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Robustness under noisy data

M = 500, N = 500, NOISE_STD = 0.1

True OE parameters

parameter value
$b_1$ 1.00000000
$f_1$ -1.10000000
$f_2$ 0.26250000

OE-structure estimates (SM and OE)

method parameter mean std
SM $b_1$ 1.00035237 0.00436880
SM $f_1$ -1.09972652 0.00382553
SM $f_2$ 0.26226868 0.00330754
OE $b_1$ 1.00028169 0.00437836
OE $f_1$ -1.09978869 0.00383730
OE $f_2$ 0.26232151 0.00331758

ARX baseline parameters (not directly comparable to OE parameters)

parameter mean std
$\theta_{1}$ -0.96402559 0.01213341
$\theta_{2}$ 0.14247447 0.01069840
$\theta_{3}$ 1.15416775 0.01383448