Data captured by a Synthetic Aperture Sonar (SAS) near Mobile Bay during the 2021 Undersea Remote Sensing experiment funded by the Office of Naval Research reveals near surface bubble clouds from wave breaking events and a large aggregation of fish. Tools developed for using SAS data to image hydrodynamic features in the water column were applied to observations of the bubble clouds and fish aggregation. Combining imagery and height data captured by the sonar array with a detection and tracking algorithm enables the trajectories, velocities, and behavior of fish in the aggregation to be observed. Fitting the velocity and height data of the tracked objects to a Gaussian mixture model and performing cluster analysis enables an estimate of the near-surface ambient velocity via observation of the movement of the bubble traces and the general direction of motion of the fish aggregation. We find that the velocity traces associated with bubbles are consistent with ambient currents as opposed to the direction of propagating wave crests while velocities of fish indicate relatively large, pelagic species.

Synthetic aperture sonar (SAS) is an active sonar imaging technique in which an extended aperture is created by coherently combining echo data captured at multiple positions along a trajectory. The coherent combination of data captured from multiple positions enables the length of the array used for imaging to be extended beyond the physical length of the sonar, hence the name “synthetic aperture.” Synthetic aperture systems have resolution that is theoretically independent of range and frequency,1 and the ability to create high resolution images at long ranges has made this type of imaging applicable for defense applications such as mine countermeasures.2,3 The technology is finding increasing application beyond the defense sector however, with synthetic aperture sonar now being used for surveying,4,5 archaeology,6,7 oceanography,8,9 pipeline inspection,10,11 resource identification,12 and habitat monitoring, such as for coral reefs.13 

The speed of sound in water introduces a practical limitation on the ability to achieve both high resolution and high area coverage rates.14 Both military and commercial synthetic aperture sonar systems address this challenge by leveraging physical designs incorporating “real-aperture” arrays of receivers with multiple elements in the along-track dimension.14 Using the along-track array of receivers enables the sonar system to create large synthetic apertures from a much smaller number of pings because the aperture can be sampled set-by-set rather than point-by-point. The practical ramification of this design is that the sonar can travel farther between pings without creating an under-sampled array, significantly raising the area coverage rate. As noted in Hansen14 (Chap. 2.3), a secondary implication is that real-aperture “sector-scan” images can be created from every ping. These images have a lower resolution than the synthetic aperture imagery, however, they are more useful for imaging moving objects. The coherent beamforming processes used to create synthetic aperture imagery make assumptions about the delays to scatterers that can be broken by moving objects15 and moving objects are often significantly blurred. In contrast, moving objects generally retain focus in single-ping real-aperture imagery, a fact that was leveraged in Marston et al.8 to track and image ebb-plume fronts.

As in Marston et al., the current work represents an additional investigation into a non-traditional use of a synthetic aperture sonar array. While previous work focused on observations and quantitative analysis of bubble plumes at the Connecticut River ebb plume front, this work focuses on transient signals attributed to localized bubble plumes from breaking waves and measurements of a large aggregation of relatively fast-moving biological scatterers that are presumed to be fish.

During the Undersea Remote Sensing Directed Research Initiative (USRS-DRI) sponsored by the Office of Naval Research, several estuaries along the coast of the United States were surveyed using various sensors including echo-sounders, multibeam-sonars, marine radar, optical drones, and a synthetic aperture sonar. One of the goals of the DRI was to determine how the remote-sensing capabilities of synthetic aperture sonar systems can used to further oceanography. The work described here was performed in and around the mouth of Mobile Bay in 2021 as a part of the USRS DRI. Among other objectives, USRS has focused on forming a synoptic view of the estuarine environment via synthesizing data captured by a broad range of in situ and remote sensing techniques and numerical modelling approaches. The goal of the synthesis is to better understand the temporal and spatial variability of estuarine systems and measure this variability using unconventional sampling methods. To this end, comparable studies were performed in the Connecticut River and James River prior to the Mobile Bay work. In the two prior systems, bubble entrainment attributed to wave breaking and downwelling associated with surface velocity convergence was a dominant feature in acoustic imagery.8,16

Mobile Bay, into which the Mobile River and its tributaries discharge, is a large (1070 km2) and shallow bay located in the northern Gulf of Mexico. The system's mean daily discharge makes it one of the largest river systems in the United States.17 Approximately 85% percent of the exchange between Mobile Bay and the Gulf of Mexico passes through Main Pass at the southern end of the Bay. Although many kilometers wide, most of the pass is only a few meters deep with the exception of a dredged navigation channel approximately 10 meters deep. This relatively deep channel extends southward into the Gulf of Mexico with shallow shoals to the east and west. Peak tidally-driven currents through Main Pass Bay are approximately 1 m/s.

