Background
Affine projection and kernel affine projection algorithms
Affine projection algorithm
Kernel affine projection algorithm
Fractional signal processing approach
Introduction to fractional derivative
Proposed kernel fractional affine projection algorithm
Experimental results
Time series prediction
Lorenz time series
Algorithm | LMS | APA | KAPA | KFAPA |
---|---|---|---|---|
Training MSE (σ = 0.05) | 0.02250 ± 1.75e−005 | 0.01454 ± 5.26e−004 | 0.041827 ± 1.93e−065 | 0.02156 ± 1.39e−005 |
Training MSE (σ = 0.05) | 0.01583 ± 0.22e−005 | 0.07820 ± 0.00306 | 0.017738 ± 2.28e−003 | 0.091538 ± 1.367e−004 |
Training MSE (σ = 0.02) | 0.01903 ± 0.003149 | 0.025175 ± 0.000198 | 0.001399 ± 0.000189 | 0.0020052 ± 6.50e−005 |
Training MSE (σ = 0.02) | 0.002970 ± 0.00170 | 0.005556 ± 0.0004324 | 0.001356 ± 0.000131 | 0.0027892 ± 9.49e−004 |
Training MSE (σ = 0.04) | 0.004349 ± 0.0003927 | 0.00680 ± 0.0007169 | 0.004117 ± 0.000251 | 0.0048219 ± 0.0001680 |
Training MSE (σ = 0.04) | 0.0049979 ± 0.0004128 | 0.007162 ± 0.0009767 | 0.005117 ± 0.000382 | 0.005822 ± 0.0003391 |
Training MSE (σ = 0.1) | 0.015863 ± 0.0009678 | 0.010932 ± 0.0025963 | 0.026628 ± 0.00094904 | 0.045301 ± 0.00086739 |
Training MSE (σ = 0.1) | 0.016166 ± 0.007296 | 0.019066 ± 0.0044241 | 0.035729 ± 0.00128194 | 0.0555606 ± 0.0023143 |
Training MSE (σ = 0.5) | 0.42356 ± 0.10011 | 0.50001 ± 0.010242 | 0.82530 ± 0.2115 | 0.4209 ± 0.030332 |
Training MSE (σ = 0.5) | 0.51752 ± 0.22074 | 0.69218 ± 0.028178 | 0.91918 ± 0.32231 | 0.52013 ± 0.047689 |
Nonlinear channel equalization
Algorithm | MSE (dB) |
---|---|
APA | 0.6 ± 0.2 |
KAPA | 0.55 ± 0.05 |
KFAPA | 0.4 ± 0.1 |
Atmospheric CO2 concentration forecasting
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66 | 0.075 | 0.40 | 0.0576 | 1.0878 | 0.6600 | 0.4167 | 0.78 | 0.18 | 3.7509 | 0.1900 |
Static function approximation
Algorithm | Training MSE | Testing MSE |
---|---|---|
APA | 0.35 ± 0.05 | 0.3 ± 0.02 |
KAPA | 0.2 ± 0.04 | 0.22 ± 0.05 |
KFAPA | 0.11 ± 0.1 | 0.13 ± 0.3 |