# Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. The RBF-Kernel-Based Adaptive Filtering

#### 2.2. The Evolutionary Metaheuristic Optimization Algorithms

#### 2.2.1. Traditional PSO Algorithm

#### 2.2.2. Enhanced Partial Search Particle Swarm Optimization (EPS-PSO) Algorithm

#### 2.2.3. Multiswarm Particle Swarm Optimization (MSPSO)

#### 2.2.4. Genetic Algorithm (GA)

## 3. Results and Discussion

#### 3.1. Simulation Results

#### 3.1.1. Blocks Signal

#### 3.1.2. Bumps Signal

#### 3.1.3. Doppler Signal

#### 3.1.4. HeaviSine Signal

#### 3.1.5. Piece-Regular Signal

#### 3.1.6. Sing Signal

#### 3.1.7. Parameters Sensitivity

#### 3.1.8. Effects of the Signal Length

#### 3.2. Parameters Optimization

#### 3.3. Experimental Results for Real-Life Signals

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Algorithm A1 PSO algorithm-general |

Require:$s,MaxIt,{w}_{min},{w}_{max},{c}_{1},{c}_{2}$Ensure:${p}_{g}$1: Initialization:2: for$i\leftarrow 1$tosdo3: Initialize position ${x}_{i}$, velocity ${v}_{i}$ and particle’s personal best ${p}_{i}$; 4: Perform the function evaluation $f\left({x}_{i}\right)$; 5: ${p}_{i}\leftarrow {x}_{i};$ 6: if $f\left({p}_{i}\right)<f\left({p}_{g}\right)$ then7: ${p}_{g}\leftarrow {p}_{i}$; 8: end if9: end for10: Main loop:11: for $it\leftarrow 1$ to $MaxIt$ do12: (17); 13: for $i\leftarrow 1$ to s do14: (15), (16); 15: Perform the function evaluation $f\left({x}_{i}\right)$; 16: if $f\left({x}_{i}\right)<f\left({p}_{i}\right)$ then17: ${p}_{i}\leftarrow {x}_{i}$; 18: end if19: if $f\left({p}_{i}\right)<f\left({p}_{g}\right)$ then20: ${p}_{g}\leftarrow {p}_{i}$; 21: end if22: end for23: end for |

Algorithm A2 EPS-PSO algorithm-general |

Require:$s,MaxIt,{w}_{min},{w}_{max},{c}_{1},{c}_{2},{t}_{g}$Ensure:${p}_{T-g}$1: Initialization:2: for each particle in both swarms do3: Initialize position ${x}_{i}$, velocity ${v}_{i}$ and particle’s personal best ${p}_{i}$; 4: Perform the function evaluation $f\left({x}_{i}\right)$; 5: ${p}_{i}\leftarrow {x}_{i};$ 6: if $f\left({p}_{i}\right)<f\left({p}_{g}\right)$ then7: ${p}_{g}\leftarrow {p}_{i}$; 8: end if9: end for10: Main loop:11: for $it\leftarrow 1$ to $MaxIt$ do12: (17); 13: for each particle in both swarms do14: (15), (16); 15: Perform the function evaluation $f\left({x}_{i}\right)$; 16: if the criterion of the reinitialization period ${t}_{g}$ for the cosearch swarm is met then17: for each particle in the cosearch swarm do18: Reinitialize position ${x}_{i}$, velocity ${v}_{i}$ and particle’s personal best ${p}_{i}$; 19: Perform the evaluation $f\left({x}_{i}\right)$; 20: if $f\left({p}_{CO-g}\right)<f\left({p}_{T-g}\right)$ then21: ${p}_{T-g}\leftarrow {p}_{CO-g}$; 22: end if23: end for24: end if25: end for26: end for |

Algorithm A3 MSPSO algorithm-general |

Require:$s,nSwarm,MaxIt,{w}_{min},{w}_{max},{c}_{1},{c}_{2}$Ensure:${p}_{g}$1: Initialization:2: for$j\leftarrow 1$ to $nSwarm$ do3: for $i\leftarrow 1$ to s do4: Initialize position ${x}_{i,j}$, velocity ${v}_{i,j}$ and particle’s personal best ${p}_{i,j}$ 5: Perform the function evaluation $f\left({x}_{i,j}\right)$ 6: ${p}_{i,j}\leftarrow {x}_{i,j}$; 7: if $f\left({p}_{i,j}\right)<f\left({p}_{g,j}\right)$ then8: ${p}_{g,j}\leftarrow {p}_{i,j}$; 9: end if10: end for11: end for12: Main loop:13: for $it\leftarrow 1$ to $MaxIt$ do14: (17); 15: for $j\leftarrow 1$ to $nSwarm$ do16: for $i\leftarrow 1$ to s do17: (15), (16); 18: Perform the function evaluation $f\left({x}_{i,j}\right)$ 19: if $f\left({x}_{i,j}\right)<f\left({p}_{i,j}\right)$ then20: ${p}_{i,j}\leftarrow {x}_{i,j}$; 21: end if22: if $f\left({p}_{i,j}\right)<f\left({p}_{g,j}\right)$ then23: ${p}_{g,j}\leftarrow {p}_{i,j}$; 24: end if25: end for26: end for27: ${p}_{g}\leftarrow \mathrm{min}\left({p}_{g,j}\right)$ 28: end for |