During ebb tides the relatively fresh waters expand out from Main Pass, spilling over the shoals and navigation channel forming a narrow, expanding plume over the dense ambient Gulf of Mexico waters. Mobile Bay's plume has been observed to extend as much as 30 km from shore with thicknesses as large as a meter thick while plume thicknesses are greater near Main Pass.18 Regardless of depth, this stratification makes the Mobile Bay plume sensitive to ambient wind conditions. Strong stratification inhibits the transfer of momentum imparted by the wind on the plume, allowing for strong wind-driven currents in the upper water column.19 Because of the large fetch in many directions the surface conditions are highly sensitive to winds. While surface roughness can also impact sonar performance,20,21 the generation of bubble plumes from wave breaking, a process that is enhanced at fronts,19,22,23 can be widely observed in Mobile Bay. With each breaking wave event, a bubble plume is injected into the water column. While relatively large entrained bubbles will rapidly rise to the surface and create residual surface foam, smaller bubbles with low rise velocities can remain in the water column for many minutes or longer, where they can be transported passively by currents and turbulence. Whitecapping, a clear indicator of aeration of surface waters by wave breaking, begins to occur for sustained wind speeds as low as ∼3.5 m/s,24,25 while plume depths for entrained bubbles scale with wave height and the ability of the wave to do work against the buoyancy of the gas. Entrained bubbles are efficient scatterers of sound and have been the focus of acoustic studies for decades.26–28 In this work, we identify and track the presence of individual bubble plumes from wave breaking events and track their advection with ambient currents.

In Mobile Bay, near-surface signals attributed to bubbles were commonly observed but were not the only notable feature observed by the synthetic aperture sonar during the survey. Of particular interest is a large aggregation of biological scatterers, presumed to be large fish. The size and spacing of the fish, and their direction of motion were such that individual fish could be observed for multiple pings, and throughout much of the field of view of the sonar.

Both the bubble plumes and fish applications require the use of detection and tracking algorithms. Despite moving-object tracking being a well-established sub-field of synthetic-aperture-radar,15 research on the subject is nearly non-existent in SAS literature, with the closest work being related to tracking of objects in harbors using a distributed multiple-input multiple-output (MIMO) acoustic array29 or bistatically imaging submarines.30 The approach taken in the present study is to perform detection and tracking using imagery created by the previously described real aperture arrays used to boost area coverage rate. These arrays are often modular, with customizable lengths that can be in excess of two meters,31 and have far-field angular resolutions of just fractions of a degree. These real-aperture arrays can be used to create “sector scan” images analogous to the images created by forward looking sonars for which tracking methodologies are well established, particularly for fish detection.

A recent overview of the field of fish tracking and identification techniques using imaging sonar is given in Wei et al.32 According to Wei et al., current state-of-the-art leverages high resolution forward-looking sonar systems with center frequencies in the megahertz. Benefits of these high resolution systems include the ability to classify fish based on features visible in imagery, and the ability to perform tracking in both range and azimuth dimensions. Recent approaches have leveraged machine-learning augmented trackers like YOLO (“You only look once”33) to track and classify fish species with high resolution acoustic imaging systems.34 A limitation, however, is the rapid attenuation experienced by the high frequency signals, which generally limits the practical ability of feature identification in high resolution sonar imagery to maximum ranges from 15 to 20 meters.32 Detection of fish at 40 meters with high resolution “acoustic camera” systems like the Dual Frequency Identification Sonar (DIDSON35) have been demonstrated, but long range imaging is accompanied by image and feature degradation.36 

The present research demonstrates that SAS arrays can be used to track the behavior of moving objects, such as fish or bubble clouds, over much larger ranges than comparable forward looking sonars, provided that the size and spacing of objects being tracked is compatible with the resolution of the sonar. Additionally, vertical staves normally used for bathymetry estimation can be leveraged in the present application to provide a third dimension to the location of tracked objects. Whereas several papers on fish tracking have exploited open-source, customizable deep-network image-based detectors such as YOLO,33 the present study assumes that the sector-scan resolution of SAS images is insufficient to provide image features that can be leveraged by such trackers in a meaningful way. The tracking problem is reduced to point detection and inter-frame data association to estimate velocities and paths of motion. Subsequent sections will describe the method used for determining scatterer velocity, and the data-association method used to track objects between frames. Results of applying the tracker to data captured at Mobile Bay by the deployed SAS system will then be given along with clustering results based on the behavior of tracked objects.

The sector-scan imaging approach taken in the present study is identical to that used in Marston et al.8 to study tidal plume front features. In this approach, data is assumed to have been captured by a receiver array composed of M samples in the along-track dimension and N samples in the vertical dimension, where N > 2. A set of N polar coordinate images with dimensions range and azimuthal angle are created using delay-and-sum beamforming. Subsequently, the images are binned in the range dimension, and correlation beamforming8,37 is used to estimate vertical angle-of-arrival. This process results in two J x K matrices: Ij,k and φj,k, where J ≈ M, the number of along-track array elements, and K is the number of range-bins used for performing cross-correlations. Ij,k contains magnitude values and resembles a standard sector-scan image. φj,k, contains vertical angles-of-arrival. Figure 1 depicts an example of these two data products, and how they can be combined to create an xyz scatterplot (or “point cloud”).

FIG. 1.

(Color online) An example of a log-scale single-ping polar coordinate image (a) and associated angles of arrival (b) created from data captured by the SAS system deployed at Mobile Bay. In (c), a xyz scatterplot in Cartesian coordinates is created from the data in (a) and (b). Hue in (c) is based on depth as the color-bar on the right shows, and lightness is proportional to log-scale image intensity.

