Abstract

This paper presents a novel biometric system for real-time walker recognition using a pyroelectric infrared sensor, a Fresnel lens array and signal processing based on the linear regression of sensor signal spectra. In the model training stage, the maximum likelihood principal components estimation (MLPCE) method is utilized to obtain the regression vector for each registered human subject. Receiver operating characteristic (ROC) curves are also investigated to select a suitable threshold for maximizing subject recognition rate. The experimental results demonstrate the effectiveness of the proposed pyroelectric sensor system in recognizing registered subjects and rejecting unknown subjects.

©2007 Optical Society of America

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References

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  1. A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
    [Crossref]
  2. V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
    [Crossref]
  3. N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
    [Crossref] [PubMed]
  4. M. Planck, “On the law of distribution of energy in the normal spectrum,” Annalen der Physik 4, 533 ff (1901).
  5. U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
    [Crossref] [PubMed]
  6. A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
    [Crossref]
  7. Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
    [Crossref]
  8. T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
    [Crossref]
  9. Glolab Corporation, “Infrared parts manual,” http://www.glolab.com/pirparts/infrared.html.
  10. Fresnel Technologies Inc., http://www.fresneltech.com/arrays.html.
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    [Crossref] [PubMed]
  12. J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
    [Crossref] [PubMed]
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    [Crossref]
  14. M. N. Leger and P. D. Wentzell, “Maximum likelihood principal components regression on wavelet-compressed data,” Appl. Spectrosc. 58,855–862, (2004).
    [Crossref] [PubMed]
  15. D. Green and J. Swets, Signal Detection Theory and Psychophysics (John Wiley and Sons, New York, 1989).
  16. J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143,29–36 (1982).
    [PubMed]
  17. C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8,283–298 (1978).
    [Crossref] [PubMed]
  18. A. P. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30,1145–1159, (1997).
    [Crossref]
  19. D. J. Hand and R. J. Till, “A simple generalisation of the area under the ROC curve for multiple class classification problems,” Mach. Learn. 45,171–186, (2001).
    [Crossref]
  20. M. Faundez-Zanuy and E. Monte-Moreno, “State-of-the-art in speaker recognition,” IEEE Aerosp. Electron. Syst. Mag 20,7–12 (2005
    [Crossref]

2006 (3)

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

2005 (1)

M. Faundez-Zanuy and E. Monte-Moreno, “State-of-the-art in speaker recognition,” IEEE Aerosp. Electron. Syst. Mag 20,7–12 (2005
[Crossref]

2004 (2)

M. N. Leger and P. D. Wentzell, “Maximum likelihood principal components regression on wavelet-compressed data,” Appl. Spectrosc. 58,855–862, (2004).
[Crossref] [PubMed]

A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
[Crossref]

2003 (1)

U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
[Crossref] [PubMed]

2002 (2)

A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
[Crossref]

S. K. Schreyer, M. Bidinosti, and P. D. Wentzell, “Application of maximum likelihood principal components regression to fluorescence emission spectra,” Appl. Spectrosc. 56,789–796, (2002).
[Crossref]

2001 (2)

D. J. Hand and R. J. Till, “A simple generalisation of the area under the ROC curve for multiple class classification problems,” Mach. Learn. 45,171–186, (2001).
[Crossref]

N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
[Crossref] [PubMed]

1997 (1)

A. P. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30,1145–1159, (1997).
[Crossref]

1996 (1)

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

1995 (1)

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

1982 (1)

J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143,29–36 (1982).
[PubMed]

1978 (1)

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8,283–298 (1978).
[Crossref] [PubMed]

1901 (1)

M. Planck, “On the law of distribution of energy in the normal spectrum,” Annalen der Physik 4, 533 ff (1901).

Ackerman, M.

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

Ahmed, A.

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

Baig, A.

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

Bidinosti, M.

Bradley, A. P.

A. P. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30,1145–1159, (1997).
[Crossref]

Brady, D. J.

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
[Crossref] [PubMed]

Burchett, J.

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

D. J., Brady

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

Fang, J. S.

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

Faundez-Zanuy, M.

M. Faundez-Zanuy and E. Monte-Moreno, “State-of-the-art in speaker recognition,” IEEE Aerosp. Electron. Syst. Mag 20,7–12 (2005
[Crossref]

Feller, S.

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

Gopinathan, U.

U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
[Crossref] [PubMed]

Green, D.

D. Green and J. Swets, Signal Detection Theory and Psychophysics (John Wiley and Sons, New York, 1989).

Guenther, B. D.

