This preprint tests two PAMGuard location pipelines with simulated whale calls and reports large errors under several uncertainties. Explore the seven scenarios, two different error metrics, and how clock differences enter the geometry.

01 / First, what counts as an error?

A dot on a map looks like an answer. This paper asks how much trust that answer deserves.

Start with a small surprise: a reported error of zero can coexist with a point that misses the whale. It depends on what you measure.

The paper uses two different error definitions: Section V, PDF pp. 10–12.

One location. Two error measures.

Move the true source. Watch when the region’s error becomes zero.

The true source lies outside the region. The two distances differ by the radius.

This is an original horizontal slice through a cylinder, with a teaching radius of 80 m. The source stays at the cylinder’s mid-height. Point error is the center-to-source distance d; region error is max(0, d − 80 m). It is a slider-controlled geometric state, not motion through time.

The paper’s simplex metric uses distance outside an expanded confidence cylinder; its hyperbolic metric uses distance to an estimated point. Real outputs have different centers and region sizes. This model illustrates those definitions only; it does not run either localizer or reproduce the paper’s results. Section V, pp. 10–12; Appendix A.3, p. 28.

Test against a whale whose location is known.

The researchers generated synthetic click recordings, fed them through PAMGuard, then compared the returned locations with the simulated truth. They changed receiver-position, clock, or sound-speed uncertainty across seven scenarios.

Sections III–V, pp. 7–12; Figure 1, p. 6. These are simulations, not recordings of tracked whales.

The receivers span roughly 1 km horizontally and 200 m in depth by the coordinates on p. 10. All receivers receive loud clicks in this deliberately favorable setup (Section III, p. 7).

02 / Inspect the reported evidence

Change the uncertainty. Compare the consequences.

Choose a scenario to inspect its largest reported error among 100 calls . These are summaries from the paper’s detailed results—not typical errors, raw call records, or a new simulation.

A / Almost perfect inputs

Receiver position, clock and sound-speed uncertainties are all minuscule.

How far the truth falls outside its expanded confidence cylinder . Inside counts as zero.

Fixed logarithmic scale · each equal step multiplies distance

How far the truth lies from the estimated point . No confidence region was returned.

Same scale · different error definition

Even with almost perfect inputs, the evaluated hyperbolic pipeline produced a maximum point error of 41 km.

Detailed results: Section V.B, p. 14; Figures 3A and 4A, pp. 11–12.

The reviewed Figure 3 histograms show simplex region errors spreading markedly in the sound-speed scenarios. Figure 4’s hyperbolic point errors remain concentrated around hundreds to thousands of meters across the scenarios. A maximum alone does not tell you how common an error is. We have not reconstructed call-level data or histogram counts.

On the paper’s logarithmic error axes, exact zero has no finite position. Low-end histogram bars therefore cannot be treated as exact coverage counts. Read the paper’s explicit counts with its inconsistencies in mind.

Inspect original Figure 3 (simplex), p. 11 · Figure 4 (hyperbolic), p. 12. Source figures are linked rather than reproduced because the supplied inventory approves none for display.

This explorer uses the explicit maxima in Sections V.B–V.E: simplex 1.3, 0.72, 168, 1,046, 4,700, 1.5 × 10⁹ and 7.1 × 10¹² m; hyperbolic 41,000, 22,000, 15,000, 7,900, 6,800, 3,200 and 12,000 m. Section V.A and the abstract give different rounded or order-of-magnitude figures, particularly for sound speed. We preserve the detailed results without treating the discrepancies as resolved.

For B1, Section V.C reports both 100/100 simplex coverage and a positive maximum region error of 0.72 m. Under the stated metric these cannot both hold. For sound speed, Section V.E selects a mean in [1450, 1468] m/s but also states that path speeds are restricted to [1460, 1468] m/s; the sampling procedure is not fully clear.

The paper calls the expanded simplex cylinder a 99.5% interval on p. 10 and describes a three-standard-deviation expansion in Appendix A.3. We call it an “expanded region” rather than presenting that coverage level as established.

03 / A map made from time differences

A tiny clock difference enters the geometry.