Algorithm A4 GA algorithm-general |

Require: $s,MaxIt,{p}_{c},{p}_{m}$Ensure:${p}_{g}$1: Initialization:2: for$i\leftarrow 1$tosdo3: Initialize position ${x}_{i}$, velocity ${v}_{i}$ and particle’s personal best ${p}_{i}$ 4: Perform the function evaluation $f\left({x}_{i}\right)$ 5: end for6:Sort population in descending order; 7:${p}_{g}\leftarrow population\left(1\right)$; 8: Main loop:9: for $it\leftarrow 1$ to $MaxIt$ do10: for $j\leftarrow 1$ to ${n}_{c}/2$ do11: Compute crossovers and form new subpopulation; 12: end for13: for $j\leftarrow 1$ to ${n}_{m}$ do14: Compute mutation and form new subpopulation; 15: end for16: Create merged population; 17: Sort population in descending order; 18: Truncate population to s best performing particles; 19: ${p}_{g}\leftarrow population\left(1\right)$; 20: end for |

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**Figure 1.**Blocks signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =1.44,{R}_{c}=0.67$). (

**d**) Filtering error.

**Figure 2.**Bumps signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =0.82,{R}_{c}=0.33$). (

**d**) Filtering error.

**Figure 3.**Doppler signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =2.29,{R}_{c}=0.94$). (

**d**) Filtering error.

**Figure 4.**HeaviSine signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =4.98,{R}_{c}=0.99$). (

**d**) Filtering error.

**Figure 5.**Piece-Regular signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =1.44,{R}_{c}=0.81$). (

**d**) Filtering error.

**Figure 6.**Sing signal: (

**a**) Original signal. (

**b**) Noisy signal (SNR = 7 dB). (

**c**) Original and RBF-RICI filtered signal ($\Gamma =0.99,{R}_{c}=0.01$). (

**d**) Filtering error.

**Figure 7.**The filtering quality indicator MSE as a function of the RBF-RICI algorithm’s parameters $\Gamma $ and ${R}_{c}$ for noisy signals at 7 dB SNR: (

**a**) Blocks. (

**b**) Bumps. (

**c**) Doppler. (

**d**) HeaviSine. (

**e**) Piece-Regular. (

**f**) Sing.

**Figure 8.**Convergence comparison between the considered optimization algorithms for signals: (

**a**) Blocks. (

**b**) Bumps. (

**c**) Doppler. (

**d**) HeaviSine. (

**e**) Piece-Regular. (

**f**) Sing.

**Figure 9.**Sea temperature: (

**a**) Noisy measured signal. (

**b**) RBF-RICI filtered signal. (

**c**) Savitzky–Golay filtered signal.

**Figure 10.**Significant wave height: (

**a**) Noisy measured signal. (

**b**) RBF-RICI filtered signal. (

**c**) Savitzky–Golay filtered signal.

**Figure 11.**Wave direction: (

**a**) Noisy measured signal. (

**b**) RBF-RICI filtered signal. (

**c**) Savitzky–Golay filtered signal.

**Figure 12.**Individual maximum wave height: (

**a**) Noisy measured signal. (

**b**) RBF-RICI filtered signal.(

**c**) Savitzky–Golay filtered signal.

**Table 1.**Blocks signal (SNR = 5 dB)—Filtering results. The best filtering quality indicators are marked in bold.

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=3.67$, ${\mathit{R}}_{\mathit{c}}=0.95$ | LPA-RICI $\mathbf{\Gamma}=4.03$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.73$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|---|

MSE | 0.1409 | 0.1459 | 0.2114 | 0.3276 |

MAE | 0.2132 | 0.2100 | 0.3264 | 0.4219 |

MAXE | 3.6682 | 3.6471 | 4.0740 | 2.5848 |

PSNR (dB) | 22.8307 | 22.6801 | 21.0700 | 19.1668 |

ISNR (dB) | 11.4673 | 11.3166 | 9.7065 | 7.8033 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.44$, ${\mathit{R}}_{\mathit{c}}=0.67$ | LPA-RICI $\mathbf{\Gamma}=4.12$, ${\mathit{R}}_{\mathit{c}}=0.98$ | LPA-ICI $\mathbf{\Gamma}=0.62$ | Savitzky- Golay $\mathit{h}=21$ |
---|---|---|---|---|

MSE | 0.0849 | 0.0973 | 0.1305 | 0.2599 |

MAE | 0.1797 | 0.1864 | 0.2550 | 0.3684 |

MAXE | 3.2267 | 2.8130 | 2.9652 | 2.3588 |

PSNR (dB) | 25.0323 | 24.4376 | 23.1630 | 20.1717 |

ISNR (dB) | 11.6688 | 11.0741 | 9.7996 | 6.8082 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.60$, ${\mathit{R}}_{\mathit{c}}=0.84$ | LPA-RICI $\mathbf{\Gamma}=1.56$, ${\mathit{R}}_{\mathit{c}}=0.89$ | LPA-ICI $\mathbf{\Gamma}=0.47$ | Savitzky- Golay $\mathit{h}=19$ |
---|---|---|---|---|

