Systems and methods for security breach detection

1. A system for detecting and classifying a security breach, the system comprising:

at least one sensor configured to detect seismic vibration from a source, and to generate an output signal that represents the detected seismic vibration; and

a controller configured to extract a feature vector from the output signal of the sensor and to compute one or more likelihoods of the extracted feature vector relative to set {b i } (i=1, . . . , i max ) of breach classes b i , the controller further configured to classify the source of the detected seismic vibration as a security breach belonging to one of the breach classes b i by choosing a breach class within the set {b i } that has a maximum likelihood relative to the extracted feature vector.

2. The system of claim 1 ,

wherein the breach classes b i comprise at least one of: a moving vehicle, a human footstep, and background noise.

3. The system of claim 1 , wherein the controller is further configured to extract the feature vector from the output signal by applying a Fourier transform to the output signal so as to convert the output signal from a time domain signal into a frequency domain signal; applying to the converted signal a plurality of weighting functions at different frequency bands; calculating energy of each of the bands; and applying a discrete cosine transform to the weighted frequency signals.

4. The system of claim 2 ,

wherein the controller is further configured to input and store a time sequence O of feature vectors o i ( i=1, . . . , T )=o 1 , o 2 , . . . , o T , where o t represents a feature vector observed at a time t, and the time sequence O represents one or more segments of the output signal of the sensor; and

wherein a mathematical formulation for the likelihood that the extracted feature vector is a member b i of a breach class set {b i } comprises:

arg max i {P(b i |O)},

where P(b i |O) represents the likelihood of b i given O.

5. The system of claim 4 , wherein the controller is further configured to compute the likelihood P(b i |O) by using Bayes' rule given by:

P ( b i |O )= P ( O|b i ) P ( b i )/ P ( O ),

where

P(O|b i ) represents the likelihood of O given b i ,

P(b i ) represents the likelihood of b i , and

P(O) represents the likelihood of O.

6. The system of claim 5 , wherein the controller is further configured to compute the one or more likelihoods by adopting a GMM (Gaussian Mixture Model) parametric model for each member b i of the set {b i }, and estimating one or more GMM parameters for said parametric model to compute a conditional density P(O|b i ), where P(O|b i ) represents the probability of O given b i .

7. The system of claim 6 , wherein a mathematical formulation of the likelihood P(b i |O), in the adopted GMM parametric model, comprises:

P

⁡

(

b

i

|

O

)

=

∑

m

=

1

M

⁢

C

i

⁢

N

⁡

(

O

;

μ

m

;

Σ

m

)

;

wherein

N(O; μ m ; Σ m ) is a multivariate Gaussian distribution,

C i are constants,

μ m are mean vectors, and

Σ m are covariance matrices; and

wherein C i , μ m , and Σ m are unknown GMM parameters.

8. The system of claim 7 , wherein the controller is configured to estimate the unknown GMM parameters C i , μ m , and Σ m using one of:

a Baum-Welch re-estimation;

an EM (expectation-maximization) algorithm; and

an MLE (maximum likelihood estimation) algorithm.

9. The system of claim 8 , wherein the controller is further configured to choosing the breach class within the set {b i } that has the maximum likelihood by performing Viterbi decoding.

10. The system of claim 1 , further comprising an amplifier subsystem, wherein the amplifying subsystem includes a variable gain pre-amplifier configured to remotely adjust gain of the output signal by normalizing energy level of background and noise in the output signal.

11. The system of claim 10 , wherein the amplifier subsystem further includes a bandpass filter having a variable frequency range and a variable cutoff frequency; and wherein the frequency range of the bandpass filter is remotely adjustable.

12. The system of claim 10 , wherein the source of the seismic vibration is a human footstep, and wherein the frequency range of the bandpass filter is between about 0.1 Hz to about 50 Hz.

