Bridging Echolocation Gaps in Automated Beaked Whale Tracking

I. INTRODUCTION

• Beaked whales are difficult to study visually because they dive deeply and are rarely observed in visual surveys, and they are of interest because of sensitivity to intense anthropogenic sound.Their mass strandings have been associated with naval mid-frequency active sonar events [5–8].Source: §I · p. 3
• Small-group detections can be ambiguous, directional clicks can be missed when whales face away from sensors, and large PAM datasets make manual processing difficult.Source: §I · pp. 3–4
• The study analyzes goose-beaked whale recordings from bottom-mounted volumetric hydrophone arrays and automates click labeling and 2-D localization with belief propagation-based multi-target tracking.Source: §I · p. 4

A. State of the Art

• Conventional whale tracking often relies on human operators to inspect click sequences, while automated multi-target tracking offers an alternative to hand labeling.Prior whale-tracking approaches described here do not reconnect track fragments across extended detection gaps [52–54].Source: A. State of the Art · pp. 5, 7
• The proposed method combines multisensor belief propagation-based tracking with smoothing and stitching to connect non-overlapping track fragments across extended detection gaps.Unlike track-to-track fusion of concurrent estimates, the approach associates fragments from before and after a gap and concatenates their histories.Source: A. State of the Art · p. 6
• A beaked-whale approach uses two BP-based MTT stages to track in the TDOA domain and then fuse estimates for 3-D tracking.It tracks directly from TDOA measurements without an intermediate localization step, using a nonlinear measurement model implemented with particle flow.Source: A. State of the Art · p. 8
• Longer gaps in humpback whale song can fragment one trajectory into multiple tracks, with joining the fragments identified as future work.The cited work reports this problem for 2-D track fragments.Source: A. State of the Art · p. 8
• Existing automated marine-mammal tracking methods lack a dedicated mechanism to reconnect fragments across prolonged, behavior-driven detection gaps; this paper proposes probabilistic stitching.The stitching stage is intended to address the continuity problem.Source: A. State of the Art · p. 8

B. Contributions, Paper Organization, and Notations

• Beaked-whale click gaps can violate standard MTT detection assumptions, causing tracks to terminate prematurely and later restart.The gaps can occur when whales stop clicking or turn away from receivers.Source: B. Contributions, Paper Organization,… · p. 9
• The three-stage pipeline applies BP-based multi-target tracking, smooths noisy track estimates, then stitches fragments using lowest-cost pairings.For stitching, it predicts an earlier segment's endpoint forward to a later segment's start time.Source: B. Contributions, Paper Organization,… · p. 9
• The stitching stage treats fragment matching as temporal track-to-track association by predicting state estimates to a common time.It concatenates disjoint track histories rather than fusing concurrent state estimates.Source: B. Contributions, Paper Organization,… · p. 10
• The evaluation uses Ziphius cavirostris echolocation recordings in five real-data examples spanning varying complexity, with reference labels from trained human operators.The paper describes the tracking domain as 2-D azimuth–elevation DOA.Source: B. Contributions, Paper Organization,… · pp. 8–10
• The authors report performance advantages over state-of-the-art reference methods, quantified using GOSPA metrics.The paper identifies this as an advance over its preliminary account.Source: B. Contributions, Paper Organization,… · p. 10
• The notation section distinguishes random variables from realizations and vectors from matrices, and defines PDF shorthand and the identity matrix.It also uses ∝ for equality up to a normalization factor.Source: B. Contributions, Paper Organization,… · pp. 10–11

II. BP-BASED MTT

• MTT estimates the number and states of multiple targets from the collected measurements.The method computes marginal posterior state distributions for potential targets and uses them for state estimation.Source: §II · pp. 11–12
• A target state is a four-dimensional vector of azimuth, elevation, and their respective velocities relative to the sensor.Source: §II · p. 11
• Each potential target has a state and an existence indicator, with existence decided by whether its posterior probability exceeds a predefined threshold.For existing potential targets, the method performs minimum mean-square error state estimation.Source: §II · pp. 11–12
• Real-time estimation is filtering using past and current measurements, while post-processing smoothing uses past, current, and future measurements.Source: §II · p. 12

A. Statistical Model

• Targets survive between time steps with probability ps and otherwise die; newborn targets are modeled by a Poisson point process.The model uses a constant-velocity state transition, with survival probability potentially depending on the interval between steps on an irregular time grid.Source: A. Statistical Model · pp. 13, 15
• Surviving targets are represented by legacy potential targets, while new potential targets account for possible births associated with measurements.Source: A. Statistical Model · p. 13
• Each target is detected with probability pd and, if detected, generates one measurement; non-target clutter is modeled as a Poisson point process.Source: A. Statistical Model · p. 13
• The target-oriented association variables encode which legacy target generated each measurement, while a one-to-one constraint prevents two legacy targets sharing a measurement.Source: A. Statistical Model · pp. 13, 14, 16

B. Message Passing and Selected Processing Steps

• Loopy factor-graph recursion yields approximate marginal PDFs and PMFs, but is guaranteed to converge to the global optimum of its corresponding convex optimization problem with bounded iterations.The resulting approximations are described as efficient to compute and highly accurate.Source: B. Message Passing and Selected… · pp. 16–17
• Prediction messages for legacy potential targets are combined with the current measurement model, and the resulting messages provide inputs to probabilistic data association.Source: B. Message Passing and Selected… · pp. 17–18
• After data association, measurement-update messages produce beliefs that approximate current-time marginal posteriors for state estimation.Source: B. Message Passing and Selected… · p. 18