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

Hand, D. J.

D. J. Hand and R. J. Till, “A simple generalisation of the area under the ROC curve for multiple class classification problems,” Mach. Learn. 45,171–186, (2001).
[Crossref]

Hanley, J. A.

J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143,29–36 (1982).
[PubMed]

Hao, Q.

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

Hsu, K. Y.

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

Hussian, T.

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

Jain, A. K.

A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
[Crossref]

Kakuta, N.

N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
[Crossref] [PubMed]

Kawamura, K.

A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
[Crossref]

Leger, M. N.

McNeil, B. J.

J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143,29–36 (1982).
[PubMed]

Metz, C. E.

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8,283–298 (1978).
[Crossref] [PubMed]

Monte-Moreno, E.

M. Faundez-Zanuy and E. Monte-Moreno, “State-of-the-art in speaker recognition,” IEEE Aerosp. Electron. Syst. Mag 20,7–12 (2005
[Crossref]

Nakamura, M.

N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
[Crossref] [PubMed]

Pitsianis, N. P.

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
[Crossref] [PubMed]

Planck, M.

M. Planck, “On the law of distribution of energy in the normal spectrum,” Annalen der Physik 4, 533 ff (1901).

Prabhakar, S.

A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
[Crossref]

Ross, A.

A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
[Crossref]

Saadawi, T.

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

Scherzinger, A.

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

Schreyer, S. K.

Sekmen, A. S.

A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
[Crossref]

Shankar, M.

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

Spitzer, V.

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

Swets, J.

D. Green and J. Swets, Signal Detection Theory and Psychophysics (John Wiley and Sons, New York, 1989).

Till, R. J.

D. J. Hand and R. J. Till, “A simple generalisation of the area under the ROC curve for multiple class classification problems,” Mach. Learn. 45,171–186, (2001).
[Crossref]

Wentzell, P. D.

Whitlock, D.

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

Wilkes, M.

A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
[Crossref]

Yokoyama, S.

N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
[Crossref] [PubMed]

Annalen der Physik (1)

M. Planck, “On the law of distribution of energy in the normal spectrum,” Annalen der Physik 4, 533 ff (1901).

Appl. Spectrosc. (2)

IEEE Aerosp. Electron. Syst. Mag (1)

M. Faundez-Zanuy and E. Monte-Moreno, “State-of-the-art in speaker recognition,” IEEE Aerosp. Electron. Syst. Mag 20,7–12 (2005
[Crossref]

IEEE Sens. J. (1)

Q. Hao, D. J. Brady, B. D. Guenther, J. Burchett, M. Shankar, and S. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 06,1683–1694 (2006).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

N. Kakuta, S. Yokoyama, and M. Nakamura, “Estimation of radiative heat transfer using a geometric human model,” IEEE Trans. Biomed. Eng. 48,324–331 (2001).
[Crossref] [PubMed]

IEEE Trans. Circuits syst. Video Technol. (1)

A. K. Jain, A. Ross, and S. Prabhakar, “An introduction to biometric recognition,” IEEE Trans. Circuits syst. Video Technol. 14,4–20 (2004).
[Crossref]

IEEE Trans. Syst., Man Cybern. A (1)

A. S. Sekmen, M. Wilkes, and K. Kawamura, “An application of passive human-robot interaction: human tracking based on attention distraction,” IEEE Trans. Syst., Man Cybern. A 32,248–259 (2002).
[Crossref]

IEEE Trans. Veh. Technol. (1)

T. Hussian, A. Baig, T. Saadawi, and A. Ahmed “Infrared pyroelectric sensor for detection of vehicular traffic using digital signal processing techniques,” IEEE Trans. Veh. Technol. 44,683–689 (1995).
[Crossref]

J. Am. Med. Assoc. (1)

V. Spitzer, M. Ackerman, A. Scherzinger, and D. Whitlock, “The visible human male: A technical report,” J. Am. Med. Assoc. 3,118–130 (1996).
[Crossref]

Mach. Learn. (1)

D. J. Hand and R. J. Till, “A simple generalisation of the area under the ROC curve for multiple class classification problems,” Mach. Learn. 45,171–186, (2001).
[Crossref]

Opt. Express. (3)

U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express. 11,2142–2152 (2003).
[Crossref] [PubMed]

J. S. Fang, Q. Hao, D. J. Brady, M. Shankar, B. D. Guenther, N. P. Pitsianis, and K. Y. Hsu, “Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays,” Opt. Express. 14,609–624, (2006).
[Crossref] [PubMed]