MSE | 0.0311 | 0.0298 | 0.0595 | 0.1889 |

MAE | 0.1000 | 0.1059 | 0.1703 | 0.2939 |

MAXE | 2.4207 | 2.4023 | 2.4001 | 2.3602 |

PSNR (dB) | 29.3877 | 29.5756 | 26.5776 | 21.5585 |

ISNR (dB) | 13.0243 | 13.2121 | 10.2142 | 5.1951 |

**Table 4.**Blocks signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.03$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.73$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|

MSE | 3.43% | 33.35% | 56.99% |

MAE | −1.52% | 34.68% | 49.47% |

MAXE | −0.58% | 9.96% | −41.91% |

PSNR (dB) | 0.66% | 8.36% | 19.12% |

ISNR (dB) | 1.33% | 18.14% | 46.95% |

**Table 5.**Blocks signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.12$, ${\mathit{R}}_{\mathit{c}}=0.98$ | LPA-ICI $\mathbf{\Gamma}=0.62$ | Savitzky- Golay $\mathit{h}=21$ |
---|---|---|---|

MSE | 12.74% | 34.94% | 67.33% |

MAE | 3.59% | 29.53% | 51.22% |

MAXE | −14.71% | −8.82% | −36.79% |

PSNR (dB) | 2.43% | 8.07% | 24.10% |

ISNR (dB) | 5.37% | 19.07% | 71.39% |

**Table 6.**Blocks signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=1.56$, ${\mathit{R}}_{\mathit{c}}=0.89$ | LPA-ICI $\mathbf{\Gamma}=0.47$ | Savitzky- Golay $\mathit{h}=19$ |
---|---|---|---|

MSE | −4.36% | 47.73% | 83.54% |

MAE | 5.57% | 41.28% | 65.97% |

MAXE | −0.77% | −0.86% | −2.56% |

PSNR (dB) | −0.64% | 10.57% | 36.32% |

ISNR (dB) | −1.42% | 27.51% | 150.70% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky–Golay |

5 | 0.1439 | 0.2301 | 0.1482 | 0.0006 |

7 | 0.2655 | 0.0839 | 0.1351 | 0.0004 |

10 | 0.2136 | 0.2353 | 0.1413 | 0.0010 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.13$, ${\mathit{R}}_{\mathit{c}}=0.49$ | LPA-RICI $\mathbf{\Gamma}=2.05$, ${\mathit{R}}_{\mathit{c}}=0.90$ | LPA-ICI $\mathbf{\Gamma}=0.57$ | Savitzky- Golay $\mathit{h}=9$ |
---|---|---|---|---|

MSE | 0.0277 | 0.0356 | 0.0382 | 0.0626 |

MAE | 0.0966 | 0.1093 | 0.1215 | 0.1880 |

MAXE | 1.1582 | 1.2638 | 1.2638 | 1.7304 |

PSNR (dB) | 29.6493 | 28.5563 | 28.2463 | 26.1023 |

ISNR (dB) | 7.8378 | 6.7449 | 6.4348 | 4.2909 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=0.82$, ${\mathit{R}}_{\mathit{c}}=0.33$ | LPA-RICI $\mathbf{\Gamma}=1.57$, ${\mathit{R}}_{\mathit{c}}=0.88$ | LPA-ICI $\mathbf{\Gamma}=0.48$ | Savitzky- Golay $\mathit{h}=9$ |
---|---|---|---|---|

MSE | 0.0181 | 0.0251 | 0.0279 | 0.0454 |

MAE | 0.0806 | 0.0944 | 0.1028 | 0.1546 |

MAXE | 0.9612 | 1.0178 | 1.0178 | 1.7418 |

PSNR (dB) | 31.4981 | 30.0755 | 29.6152 | 27.4996 |

ISNR (dB) | 7.6866 | 6.2640 | 5.8038 | 3.6881 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=0.61$, ${\mathit{R}}_{\mathit{c}}=0.26$ | LPA-RICI $\mathbf{\Gamma}=1.55$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.34$ | Savitzky- Golay $\mathit{h}=7$ |
---|---|---|---|---|

MSE | 0.0101 | 0.0148 | 0.0166 | 0.0276 |

MAE | 0.0599 | 0.0777 | 0.0790 | 0.1228 |

MAXE | 0.7072 | 0.7327 | 0.8098 | 1.3599 |

PSNR (dB) | 34.0275 | 32.3577 | 31.8621 | 29.6602 |

ISNR (dB) | 7.2161 | 5.5462 | 5.0506 | 2.8487 |

**Table 11.**Bumps signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=2.05$, ${\mathit{R}}_{\mathit{c}}=0.90$ | LPA-ICI $\mathbf{\Gamma}=0.57$ | Savitzky- Golay $\mathit{h}=9$ |
---|---|---|---|

MSE | 22.19% | 27.49% | 55.75% |

MAE | 11.62% | 20.49% | 48.62% |

MAXE | 8.36% | 8.36% | 33.07% |

PSNR (dB) | 3.83% | 4.97% | 13.59% |

ISNR (dB) | 16.20% | 21.80% | 82.66% |

**Table 12.**Bumps signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=1.57$, ${\mathit{R}}_{\mathit{c}}=0.88$ | LPA-ICI $\mathbf{\Gamma}=0.48$ | Savitzky- Golay $\mathit{h}=9$ |
---|---|---|---|

