Earlier articles assigned people to work. Now consider a different choice: which observations refer to the same object? This is data association, one problem encountered in data fusion.1

In a toy warehouse, cameras detect carts at North and South at 10:00, then at East and West at 10:02. Identifiers are unreadable. Assume exactly two carts, accurate locations, synchronized clocks, and one detection per cart in each snapshot, with no extra detections.

The available routes have these minimum travel times. A cart may wait after arriving. Every proposed pairing has a two-minute gap:

Sighting at 10:00East at 10:02West at 10:02
North1 minute: fits1 minute: fits
South1 minute: fits3 minutes: too late

Matching North to East looks feasible. That leaves South paired with West, which requires three minutes. Both pairings must fit together, so this arrangement fails. Assigning both earlier sightings to East would also fail: it would reuse one observation and leave West unexplained.

The surviving pairing links North to West and South to East. Each cart receives one observation from each snapshot, and both journeys fit the available time. Cart 1 and Cart 2 below are temporary labels for these identity hypotheses.

Proposed cart associations and their recorded sighting times The surviving candidate associates the North camera sighting at 10:00 and the West camera sighting at 10:02 with Cart 1 hypothesis. It associates the South camera sighting at 10:00 and the East camera sighting at 10:02 with Cart 2 hypothesis. Observation cards are square-cornered; cart hypotheses are labelled ellipses, not observed identifiers or people. In the timeline, four dots mark recorded sightings and dashed links show the same proposed associations. No intermediate position, route, or observed journey is asserted. Relationships in the surviving candidate N: North camera 10:00 sighting Cart 1 hypothesis W: West camera 10:02 sighting S: South camera 10:00 sighting Cart 2 hypothesis E: East camera 10:02 sighting associated with associated with associated with associated with Sightings on a timeline 10:00 10:01 10:02 Cart 1 hypothesis Cart 2 hypothesis N: North W: West S: South E: East Dots are sightings; dashed links are proposed associations, not observed journeys.
The same proposed associations appear in both views. Dots mark recorded sightings. Dashed connections link observations assigned to the same cart hypothesis; they do not show an observed journey.

The vocabulary from Article 8 now names observations, cameras, times, locations, and cart hypotheses. An illustrative statement is “Observation N is associated with cart hypothesis 1.” The camera records a sighting; the association is an inference about what it saw.

Missed detections, extra detections, or uncertain clocks could change the admissible pairings. One observation per cart per snapshot is an assumption here; overlapping sensors can observe the same cart. Keep multiple surviving explanations available for assessment.

A compatible association is a candidate explanation under a model. Estimating positions or speeds also needs an uncertainty model. The arrangement step identifies observations that can be considered together; evidence is still needed to verify inferred identities.

For your data, state what each source observed, which connections you propose, and which rules those connections must satisfy together. Preserve the original observations so a later correction can reopen the explanation.

Next: Which Agent Should Act Next—and What Must Happen Afterward? We turn to agent routing and handoffs.

References

  1. Stone Soup, Data association—multi-target tracking tutorial. The warehouse example is illustrative. ↩