Fig 1.
Graphical representation of the TDOA for both large and small aperture separation between two sensors. A) Example of a hyperboloid of possible source locations when the TDOA between two widely spaced receivers is known. B) Small-aperture TDOA when the signal’s propagation through the array is approximated as a plane wave. The dashed line represents the wave-front, and is the unit vector normal to the wavefront.
Fig 2.
The typical workflow used to estimate whale tracks via TDOA localization. The parallelograms indicate data inputs or outputs; the rectangles represent an automated process; the trapezoids indicate a graphical user interface (GUI).
Fig 3.
The brushDOA user interface for editing detections on two 4-channel arrays.
The brushDOA user interface allows analysts to select detections, remove false detections, and assign color labels to the detections originating from the same source. The interface includes six plots: azimuth vs. time and elevation vs. time for both arrays, and the azimuth vs. elevation for both arrays. Each frame above shows the brushDOA interface during four stages of labeling encounters: 1. The analyst removes false detections caused by other nearby sound sources (e.g. ADCP pings, dolphins, instrument noise); 2. The analyst assigns labels on one array to each of the animals present in the encounter using a combination of spatial and temporal separation of detections; 3. Click-Train Correlation is used to automatically associate detections on the labeled array with their corresponding detections on the unlabeled array; and 4. The remaining detections are assigned labels.
Fig 4.
An example of click-train correlation (CTC) using a window of detections arriving from two sources. The labeled detections (left column) are separated into two click trains, and each is cross-correlated with the unlabeled click train. CTC is used to associate detections across instruments and determine the delay which would align the clicks.
Fig 5.
Visualization of the DOA intersect localization method.
An alternative method of localization when detections are present on both 4-channel arrays is to find the intersection of the two DOA lines, and
. This is done by solving the Eq 8 using MATLAB’s mldivide function (Eq 9).
Fig 6.
The case study site where Zc tracks were reconstructed using the Where’s Whaledo MATLAB toolkit. Site is in Tanner Basin, ≈ 200 km southwest of Los Angeles, California. Two instrument types were used: single channel instruments (black circles on the left plot) and 4-channels (black squares). Bathymetry data from Global Multi-Resolution Topography (GMRT) [48].
Fig 7.
Zc track reconstructions with clear source association.
The left panel is a map view with time annotations along two separate animal tracks, and the right panel shows the animals’ depth versus time. The colors represent different whales, and the semi-transparent shading represents their 95% confidence intervals. Points with circles are localized with two 4-channel instruments, whereas points with “x” were detected on only one 4-channel and one or two single-channels, Confidence intervals vary due to differences in the number of instruments used to localize, the position of the whale, or the precision and accuracy of the TDOAs.
Fig 8.
Zc tracks with large group sizes.
An encounter with five whales vocalizing concurrently. Panels A and B show the map view and the depth vs. time of the track estimates of all five animals, where the colors correspond to the same detections shown in the other panels. Panel C shows the map view and depth vs. time views for each individual separately, where the different colors represent different whales and the semi-transparent shading represents their 95% confidence intervals. Panel D shows the labeled azimuths and elevation angles of each of the animals in the encounter.
Fig 9.
Reconstructing Zc tracks in the presence of false-detections.
Top left panel shows array-two detections, including: (yellow box) echolocating dolphins and (red box) two echolocating Zc. Upper right panel illustrates removal of dolphin detections, due to their higher elevation angles, periodicity (where detections fade in and out on an ≈ 1 min cycle), and “fuzziness” (where multiple dolphin clicks present in one window gave erroneous DOAs). Middle panels show array-one detections (left) before and (right) after dolphin echolocation removal. Lower panels show maps with tracks of (left) both Zc and (middle and right) individual animals.