MSE | 27.89% | 35.13% | 60.13% |

MAE | 14.62% | 21.60% | 47.87% |

MAXE | 5.56% | 5.56% | 44.82% |

PSNR (dB) | 4.73% | 6.36% | 14.54% |

ISNR (dB) | 22.71% | 32.44% | 108.42% |

**Table 13.**Bumps signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=1.55$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.34$ | Savitzky- Golay $\mathit{h}=7$ |
---|---|---|---|

MSE | 31.76% | 39.16% | 63.41% |

MAE | 22.91% | 24.18% | 51.22% |

MAXE | 3.48% | 12.67% | 48.00% |

PSNR (dB) | 5.16% | 6.80% | 14.72% |

ISNR (dB) | 30.11% | 42.88% | 153.31% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky-Golay |

5 | 0.1740 | 0.1614 | 0.1117 | 0.0002 |

7 | 0.1974 | 0.1206 | 0.0937 | 0.0001 |

10 | 0.1812 | 0.0742 | 0.0845 | 0.0001 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=2.15$, ${\mathit{R}}_{\mathit{c}}=0.88$ | LPA-RICI $\mathbf{\Gamma}=4.82$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.58$ | Savitzky- Golay $\mathit{h}=23$ |
---|---|---|---|---|

MSE | 0.0037 | 0.0046 | 0.0059 | 0.0044 |

MAE | 0.0452 | 0.0496 | 0.0590 | 0.0481 |

MAXE | 0.2647 | 0.3061 | 0.3028 | 0.2949 |

PSNR (dB) | 18.2042 | 17.1874 | 16.1235 | 17.4454 |

ISNR (dB) | 8.8026 | 7.7858 | 6.7220 | 8.0439 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=2.29$, ${\mathit{R}}_{\mathit{c}}=0.94$ | LPA-RICI $\mathbf{\Gamma}=3.61$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.46$ | Savitzky- Golay $\mathit{h}=21$ |
---|---|---|---|---|

MSE | 0.0027 | 0.0033 | 0.0045 | 0.0034 |

MAE | 0.0373 | 0.0417 | 0.0512 | 0.0412 |

MAXE | 0.3212 | 0.2803 | 0.3177 | 0.2776 |

PSNR (dB) | 19.5106 | 18.6596 | 17.3110 | 18.5490 |

ISNR (dB) | 8.1091 | 7.2581 | 5.9094 | 7.1475 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=2.85$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-RICI $\mathbf{\Gamma}=2.55$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.35$ | Savitzky- Golay $\mathit{h}=17$ |
---|---|---|---|---|

MSE | 0.0017 | 0.0021 | 0.0030 | 0.0023 |

MAE | 0.0293 | 0.0319 | 0.0411 | 0.0332 |

MAXE | 0.2097 | 0.2553 | 0.2809 | 0.2643 |

PSNR (dB) | 21.5377 | 20.6978 | 19.1250 | 20.2577 |

ISNR (dB) | 7.1362 | 6.2962 | 4.7235 | 5.8561 |

**Table 18.**Doppler signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.82$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.58$ | Savitzky- Golay $\mathit{h}=23$ |
---|---|---|---|

MSE | 19.57% | 37.29% | 15.91% |

MAE | 8.87% | 23.39% | 6.03% |

MAXE | 13.52% | 12.58% | 10.24% |

PSNR (dB) | 5.92% | 12.90% | 4.35% |

ISNR (dB) | 13.06% | 30.95% | 9.43% |

**Table 19.**Doppler signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=3.61$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.46$ | Savitzky- Golay $\mathit{h}=21$ |
---|---|---|---|

MSE | 18.18% | 40.00% | 20.59% |

MAE | 10.55% | 27.15% | 9.47% |

MAXE | −14.59% | −1.10% | −15.71% |

PSNR (dB) | 4.56% | 12.71% | 5.18% |

ISNR (dB) | 11.72% | 37.22% | 13.45% |

**Table 20.**Doppler signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=2.55$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.35$ | Savitzky- Golay $\mathit{h}=17$ |
---|---|---|---|

MSE | 19.05% | 43.33% | 26.09% |

MAE | 8.15% | 28.71% | 11.75% |

MAXE | 17.86% | 25.35% | 20.66% |

PSNR (dB) | 4.06% | 12.62% | 6.32% |

ISNR (dB) | 13.34% | 51.08% | 21.86% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky–Golay |

5 | 0.1600 | 0.0658 | 0.0947 | 0.0010 |

7 | 0.1177 | 0.0464 | 0.0836 | 0.0004 |

10 | 0.0512 | 0.0555 | 0.0702 | 0.0007 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=4.98$, ${\mathit{R}}_{\mathit{c}}=0.98$ | LPA-RICI $\mathbf{\Gamma}=4.97$, ${\mathit{R}}_{\mathit{c}}=0.99$ | LPA-ICI $\mathbf{\Gamma}=0.61$ | Savitzky- Golay $\mathit{h}=217$ |
---|---|---|---|---|

