Manuscript En01-C@1 · En01-C.tex · section · 00a2161c

Settings and declared competing sources

Structured-force identifiability from four free times › Settings and declared competing sources · lines 1456–1498

Choose

t_{i} = t_{0} + i Δ, i = 0, 1, 2, 3, t_{0} \geq 0, Δ > 0,

and use weights

a = (- 1, 3, - 3, 1) .

They satisfy

i \sum a_{i} t_{i}^{j} = 0 (j = 0, 1, 2), i \sum a_{i} t_{i}^{3} = 6 Δ^{3} .

The cooling and boost procedure is identical across these settings. Its output second moments may depend arbitrarily on the hypothesis, support amplitude, and other shared nuisance parameters. The free interval is exactly flat. Forces from white support displacement consequently vanish there.

Other admitted flat-stage sources have a constant aggregate second-moment coefficient $D_{f} \geq 0$ . Under the two hypotheses,

D_{f, 0} = D_{f}, D_{f, 1} = D_{f} + λ A_{r_{c}} .

This notation includes any ordinary kick source with the same constant second-moment heating action, not only Gaussian force diffusion.

The four sensing stages have identical duration, strength, curvature, and electronic normalization. White increments after the free interval are independent of earlier ones. Their integrated source offset is common across the four settings of each hypothesis.

Displayed formulas in this passage

unlabeled · line 1459
$t_{i} = t_{0} + i Δ, i = 0, 1, 2, 3, t_{0} \geq 0, Δ > 0,$
unlabeled · line 1465
$a = (- 1, 3, - 3, 1) .$
unlabeled · line 1469
$i \sum a_{i} t_{i}^{j} = 0 (j = 0, 1, 2), i \sum a_{i} t_{i}^{3} = 6 Δ^{3} .$
unlabeled · line 1484
$D_{f, 0} = D_{f}, D_{f, 1} = D_{f} + λ A_{r_{c}} .$

Settings and declared competing sources

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