Noise reduction technique for monitoring electromagnetic signals

1. A method for analyzing a target electromagnetic signal radiating from a monitored system, comprising:

monitoring the target electromagnetic signal using a set of antennas to obtain a set of received target electromagnetic signals from the monitored system;

calculating a weighted mean of the received target electromagnetic signals using a first pattern-recognition model;

subtracting the received target electromagnetic signals from the weighted mean of the received target electromagnetic signals to obtain a set of noise-reduced signals for the monitored system; and

assessing the integrity of the monitored system by analyzing the noise-reduced signals using a second pattern-recognition model.

2. The method of claim 1 , wherein the first pattern-recognition model and second pattern-recognition model are created using a nonlinear, nonparametric regression technique.

3. The method of claim 2 , wherein the first pattern-recognition model is created by:

monitoring a reference electromagnetic signal radiating from the monitored system using a set of reference antennas to obtain a set of received reference electromagnetic signals;

generating a set of frequency-domain representations of the received reference electromagnetic signals;

dividing each of the frequency-domain representations of the received reference electromagnetic signals into a set of frequencies;

selecting a set of well-correlated frequencies from the frequency-domain representations of the received reference electromagnetic signals;

constructing a set of reference electromagnetic-signal amplitude-time series for each of the well-correlated frequencies based on the received reference electromagnetic signals collected over a first predetermined time period; and

training the first pattern-recognition model using the reference electromagnetic-signal amplitude-time series.

4. The method of claim 3 , wherein the second pattern-recognition model is created by:

calculating a weighted mean of the received reference electromagnetic signals obtained from the reference antennas using the first pattern-recognition model;

subtracting the received reference electromagnetic signals from the weighted mean of the received reference electromagnetic signals to obtain a set of reference noise-reduced signals for the monitored system;

constructing a set of reference electromagnetic-signal fingerprints for each of the well-correlated frequencies from the reference noise-reduced signals obtained over a second predetermined time period; and

training the second pattern-recognition model using the reference electromagnetic-signal fingerprints.

5. The method of claim 4 , wherein calculating the weighted mean of the received target electromagnetic signals involves:

for each frequency from the frequencies of each of the received target electromagnetic signals:

determining a standard deviation of the frequency using the first pattern-recognition model;

calculating a weight for the frequency, wherein the weight is inversely proportional to the standard deviation of the frequency;

multiplying a monitored amplitude-time series of the frequency with the weight to obtain a weighted amplitude-time series for the frequency; and

using the weighted amplitude-time series to calculate an average amplitude-time series for the frequency.

6. The method of claim 5 , wherein obtaining the noise-reduced signals for the monitored system involves:

for each frequency from the frequencies of each of the received target electromagnetic signals:

subtracting the received target electromagnetic signals from the average amplitude-time series to obtain a noise-reduced amplitude-time series.

7. The method of claim 1 , wherein analyzing the noise-reduced signals using the second pattern-recognition model involves:

generating a target electromagnetic-signal fingerprint from the noise-reduced signals;

feeding the target electromagnetic-signal fingerprint into the second pattern-recognition model;

producing an estimated electromagnetic-signal fingerprint using the second pattern-recognition model; and

comparing the target electromagnetic-signal fingerprint to the estimated electromagnetic-signal fingerprint to detect a statistical deviation in the noise-reduced signals.

8. The method of claim 7 , wherein the statistical deviation is detected using a sequential probability ratio test (SPRT).

9. The method of claim 1 , wherein the antennas include at least one of a near-isotropic antenna and a Universal Serial Bus (USB) interface.

10. A system for analyzing a target electromagnetic signal radiating from a monitored system, comprising:

a set of antennas configured to monitor the target electromagnetic signal to obtain a set of received target electromagnetic signals from the monitored system; and

an analysis apparatus configured to:

calculate a weighted mean of the received target electromagnetic signals using a first pattern-recognition model;

subtract the received target electromagnetic signals from the weighted mean of the received target electromagnetic signals to obtain a set of noise-reduced signals for the monitored system; and

assess the integrity of the monitored system by analyzing the noise-reduced signals using a second pattern-recognition model.

11. The system of claim 10 , wherein the first pattern-recognition model is created by:

monitoring a reference electromagnetic signal radiating from the monitored system using a set of reference antennas to obtain a set of received reference electromagnetic signals;

generating a set of frequency-domain representations of the received reference electromagnetic signals;

dividing each of the frequency-domain representations of the received reference electromagnetic signals into a set of frequencies;

selecting a set of well-correlated frequencies from the frequency-domain representations of the received reference electromagnetic signals;

constructing a set of reference electromagnetic-signal amplitude-time series for each of the well-correlated frequencies based on the received reference electromagnetic signals collected over a first predetermined time period; and

training the first pattern-recognition model using the reference electromagnetic-signal amplitude-time series.