MSE | 0.1683 | 0.2022 | 0.3517 | 0.0995 |

MAE | 0.3264 | 0.3432 | 0.4737 | 0.2217 |

MAXE | 1.2817 | 1.8795 | 2.7010 | 1.0594 |

PSNR (dB) | 19.7793 | 18.9828 | 16.5791 | 22.0611 |

ISNR (dB) | 12.6436 | 11.8471 | 9.4434 | 14.9254 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=4.98$, ${\mathit{R}}_{\mathit{c}}=0.99$ | LPA-RICI $\mathbf{\Gamma}=4.54$, ${\mathit{R}}_{\mathit{c}}=0.99$ | LPA-ICI $\mathbf{\Gamma}=0.51$ | Savitzky- Golay $\mathit{h}=101$ |
---|---|---|---|---|

MSE | 0.1070 | 0.1280 | 0.2540 | 0.0763 |

MAE | 0.2526 | 0.2763 | 0.3987 | 0.2001 |

MAXE | 1.1832 | 1.8756 | 2.6166 | 1.0451 |

PSNR (dB) | 21.7477 | 20.9676 | 17.9928 | 23.2185 |

ISNR (dB) | 12.6119 | 11.8319 | 8.8571 | 14.0828 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=4.85$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-RICI $\mathbf{\Gamma}=4.67$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.38$ | Savitzky- Golay $\mathit{h}=101$ |
---|---|---|---|---|

MSE | 0.0594 | 0.0668 | 0.1549 | 0.0536 |

MAE | 0.1782 | 0.1924 | 0.3101 | 0.1578 |

MAXE | 1.0415 | 0.9900 | 2.4188 | 1.0251 |

PSNR (dB) | 24.3045 | 23.7948 | 20.1394 | 24.7476 |

ISNR (dB) | 12.1688 | 11.6591 | 8.0037 | 12.6118 |

**Table 25.**HeaviSine signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.97$, ${\mathit{R}}_{\mathit{c}}=0.99$ | LPA-ICI $\mathbf{\Gamma}=0.61$ | Savitzky- Golay $\mathit{h}=217$ |
---|---|---|---|

MSE | 16.77% | 52.15% | −69.15% |

MAE | 4.90% | 31.10% | −47.23% |

MAXE | 31.81% | 52.55% | −20.98% |

PSNR (dB) | 4.20% | 19.30% | −10.34% |

ISNR (dB) | 6.72% | 33.89% | −15.29% |

**Table 26.**HeaviSine signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.54$, ${\mathit{R}}_{\mathit{c}}=0.99$ | LPA-ICI $\mathbf{\Gamma}=0.51$ | Savitzky- Golay $\mathit{h}=101$ |
---|---|---|---|

MSE | 16.41% | 57.87% | −40.24% |

MAE | 8.58% | 36.64% | −26.24% |

MAXE | 36.92% | 54.78% | −13.21% |

PSNR (dB) | 3.72% | 20.87% | −6.33% |

ISNR (dB) | 6.59% | 42.39% | −10.44% |

**Table 27.**HeaviSine signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.67$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.38$ | Savitzky- Golay $\mathit{h}=101$ |
---|---|---|---|

MSE | 11.08% | 61.65% | −10.82% |

MAE | 7.38% | 42.53% | −12.93% |

MAXE | −5.20% | 56.94% | −1.60% |

PSNR (dB) | 2.14% | 20.68% | −1.79% |

ISNR (dB) | 4.37% | 52.04% | −3.51% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky–Golay |

5 | 0.2017 | 0.1275 | 0.1274 | 0.0010 |

7 | 0.1428 | 0.1061 | 0.1534 | 0.0009 |

10 | 0.0942 | 0.1177 | 0.1102 | 0.0015 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.72$, ${\mathit{R}}_{\mathit{c}}=0.82$ | LPA-RICI $\mathbf{\Gamma}=4.80$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.57$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|---|

MSE | 10.6693 | 14.1213 | 18.3593 | 13.3110 |

MAE | 2.3735 | 2.7457 | 3.1596 | 2.7866 |

MAXE | 17.7053 | 19.0331 | 18.5048 | 15.9277 |

PSNR (dB) | 22.4826 | 21.2653 | 20.1255 | 21.5219 |

ISNR (dB) | 9.9092 | 8.6918 | 7.5520 | 8.9485 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.44$, ${\mathit{R}}_{\mathit{c}}=0.81$ | LPA-RICI $\mathbf{\Gamma}=3.77$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.47$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|---|

MSE | 7.0609 | 9.5441 | 13.0202 | 9.9522 |

MAE | 1.9533 | 2.2509 | 2.6585 | 2.3151 |

MAXE | 12.7040 | 18.3339 | 15.7328 | 15.2692 |

PSNR (dB) | 24.2754 | 22.9667 | 21.6178 | 22.7848 |

ISNR (dB) | 9.7020 | 8.3932 | 7.0444 | 8.2114 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.19$, ${\mathit{R}}_{\mathit{c}}=0.84$ | LPA-RICI $\mathbf{\Gamma}=2.86$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.35$ | Savitzky- Golay $\mathit{h}=19$ |
---|---|---|---|---|

