Non-line-of-sight Time-of-flight Positioning Method Based on Coincidence Count Optimization

Mu Zhou; Linli Zhou; Wei He; Liangbo Xie

doi:10.3788/AOS250697

Acta Optica Sinica, Volume. 45, Issue 16, 1628002(2025)

Non-line-of-sight Time-of-flight Positioning Method Based on Coincidence Count Optimization

Mu Zhou^*, Linli Zhou, Wei He, and Liangbo Xie

School of Communications and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

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Abstract Get PDF(in Chinese)

Figures & Tables(18)

Fig. 1. System flowchart

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Fig. 2. System model. (a) Principle of entangled source preparation; (b) non-line-of-sight signal photon transmission

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Fig. 3. Principle of coincidence counting

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Fig. 4. ToF back projection positioning. (a) Time probability distribution; (b) positioning principle

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Fig. 5. Experimental platform

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Fig. 6. Positional relationship between scan points and target

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Fig. 7. Comparison of time errors extraction by different methods

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Fig. 8. Comparison of time precision extraction under different light path lengths. (a) Time extraction errors; (b) error variations

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Fig. 9. Comparison of extracted ToF errors under different target positions. (a) ToF errors; (b) relative errors

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Fig. 10. Comparison of different coincidence counting methods under different gate widths. (a) Time errors under different gate widths; (b) time cost under different coincidence gate widths

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Fig. 11. Comparison of different coincidence counting methods. (a) Comparison of time overhead under different photon numbers; (b) relationship between total photon number and remaining photon number

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Fig. 12. Time probability distribution by different methods. (a) Gaussian filtering; (b) median filtering; (c) wavelet filtering; (d) quantum coincidence counting; (e) proposed method

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Fig. 13. Position estimation by different methods. (a) Gaussian filtering; (b) median filtering; (c) wavelet filtering; (d) quantum coincidence counting; (e) proposed method

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Fig. 14. Positioning errors under different scan points. (a) Horizontal errors; (b) vertical errors; (c) total errors

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Fig. 15. Comparison of positioning error curves by different methods

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Table 1. Entangled photon pair selection algorithm based on time correlation

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Table 1. Entangled photon pair selection algorithm based on time correlation

Input: Photon arrival time

t_{1 K}

recorded by SPD 1, photon arrival time

t_{2 K}

recorded by SPD 2,

N

, iteration count

Q

, iteration step size

s

g_{τ}

t_{p}

, maximum photon arrival time

K

within acquisition windowOutput: Optimized photon ToF

T_{f}

(1) For $q = 1 : Q$ do

(2) $τ_{q} = s \times q, c o u n t (τ_{q}) \leftarrow 0$ ;

(3) $f_{f l a g} \leftarrow 1$ ;

(4) For $i = 1 : N$ do

(5) For $j = 1 : N$ do

(6) $j = f_{f l a g}$ ;

(7) If $|t_{1 i} + τ_{q} - t_{2 j}| \leq g_{τ}$ do

(8) $c o u n t (τ_{q}) = c o u n t (τ_{q}) + 1$ ;

(9) $f_{f l a g} = j + 1$ ;

(10) Break

(11) End if

(12) $j = j + 1$ ;

(13) End for

(14) End for

(15) End for

(16) $f i n d (c o u n t (τ)) = = m a x (c o u n t (τ_{q}))$ ; coincidence count delay value $τ_{q}$ for the $q$ iteration; coincidence count values $c o u n t (τ_{q})$ after delay $τ_{q}$

(17) Obtaining the preliminary ToF delay $t_{f 1} = τ$

(18) For $j = 1 : K$ do

(19) For $i = 1 : K$ do

(20) If $t_{f 1} - t_{p} \leq |t_{1 j} - t_{2 i}| \leq t_{f 1} + t_{p}$ do

(21) $V_{v a l i d_p a i r s} = [v_{P a i r s}; i, j]$ , $V_{v a l i d_p a i r s}$ denotes the time sequence of temporally entangled photons after post-selection

(22) End if

(23) End for

(24) End for

(25) Returning entangled photon time sequences $t_{1 i}^{'} (t_{1 k} (v_{P a i r s} (;, 1)))$ , $t_{2 j}^{'} (t_{1 k} (v_{P a i r s} (;, 2)))$

(26) Coincidence counting between channels $t_{1 i}^{'}$ and $t_{2 j}^{'}$ , Obtaining the optimized photon ToF $T_{f}$

(27) End

Table 2. Main parameters

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Table 2. Main parameters

Parameter	Value
Laser power /mw	120
Pump light wavelength /nm	405
Nonlinear crystal dimensions /(mm×mm×mm)	$1 \times 2 \times 20$
SPD efficiency /%	$> 60$
SPD dark count rate /Hz	$< 500$
SPD saturation count rate /MHz	$35$
SPD dead time /ps	$\leq 20$
SPD temporal resolution /ps	350
Time-to-digital converter temporal resolution /ps	2

Table 3. Positioning errors by different methods

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Table 3. Positioning errors by different methods

Method	Estimated coordinate /m	Horizontal error /m	Vertical error /m	Total error /m
Gaussian filtering^[15]	(1.8619, －0.5555)	0.1381	0.4444	0.5825
Median filtering^[35]	(1.9069, －0.2702)	0.0931	0.9069	1.0000
Wavelet filtering^[36]	(1.7417, －0.9159)	0.2583	0.0840	0.3423
Coincidence counting^[27]	(1.9820, －1.0260)	0.0180	0.0260	0.0440
Proposed	(1.9970, －0.9909)	0.0030	0.0090	0.0120

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Mu Zhou, Linli Zhou, Wei He, Liangbo Xie. Non-line-of-sight Time-of-flight Positioning Method Based on Coincidence Count Optimization[J]. Acta Optica Sinica, 2025, 45(16): 1628002

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Paper Information

Category: Remote Sensing and Sensors

Received: Mar. 5, 2025

Accepted: May. 20, 2025

Published Online: Aug. 15, 2025

The Author Email: Mu Zhou (zhoumu@cqupt.edu.cn)

DOI:10.3788/AOS250697

CSTR:32393.14.AOS250697

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology