Table 6 Comparative results of the K-MHFLMS estimates and errors for the example with \(p = 1,2,3,4\),\(\sigma = 0.8\),\(\delta { = 1}{\text{.2}}\).

From: Design of multi-innovation hierarchical fractional adaptive algorithm for generalized bilinear-in-parameter system using the key term separation principle

 

\(t\)

\(a_{1}\)

\(a_{2}\)

\(\lambda_{1}\)

\(\lambda_{1}\)

\(\rho_{1}\)

\(\rho_{2}\)

\(\theta_{1}\)

\(\theta_{2}\)

Fitness

\(1\)

2000

 − 0.35620

0.95807

0.16274

0.56981

0.68748

 − 0.35620

 − 0.27733

0.27729

0.82496

4000

 − 0.52588

1.40056

0.44406

1.19871

1.10893

 − 0.52588

 − 0.12459

0.12456

0.69836

6000

 − 0.56961

1.61346

0.52277

1.41076

1.37240

 − 0.56961

 − 0.06557

0.06556

0.65050

8000

 − 0.60222

1.75817

0.58662

1.41571

1.59314

 − 0.60222

 − 0.06843

 − 0.04941

0.61906

10,000

 − 0.59676

1.84439

0.57241

1.41924

1.79246

 − 0.59676

 − 0.09348

 − 0.16418

0.59283

\(2\)

2000

 − 0.50204

1.42755

0.37003

1.16355

1.10721

 − 0.50204

 − 0.15144

0.15141

0.70438

4000

 − 0.61358

1.74481

0.58748

1.37233

1.62211

 − 0.61358

 − 0.08322

 − 0.07831

0.61563

6000

 − 0.59644

1.83969

0.56618

1.30247

1.96571

 − 0.59644

 − 0.15990

 − 0.16691

0.58599

8000

 − 0.62366

1.90060

0.59675

1.22241

2.27463

 − 0.62366

 − 0.17713

 − 0.24199

0.56582

10,000

 − 0.61077

1.91205

0.54376

1.29875

2.55515

 − 0.61077

 − 0.16872

 − 0.31810

0.54083

\(3\)

2000

 − 0.58086

1.66547

0.47880

1.35520

1.39634

 − 0.58086

 − 0.09014

0.09014

0.65388

4000

 − 0.63341

1.84412

0.57428

1.24048

1.99949

 − 0.63341

 − 0.10613

 − 0.14115

0.58550

6000

 − 0.59087

1.86301

0.57717

1.23432

2.42077

 − 0.59087

 − 0.16494

 − 0.24189

0.55443

8000

 − 0.63148

1.86928

0.60548

1.14740

2.78419

 − 0.63148

 − 0.21157

 − 0.30325

0.54661

10,000

 − 0.62197

1.84813

0.55664

1.28137

3.11822

 − 0.62197

 − 0.19481

 − 0.39779

0.52715

\(4\)

2000

 − 0.63509

1.80564

0.52436

1.33201

1.62110

 − 0.63509

 − 0.08029

0.04504

0.62935

4000

 − 0.64703

1.86194

0.54538

1.15388

2.31533

 − 0.64703

 − 0.15472

 − 0.20334

0.56697

6000

 − 0.59480

1.83321

0.60006

1.20974

2.80187

 − 0.59480

 − 0.17708

 − 0.30667

0.53800

8000

 − 0.64711

1.81077

0.61534

1.09579

3.20222

 − 0.64711

 − 0.23893

 − 0.35477

0.54609

10,000

 − 0.64241

1.77714

0.56999

1.25834

3.57081

 − 0.64241

 − 0.20927

 − 0.46204

0.53667

\({{\varvec{\Sigma}}}\)

 

0.80000

1.40000

0.40000

1.90000

3.00000

 − 2.00000

0.65000

 − 1.20000

 
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