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Table 1 Comparison of MSD in case of noisy input and noisy output

From: \(\ell _1\)-regularized recursive total least squares based sparse system identification for the error-in-variables

Forgetting factor

Algorithm

S = 4 (dB)

S = 8 (dB)

S = 16 (dB)

S = 64 (dB)

0.999

RLS

−34.0

−33.5

−33.8

−33.7

\(\ell _1\)-RLS

−34.8

−33.6

−33.5

−33.7

\(\ell _1\)-RTLS

−35.4

−35.0

−34.9

−34.8

(\(\ell _1\)-RLS)-(\(\ell _1\)-RTLS)

0.6

1.4

1.4

1.1

0.9995

RLS

−35.7

−35.9

−36.1

−35.9

\(\ell _1\)-RLS

−36.0

−35.8

−35.8

−35.9

\(\ell _1\)-RTLS

−38.1

−38.0

−38.0

−38.0

(\(\ell _1\)-RLS)-(\(\ell _1\)-RTLS)

2.1

2.2

2.2

2.1

0.9999

RLS

−39.0

−39.3

−38.6

−38.6

\(\ell _1\)-RLS

−38.9

−39.1

−38.5

−38.6

\(\ell _1\)-RTLS

−44.0

−44.1

−43.6

−43.6

(\(\ell _1\)-RLS)-(\(\ell _1\)-RTLS)

5.1

5.0

5.1

5.0

1

RLS

−39.0

−38.5

−38.6

−38.9

\(\ell _1\)-RLS

−39.0

−38.5

−38.6

−38.9

\(\ell _1\)-RTLS

−45.0

−44.6

−44.8

−44.7

(\(\ell _1\)-RLS)-(\(\ell _1\)-RTLS)

6.0

6.1

6.2

5.8

  1. *\(\ell _1\)-RLS is the algorithm in Eksioglu and Tanc (2011)