FIG. 1.

(Color online) An example of a log-scale single-ping polar coordinate image (a) and associated angles of arrival (b) created from data captured by the SAS system deployed at Mobile Bay. In (c), a xyz scatterplot in Cartesian coordinates is created from the data in (a) and (b). Hue in (c) is based on depth as the color-bar on the right shows, and lightness is proportional to log-scale image intensity.

Close modal

A thorough description of the method used to create the type of data shown in Fig. 1 is given in Sec. II of Marston et al.8 Note that this type of beamforming is not required for the subsequent tracker, which only assumes a geo-rectified polar-coordinate intensity image with an accompanying matrix of vertical angles-of-arrival having equal size to the image matrix. In the present case, the angular sample spacing in the azimuthal dimension of the sector scan images created in the current study is ∼0.25 degrees. The range resolution of the image shown in Fig. 1 is approximately 20 cm and is significantly reduced from the true bandwidth-limited range resolution of the system due to the necessity for block-processing data in range to perform cross-correlations.

The detection process is applied to the sector scan image data, an example of which is shown in Fig. 1(a). Due to the use of real-aperture processing, along-track resolution varies as a function of range in sector-scan images. The present implementation limits the maximum range to r = 110 meters, at which point the minimum resolvable distance between objects in the azimuthal dimension is 2rsin(θrez)= ∼1 meter. The focus of this manuscript is on bubble plumes from breaking waves and aggregations of fish, both of which can vary significantly in scale. The average peak period and significant wave height observations in the vicinity of the SAS observations were approximately 3.7 s. The water column depth was 10 meters. Using the linear wave equation,38 these constitute deep water waves and estimated wave speeds and wavelengths are approximately of 5 m/s and 16 m, respectively. Under these conditions and expected spatial scales bubble plumes injected by breaking wave crests are expected to be resolvable in the sector scan imagery.

Fish, on the other hand, aggregate with highly variable packing densities. The volume occupied by a fish in a school has been shown to roughly follow N L body 3 m3, where N is the number of fish and L body is the average fish body length.39 Given the resolution limitations of the current sector scan imagery (∼1 m at 110 m), the ability to track individual scatterers is an indicator of fish size; i.e., average body length is > 1 m in length due to fish packing behavior. The inshore waters of the northern Gulf of Mexico host numerous moderate to large, schooling pelagic species that can approach or exceed this length. These include, but are not limited to, Spanish mackerel (Scomberomorus maculatus) and Crevalle jack (Caranx hippos).

Figure 2 shows a flow chart of the detection process. To detect bubble plumes, fish, or other targets the first stage of the detection process applies a range-variant smoothing filter in the range and angle dimensions to place a lower-bound on the minimum resolvable distance in the along-track dimension. The purpose of this filter is to prevent a single detection from splitting into multiple detections on the same object as the object moves closer to the sonar. The filter is applied in two stages: the first is a range-variant smoother in angle, where the smoothing kernel is defined via:
f θ θ , r = W r e θ 2 / 2 θ f r 2 ,
(1)
W r = π θ f r 8 + Δ θ 2 8 1 / 8 ,
(2)
θ f r = sin 1 L f r .
(3)
FIG. 2.

(Color online) A flow chart of the detection process.

FIG. 2.

(Color online) A flow chart of the detection process.

Close modal
In Eqs. (1)–(3), θ is azimuthal angle, r is the range, Δ θ is the sector-scan sample spacing in θ, and Lf is the approximate length of the object of interest. The Gaussian smoothing kernel in Eq. (1) is accompanied by a weighting function W r that is described in Eq. (2). This weighting function bridges the reciprocal of the integral of the Gaussian function in (1) [i.e., 1 / π θ f r], with a limiting value determined by the angular sample spacing of the sector scan image ( Δ θ / 2). The latter value represents the angular limit below which θ f r produces a filtering kernel via Eq. (1) that looks like a delta-function due to sample spacing Δ θ. The weighting function in Eq. (3) provides the normalization for the convolution operation, preventing near range values from becoming excessively large. The function θ f r defined in Eq. (3) is the angular span of the characteristic length Lf in the sonar field of view as a function of range from the sonar. Range variant smoothing in the angular dimension is followed by smoothing in the range dimension using another Gaussian kernel defined as
f r ( r ) = e r 2 / 2 ( r f ) 2 ,
(4)
which, as with Eq. (1), is applied as a convolution but in the range dimension. In the present implementation, Lf = 0.125 m and rf = 0.1 m.