J. S. Fang, Q. Hao, Brady D. J., B. D. Guenther, and K. Y. Hsu, “Real-time human identification using a pyroelectric infrared detector array and hidden Markov models,” Opt. Express. 14,6643–6658 (2006).
[Crossref] [PubMed]

Pattern Recogn. (1)

A. P. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30,1145–1159, (1997).
[Crossref]

Radiology (1)

J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143,29–36 (1982).
[PubMed]

Semin. Nucl. Med. (1)

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8,283–298 (1978).
[Crossref] [PubMed]

Other (3)

D. Green and J. Swets, Signal Detection Theory and Psychophysics (John Wiley and Sons, New York, 1989).

Glolab Corporation, “Infrared parts manual,” http://www.glolab.com/pirparts/infrared.html.

Fresnel Technologies Inc., http://www.fresneltech.com/arrays.html.

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Figures (12)

Fig. 1.
Fig. 1. The diagram of the recognition process
Fig. 2.
Fig. 2. A sensor module (including a PIR detector, a Fresnel lens arrary, Texas Instrument micro-controller (MSP430149) and RF transceiver (TRF6901) module)
Fig. 3.
Fig. 3. The experiment setup for real-time walker recognition.
Fig. 4.
Fig. 4. Flow chart of real-time feature extraction.
Fig. 5.
Fig. 5. Event window detection from windowed power spectrum density of sensory data. (a) Raw data. (b) WPSD of the raw data. (c) Digitized signals. (d) Event windows.
Fig. 6.
Fig. 6. Two event data sets generated by two different individuals.
Fig. 7.
Fig. 7. The spectral features for two different individuals derived from the event data in Fig. 6.
Fig. 8.
Fig. 8. Each column is for different speed levels. Each subfigure contains 40 superimposed data sets.
Fig. 9.
Fig. 9. Results for leave-one-out cross-validation of calibration data
Fig. 10.
Fig. 10. The supervised clustering results upon 3 labels for 120 data sets with contours of the probability density distributions. (a) From Jason“s training data. (b) From Bob’s training data.
Fig. 11.
Fig. 11. The RMSEP results for different value of additive noise.
Fig. 12.
Fig. 12. ROC curves of four registered people

Tables (2)

Tables Icon

Table 1. Summary of parameters of PIR detector

Tables Icon

Table 2. The recognition results of 4 registered and 6 unregistered subjects. During the experiment, each subject walks 20 rounds along a fixed path. The detection of unregistered subject yields a report of “Others”.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

M = F R .
M = F ˜ R + ε ,
F m × n = U m × m m × n V n × n T ,
F F ˜ k = U ˜ m × k ˜ k × k V ˜ n × k T ,
F PJ T ,
M m × 1 = P m × k R ̂ k × 1 + ε ̂ m × 1 .
Q = 1 ( 2 π ) m / 2 C ε ̂ 1 / 2 exp [ 1 2 ( M P R ̂ ) T C ε ̂ 1 ( M P R ̂ ) ] ,
Q ' = ( M P R ̂ ) T C ε ̂ 1 ( M P R ̂ ) .
R ̂ [ ( M P R ̂ ) T C ε ̂ 1 ( M P R ̂ ) ] | R ̂ = R ̂ MLE = 0 .
P T C ε ̂ 1 ( M P R ̂ MLE ) = 0 .
R ̂ MLE = ( P T C ε ̂ 1 P ) 1 P T C ε ̂ 1 M .
R n × 1 = J n × k R ̂ k × 1 , MLE
= V ˜ n × k ( P T C ε ̂ 1 P ) 1 P T C ε ̂ 1 M
= V ˜ n × k [ ( U ˜ m × k ˜ k × k ) T C ε ̂ 1 ( U ˜ m × k ˜ k × k ) ] 1 ( U ˜ m × k ˜ k × k ) T C ε ̂ 1 M m × 1 .
μ = W ¯ = l = 1 n W 1 n ,
C = [ cov ( p , p ) cov ( p , q ) cov ( q , p ) cov ( q , q ) ] .
cov ( X , Y ) = l = 1 n ( X l X ¯ ) ( Y l Y ¯ ) ( n 1 ) .
m { H 0 , if max i { p ( m H i ) } < γ i H i : i = arg max i { p ( m H i ) } otherwise ,
p ( m H i ) = 1 ( 2 π ) C i 1 / 2 exp [ 1 2 ( m μ i ) T C i 1 ( m μ i ) ] .
RMSEP = i = 1 n ( M i M ̂ i ) 2 n = i = 1 n e i 2 n ,

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