Knowledge / Navigation and collision

Encounter uncertainty and ship domains: the limits of a single safe distance

How to interpret ship-domain geometry, prediction uncertainty and sensitivity without treating a modelled boundary as a universal safe passing distance.

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A ship domain is a modelled area around a vessel used to describe desired separation or screen encounters. It can support an assessment, but a coloured boundary is not a physical wall, a probability of collision or a legal permission to proceed. Its usefulness depends on what it represents, which reference point it surrounds and how uncertainty changes with time. This article develops a transparent way to read domain-based results, using deliberately hypothetical numbers. It complements basic closest-point-of-approach analysis without replacing navigational judgment, the applicable collision regulations or ship-specific procedures.

1. Define the question before drawing the boundary

A domain can describe observed passing behaviour, a planner’s preferred clearance, a screening threshold or the space needed to preserve manoeuvring options. Those are different questions. An empirical contour enclosing most observed traffic does not establish that the traffic was safe. A design clearance selected for an experiment does not become a requirement for other ships. Write the intended meaning beside every diagram and label.

There is no single internationally prescribed passing distance for every encounter. The US Coast Guard’s navigation-rules FAQ explicitly explains this. A numerical screen is therefore supplementary: an encounter may deserve attention even when its predicted track remains outside the selected domain. Conversely, a domain intrusion is not by itself a finding of legal fault or proof that a collision will occur.

2. Separate the hull, the reference point and the margin

A position report usually refers to a sensor or an internally defined ship reference point. Clearance concerns occupied hull geometry, including orientation. For a long ship, a reference point can remain outside an obstacle boundary while the bow or stern sweeps through it. Two point tracks that do not intersect can still correspond to overlapping hulls.

Before adding a margin, establish whether the reported separation is centre-to-centre, antenna-to-antenna or hull-to-hull. In a generic calculation, a 300-metre point separation minus two assumed 40-metre projected half-widths leaves 220 metres of geometric clearance. That subtraction is valid only for those projected dimensions at that instant. It ignores uncertainty and future rotation; it is not a universal conversion from radar range to clear water.

3. Understand what a statistical domain has learned

The primary research by Rawson and Brito on context-aware domains investigates how encounter context changes observed spacing. This is a useful reason to resist treating one fitted boundary as universal. A model’s population and setting belong in its description.

Suppose a hypothetical training set mainly contains large ships in an organized offshore lane. Applying its spacing contour to fishing traffic near a harbour changes both the vessel population and the available water. More data from the original lane may improve precision there without resolving that transfer problem. Record which conditions are represented, which are scarce, and which are outside scope. Precision within the wrong population is not evidence of suitability for a new one.

4. Divide uncertainty into distinct causes

Measurement uncertainty concerns the present state: position, heading, speed and time. Prediction uncertainty concerns what happens next: another vessel’s manoeuvre, engine response or current variation. Model inadequacy concerns a missing mechanism, such as treating a turning vessel as travelling forever on a straight line. These causes require different remedies.

Additional observations can reduce some measurement uncertainty, but they cannot guarantee another ship’s future intention. A more elaborate motion model can represent turning without knowing when a turn will begin. An analyst should therefore avoid compressing every concern into one unexplained distance allowance. List assumptions, show plausible alternatives and identify which new evidence would change the assessment. Missing information should remain visible rather than being converted into a falsely precise number.

5. Keep time, axes and motion references consistent

An encounter combines measurements taken at different times. A correct position with an old timestamp can be misleading when placed beside a fresh target track. At an illustrative relative speed of 12 knots, 30 seconds represents 0.10 nautical miles, approximately 185.2 metres, of relative travel. This is a time-alignment calculation, not a recommended alarm allowance.

Use one clearly defined horizontal coordinate frame and express velocities consistently. Ground-referenced relative motion and water-referenced manoeuvring response answer different questions. Likewise, heading is not automatically course over ground. If a calculation rotates a domain using heading but propagates its centre using ground velocity, that choice may be reasonable, but it must be explicit. Otherwise a visually smooth animation can conceal incompatible quantities.

6. Propagate a simple uncertainty example honestly

Consider a teaching model for one cross-track coordinate. Let its present error have a standard deviation of 20 metres and its cross-track velocity error a standard deviation of 0.10 metres per second. Assume both are zero-mean, independent and constant over the prediction interval. After 600 seconds, the position standard deviation is the square root of 20 squared plus 600 squared times 0.10 squared: approximately 63.25 metres.

Under an additional normal-distribution assumption, a two-sided interval of approximately 1.96 standard deviations is about plus or minus 124 metres for that coordinate. It is not a two-dimensional 95% containment circle or a guarantee against collision. Correlation, bias, changing velocity and another ship’s manoeuvre invalidate this simplified interpretation. The calculation demonstrates why a fixed uncertainty ring can become misleading as the prediction horizon grows.