MSE | 3.7850 | 5.2971 | 7.6770 | 6.7829 |

MAE | 1.4513 | 1.6479 | 2.0257 | 1.8895 |

MAXE | 8.7759 | 16.1955 | 12.8774 | 14.5437 |

PSNR (dB) | 26.9834 | 25.5236 | 23.9121 | 24.4498 |

ISNR (dB) | 9.4099 | 7.9502 | 6.3386 | 6.8764 |

**Table 32.**Piece-Regular signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=4.80$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.57$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|

MSE | 24.45% | 41.89% | 19.85% |

MAE | 13.56% | 24.88% | 14.82% |

MAXE | 6.98% | 4.32% | −11.16% |

PSNR (dB) | 5.72% | 11.71% | 4.46% |

ISNR (dB) | 14.01% | 31.21% | 10.74% |

**Table 33.**Piece-Regular signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=3.77$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.47$ | Savitzky- Golay $\mathit{h}=25$ |
---|---|---|---|

MSE | 26.02% | 45.77% | 29.05% |

MAE | 13.22% | 26.53% | 15.63% |

MAXE | 30.71% | 19.25% | 16.80% |

PSNR (dB) | 5.70% | 12.29% | 6.54% |

ISNR (dB) | 15.59% | 37.73% | 18.15% |

**Table 34.**Piece-Regular signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=2.86$, ${\mathit{R}}_{\mathit{c}}=1$ | LPA-ICI $\mathbf{\Gamma}=0.35$ | Savitzky- Golay $\mathit{h}=19$ |
---|---|---|---|

MSE | 28.55% | 50.70% | 44.20% |

MAE | 11.93% | 28.36% | 23.19% |

MAXE | 45.81% | 31.85% | 39.66% |

PSNR (dB) | 5.72% | 12.84% | 10.36% |

ISNR (dB) | 18.36% | 48.45% | 36.84% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky–Golay |

5 | 0.1522 | 0.0670 | 0.0862 | 0.0003 |

7 | 0.1459 | 0.0532 | 0.0975 | 0.0007 |

10 | 0.1366 | 0.0674 | 0.0873 | 0.0005 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=1.12$, ${\mathit{R}}_{\mathit{c}}=0.11$ | LPA-RICI $\mathbf{\Gamma}=2.81$, ${\mathit{R}}_{\mathit{c}}=0.94$ | LPA-ICI $\mathbf{\Gamma}=0.82$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|---|

MSE | 83.8782 | 141.4546 | 177.6915 | 1962.6767 |

MAE | 3.8877 | 6.4314 | 6.8539 | 33.8149 |

MAXE | 111.5364 | 211.4573 | 193.0249 | 303.2041 |

PSNR (dB) | 46.9901 | 44.7204 | 43.7299 | 33.2981 |

ISNR (dB) | 15.9259 | 13.6562 | 12.6657 | 2.2339 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=0.99$, ${\mathit{R}}_{\mathit{c}}=0.01$ | LPA-RICI $\mathbf{\Gamma}=1.87$, ${\mathit{R}}_{\mathit{c}}=0.91$ | LPA-ICI $\mathbf{\Gamma}=0.73$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|---|

MSE | 64.1788 | 80.2616 | 132.0162 | 1338.2816 |

MAE | 3.3283 | 5.4335 | 5.8075 | 27.0899 |

MAXE | 108.9616 | 114.1618 | 171.9973 | 300.6734 |

PSNR (dB) | 48.1527 | 47.1815 | 45.0203 | 34.9611 |

ISNR (dB) | 15.0885 | 14.1173 | 11.9561 | 1.8969 |

Filtering Quality Indicator | RBF-RICI $\mathbf{\Gamma}=0.68$, ${\mathit{R}}_{\mathit{c}}=0.11$ | LPA-RICI $\mathbf{\Gamma}=2.11$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.44$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|---|

MSE | 35.3108 | 50.3365 | 73.5058 | 804.6591 |

MAE | 2.4840 | 4.0478 | 4.7087 | 19.5046 |

MAXE | 84.0245 | 99.7517 | 115.0057 | 297.8189 |

PSNR (dB) | 50.7475 | 49.2078 | 47.5634 | 37.1705 |

ISNR (dB) | 14.6833 | 13.1435 | 11.4992 | 1.1062 |

**Table 39.**Sing signal (SNR = 5 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=2.81$, ${\mathit{R}}_{\mathit{c}}=0.94$ | LPA-ICI $\mathbf{\Gamma}=0.82$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|

MSE | 40.70% | 52.80% | 95.73% |

MAE | 39.55% | 43.28% | 88.50% |

MAXE | 47.25% | 42.22% | 63.21% |

PSNR (dB) | 5.08% | 7.46% | 41.12% |

ISNR (dB) | 16.62% | 25.74% | 612.93% |

**Table 40.**Sing signal (SNR = 7 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=1.87$, ${\mathit{R}}_{\mathit{c}}=0.91$ | LPA-ICI $\mathbf{\Gamma}=0.73$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|

MSE | 20.04% | 51.39% | 95.20% |

MAE | 38.74% | 42.69% | 87.71% |

MAXE | 4.56% | 36.65% | 63.76% |

PSNR (dB) | 2.06% | 6.96% | 37.73% |

ISNR (dB) | 6.88% | 26.20% | 695.43% |

**Table 41.**Sing signal (SNR = 10 dB)—Filtering quality improvement of the RBF-RICI-based filtering over other tested algorithms.