A call reaches two receivers at different times. If sound speed is known, that time gap tells us the difference between the two travel distances. More receiver pairs constrain the source location.

A residual difference between the clocks contaminates that time gap. A common shift of all clocks cancels when times are subtracted.

The paper corrected its simulated clocks with a straight line between start and end measurements. Nonlinear drift left residual differences of a few milliseconds.

Section II, p. 4; Section V.D, pp. 15–17. Figure 5’s caption and discussion support the clock description; its image was not supplied for inspection.

What does 4 milliseconds change?

Hold sound speed at 1450 m/s and change the residual clock difference.

This is an input bias, not a location error. The final location also depends on geometry, other uncertainties and the software pipeline. This arithmetic does not explain the paper’s kilometer-scale errors.

For a known common speed c, a time-difference-of-arrival (TDOA), τ, corresponds to a path-length difference δd = cτ. A residual clock difference ε adds the bias cε. Here c = 1450 m/s and ε = 0.004 s give 5.8 m. These example inputs illustrate Section II, p. 4 and Section V.D, pp. 15–16.

In three dimensions, points with a given distance difference form a hyperboloid. Intersections of these surfaces constrain location. The paper’s simplex method searches for a best fit using a likelihood; the hyperbolic method uses an analytical solution (Section II.A–B, pp. 4–5).

04 / Where the evidence stops

Test the pipeline. Keep the uncertainty.

The configured pipelines sometimes returned large errors. The simplex regions often failed to contain the simulated truth. A visually plausible point is not sufficient validation. Sections V–VII, pp. 13–23.

The authors did not isolate the cause. These results do not establish that every PAMGuard version, configuration or field use has the same failures. Sections IV and VI.A; Conclusion, pp. 8–9, 18–19, 22–23.

With four receivers, there can be two mathematical solutions in three dimensions. In the separate Figure 6 example, two separated SBE regions represent candidate locations, while the simplex output supplies one displaced estimate. This uses the older PAMGuard 2.02.11c version and is not a panel from the five-receiver experiment.

Additional information, such as whether a candidate lies outside the ocean or far from a previous known location, can sometimes reject one alternative. This example illustrates ambiguity, not universal performance. Section VI.B, pp. 20–21; Figure 6, p. 21.

Sequential bound estimation (SBE) explicitly treats bounds on the uncertain variables. The authors report that its regions contained the true location for all simulated calls in every tested scenario. That is a result for these tests, not proof of universal 100% coverage under arbitrary conditions.

The paper gives only a brief comparison and refers elsewhere for the method. It declares that SBE and related technologies are a commercial location service. Section VI.C and Conclusion, pp. 22–23; Section IX.A, p. 24.

The simulator gives every receiver a loud, omnidirectional click, unlike real whale clicks that can be strongly directional. Added white noise yields a reported signal-to-noise ratio of 30–55 dB. Temperature and physical-shock effects on clocks are not simulated. Section III, p. 7; Section V.D, p. 17.

The study uses specified receiver geometry, a limited volume and 100 calls per scenario. It does not establish error rates for all whale species, ocean conditions or array designs.

Section IV names version 2.02.28 for the main work; Section VI.B calls the preceding simulations version 2.02.18. This source inconsistency remains unresolved. The older four-receiver example is identified as 2.02.11c.

The researchers used a configuration supplied by PAMGuard scientists, modified to use waveform-envelope peak selection. They tested the full pipeline rather than isolated location algorithms. When more than one database result matched a call’s time, they chose the location nearest the known truth. That favorable selection is part of the evaluation. Section IV, pp. 8–9; Appendix A.1–A.2, pp. 25–28.

The source

Read the research

Unreported large errors from two PAMGuard three-dimensional localizers of whale calls

Maya Mathur, Luke Stoner-Eby, Devin Pascoe and John L. Spiesberger. arXiv:2609.20350v1, 17 September 2026. Preprint.

About this experience

Built from the complete supplied 35-page paper and checked against the supplied figure reviews. All page references use PDF page numbers. The interactive diagrams are original educational models; the result summaries are transcribed from the paper. No software failure is diagnosed here.

No source artwork is reproduced. No conceptual illustrations are planned. Scientific review is still required.