7. Compare alternatives instead of hiding them in one prediction

Suppose the nominal predicted hull clearance is 260 metres and an analyst-selected screening margin is 200 metres. Nominal margin above the screen is 60 metres. If a separately justified adverse sensitivity case reduces clearance by 90 metres, its result is 170 metres, or 30 metres below the screen. The useful output is that the classification changes under the assumed variation.

It would be incorrect to announce a collision probability from these two cases. No distribution or collision-event model has been supplied. It would also be incorrect to combine the 90-metre sensitivity change with the previous statistical interval without considering whether they represent the same uncertainty twice. Present the nominal case, adverse case and reason for the change. This gives a reviewer something to challenge and verify.

8. Use direction-dependent geometry with restraint

An ellipse can represent different longitudinal and transverse extents. For an illustrative ellipse with forward-axis coordinate x, lateral coordinate y and semi-axes a and b, the normalized score is x squared divided by a squared plus y squared divided by b squared. A score below one lies inside the ellipse. This is geometry, not a collision-risk law.

With a equal to 600 metres, b equal to 200 metres, x equal to 300 metres and y equal to 100 metres, the score is 0.50. At the same x and y equal to 180 metres, it is 1.06. A small lateral change can cross the chosen boundary. Neither score establishes safety: orientation, ship dimensions, the other vessel’s domain and the time at which positions are compared still matter.

9. Evaluate the encounter through time

A single minimum-distance value removes the sequence of events. It does not say how long a domain is occupied, when uncertainty becomes important or whether an avoiding manoeuvre creates a later problem. An analysis can instead report earliest possible intrusion within its assumptions, duration of modelled intrusion and the time remaining before options become constrained.

These outputs should not be treated as countdown instructions. Their meaning depends on the assumed response of both ships. A trajectory that clears one vessel but approaches another is not adequately described by its first encounter alone. In multi-ship situations, preserve a common timeline and assess the consequences of a manoeuvre for all relevant traffic and fixed hazards. Pairwise scores cannot simply be added as if encounters were independent.

10. Keep evidence sources genuinely distinct

Radar, visual observations, AIS and electronic displays can provide complementary information, but multiple screens do not necessarily mean independent evidence. Several displayed values may originate from the same position sensor or share the same incorrect time base. Apparent agreement can therefore survive a common input error.

The MCA guidance on electronic navigational aids discusses the need to understand aid limitations. In an educational review, draw a simple provenance chain from sensor to display to calculated domain result. Ask what information is genuinely new and what is merely repeated. A disagreement is a reason to investigate the data and situation, not automatically to average the displays into a more reassuring value.

11. Keep regulatory judgment outside an arbitrary score

The International text in the USCG rules compilation places collision-risk assessment and avoiding action within prevailing circumstances, available information and the relevant encounter rules. International and US Inland provisions must not be mixed indiscriminately. A research domain does not replace these duties.

For a scenario review, retain the encounter classification, visibility, vessel status and sequence of observations alongside numerical results. A distance-only threshold may miss an inappropriate manoeuvre or an action taken too late. Conversely, a rule label generated from one uncertain bearing may change when the track is revised. If the evidence does not support a stable classification, record that uncertainty rather than presenting software output as an authoritative legal conclusion.

12. Build an auditable result and avoid familiar mistakes

A useful result identifies the domain’s purpose, geometry, reference point, time horizon, motion assumptions, uncertainty treatment and excluded conditions. It reports what changed when plausible inputs changed. It also separates observed quantities from inferred states and analyst-selected margins. This makes the conclusion reproducible without exposing any proprietary implementation.

Common mistakes include treating an AIS antenna as a hull centre, using an unlabelled nautical-mile/metre conversion, interpreting a one-dimensional interval as a two-dimensional guarantee, and claiming that a domain boundary is mandated by COLREG. Another is tuning a screen until historic incidents look well separated and then evaluating it on the same cases. Keep development and evaluation evidence distinct, including unsuccessful examples and conditions where no reliable conclusion can be reached.

13. Practical synthesis and scope

For any domain-based plot, ask five questions: what does the boundary mean, where is its reference point, how old are its inputs, how does uncertainty grow, and what decision is the plot intended to support? Then ask whether the answer remains stable when reasonable alternatives are tested. The most useful conclusion may be that more evidence or a broader assessment is needed.

The numerical situations are original teaching examples, not observed vessel data, approved separation criteria or operating instructions. Public sources support the stated context; the analytical examples expose their own assumptions. Local requirements, vessel procedures and competent professional judgment govern real operations.

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