Live EO-MTT examples

Same ten measurements, threshold-selected cells

Dashed ellipses mark the two unknown extended objects; m₉ is ambiguous and m₁₀ is clutter.

A · restricted set

Combinatorial load

B(10) = 115 975

Measurements M 10

B(M) counts set partitions only; cell-to-object assignments add more possibilities.

Single-linkage threshold

d = 8.0

Merge when closest pair ≤ d

cells now—

distinct sweep candidates9

of all B(10)0.0078%

The heuristic decides which hypotheses can receive non-zero weight. Move d to watch the candidate set change.

Teaching simplification. Geometry and the single-linkage sweep match the source page’s ten-point example. This is not a complete PHD/CPHD update or calibrated likelihood.

A PMBM mixture branches; management keeps it finite

Each global hypothesis carries one partition–association history and its own weight.

B1 · retain hypotheses

→ 4 global hypotheses

Two approximations, two different outputs

Sampling explores joint hypotheses. This Family C SPA schematic passes messages to approximate marginals without enumerating those hypotheses.

JOINT SEARCH ≠ MARGINAL INFERENCE

B2a

Gibbs-style search

0 moves

Visits high-weight joint partition hypotheses; finite runs may miss modes.

Deterministic-seed toy chain with a CRP-flavored Gaussian score; visit frequencies are not a calibrated posterior.

C · SCHEMATIC

Per-measurement SPA

iteration 0

Approximates association marginals; it does not enumerate or sample partitions.

Simplified per-measurement SPA teaching update for association/existence only. Reference [32] also uses BP, but in a distinct trajectory-PMB model; real trackers also infer kinematics and extent.