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computer-science engineering-and-technology transportation

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Dead reckoning

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Description

Dead reckoning estimates where you are now by starting from the last position you actually knew and adding up everything you’ve done since — your heading, speed, and elapsed time, or your wheel rotations, or your integrated accelerations — without looking outside. It is navigation by bookkeeping rather than observation. Its defining structural feature is that error compounds: each new estimate is built on top of the previous estimate, so every increment’s small measurement error is carried forward and added to, and total uncertainty grows without bound the longer you go without an external fix. The diagnostic question — “is this estimate built by integrating internal increments since the last known fix, and how long since that fix?” — flags the load-bearing risk: a dead-reckoned estimate is precise-looking but progressively less trustworthy, and there is no way to know how wrong it has become from the inside. The only cure is re-anchoring against an external reference. The pattern generalizes past navigation to any state extrapolated forward between check-ins: a mental model of a colleague’s project updated only by inference since you last spoke, a financial projection rolled forward between audits, a simulation advanced many steps from a known initial condition.

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Triggers

User-initiated: User describes estimating a current state by extrapolating from a last-known point without fresh external data, or worries that an estimate has compounded error since the last checkpoint (“we haven’t synced since the kickoff,” “projecting forward from the last audit”). Agent-initiated: Agent notices a state is being trusted that was extrapolated, not observed, and that no external fix has occurred recently. Candidate inference: “this is dead-reckoned — how stale is the last fix, and how fast does error compound here?” Situation-shape signals: A current estimate computed by summing increments from a prior known state; growing-but-uncheckable uncertainty; a long interval since the last external observation; a planned re-anchoring (audit, GPS fix, sync) that bounds the error.

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Exclusions

  • Drift — drift is a passive divergence property; dead-reckoning is an active estimate-by-integration method whose error compounds. The method-vs-phenomenon distinction is the sharpest boundary (and the easiest to blur, since reckoned error presents as drift).
  • Calibration — calibration is the external-fix re-anchoring; dead-reckoning is what runs between fixes with no reference.
  • Direct measurement — reading state from an external observation is the fix that bounds reckoned error, not reckoning.
  • Snowball-effect — snowball-effect compounds advantage; dead-reckoning compounds error. Same shape, opposite valence.

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Structure

Internal structure of dead-reckoning: a table of its component slots and the concepts that fill them.

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Relationships

Relationship neighborhood of dead-reckoning: a graph of the concepts it connects to and the concepts it is a part of.
  • drift — active method vs passive phenomenon; reckoned error often manifests as drift, but the concepts are distinct.
  • calibration — the external fix that ends a reckoning run is a calibration; dead-reckoning structurally requires periodic re-anchoring to stay bounded.
  • snowball-effect — shared compounding shape, opposite valence (advantage vs error) and controllability.

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Examples

Nathaniel Bowditch, "The American Practical Navigator: An Epitome of Navigation", U.S. National Geospatial-Intelligence Agency, Publication No. 9 (originally 1802; modern editions ongoing) · transportation

The classic maritime method: from the last well-determined fix, a navigator advances the ship’s position by applying the vector of true course steered and distance run over elapsed time. No external observation is consulted — the new position is computed purely from heading, speed, and time. Bowditch’s text codifies the practice and its central caution: because each leg’s estimate is laid off from the previous estimate, errors in steering and speed-through-water accumulate, and the reckoned position grows progressively less reliable until a celestial sight, landmark bearing, or modern electronic fix re-establishes a known position.Inference: A dead-reckoned position is a running extrapolation, trustworthy only in proportion to how recently it was anchored. The structure makes the failure mode legible: the chart shows a confident pencil line, but its uncertainty grows with every plotted leg. The navigator’s discipline is not to trust the line but to know when the last fix was — and to seek the next one before accumulated error becomes dangerous.

Sebastian Thrun, Wolfram Burgard & Dieter Fox, "Probabilistic Robotics", MIT Press (2005) · computer-science

A mobile robot estimates its pose by odometry: integrating wheel-encoder counts to accumulate how far and which way it has moved since a known starting pose. Thrun, Burgard and Fox formalize the consequence — pose uncertainty grows without bound, because each motion update convolves the previous (already uncertain) estimate with fresh noisy motion, so the error covariance only ever increases under pure odometry. The standard remedy is to periodically reset the accumulated error against external sensor observations of landmarks, the core move in localization and SLAM.Inference: Robot odometry is dead-reckoning rendered explicitly probabilistic: the growing covariance is the compounding error, quantified. The architecture pairs an unbounded-error internal estimator with periodic external fixes precisely because the integrator alone diverges. This is the same fix-and-reckon loop as marine navigation, now with the uncertainty made mathematically visible — and it shows why a system that only dead-reckons must eventually re-anchor or be lost.

David H. Titterton & John L. Weston, "Strapdown Inertial Navigation Technology", 2nd edition, American Institute of Aeronautics and Astronautics / IET (2004) · engineering-and-technology

An inertial navigation system computes position by double-integrating accelerometer and gyroscope measurements forward from a known initial state, with no external reference. Titterton and Weston detail the consequence: even a tiny constant sensor bias, integrated twice over time, produces a position error that grows as a cubic function of elapsed time. Left unaided, an INS therefore “walks away” from truth, which is why high-grade systems are mechanized to accept periodic external aids — GNSS fixes, star trackers — that bound the otherwise-unbounded accumulation.Inference: Inertial navigation is dead-reckoning at the level of physical integration: the error growth is not incidental but a mathematical inevitability of integrating a noisy increment stream. The system design encodes the concept’s central truth — an integrating estimator with no external fix diverges — by building the re-anchoring (the external aid) directly into the architecture as a non-optional bound on accumulated error.