III. TRACK SMOOTHING AND STITCHING

• The model assumes target-measurement generation is independent across time, so multiple missed steps terminate a track and resumed detections initialize a new one.The text notes that click detections are not independent or identically distributed across time, and long missed-detection sequences commonly occur when whales are not vocalizing or their directional clicks cannot be detected above noise.Source: §III · pp. 18–19
• MTT alone can produce highly fragmented trajectories that require additional processing to form a continuous track for each target.Source: §III · p. 19
• Track smoothing and stitching are introduced to improve track continuity and accuracy in the presence of missing detections.Source: §III · p. 19

A. Track Smoothing

• Track smoothing uses measurements from both past and future time steps to improve target-state estimates at each time step.Approximate marginal posteriors are computed forward and backward with BP message passing, then combined into smoothed tracks.Source: A. Track Smoothing · pp. 19–20

B. Track Stitching

• Only fragments where the old track ends before the new track starts are admissible; accepted fragments are concatenated without state-estimate fusion at the join.Assignments are made within a sliding window of length B seconds.Source: B. Track Stitching · pp. 21, 22, 24, Figure 2 · p. 23
• Track stitching predicts each old track’s final state to a new track’s initial time and assigns fragment pairings by minimizing their costs.The assignment compares predicted and observed states at a common time and uses a one-to-one association.Source: B. Track Stitching · pp. 22–23
• The current endpoint-only association leaves residual dependence from shared motion uncertainty as a potential improvement area.The authors identify estimating that dependence or using multiple states near fragment endpoints as possible directions.Source: B. Track Stitching · p. 24
• The association cost uses endpoint states and accounts for old-track survival and newly born tracks through dummy pairings.A non-dummy old track paired with a dummy represents a trajectory ending; a new track paired with a dummy represents one beginning.Source: B. Track Stitching · p. 24
• A greedy window-assignment alternative yielded no significant improvement over updating tracks after each window assignment on the beaked whale data.The greedy variant sorts assignments across windows by cost and discards merges that conflict with earlier ones.Source: B. Track Stitching · p. 25

IV. SIMULATION EXPERIMENTS

• The simulation uses two tracks over 300 time steps, with 10 randomized gaps per track lasting up to 14 seconds each.Each time step represents one second; the gaps model whales stopping vocalization or turning away from receivers.Source: §IV · p. 25
• In the illustrated two-track simulation, stitching correctly links track segments separated by detection gaps that otherwise terminate tracks.The figure contrasts BP-based MTT before smoothing and stitching with results after both steps.Source: Figure 3 · p. 26, §IV · p. 27
• The comparison includes GM-PHD, which omits probabilistic data association and therefore reduces computational complexity at the potential cost of tracking performance.GM-PHD had previously been applied to tracking false killer whales using TDOA measurements.Source: §IV · p. 27
• BP-based MTT with track smoothing and stitching has significantly lower missed-target and total GOSPA errors than BP-based MTT without those steps or GM-PHD.The remaining GOSPA error components differ only slightly among methods.Source: §IV · pp. 27–28, Figure 4 · p. 28

• PAM detectability depends on signal-to-noise ratio and directional clicks, varies with whale movement, and is difficult to model accurately.Source: §V · pp. 29–30
• Because click availability changes with dive cycle and pauses between trains, the method used a lower detection probability and track stitching to address resulting gaps.Source: §V · p. 30
• To accommodate irregular clicks, the method formed time steps from 0.4-s intervals using each interval’s highest-amplitude click and omitted empty intervals to avoid treating pauses as multiple missed detections.Source: §V · p. 30
• The comparison is descriptive and post-selection rather than a held-out performance estimate because pruning settings were selected using the same random seeds.Source: §V · p. 32
• With smoothing and stitching, tracks closely followed human-labeled clicks and resolved many small gaps between click sequences, but larger gaps lasting approximately 2–5 min remained unresolved.Source: §V · p. 32
• In denser overlapping encounters, tracks largely followed labels but sometimes duplicated whales or made incorrect associations at crossings, leaving gaps or switching targets; human verification may be needed.Source: §V · p. 34, Figure 6 · p. 34

V. REAL-WORLD APPLICATION

• Nonrandom click clutter from a likely dolphin target can readily produce false-positive tracks in MTT.The click sequences were observed from 0 to 2400 and were considered most likely to belong to a dolphin species rather than the target species.Source: §V · p. 35
• Across five encounters, smoothing and stitching reduced standalone BP-based MTT mean total GOSPA error from 2.349 to 1.534 (approximately 34.7%), primarily by lowering missed-target error from 1.811 to 0.570.Source: §V · pp. 35–36
• Localization error increased from 0.383 to 0.598 and false-target error from 0.154 to 0.367 after smoothing and stitching.These increases can result from incorrect associations between track fragments during stitching.Source: §V · p. 36
• Standalone BP-based MTT had a slightly lower mean total GOSPA error than GM-PHD (2.349 versus 2.358) and lower total error for nine of ten seeds.Source: §V · p. 36

VI. CONCLUSION

• The automated method tracks beaked whales from passive-acoustic echolocation recordings in the direction-of-arrival domain.Source: §VI · p. 36
• Track smoothing and stitching improve state estimation for complex data and bridge gaps caused by consecutive missed detections that violate standard MTT assumptions.Source: §VI · p. 36
• The method produces lower-error tracking than other state-of-the-art methods and results comparable to reference labels provided by trained human operators.Source: §VI · p. 36
• The approach may reduce researchers’ effort to process PAM data, enabling more effective studies of important species.Source: §VI · p. 36
• Future work will demonstrate a fully automated tracking pipeline and extend the 2-D method to 3-D.Source: §VI · p. 36

A. Conflict of Interest

• The authors report no conflicts to disclose.Source: A. Conflict of Interest · p. 37