: stop while

5. Experimental Results

We have conducted experiments in ii different scenarios to evaluate the performance and accuracy of the proposed methods. One prepare of experiments have been carried on in a controlled environs, a circular swimming pool, while the other set of experiments is carried on at sea, in a harbor dock. The former scenario allows us to evaluate the sensor modeling and localization in a structured environment. Nosotros have an external vision organisation that tracks the position of the vehicle in the controlled environment. This location estimation serves equally a ground-truth and allows u.s. to correlate the position estimates using the navigation organisation and the ground-truth. The latter scenario presents the navigation arrangement operating in a more complex scenario without whatsoever arrangement to estimate the ground-truth. In this instance, we evaluate the accuracy of the arrangement comparing the last estimated underwater position with the first stable GPS position obtained when surfacing. Care has been taken to emerge vertically so that the fault associated with emerging is negligible.

We perform the experiments running the intensive computation in a remote computer. We communicate with the Raspberry Pi using TCP/UDP protocols through the Ethernet of the umbilical cable. We also use this computer for monitoring, configuring, and operating the underwater vehicle. This computer installs an Intel Core i7 running at 3.3 GHz. We configure the image acquisition with 480 × 360 resolution, which allows u.s.a. to compute 15 frames per second in the remote estimator. In particular, vision processing takes most 25 milliseconds on average. Apropos the localization approach, information technology takes about iii milliseconds per update. This timing is tessellating the variable of interest using 1000 samples. Past adjusting this timing allows us to perform the localization update every 150 milliseconds.

5.1. Experiments in the Swimming Pool Scenario

The experiments in the swimming pool consist of the submerged navigation of the underwater vehicle performing inspection tasks. Figure 12 shows the pond pool scenario and the external vision system designed to provide the ground-truth. The swimming pool has six meters in bore and has different objects simulating working weather for inspection tasks. The shallow depth of the swimming puddle is plenty to degrade the GNSS signal. Thus, the particle filter becomes mandatory for underwater navigation. The vehicle uses the mechanical sonar scanner Ping360 to perceive arcs corresponding to the pond pool walls. Nosotros use the standard camera of the Sibiu Pro platform to detect the Aruco markers. We apply the sensor modeling techniques presented to a higher place to estimate the features surrounding the vehicle during underwater navigation. Nosotros fuse these features with the motion estimation to calculate the vehicle belief using the particle filter.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g012.jpg

(a) Structured pond pool scenario and (b) ground-truth estimation organization.

Effigy thirteen shows the path followed past the vehicle in underwater navigation performing inspection tasks. The brown circle represents the ground-truth position estimation using the external vision system, and the brown segment-lines the connection between location estimations. The dark-green circumvolve represents the location estimation using the corresponding sensory data. The pink line segments represent the connection between position estimates with the navigation arrangement of the vehicle. We evaluate the estimated path followed by the immersed vehicle in three situations: navigation using dead-reckoning, using the vision markers, and using the sonar scanner observations. We tin observe that the footing-truth is similar for the three cases since we represent the same experiment using different sensory information.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g013.jpg

Position interpretation doubtfulness using (top) dead-reckoning, (middle) vision markers, and (bottom) sonar perceptions in the structured pond puddle scenario.

The dead-reckoning experiment only uses the INS of the Vectornav VN-200 navigation organization and the DVL-1000 speed estimations. We can discover that the path followed using dead-reckoning approximates the road followed past the underwater vehicle. However, the position error is cumulative or compounding over time using such an arroyo. Thus, nosotros can observe that the underwater vehicle goes through the piping in the structured surroundings because the estimated position degrades over fourth dimension. We also have noted that the correlation coefficient $σ$ grows unbounded during the navigation. We simply introduce three Aruco markers in the structured environment, which are detected sporadically during the navigation. We represent these Aruco markers using empty squares with the corresponding ID. These sporadic observations allow u.s. to correct the position estimation and the uncertainty of the vehicle belief represented by the correlation coefficient $σ$ , equally shown in Figure thirteen(centre). Withal, nosotros can observe that the position estimation compared to the ground-truth is of the order of one-half a meter. We have to remark that we can enhance the accuracy of position estimation past adding vision markers. The Video S1 in the Supplementary Materials shows the navigation and position estimates using the Aruco markers. Finally, we tin observe that the all-time position estimation is obtained using the features from the sonar scanner observations, in particular the circumference arcs obtained using the circular model fitting presented above. The representation surrounding the vehicle during the underwater navigation allows usa to feed the localization approach with coherent information that allows united states of america to track the vehicle with a high caste of accurateness. We can likewise notice that the estimation $σ$ of the doubt of vehicle location is kept under one-half a meter during the navigation. This information is coherent with the location interpretation provided by the footing-truth.

