Statistical Picking of Multivariate Waveforms

. 2022 Dec 8;22(24):9636. doi: 10.3390/s22249636

Algorithm 1changepost

Require: ${\hat{ψ}}^{*} = {{\hat{ψ}}_{1}^{*}, \dots, {\hat{ψ}}_{K^{*}}^{*}}$ ; $s_{i} = {(Y_{i} - {\hat{Y}}_{i})}^{2} / w_{i}$ ; $S = {s_{1}, \dots, s_{n}}$ ; $s t a r t = 1$ ; $e n d = n$

Ensure: $\hat{ψ}$

1:
for $(i i n 1 : K^{*})$ do
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if $(i = = 1)$ then
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$r a t i o [i] \leftarrow \frac{var (S [s t a r t : {\hat{ψ}}_{i}^{*}])}{var (S [s t a r t : {\hat{ψ}}_{i + 1}^{*}])}$
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end if
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if $(1 < i < K^{*})$ then
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$r a t i o [i] \leftarrow \frac{var (S [{\hat{ψ}}_{i - 1}^{*} : {\hat{ψ}}_{i}^{*}])}{var (S [{\hat{ψ}}_{i - 1}^{*} : {\hat{ψ}}_{i + 1}^{*}])}$
7:
end if
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if $(i = = K^{*})$ then
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$r a t i o [i] \leftarrow \frac{var (S [{\hat{ψ}}_{i - 1}^{*} : {\hat{ψ}}_{i}^{*}])}{var (S [{\hat{ψ}}_{i - 1}^{*} : e n d])}$
10:
end if
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end for
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$r a t i o [r a t i o < 1] \leftarrow {(r a t i o [r a t i o < 1])}^{- 1}$
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$\hat{ψ} \leftarrow {\hat{ψ}}^{*} [which (rank (r a t i o) > K^{*} - 2)]$