13. The system of claim 10 , wherein the source of the seismic vibration comprises one of a human footstep and a moving vehicle, wherein the controller is further configured to discriminate between the human footstep and the moving vehicle, and wherein the frequency range of the bandpass filter is between about 0.1 Hz to about 200 Hz.

14. The system of claim 1 , wherein the at least one sensor comprises a geophone.

15. The system of claim 1 , wherein the at least one sensor comprises a wireless sensor network.

16. A method of detecting and identifying a security breach, comprising:

detecting seismic vibration from a source, and generating an output signal that represents the detected seismic vibration;

extracting a feature vector from the output signal;

computing one or more likelihoods for the extracted feature vector relative to set {b i } (i=1, . . . , i max ) of breach classes b i ; and

classifying the source of the seismic vibration as a security breach belonging to one of the breach classes b i by choosing a breach class within the set {b i } that has a maximum likelihood.

17. The method of claim 16 , wherein the act of extracting the feature vector from the output signal comprises the acts of:

applying a Fourier transform to the output signal so as to convert the output signal from a time domain signal into a frequency domain signal;

applying to the converted signal a plurality of weighting functions at different frequency bands;

calculating energy of each of the bands; and

applying a discrete cosine transform to the weighted frequency signals based on the computed likelihood, as one of a plurality of security breach events or as background noise.

18. The method of claim 16 , wherein the act of computing the one or more likelihoods for the extracted feature vector relative to set {b i } (i=1, . . . , i max ) of breach classes b i comprises the acts of:

adopting a GMM (Gaussian Mixture Model) parametric model for each member b i of the set {b i }; and

estimating one or more GMM parameters for said parametric model to compute a conditional density P(O|b i ), where P(O|b i ) represents the probability of O given b i .

19. The method of claim 18 , wherein a mathematical formulation of the likelihood P(b i |O) in the adopted GMM parametric model comprises:

P

⁡

(

b

i

|

O

)

=

∑

m

=

1

M

⁢

C

i

⁢

N

⁡

(

O

;

μ

m

;

Σ

m

)

;

wherein

N(O; μ m ; Σ m ) is a multivariate Gaussian distribution,

C i are constants,

μ m are mean vectors, and

Σ m are covariance matrices; and

wherein C i , μ m and Σ m are GMM parameters.

20. The method of claim 19 , wherein the act of estimating the GMM parameters C i , μ m and Σ m comprises at least one of:

performing a Baum-Welch re-estimation;

using an EM (expectation-maximization) algorithm; and

using an MLE (maximum likelihood estimation) algorithm.

21. The method of claim 16 , wherein the act of choosing the breach class within the set {b i } that has the maximum likelihood comprises the act of performing Viterbi decoding.

22. The method of claim 16 , further comprising the act of wirelessly transmitting to a command center one of:

data representative of the detected seismic vibration; and

data representative of the classified security breach.

23. A computer-readable storage medium having stored therein computer-readable instructions for a processing system, wherein said instructions when executed by said processor cause said processing system to:

extracting a feature vector from an output signal of a seismic sensor;

compute one or more likelihoods for the extracted feature vector relative to a set {b i } (i=1, . . . , i max ) of breach classes b i ; and

choose a breach class within the set {b i } that has a maximum likelihood.

24. A wireless transmitter, wherein the wireless transmitter is configured to:

receive from one or more geophones vibration data representative of seismic vibration detected by the geophones, and transmit the vibration data to a command center;

receive from a detecting system security breach data representative of a security breach that has been detected by the detecting system by extracting a feature vector from the vibration data detected by the geophones, and computing one or more likelihoods of the extracted feature vector relative to set {bi} (I=1, . . . , imax) of breach classes bi, and choosing a breach class within the set {bi} that has a maximum likelihood relative to the extracted feature vector; and

transmit the security breach data to the command center.

25. The system of claim 1 , further comprising a wireless transmitter configured to transmit, to a command center, one of:

data representative of the detected seismic vibration; and

data representative of the detected security breach.