5.two. Experiments in the Dock Harbor Scenario

The experiments in the harbor dock consist of the submerged navigation of the underwater vehicle performing inspection tasks. In particular, nosotros follow the dock harbor wall to perform such inspection tasks [34]. Figure xiva shows the satellite image of the dock harbor scenario. Effigy 14b depicts a representation of the environment around the vehicle using the fuzzy segment representation. We update the belief of the variable of interest using the speed estimates provided by the INS of the Vectornav VN-200 navigation system and the DVL-1000. The vehicle uses the mechanical sonar scanner Ping360 to perceive the walls of the dock harbor. We use the sensor modeling techniques presented above to perceive the features surrounding the vehicle during underwater navigation. We fuse these features with the motion estimation to estimate the vehicle conventionalities and the location uncertainty using the particle filter.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g014.jpg

(a) Harbor dock scenario and (b) the fuzzy segment representation of the environs surrounding the vehicle.

In this scenario, nosotros do not have an external organisation providing the footing-truth. We only can evaluate the accuracy of the localization when the vehicle emerges. We do it by comparing the GPS location with the position estimation in submerged navigation. As previously mentioned, we initialize the structured representation of the surroundings from the last GPS estimation using UTM coordinates, and when the vehicle emerges, we transform the estimated underwater position in the structured local representation to UTM coordinates once more. Figure 15 shows the position estimation of the submerged vehicle during underwater navigation. The xanthous line segments represent the connection of position estimates using the GPS information, whereas the pink line segments represent the connexion betwixt position estimates in submerged conditions. The localization system performs this switch using the barometer readings, equally shown in Figure 11.

An external file that holds a picture, illustration, etc. Object name is sensors-21-01549-g015.jpg

Position estimation doubt using (top) expressionless-reckoning and (lesser) particle-based localization arrangement sensing uncertain line segments in the harbor scenario.

Figure 15(top) shows the path followed using expressionless-reckoning with the speed interpretation provided past the INS of the VectorNav and DVL-1000. We tin can observe that the correlation coefficient $σ$ representing the location uncertainty grows unbounded during the navigation. We also notation that the position estimation is drifting further and further away from the wall that it is inspecting. When the vehicle emerges, we observe that the GPS position is at a distance of more than 5 meters from the location estimated by the underwater navigation organisation. The drastic changes of the GPS position estimates are attributed to the initialization of the Kalman filters of the Vectornav VN-200 navigation organisation. Figure 15(bottom) shows the path followed past the underwater vehicle using the sonar scanner observations with the line fitting arroyo and the fuzzy segment representation. The representation effectually the underwater vehicle allows united states to feed the localization approach with coherent information, which allows u.s. to track the vehicle with a high caste of accuracy. We have to remark that a wall does not provide data to locate the vehicle, but ensuring that the vehicle location is posed at the corresponding distance from the wall. For these reasons, the interpretation $σ$ of the uncertainty of vehicle position is only reduced in 1 dimension. The localization algorithm would need more information to perform some kind of triangulation to locate the vehicle. In any example, the position estimated by the particle filter is located at a altitude of less than one meter from the GPS location when the underwater vehicle emerges.

6. Conclusions and Future Works

We have presented the processing, modeling, and fusing of unlike underwater sensor signals to provide a reliable representation for underwater localization in structured environments. In particular, we have presented the feature extraction from the buffered data of underwater observations using a photographic camera and a mechanical sonar scanner. The underwater sensor readings using these sensors are noisy and uncertain, and thus nosotros propose a mechanism to verify such measures by coherent consecutive and redundant data observations, which are removed from the buffer by aging and disparity. We propagate the uncertainty of such perceptions to the set of features surrounding the underwater vehicle, which provides a coherent representation of the surroundings. We also update and remove these features using the factors previously mentioned. This processing filters out inconsistent information that tin can deteriorate the position estimations of the localization approach. We apply the extracted features from noisy underwater sensors to feed the update stage of a particle filter localization method. However, we can besides use the proposed sensor modeling techniques with other localization approaches. We evaluate the underwater sensor modeling with the accuracy of the localization system when the vehicle submerges. The experimental results show meaning accurateness improvements in comparing with dead-reckoning underwater navigation. As futurity works, we plan to include acoustic sensor readings in the proposed framework, fusing these measurements with the perceptions using sonar and optical sensors. Nosotros also programme to estimate the location by combining a local (tracking) and a global localization method. This volition allows us to amend the accuracy and robustness of the position estimation.

Acknowledgments

We admit the back up of the Nido Robotics company.

Author Contributions

H.M.-B.: Conceptualization, funding acquisition, software and supervision; P.B.-P.: Formal analysis, investigation, and software; D.H.-P.: Conceptualization, formal analysis, investigation, software, and writing. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Argument

We include a video showing the development working in real-earth weather condition.

Conflicts of Involvement

The authors declare no conflict of interest.

Footnotes

Publisher's Annotation: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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