Detection of transient signals in doppler spectra

• US 8,022,864 B2
• Filed: 11/08/2007
• Issued: 09/20/2011
• Est. Priority Date: 11/08/2007
• Status: Expired due to Fees

• Current Assignee: The United States of America As Represented By The Secretary of Commerce
• Original Assignee: THE GOVERNMENT OF THE UNITED STATES OF AMERICA, AS REPRESENTED BY THE SECRETARY OF COMMERCE
• Inventors: Jordan, James Ronald, Churnside, James Harwood, Johnston, Paul Ernest
• Primary Examiner(s): Gregory; Bernarr
• Application Number:
  US11/937,262
• Publication Number:
  US 20110034142A1
• Time in Patent Office: 1,412 Days
• Field of Search: 342 89-103, 342/159, 342/175, 342192-197, 342/13, 342 26 R- 26 D, 342/27, 342/28, 342/42, 342/44, 342/198, 342/350, 342/351, 342/378, 342/379, 342/381, 342/385, 342/417, 342/418, 342/448, 342450-465, 367/135, 702 1- 4, 702/57, 324/72, 731/701.6, 731/702.4
• US Class Current: 342/192
• CPC Class Codes: G01S 7/021 Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals

Abstract

Signal processing is used to detect transient signals in the presence of noise. Two embodiments are disclosed. In both embodiments, the time series from a remote sensor is broken into a number of short time series. The power spectrum of each short time series are then calculated along with the mean noise level. The moments of each peak in every power spectrum are calculated and the peak with the largest power selected from each power spectrum. A histogram of the moments from these selected peaks is generated and normalized to become a measured PDF. In addition, a pre-determined PDF is derived, in the same method as above, from theoretically calculated noise, numerically simulated noise, or measured noise. Comparison between the measured and pre-determined PDF'"'"'s establish the detection of a transient signal. The first embodiment compares the area between the measured and pre-determined PDF'"'"'s against a threshold to determine detection. In a second embodiment, the differences between the measured and pre-determined PDF'"'"'s are weighted and summed to form a score. This score is compared to a threshold to determine detection.

Claims

1. A method of detecting transient signals in a power spectrum comprising a measured signal and noise, the method comprising the steps of:

generating a power spectrum from the measured signal and noise;

determining, from the power spectrum, peaks in the power spectrum;

generating at least one histogram of moments for peaks in the power spectrum;

normalizing the at least one histogram of the moments by its area to produce a measured Probability Density Function (PDF);

comparing a difference between the measured PDF with a predetermined PDF to determine if a signal is present.

2. The method of claim 1, wherein the step of generating a power spectrum comprises the steps of:

breaking up the measured signal and noise into a series of short blocks to generate a histogram of spectral width.

3. The method of claim 1, wherein the step of determining, from the power spectrum, peaks in the power spectrum comprises the steps of:

determining, from the power spectrum, a mean noise level; and

determining, from the mean noise level, peaks in the power spectrum.

4. The method of claim 1, wherein the step of generating at least one histogram of moments for peaks in the power spectrum comprises the steps of:

calculating moments for at least one or more of power, velocity, spectral width, skewness, and kurtosis for each peak in the power spectrum;

selecting the largest signal power peak from each individual power spectrum; and

generating a histogram of the moments.

5. The method of claim 1, wherein the step of comparing a difference between the measured PDF with a pre-determined PDF to determine if a signal is present comprises the steps of:

assigning a weight to each of a plurality of bins in the PDF;

calculating differences between the measured PDF with the pre-determined PDF;

multiplying the differences by a weight assigned to a corresponding bin to produce weighted differences;

summing the weighted differences between the measured PDF and the pre-determined PDF to produce a summed value; and

comparing the summed value with a predetermined threshold value to determine if a signal is present.

6. The method of claim 5, wherein the step of comparing the summed value with a pre-determined threshold value to determine if a signal is present comprises the steps of:

comparing the spectral width using a predetermined number of bins narrower than an expected transient signal;

if the measured PDF value is larger than the pre-determined PDF value, weighting the difference by multiplying the difference by an associated weight for each bin;

summing the weighted differences as a score for each group of data; and

comparing each score against an empirically determined output threshold, wherein scores greater than the predetermined threshold are considered signal detections.

7. The method of claim 1, wherein the predetermined PDF is determined from the steps of:

generating, using a model, simulated spectra containing pure noise;

generating moments from the simulated spectra to generate the predetermined PDF.

