Optimization of Time Delay Estimation by Singular Spectral Decomposition and Improved Generalized Correlation Method

Yuhua Xing; Heng Wang

doi:10.3788/LOP223315

Laser & Optoelectronics Progress, Volume. 61, Issue 5, 0506008(2024)

Optimization of Time Delay Estimation by Singular Spectral Decomposition and Improved Generalized Correlation Method

Yuhua Xing and Heng Wang^*

Author Affiliations

School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, Shaanxi, China

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Abstract Get PDF(in Chinese)

Figures & Tables(12)

Fig. 1. Results of autocorrelation normalization of transmitted signals

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Fig. 2. (a) Time-domain waveform diagram and (b) spectrum diagram of aliasing signal without noise

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Fig. 3. (a) Time-domain waveform diagram and (b) spectrum diagram of aliasing signal under $-$ 5 dB noise

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Fig. 4. Results of SSC component by SSD

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Fig. 5. (a) Time-domain waveform diagram and (b) spectrum diagram of signal reconstructed by SSD

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Fig. 6. Normalized results of time delay estimation for each method when circuit is open. (a) Secondary cross correlation; (b) SCOT-GCC; (c) SCOT-GCC after SSD processing; (d) proposed method

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Fig. 7. Normalized results of time delay estimation for each method when circuit is short. (a) Secondary cross correlation; (b) SCOT-GCC; (c) SCOT-GCC after SSD processing; (d) proposed method

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Fig. 8. PLSR comparison under different signal-to-noise ratio (SNR) conditions

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Fig. 9. N comparison under different SNR conditions

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Fig. 10. Comparison of accuracy under different SNR conditions

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Table 1. Common generalized cross correlation (GCC) weighted functions
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Table 1. Common generalized cross correlation (GCC) weighted functions
GCC function Expression of function
PHAT $\frac{1}{|φ_{y 1, y 2} (f)|}$
ROTH $\frac{1}{φ_{y 1, y 2} (f)}$
SCOT $\frac{1}{\sqrt[]{φ_{y 1, y 1} (f) * φ_{y 2, y 2} (f)}}$
ML/HT $\frac{1}{φ_{y 1, y 2} (f)} * \frac{{|γ_{y 1, y 2} (f)|}^{2}}{1 - {|γ_{y 1, y 2} (f)|}^{2}}$

Table 2. Performance comparison of different delay estimation methods

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Table 2. Performance comparison of different delay estimation methods

Fault type	Calculation method	Main peak sidelobe ratio，PSLR /dB	Misjudgment peak ratio N
Open circuit method	Secondary cross correlation	$-$ 5.5674	0.6818
	SCOT-GCC	$-$ 5.3298	0.5831
	SCOT-GCC after SSD processing	$-$ 6.4047	0.2288
	Proposed method	$-$ 7.3595	0.1837
Short circuit fault	Secondary cross correlation	$-$ 7.5380	0.6189
	SCOT-GCC	$-$ 14.6100	0.7418
	SCOT-GCC after SSD processing	$-$ 23.9800	0.6951
	Proposed method	$-$ 18.6900	0.5285

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Yuhua Xing, Heng Wang. Optimization of Time Delay Estimation by Singular Spectral Decomposition and Improved Generalized Correlation Method[J]. Laser & Optoelectronics Progress, 2024, 61(5): 0506008

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