Following application of the smoothers for de-speckling, all peaks greater than their 8-pixel neighbors are found. Peak location estimates at sub-pixel precision in θ and r are found via parabolic interpolation and peak estimation. Sub-pixel peak localization via parabolic interpolation is a common technique in particle image velocimetry literature; a discussion of sub-pixel peak estimation techniques such as the one employed here and others may be found in Chen and Katz40 or chapter 5.4 of Raffel.41 

Most peaks correspond to noise and are not of interest, therefore the peaks are culled or preserved based on an estimate of the signal-to-background ratio. This is done by normalizing the de-speckled image by a moving median filter, i.e.,
I nrm r , θ = I f r , θ M I f r , θ + σ I ,
(5)
where I f r , θ is the sector-scan image having been de-speckled using the Gaussian filter kernels described in Eqs. (1) and (4), M( ) represents the median-filter operator, in this case using a 15 × 15 pixel sliding window for normalization, and σ I prevents very low amplitude signals from being amplified by the normalization operation. In the present case σ I is defined as
σ I = 1 J K r , θ I f r , θ .
(6)
Following normalization, a binary mask is created using a prominence threshold Ithresh,
I mask r , θ = { 0 , I mask r , θ < I thresh , 1 , I mask r , θ > I thresh .
(7)
All detected peaks lying within pixels having prominences greater than I thresh are retained, and a third coordinate dimension, elevation angle, is assigned to each detection from the values in φ( r , θ) corresponding to the index in I( r , θ) of the detections. These points are then transformed from vehicle body coordinates r , θ , φ into geo-rectified Universal Transverse Mercator (UTM) coordinates using the navigation state values from the inertial navigation system of the autonomous underwater vehicle on which the SAS array is mounted.

Figure 3 shows an example of a sector-scan image in polar coordinates [Fig. 3(a)], the image after de-speckling using the convolution filters defined in Eqs. (1) and (4) [Fig. 3(b)], and the detections (green circles) resulting from the application of the detection process described in Fig. 3(c).

FIG. 3.

(Color online) A sector scan image showing a shoal of fish before (a) and after (b) de-speckling. Plot (c) overlays detections on top of the sector scan image.

FIG. 3.

(Color online) A sector scan image showing a shoal of fish before (a) and after (b) de-speckling. Plot (c) overlays detections on top of the sector scan image.

Close modal
To estimate the velocities of individual detections, the current approach associates detections across multiple pings using a constant velocity model. This is done by finding the velocities in the x and y dimensions that maximize a density function ρ v x , v y created using detection points from a span of adjacent pings. Denoting the current detection point location in the horizontal plane as x n , m , y n , m, where bold m represents the index of the current ping and bold n indicates the index of the detection within ping m,
ρ n , m v x , v y = 1 K e α D k 2 ,
(8)
D k = x n , m x k + Δ t m v x 2 + y n , m y k + Δ t m v y 2 ,
(9)
where Dk is the distance between the currently evaluated detection point located at x n , m , y n , m and the kth detection point located at x k , y k, captured during ping m m, which is separated temporally from the current ping by the time span Δ t m. The kth detection point is a member of the K-length set of all detection points for which m m P m + P , m m. The constant velocity assumption is therefore applied over a span of pings of length 2 P + 1. For the present system P = 4, creating a total time span of nine pings for which velocity is assumed to be constant or, equivalently, for about 1.5 s based on the operation settings of the sonar during acquisition. The variable α in Eq. (8) represents a fitting parameter that determines how much deviation from the model can be tolerated to increase the value of ρ n , m v x , v y; its value in the current implementation is α = 2.5.

Note that the location of the detection is three dimensional, but the velocity is only being calculated in the x- and y-dimensions. There are multiple reasons for this: ρ n , m v x , v y is often a multimodal, non-convex function and determination of the values of v x and v y that maximize ρ n , m v x , v y is currently being performed by a brute-force search over v x and v y. Adding v z as a search parameter was found to slow velocity estimation considerably. The sparsity of the measurement in the elevation direction, however, implies that distributions of moving scatterers for which multiple objects occupy the same region in the x- and y-dimensions but have different locations and velocities in z will not be measurable with this system; thus, the search limitation models a true limitation of the array used for acquisition.

The search for the velocities that maximize ρ n , m v x , v y is limited to a range of −3 to 3 m/s in both dimensions and is performed at a resolution of 37.5 cm/s. Computational efficiency is improved by reducing n from being the set of all detection points found in the ping set M to the subset of points that could be potential candidates given the limitations on velocity. Evaluation of Eq. (8) using this approach results in a matrix with a well-defined peak indicating the velocity in the x- and y-dimensions if a velocity model fits the detection data well. The location of the peak of ρ n , m v x , v y is resolved to a precision finer than the sample spacing using parabolic interpolation in both dimensions.

The peak value of ρ v x , v y provides a quality value for the velocity estimate: if few points fit any candidate velocity, then the peak value of ρ v x , v y is low. Velocity estimates for which max ρ v x , v y < ρ thresh are culled; in the current implementation ρ thresh = 6. Figure 4 shows the georectified detections of Fig. 3 and their velocities estimated in the manner described above. Velocities not meeting the quality criterion have been culled.

FIG. 4.

(Color online) Velocity estimates for the detections shown in Fig. 3. Note that only detections with velocity estimates having a quality value ρ max v x , v y≥ 6 are plotted.

FIG. 4.

(Color online) Velocity estimates for the detections shown in Fig. 3. Note that only detections with velocity estimates having a quality value ρ max v x , v y≥ 6 are plotted.