12. The system of claim 11 , wherein the second pattern-recognition model is created by:

calculating a weighted mean of the received reference electromagnetic signals obtained from the reference antennas using the first pattern-recognition model;

subtracting the received reference electromagnetic signals from the weighted mean of the received reference electromagnetic signals to obtain a set of reference noise-reduced signals for the monitored system;

constructing a set of reference noise-reduced amplitude-time series for each of the well-correlated frequencies based on the reference noise-reduced signals obtained over a second predetermined time period; and

training the second pattern-recognition model using the reference noise-reduced amplitude-time series.

13. The system of claim 12 , wherein calculating the weighted mean of the received target electromagnetic signals involves:

for each frequency from the frequencies of each of the received target electromagnetic signals:

determining a standard deviation of the frequency using the first pattern-recognition model;

calculating a weight for the frequency, wherein the weight is inversely proportional to the standard deviation of the frequency;

multiplying a monitored amplitude-time series of the frequency with the weight to obtain a weighted amplitude-time series for the frequency; and

using the weighted amplitude-time series to calculate an average amplitude-time series for the frequency.

14. The system of claim 13 , wherein obtaining the noise-reduced signals for the monitored system involves:

for each frequency from the frequencies of each of the received target electromagnetic signals:

subtracting the average amplitude-time series from the received target electromagnetic signals to obtain a noise-reduced amplitude-time series.

15. The system of claim 10 , wherein the antennas include at least one of a near-isotropic antenna and a Universal Serial Bus (USB) interface.

16. The system of claim 10 , wherein analyzing the noise-reduced signals using the second pattern-recognition model involves:

generating a target electromagnetic-signal fingerprint from the noise-reduced signals;

feeding the target electromagnetic-signal fingerprint into the second pattern-recognition model;

producing an estimated electromagnetic-signal fingerprint using the second pattern-recognition model; and

comparing the target electromagnetic-signal fingerprint to the estimated electromagnetic-signal fingerprint to detect a statistical deviation in the noise-reduced signals.

17. A non-transitory computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for analyzing a target electromagnetic signal radiating from a monitored system, the method comprising:

monitoring the target electromagnetic signal using a set of antennas to obtain a set of received target electromagnetic signals from the monitored system;

calculating a weighted mean of the received target electromagnetic signals using a first pattern-recognition model;

subtracting the received target electromagnetic signals from the weighted mean of the received target electromagnetic signals to obtain a set of noise-reduced signals for the monitored system; and

assessing the integrity of the monitored system by analyzing the noise-reduced signals using a second pattern-recognition model.

18. The non-transitory computer-readable storage medium of claim 17 , wherein the first pattern-recognition model is created by:

monitoring a reference electromagnetic signal radiating from the monitored system using a set of reference antennas to obtain a set of received reference electromagnetic signals;

generating a set of frequency-domain representations of the received reference electromagnetic signals;

dividing each of the frequency-domain representations of the received reference electromagnetic signals into a set of frequencies;

selecting a set of well-correlated frequencies from the frequency-domain representations of the received reference electromagnetic signals;

constructing a set of reference electromagnetic-signal amplitude-time series for each of the well-correlated frequencies based on the received reference electromagnetic signals collected over a first predetermined time period; and

training the first pattern-recognition model using the reference electromagnetic-signal amplitude-time series.

19. The non-transitory computer-readable storage medium of claim 18 , wherein the second pattern-recognition model is created by:

calculating a weighted mean of the received reference electromagnetic signals obtained from the reference antennas using the first pattern-recognition model;

subtracting the received reference electromagnetic signals from the weighted mean of the received reference electromagnetic signals to obtain a set of reference noise-reduced signals for the monitored system;

constructing a set of reference residual amplitude-time series for each of the well-correlated frequencies based on the reference noise-reduced signals obtained over a second predetermined time period; and

training the second pattern-recognition model using the reference residual amplitude-time series.

20. The non-transitory computer-readable storage medium of claim 19 , wherein calculating the weighted mean of the received target electromagnetic signals involves:

for each frequency from the frequencies of each of the received target electromagnetic signals:

determining a standard deviation of the frequency using the first pattern-recognition model;

calculating a weight for the frequency, wherein the weight is inversely proportional to the standard deviation of the frequency;

multiplying a monitored amplitude-time series of the frequency with the weight to obtain a weighted amplitude-time series for the frequency; and

using the weighted amplitude-time series to calculate an average amplitude-time series for the frequency.