Table 4 nMSEs and computation time for different process noise standard deviations \(w_{5}\) of the no-overflow stage (\(T_{s}\) = 1 s).

From: Realtime estimation of average sand grain diameter and sand bed height and mass for a trailing suction hopper dredger

Estimation methods

Estimation variables

Different process noises \(w_{5}\)[mm]

Computation time

0.010

0.015

0.020

0.025

BPF

\(m_{s}\)

5.2307 × 10–4

5.7777 × 10–4

7.0719 × 10–4

7.9391 × 10–4

0.0039

\(h_{s}\)

1.4703 × 10–8

7.8465 × 10–9

5.0889 × 10–9

4.1098 × 10–9

\(d_{m}\)

0.0672

0.0939

0.1409

0.2349

GPSO-PF

\(m_{s}\)

0.0065

0.0070

0.0095

0.0117

0.3892

\(h_{s}\)

4.3605 × 10–13

6.0034 × 10–13

6.5481 × 10–13

7.3998 × 10–13

\(d_{m}\)

0.1842

0.1968

0.3262

0.5634

APF

\(m_{s}\)

0.0046

0.0017

7.3345 × 10–4

5.6971 × 10–4

0.0081

\(h_{s}\)

2.1350 × 10–5

1.1937 × 10–5

3.9104 × 10–5

6.9024 × 10–6

\(d_{m}\)

0.1968

0.1090

0.0781

0.1171

CD-FPF-CG

\(m_{s}\)

3.0981 × 10–4

1.2601 × 10–4

8.4067 × 10–5

6.7902 × 10–5

0.0118

\(h_{s}\)

3.3092 × 10–5

1.7163 × 10–5

1.1482 × 10–5

8.8726 × 10–6

\(d_{m}\)

0.0643

0.0568

0.0525

0.0517

CD-FPF-GL

\(m_{s}\)

2.8262 × 10–4

1.5088 × 10–4

9.0771 × 10–5

8.6279 × 10–5

0.0230

\(h_{s}\)

3.6910 × 10–5

1.8932 × 10–5

1.2713 × 10–5

9.4248 × 10–6

\(d_{m}\)

0.0631

0.0569

0.0549

0.0521

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