Close modal
Multiple-object-tracking is an extensive sub-field of computer vision that has a broad range of applications; an overview can be found in Luo et al.42 In the present study, tracking is accomplished via a constant-velocity α-β filter43 with empirically tuned α and β weights. The constant-velocity assumption is common for multiple-object tracking problems.42 The following state update equations are used to update the position and velocity estimates of each state:
x s , y s , z s k = x p , y p , z p k + α x , y , z x m , y m , z m k x p , y p , z p k ,
(10)
v x s , v y s k = v x p , v y p k + β x , y v x m , v y m k v x p , v y p k ,
(11)
v z s k = v z p k + β z z m k z p k T ,
(12)
where index k represents the index of the current set of detections (i.e., the current ping), x,y,z indicate positions along the respective axes, vx,y,z represent velocities along the respective axes, subscript s indicates a state estimate, subscript p indicates a state prediction, subscript m indicates a measurement, and α x , y , z and β x , y , z are the parameters weighting the contributions of the prediction and measurement residuals (i.e., “innovation”) to the current state estimate. T in Eq. (12) is the time step duration between pings. Note that this is present in Eq. (12) and not Eqs. (10) and (11) because the velocity in the z-dimension is being estimated using displacements found during the tracking process. Predictions x p , y p , z p and v x p , v y p , v z p are computed from the previous state estimates and time step T using the following equations:
x p , y p , z p k = x s , y s , z s k 1 + v x s , v y s , v z s k 1 T ,
(13)
v x p , v y p , v z p k = v x s , v y s , v z s k 1 .
(14)
The state update in Eqs. (10)–(12) requires the association of the tracked object with detection to provide measurement data. This association is done via nearest neighbors using the Euclidean distance between the predicted state of the tracked object and the measurement vector of the current set of detections. The association of tracked objects to detections in a manner that minimizes a linear distance function is an optimization problem that the well-known “Hungarian” algorithm described by Munkres44 is often used to solve, and it was used in the present case.

Tracked objects that do not get matched with a detection are not immediately removed from the pool; rather their positions are updated based on their predicted states. If an object does not get associated with a detection after multiple pings, (eight in the present implementation), it is permanently removed from the pool of currently tracked objects, and trailing predictions following the last association are truncated from the track data.

The SAS measurements described in the present study were made early during an ebb tide at approximately 2105 UTC on 11 June 2021 outside of Mobile Bay, Alabama (Fig. 5). At this time, coordinated sampling using a broad range of assets was performed south southwest of the mouth of Main Pass (the inlet to Mobile Bay). Numerous data sets derived from these assets provide important context for the SAS observations discussed here. First, five Surface Wave Instrument Floats with Tracing (SWIFTs)45 were deployed north of the study site within the main channel. SWIFTs are Lagrangian drifters that, in addition to other packages, are equipped with downlooking Nortek Signature 1000 acoustic Doppler current profilers (ADCPs) to measure velocity profiles, turbulence, and acoustic backscattering. In addition, SWIFTs are used to calculate wave heights and directional wave spectra.

FIG. 5.

(Color online) (a) The coastline around Mobile Bay, Alabama, and the northern Gulf of Mexico. The dashed lines highlight the area included in (b). (b) A closer view of Mobile Bay's Main Pass, through which most of the exchange with the Gulf of Mexico occurs. Additional content shows the locations corresponding to SAS measurements, vessel-based physical oceanographic measurements, and SWIFT drifter data used in this study.

FIG. 5.

(Color online) (a) The coastline around Mobile Bay, Alabama, and the northern Gulf of Mexico. The dashed lines highlight the area included in (b). (b) A closer view of Mobile Bay's Main Pass, through which most of the exchange with the Gulf of Mexico occurs. Additional content shows the locations corresponding to SAS measurements, vessel-based physical oceanographic measurements, and SWIFT drifter data used in this study.

Close modal

Additional supporting measurements were performed using sensor packages deployed from the R/V Pelican, which performed transects (SSW-NNE) perpendicular to the predicted orientation of the expanding plume front. Three sets of measurements from the R/V Pelican are relevant to the SAS measurements discussed here. First, two Nortek Signature 1000 ADCPs were deployed on a tow-body at a depth of approximately 4 m. Data were processed to calculate 10 s averaged velocity profiles throughout the water column. To measure water properties an RBD conductivity, temperature, and depth (CTD) profiler and a RockLand Scientific MicroSquid microstructure sensor were deployed as a free-falling package controlled by a winch. Profiles were obtained by releasing a clutch on the winch, allowing the package to fall vertically into the water column to the seabed. The package was then winched to the surface and redeployed. This process was repeated as quickly as allowed by the water depth. Properties were then processed to produce a final resolution in the vertical of 10 cm. The final instrumentation package deployed from R/V Pelican was a set of five pole-mounted echosounders with center frequencies ranging from approximately 30 to 333 kHz operated by two Simrad WBT Tubes. The only unit presented here is a 70 kHz (ES70-7 °C) transducer using a 1 ms pulse duration, power level of 75 Watts, and transmitting a frequency modulated chirp from 47 to 90 kHz with a pulse repetition rate of 5 Hz. The units were calibrated using standard sphere techniques46 following the deployment and processed to produce volume backscattering coefficients.47 

These ancillary data streams were processed and aggregated in transects. For context, the distance between R/V Pelican and the SAS system was calculated during the sampling period. The closest point of approach between the vessel and the vehicle was approximately 225 meters and occurred at approach 2123 UTC, roughly 18 min after the SAS data presented here. Data from this transect are presented and additional transects, both before and after this period, were reviewed. Over this, wind speeds, water column properties, and currents did not vary significantly. Thus, the presented results are likely representative of those sampled by the SAS system during this period.

