Table 7 nMSEs and computation time for different process noise standard deviations \(w_{5}\) of the constant-volume 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

\(m_{s}\)

1.0486 × 10–4

5.6445 × 10–5

4.9427 × 10–5

5.4254 × 10–5

0.0040

\(h_{s}\)

8.9788 × 10–10

5.3484 × 10–10

3.7525 × 10–10

2.9498 × 10–10

\(d_{m}\)

0.0534

0.0278

0.0196

0.0184

GPSO-PF

\(m_{s}\)

0.0011

0.0011

0.0010

8.4229 × 10–4

0.3802

\(h_{s}\)

5.2818 × 10–15

6.3500 × 10–15

8.1890 × 10–15

1.3262 × 10–14

\(d_{m}\)

6.1590

5.2585

5.1241

2.2071

APF

\(m_{s}\)

7.5105 × 10–4

6.0064 × 10–4

5.5512 × 10–4

2.7221 × 10–4

0.0082

\(h_{s}\)

1.5007 × 10–7

5.1917 × 10–7

3.9147 × 10–7

1.3132 × 10–6

\(d_{m}\)

4.2814

3.8971

4.8321

3.3863

CD-FPF-CG

\(m_{s}\)

9.7412 × 10–6

2.7904 × 10–6

1.3798 × 10–6

7.9791 × 10–7

0.0116

\(h_{s}\)

1.0876 × 10–6

5.8859 × 10–7

3.7176 × 10–7

2.7485 × 10–7

\(d_{m}\)

0.0297

0.0207

0.0169

0.0144

CD-FPF-GL

\(m_{s}\)

1.6962 × 10–5

5.4638 × 10–6

2.8996 × 10–6

1.9224 × 10–6

0.0235

\(h_{s}\)

1.1446 × 10–6

6.3281 × 10–7

4.1049 × 10–7

2.9672 × 10–7

\(d_{m}\)

0.0344

0.0231

0.0187

0.0159

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