8. The method of claim 7, wherein the step of generating, using a model, simulated spectra containing pure noise comprises the steps of iteratively running the model a plurality of times, and wherein the step of generating moments from the simulated Doppler spectra to generate the predetermined PDF comprises the step of generating moments from each run of the model to generate the predetermined PDF.

9. The method of claim 1, wherein the predetermined PDF is determined from the steps of:

inputting noise data comprising a time series of one or more of numerically simulated noise, measured noise data, and theoretically calculated noise data generated from a model; and

generating a histogram of at least one largest signal power peak to produce the predetermined PDF.

10. The method of claim 9, wherein the step of generating a histogram of at least one largest signal power peak to produce the predetermined PDF comprises the steps of:

breaking the time series into a series of short blocks of noise data;

calculating a power spectrum of the noise data from the short blocks of noise data;

calculating a mean noise level from the power spectrum of the noise data;

determining peaks in the power spectrum of the noise data from the mean noise level of the power spectrum;

calculating moments, including one or more of power, velocity, and spectral width for each peak in the power spectrum;

selecting at least one largest signal power peak from the power spectrum;

generating a histogram of the at least one largest signal power peak; and

normalizing the histogram to produce the predetermined PDF.

11. An apparatus for detecting transient signals in Doppler spectra comprising a measured signal and noise, the apparatus comprising:

a radar receiver for receiving a radar signal comprising a measured signal and noise;

a Fast Fourier Transform, coupled to the radar receiver, for generating a power spectrum from the magnitude squared of the Fast Fourier Transform of the radar signal;

a histogram generator, coupled to the moment calculator, for selecting a largest signal power peak from each individual power spectrum, generating a histogram of the moments, and normalizing the histogram by its area to produce a measured Probability Density Function (PDF).

12. The apparatus of claim 11, wherein the moment calculator calculates moments for at least one of power, velocity, spectral width, skewness, and kurtosis for each peak in the power spectrum.

13. The apparatus of claim 11, further comprising:

a parser, coupled to the radar receiver and the Fast Fourier Transform, for parsing the measured signal and noise into a series of short data blocks to generate a statistically robust histogram of spectral widths and outputting the series of short data blocks to the Fast Fourier Transform for generating the power spectrum.

14. The apparatus of claim 11, further comprising:

a peak detector, coupled to the Fast Fourier Transform and the histogram generator, for calculating a mean noise level and detecting peaks above the noise level.

15. The apparatus of claim 14, further comprising:

moment calculator, coupled to the peak detector, for calculating moments for at least one peak in the power spectrum.

16. The apparatus of claim 11, further comprising:

a memory for storing a predetermined PDF;

a multiplier for assigning a weight to each of the bins in the PDF;

a comparator, for comparing the measured PDF with the pre-determined PDF stored in the memory by calculating differences between the bins of the measured PDF and the corresponding bins of the pre-determined PDF and multiplying the differences by corresponding weights for each bin.

17. The apparatus of claim 16, wherein the comparator sums the weighted differences between the measured PDF and the pre-determined PDF and compares the sum with a pre-determined threshold value to determine if a signal is present.

18. The apparatus of claim 17, herein the comparator uses a number of bins less than the width of an expected transient signal, and if the measured PDF value is larger than the pre-determined PDF value, the difference is weighted by multiplying the difference by an associated weight, the sum of these weighted differences is recorded as the score for each group of data, and each score is compared against an empirically determined output threshold to determine if a signal is present.

19. The apparatus of claim 11, wherein the predetermined PDF is determined from noise data comprising a time series of one or more of numerically simulated noise, measured noise data, and theoretically calculated noise data generated from a model;

and a histogram is generated of at least one largest signal power peak to produce the predetermined PDF.

20. The apparatus of claim 19, wherein the histogram is generated by breaking the time series into a series of short blocks of noise data;

calculating a power spectrum of the noise data from the short blocks of noise data;

calculating a mean noise level from the power spectrum of the noise data;

determining peaks in the power spectrum of the noise data from the mean noise level of the power spectrum;

calculating moments, including one or more of power, velocity, spectral width, skewness, and kurtosis for each peak in the power spectrum;

selecting at least one largest signal power peak from the power spectrum;

generating a histogram of the at least one largest signal power peak; and

normalizing the histogram to produce the predetermined PDF.