Salinity and temperature profiles measured along the transect show two primary water masses (Fig. 6). The upper five meters of the water column had temperatures and salinities of approximately 28.5 °C and 25 PSU, respectively. This water, likely remnant water from prior ebb plumes, was separated by a narrow pycnocline from the ambient Gulf of Mexico waters that had a salinity of approximately 32 PSU and decreasing temperatures with depth. Along the transect line, the lower layer had a relatively strong SE current, peaking at approximately 0.5 m/s mid-water. The upper layer, by contrast, exhibited more moderate currents to the SE with shear observed throughout the surface layer. We hypothesize that the current profiles exhibit decreasing southerly flow and increasing shear due to the easterly currents being driven by winds from the SW, as the region is known to be strongly affected by wind with stratification acting as a barrier to transfer of momentum, causing the upper layer to decouple from the coastal waters below.18,19 Note that the ADCP measurements in the upper water column are of relatively poor quality. This is primarily attributed to the surface waves and associated wave orbital motions which, based on linear wave equation estimates, peak at approximately 60 cm/s, driving significant variation between samples and across the beams. While suboptimal, these measurements do represent the closest available measurements to the SAS system.

FIG. 6.

(Color online) Measurements from ADCPs, the CTD profiler, and an echosounder corresponding to a transect near the SAS system. (a), (b) North and east current velocities from upward and downward looking Nortek Signature 1000 ADCPs. The gap near 5 meters corresponds to the towbody depth. (c), (d) Salinity and temperature measurements. The near-surface, along-transect variabilities (increasing temperature and decreasing salinity) are associated with the expansion of the ebb plume. (e) Volume backscattering measurements from the 200 kHz echosounder. Note that the closest point of approach to the SAS system occurred early in the first third of the transect.

FIG. 6.

(Color online) Measurements from ADCPs, the CTD profiler, and an echosounder corresponding to a transect near the SAS system. (a), (b) North and east current velocities from upward and downward looking Nortek Signature 1000 ADCPs. The gap near 5 meters corresponds to the towbody depth. (c), (d) Salinity and temperature measurements. The near-surface, along-transect variabilities (increasing temperature and decreasing salinity) are associated with the expansion of the ebb plume. (e) Volume backscattering measurements from the 200 kHz echosounder. Note that the closest point of approach to the SAS system occurred early in the first third of the transect.

Close modal

Measurements of the waves and water properties are consistent with acoustic backscattering measurements [Fig. 6(e)]. First, at a depth of approximately 5 m, there is relatively strong scattering from the pcynocline. Below this layer appears sustained, higher levels of diffuse acoustic backscattering of uncertain origin interspersed with biological backscattering, the frequency response of which is indicative of both scattering from individual fishes and aggregations of smaller, fluid like animals such as shrimps or amphipods. Backscattering in the upper water column would generally be weaker were it not for the presence of bubble plumes extending down from the surface, which were entrained by breaking waves. In some cases, these plumes are shallow, while in other cases they extend to the pycnocline. Many of these bubbles, due to their small sizes, remain in suspension for periods of minutes or longer after a wave breaking event, resulting in an upper water column dominated by scattering from bubbles.

Wind speeds were from the SW at 8 m/s. The four SWIFTs deployed in the area generally drifted S to SE, balanced by the waves and currents. Only two of the SWIFTs were analyzed due to the proximity to the SAS system. Throughout the deployment, the SWIFTs measured waves of approximately 0.75 m with dominant periods of approximately 3.7 s. Wave breaking was regularly observed in video recorded on the surface by the SWIFTs. The direction of surface wave propagation was roughly NNE while the SWIFTs drifted SSE.

The detection and tracking algorithm was applied to 1350 pings, or approximately three and a half minutes of sequential sector-scan data captured by the SAS system deployed at Mobile Bay. The autonomous underwater vehicle (AUV) executed a turning maneuver halfway through this segment and reversed heading. The shoal of fish was primarily visible from the port side of the AUV and only port-side data is shown in these results. Figure 7 shows plots of the x–y coordinates of all tracked objects that successfully were associated with detections more than 15 times.

The shoal of fish in Fig. 7 is moving in a north-westerly direction at approximately 1.5 meters per second, though there are formations near the edges in particular that contain fish, often in sets of three or more travelling in parallel, that are moving much faster—as fast as 2.5 m/s. These swimming speeds are easily obtained by some known species of inshore, schooling pelagic species in the Mobile Bay vicinity with examples including Spanish mackerel48 and Crevalle Jack.49,50 Visible in the image are also many shorter streaks moving in a south-easterly direction at a much lower velocity and with a more uniform distribution. These streaks are associated with near-surface bubble clouds created by wave breaking action and they serve as tracers for near-surface ambient current. These are made more visible in Fig. 8, which shows a perspective view enabling the z-dimension of the tracked objects to be visualized.