Filtering Quality Indicator | LPA-RICI $\mathbf{\Gamma}=2.11$, ${\mathit{R}}_{\mathit{c}}=0.96$ | LPA-ICI $\mathbf{\Gamma}=0.44$ | Savitzky- Golay $\mathit{h}=5$ |
---|---|---|---|

MSE | 29.85% | 51.96% | 95.61% |

MAE | 38.63% | 47.25% | 87.26% |

MAXE | 15.77% | 26.94% | 71.79% |

PSNR (dB) | 3.13% | 6.69% | 36.53% |

ISNR (dB) | 11.72% | 27.69% | 1227.30% |

Runtime (s) | ||||
---|---|---|---|---|

SNR (dB) | RBF-RICI | LPA-RICI | LPA-ICI | Savitzky-Golay |

5 | 1.1708 | 0.9176 | 0.8507 | 0.0001 |

7 | 1.5391 | 0.4543 | 0.8060 | 0.0001 |

10 | 1.1189 | 0.7373 | 0.5872 | 0.0001 |

**Table 43.**Filtering results obtained by applying the RBF-RICI algorithm to signals of different lengths.

Signal | Filtering Quality Indicator | Signal Length | ||||
---|---|---|---|---|---|---|

256 | 512 | 1024 | 2048 | 4096 | ||

Blocks | MSE | 0.3513 | 0.1749 | 0.0849 | 0.0366 | 0.0304 |

MAE | 0.4153 | 0.2670 | 0.1797 | 0.1101 | 0.0879 | |

MAXE | 3.3583 | 2.9265 | 3.2267 | 2.5318 | 2.9030 | |

PSNR (dB) | 18.8633 | 21.8929 | 25.0323 | 28.6845 | 29.4858 | |

ISNR (dB) | 5.3256 | 8.6348 | 11.6688 | 15.1945 | 15.9701 | |

Runtime (s) | 0.0208 | 0.0889 | 0.2655 | 1.2338 | 4.1248 | |

Bumps | MSE | 0.0404 | 0.0292 | 0.0181 | 0.0138 | 0.0094 |

MAE | 0.1331 | 0.1045 | 0.0806 | 0.0675 | 0.0554 | |

MAXE | 1.2079 | 1.0840 | 0.9612 | 0.9261 | 0.9646 | |

PSNR (dB) | 28.0066 | 29.4147 | 31.4981 | 32.6580 | 34.3455 | |

ISNR (dB) | 3.7458 | 5.7128 | 7.6866 | 8.7608 | 10.4151 | |

Runtime (s) | 0.0195 | 0.0652 | 0.1974 | 0.9162 | 2.5284 | |

Doppler | MSE | 0.0073 | 0.0041 | 0.0027 | 0.0018 | 0.0013 |

MAE | 0.0632 | 0.0442 | 0.0373 | 0.0301 | 0.0248 | |

MAXE | 0.3359 | 0.2657 | 0.3212 | 0.4062 | 0.4062 | |

PSNR (dB) | 15.2227 | 17.7765 | 19.5106 | 21.3202 | 22.8532 | |

ISNR (dB) | 3.6592 | 6.4918 | 8.1091 | 9.8028 | 11.3092 | |

Runtime (s) | 0.0134 | 0.0465 | 0.1177 | 0.4334 | 1.0760 | |

HeaviSine | MSE | 0.3413 | 0.1443 | 0.1070 | 0.0661 | 0.0593 |

MAE | 0.5009 | 0.2944 | 0.2526 | 0.2006 | 0.1873 | |

MAXE | 1.3481 | 1.4779 | 1.1832 | 1.0982 | 1.2504 | |

PSNR (dB) | 16.7101 | 20.4488 | 21.7477 | 23.8411 | 24.3073 | |

ISNR (dB) | 7.4158 | 11.4321 | 12.6119 | 14.5912 | 15.0314 | |

Runtime (s) | 0.0182 | 0.0529 | 0.1428 | 0.3319 | 0.8183 | |

Piece-Regular | MSE | 21.2851 | 8.1570 | 7.0609 | 4.2778 | 3.2621 |

MAE | 3.3795 | 2.0880 | 1.9533 | 1.3535 | 1.1571 | |

MAXE | 18.4508 | 15.2367 | 12.7040 | 24.8208 | 24.8185 | |

PSNR (dB) | 19.3473 | 23.7121 | 24.2754 | 26.4571 | 27.6479 | |

ISNR (dB) | 4.7412 | 9.2154 | 9.7020 | 11.7501 | 12.8999 | |

Runtime (s) | 0.0143 | 0.0464 | 0.1459 | 0.4298 | 1.5775 | |

Sing | MSE | 34.2950 | 74.0754 | 64.1788 | 81.2321 | 67.2775 |

MAE | 2.9835 | 3.7794 | 3.3283 | 4.2714 | 3.7723 | |

MAXE | 45.1892 | 72.1926 | 108.9616 | 96.0850 | 249.2586 | |

PSNR (dB) | 38.8331 | 41.5093 | 48.1527 | 53.1499 | 59.9891 | |

ISNR (dB) | 11.6169 | 11.5691 | 15.0885 | 16.9605 | 20.7632 | |

Runtime (s) | 0.0648 | 0.3062 | 1.5391 | 6.0509 | 27.8120 |

Algorithms | s | $\mathit{MaxIt}$ | ${\mathit{w}}_{\mathit{max}}$ | ${\mathit{w}}_{\mathit{min}}$ | ${\mathit{c}}_{1}={\mathit{c}}_{2}$ | Additional |
---|---|---|---|---|---|---|

