Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise
Abstract
:1. Introduction
2. Impulsive Noise Model
- (1)
- If , is a real number, then
- (2)
- If , m is a non-zero real number, then
- (3)
- Let and be mutually independent α-stable distribution, then
3. Parameter Estimation Method
3.1. Fractional-Order Tracking Differentiator
3.2. Parameter Estimation Model
4. Simulation Experiment
4.1. FOTD Analysis
4.2. Comparisons
4.2.1. Standard SαS Distribution Noise
4.2.2. Non-Standard SαS Distribution Noise
- (1)
- When , the correction formula is
- (2)
- When , let , the correction formula is
- (3)
- When , let , the correction formula is
4.3. Measured Noise Experiment
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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−6 dB | −5 dB | −4 dB | −3 dB | −2 dB | −1 dB | 0 dB | 1 dB | 2 dB | 3 dB | ||
---|---|---|---|---|---|---|---|---|---|---|---|
f0 | FTD-FRFT | 1.2102 | 2.2815 | 5.5838 | 7.6531 | 13.4799 | 18.5058 | 20.0341 | 20.0968 | 20.0952 | 20.0950 |
Sigmoid-FPSD | −4.7484 | 11.7004 | 10.2649 | 20.2852 | 20.2182 | 20.1562 | 20.1863 | 20.1862 | 20.1058 | 20.1158 | |
PANT-LVD | 16.0291 | 18.4695 | 19.6947 | 20.9199 | 20.9199 | 20.9199 | 20.9199 | 20.9199 | 20.9199 | 20.9199 | |
FOTD-CFRFT | 20.2796 | 20.2574 | 20.2608 | 20.2617 | 20.2639 | 20.2652 | 20.2605 | 20.2603 | 20.2649 | 20.2646 | |
k | FTD-FRFT | −3.5269 | 0.9849 | 1.3671 | 8.1601 | 25.9438 | 40.8245 | 49.4254 | 50.1678 | 50.0054 | 49.9729 |
Sigmoid-FPSD | 45.4743 | 54.6101 | 50.1517 | 50.1191 | 50.1191 | 50.1678 | 50.1840 | 50.1677 | 50.1516 | 50.1353 | |
PANT-LVD | 37.9866 | 43.9949 | 47.0189 | 50.1228 | 50.0730 | 50.1329 | 50.2327 | 50.2826 | 50.3425 | 50.3924 | |
FOTD-CFRFT | 50.0982 | 50.1338 | 50.0889 | 50.1279 | 50.1832 | 50.1652 | 50.1783 | 50.1738 | 50.2006 | 50.1938 |
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Wang, H.; Guo, Y.; Yang, L. Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise. Fractal Fract. 2023, 7, 822. https://doi.org/10.3390/fractalfract7110822
Wang H, Guo Y, Yang L. Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise. Fractal and Fractional. 2023; 7(11):822. https://doi.org/10.3390/fractalfract7110822
Chicago/Turabian StyleWang, Houyou, Yong Guo, and Lidong Yang. 2023. "Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise" Fractal and Fractional 7, no. 11: 822. https://doi.org/10.3390/fractalfract7110822