The average velocity of the near surface bubble features and fish can be determined by applying clustering to the velocity and depth information. Using a heuristic that the primary objects being tracked will belong to one of three classes: (1) wave breaking events, (2) fish in the aggregation, or (3) stationary objects on the sediment, three dimensional vectors of the average x and y velocities (m/s) and altitude (m) were fit to a Gaussian mixture model51 with three components. Cluster assignment was based on the model for which each point had the strongest probability of being a member. The results of the clustering are shown in Fig. 9.

The mean velocities, depth, and sigma values in each dimension are plotted for the different clusters in Table I, along with their nominal labels.

TABLE I.

The average (μ) and standard deviation (σ) of each cluster, in each dimension (z and northings and eastings velocities). Off diagonal components of the sigma values were very small, indicating little correlation existed between variables in the fitted Gaussian models.

μvNorth (m/s) μvEast (m/s) μz (m) σvNorth (m/s) σvEast (m/s) σvz (m/s)
Class 1 (bubble clouds)  −0.31  0.21  −0.63  0.05  0.05  0.17 
Class 2 (fish shoal)  0.63  −0.89  −9.32  0.24  0.14  0.3 
Class 3 (stationary scatterers)  0.01  0.00  −10.01  0.005  0.006  0.089 
μvNorth (m/s) μvEast (m/s) μz (m) σvNorth (m/s) σvEast (m/s) σvz (m/s)
Class 1 (bubble clouds)  −0.31  0.21  −0.63  0.05  0.05  0.17 
Class 2 (fish shoal)  0.63  −0.89  −9.32  0.24  0.14  0.3 
Class 3 (stationary scatterers)  0.01  0.00  −10.01  0.005  0.006  0.089 

The values in Table I indicate that the general speed and direction of the fish shoal was ∼1.1 m/s at 305 degrees (map direction, relative to 0 degrees = north, positive angles are clockwise). This is approximately northwesterly. The bubble plumes are travelling in almost the opposite direction but at a slower speed: 0.37 m/s in a southeasterly direction. This direction is consistent with the ambient currents in the water column and drift patterns of the SWIFT buoys shown in Fig. 10, rather than the direction of propagation of the surface waves. The average variance of the velocities of the bubble clouds is also much smaller than the average variance of the velocities of the fish (0.05 m/s vs 0.19 m/s). This is consistent with the observation that the behavior of the fish changes depending on location in the shoal and time of observation. Fish traces can be seen moving in different directions in Fig. 11, which colors the tracked traces according to their assigned cluster.

FIG. 7.

(Color online) A map of tracked detections showing the position of the tracked objects and speeds ranging from 0 to 3 m/s. Line thickness is increased from the start to the end of each trace to indicate direction of motion.

FIG. 7.

(Color online) A map of tracked detections showing the position of the tracked objects and speeds ranging from 0 to 3 m/s. Line thickness is increased from the start to the end of each trace to indicate direction of motion.

Close modal
FIG. 8.

(Color online) A perspective-view of the scatterplot traced by the detections in which the distribution of different scatterers in the altitude dimension is visible. Scatterers near the surface were associated with breaking features and generally travel in a south-easterly direction. Several fish are within the water column; however, the majority of the shoal is within a meter or two of the bottom. The vertical scaling of the plot has been expanded by a factor of four to improve feature visibility.

FIG. 8.

(Color online) A perspective-view of the scatterplot traced by the detections in which the distribution of different scatterers in the altitude dimension is visible. Scatterers near the surface were associated with breaking features and generally travel in a south-easterly direction. Several fish are within the water column; however, the majority of the shoal is within a meter or two of the bottom. The vertical scaling of the plot has been expanded by a factor of four to improve feature visibility.

Close modal
FIG. 9.

(Color online) Cluster analysis for the tracked objects shown in Figs. 7 and 8, using the average x and y velocities and vertical (z) displacements. Clustering was performed by fitting a three-component Gaussian mixture model to the data. Cluster markers are cyan circles (“class 1”), magenta points (“class 2”), and yellow stars (“class 3”). Individual scatterers corresponding to the latter class are difficult to discern because the variance of this component is very small. Interpretation is found in the text.

FIG. 9.

(Color online) Cluster analysis for the tracked objects shown in Figs. 7 and 8, using the average x and y velocities and vertical (z) displacements. Clustering was performed by fitting a three-component Gaussian mixture model to the data. Cluster markers are cyan circles (“class 1”), magenta points (“class 2”), and yellow stars (“class 3”). Individual scatterers corresponding to the latter class are difficult to discern because the variance of this component is very small. Interpretation is found in the text.

Close modal

Figure 12 shows two different sector scan images with the actively tracked objects from classes 1 and 2 superimposed on the intensity data.

The plots in Fig. 12 are frames from Mm. 1, an animation showing the movement of the tracked objects through the consecutive sector scan images captured by the sonar.

Mm. 1.

The labeled objects and their directions superimposed on the sector scan images created by the sonar, replayed as an animation. As in Fig. 12, the smaller, magenta circles represent detections labelled in class 2 (corresponding to objects moving in the water column, e.g., the school of fish), and the larger, cyan circles correspond to near-surface bubble clouds.

Mm. 1.