PSO | 50 | 50 | 0.9 | 0.4 | 2 | |

GA | 50 | 50 | / | / | / | ${p}_{c}={p}_{m}=0.5$ |

EPSPSO | $25+25$ | 50 | 0.9 | 0.4 | 2 | ${t}_{g}=5$ |

MSPSO | $25+25$ | 50 | 0.9 | 0.4 | 2 | $nSwarm=2$ |

**Table 45.**The computational results obtained by the PSO-based and GA-based optimization algorithms after 50 iterations, averaged over 50 independent runs.

Signal | Statistic | PSO | GA | EPS-PSO | MSPSO |
---|---|---|---|---|---|

Mean | 0.0850 | 0.0852 | 0.0850 | 0.0850 | |

Best | 0.0849 | 0.0849 | 0.0849 | 0.0849 | |

Blocks | Worst | 0.0854 | 0.0856 | 0.0854 | 0.0854 |

Std. Dev. | $2.1332\xb7{10}^{-4}$ | $2.7481\xb7{10}^{-4}$ | $2.5420\xb7{10}^{-4}$ | $2.0457\xb7{10}^{-4}$ | |

Median | 0.0849 | 0.0854 | 0.0849 | 0.0849 | |

Mean | 0.0181 | 0.0181 | 0.0181 | 0.0182 | |

Best | 0.0181 | 0.0181 | 0.0181 | 0.0181 | |

Bumps | Worst | 0.0187 | 0.0184 | 0.0181 | 0.0189 |

Std. Dev. | $8.8353\xb7{10}^{-5}$ | $5.3257\xb7{10}^{-5}$ | $8.3062\xb7{10}^{-6}$ | $2.4976\xb7{10}^{-4}$ | |

Median | 0.0181 | 0.0181 | 0.0181 | 0.0181 | |

Mean | 0.0027 | 0.0027 | 0.0027 | 0.0027 | |

Best | 0.0027 | 0.0027 | 0.0027 | 0.0027 | |

Doppler | Worst | 0.0027 | 0.0028 | 0.0027 | 0.0028 |

Std. Dev. | $7.0885\xb7{10}^{-7}$ | $6.2548\xb7{10}^{-6}$ | $9.6431\xb7{10}^{-7}$ | $1.2469\xb7{10}^{-5}$ | |

Median | 0.0027 | 0.0027 | 0.0027 | 0.0027 | |

Mean | 0.1131 | 0.1150 | 0.1100 | 0.1144 | |

Best | 0.1070 | 0.1070 | 0.1070 | 0.1070 | |

HeaviSine | Worst | 0.1330 | 0.1330 | 0.1330 | 0.1333 |

Std. Dev. | $1.10\xb7{10}^{-2}$ | $1.13\xb7{10}^{-2}$ | $8.10\xb7{10}^{-3}$ | $1.15\xb7{10}^{-2}$ | |

Median | 0.1070 | 0.1070 | 0.1070 | 0.1070 | |

Mean | 7.0609 | 7.0632 | 7.0628 | 7.0609 | |

Best | 7.0609 | 7.0609 | 7.0609 | 7.0609 | |

Piece-Regular | Worst | 7.0609 | 7.1043 | 7.0848 | 7.0609 |

Std. Dev. | $3.5888\xb7{10}^{-15}$ | $8.3\xb7{10}^{-3}$ | $6.6\xb7{10}^{-3}$ | $3.5888\xb7{10}^{-15}$ | |

Median | 7.0609 | 7.0609 | 7.0609 | 7.0609 | |

Mean | 65.6770 | 65.0317 | 65.0584 | 65.3961 | |

Best | 64.1788 | 64.1788 | 64.1788 | 64.1788 | |

Sing | Worst | 68.8607 | 68.8607 | 68.8607 | 68.8607 |

Std. Dev. | 2.2062 | 1.7989 | 1.8182 | 2.0745 | |

Median | 64.1788 | 64.1788 | 64.1788 | 64.1788 |

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## Share and Cite

**MDPI and ACS Style**

Lopac, N.; Jurdana, I.; Lerga, J.; Wakabayashi, N.
Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data. *J. Mar. Sci. Eng.* **2021**, *9*, 439.
https://doi.org/10.3390/jmse9040439

**AMA Style**

Lopac N, Jurdana I, Lerga J, Wakabayashi N.
Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data. *Journal of Marine Science and Engineering*. 2021; 9(4):439.
https://doi.org/10.3390/jmse9040439

**Chicago/Turabian Style**

Lopac, Nikola, Irena Jurdana, Jonatan Lerga, and Nobukazu Wakabayashi.
2021. "Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data" *Journal of Marine Science and Engineering* 9, no. 4: 439.
https://doi.org/10.3390/jmse9040439