The labeled objects and their directions superimposed on the sector scan images created by the sonar, replayed as an animation. As in Fig. 12, the smaller, magenta circles represent detections labelled in class 2 (corresponding to objects moving in the water column, e.g., the school of fish), and the larger, cyan circles correspond to near-surface bubble clouds.

Close modal

From Figs. 11 and 12 and the animation in Mm. 1, it can be seen that most of the objects in class 1, nominally bubble plumes, occur as far range detections in the sonar field of view. This is a result of the vertical beam pattern of the system: near surface bubble features, which are located above the vehicle, are not visible until longer ranges because the transmitter has a downward depression angle and near-surface scatterers are too far off the axis of the beam at closer ranges. The detections clustered in class 2 in Fig. 9 can be readily associated with discrete, bright scatterers in the sonar imagery; in contrast, detections associated with class 1 appear to be lower contrast and appear in portions of the image affected more strongly by the hazy texture features introduced by near-surface bubble clouds created by wave-breaking events.

FIG. 10.

(Color online) (a) Velocity profiles derived from one minute of sampling at the closest point of approach to the SAS system. These measurements were taken approximately 15 min after the SAS data. (b) SWIFT data showing significant wave heights, the direction of propagation of the dominant waves (black vectors), and the drift direction of the SWIFTs (gray arrows). Note that the general direction of the SWIFTs is to the SE while the winds and waves are propagating roughly NE.

FIG. 10.

(Color online) (a) Velocity profiles derived from one minute of sampling at the closest point of approach to the SAS system. These measurements were taken approximately 15 min after the SAS data. (b) SWIFT data showing significant wave heights, the direction of propagation of the dominant waves (black vectors), and the drift direction of the SWIFTs (gray arrows). Note that the general direction of the SWIFTs is to the SE while the winds and waves are propagating roughly NE.

Close modal
FIG. 11.

(Color online) Classification results from clustering velocity and height data using a three-component Gaussian mixture model. Magenta traces correspond to objects in class 2, cyan traces correspond to objects in class 1 and yellow dots correspond to objects in class 3.

FIG. 11.

(Color online) Classification results from clustering velocity and height data using a three-component Gaussian mixture model. Magenta traces correspond to objects in class 2, cyan traces correspond to objects in class 1 and yellow dots correspond to objects in class 3.

Close modal
FIG. 12.

(Color online) Labeled objects and their directions for two pings superimposed on the intensity images associated with the same pings. See Mm. 1 for an animated version. The axes are in vehicle body coordinates. Objects clustered in class one are plotted with large circles and bold direction arrows and colored cyan; class two objects are plotted with smaller circles and magenta arrows. Plot A (top) is from an earlier ping in the data set; plot B (bottom) is from a later ping, after the AUV has performed a turn and is facing nearly 180 degrees from the original direction.

FIG. 12.

(Color online) Labeled objects and their directions for two pings superimposed on the intensity images associated with the same pings. See Mm. 1 for an animated version. The axes are in vehicle body coordinates. Objects clustered in class one are plotted with large circles and bold direction arrows and colored cyan; class two objects are plotted with smaller circles and magenta arrows. Plot A (top) is from an earlier ping in the data set; plot B (bottom) is from a later ping, after the AUV has performed a turn and is facing nearly 180 degrees from the original direction.

Close modal

The real arrays exploited by many deployed synthetic aperture systems to increase range potential also allow for intermediary “sector scan” data products to be created. The present work demonstrates that, via the pairing of sector scan data with a detection and multiple-object tracking algorithm, SAS systems can be effective tools for tracking moving objects. In the present implementation, operating under the assumption that objects of interest will have size scales on the order of several pixels or less throughout most of the field of view of the sonar, the detection algorithm uses the location of intensity peaks in the sector scan imagery as candidate detections and performs a brute search over velocity to detect persistence over a limited span of pings. Candidates that meet a persistence threshold are retained as detections and their position in three-dimensional space and velocity that maximized the persistence metric are recorded. Detections from individual pings were tracked using an α-β filter with empirically determined coefficients. Associations of new detections with tracked objects was performed by minimizing the Euclidean distance between state prediction vectors and detection measurement vectors. The minimization was accomplished using the algorithm described by Munkres.44 

This combined imaging, detection, and tracking post-processing approach was applied to SAS data containing a shoal of fish and bubble cloud features. Results demonstrate that individual fish within the shoal can be successfully tracked through many pings. From cluster analysis, the statistics of the behavior of the shoal, including speed and direction, can be ascertained. Similarly, using bubble drift speed as a proxy, the near surface ambient current can be measured remotely.

This work was supported by the Office of Naval Research under Grant No. N00014-19-1-2593. The authors would also like to gratefully acknowledge the efforts of Jim Thomson (APL-UW) and Dave Ralston (Woods Hole Oceanographic Institution) for providing current measurements and additional physical oceanographic context in support of this manuscript.

The authors have no conflicts of interest to declare.

Supporting oceanographic data from SWIFT buoys, acoustic Doppler current profilers, echosounders, and conductivity, temperature, and depth profilers are available by request from the authors. Requests for access to the sonar data supporting the findings of this paper may be made to the funding institution, the Office of Naval Research (ONR).

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