Acoustic%20Source%20Estimation%20with%20Doppler%20Processing

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Acoustic Source Estimation with Doppler Processing

• Richard J. Kozick
• Bucknell University
• Brian M. Sadler
• Army Research Laboratory

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Why Doppler?
Sensor 2 fd,2
Sensor 1 fd,1
y
Source Path
Sensor 3 fd,3
Sensor 5 fd,5
Sensor 4 fd,4
x
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Outline

• Model for sensor data
• Sum-of-harmonics source
• Propagation with atmospheric scattering
• Frequency estimation w/ scattered signals
• Cramer-Rao bounds, differential Doppler
• Varies with range, frequency, weather cond.
• Examples, measured data processing
• Extension Localization accuracy with Doppler

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Source Signal Models

• Sum of harmonics
• Internal combustion engines (cylinder firing)
• Tread slap, tire rotation
• Helicopter blade rotation
• Broadband spectra from turbine engines
• Time-delay estimation may be feasible
• Focus on harmonic spectra in this talk
• Differential Doppler estimation ? localization

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Signal Observed at One Sensor

• Sinusoidal signal emitted by moving source
• Phenomena that determine the signal at the
  sensor
• Transmission loss
• Propagation delay (and Doppler)
• Additive noise (thermal, wind, interference)
• Scattering by turbulence (random)

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Transmission Loss

• Energy is diminished from Sref (at 1 m from
  source) to value S at sensor
• Spherical spreading
• Refraction (wind temperature gradients)
• Ground interactions
• Molecular absorption
• We model S as a deterministic parameterAverage
  signal energy remains constant

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Propagation Delay Doppler
Source Path (xs(t), ys(t))
to
to T
Sensor at (x1, y1)
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No Scattering

• Sensor signal with transmission loss,propagation
  delay, and additive noise
• Complex envelope at frequency fo(i.e., spectrum
  at fo shifted to 0 Hz)

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No Scattering

• Complex envelope at frequency fo
• Pure sinusoid in additive noise
• Doppler frequency shift is proportional to the
  source frequency, fo

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Signal Observed at One Sensor

• Sinusoidal signal emitted by moving source
• Phenomena that determine the signal at the
  sensor
• Transmission loss
• Propagation delay (and Doppler)
• Additive noise (thermal, wind, interference)
• Scattering by turbulence (random)

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With Scattering

• A fraction of the signal energy is scattered from
  a pure sinusoid into a zero-mean, narrowband
  random process Wilson et. al.
• Saturation parameter, W in 0, 1
• Varies w/ source range, frequency, and
  meteorological conditions (sunny, cloudy)
• Easier to see with a picture

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Power Spectrum (PSD)
PSD
(1- W)S
Area WS
AWGN, 2No
-B/2
B/2
-fd
0
Freq.
B Processing bandwidth
Bv Bandwidth of scattered component
-fd Doppler freq. shift
SNR S / (2 No B)
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Strong Scattering W 1
Weak Scattering W 0
(1- W)S
WS
WS
(1- W)S
2No
-fd
0
-fd
0
-B/2
B/2
-B/2
B/2
Bv
Bv

• Study estimation of Doppler, fd, w/ respect to
• Saturation, W (analogous to Rayleigh/Rician
  fading)
• Processing bandwidth, B, and observation time, T
• SNR S / (2 No B)
• Scattering bandwidth, Bv (correlation time
  1/Bv)
• Scattering (W gt 0) causes signal energy
  fluctuationsmay have low signal energy if (Bv
  T) is small

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PDF of Signal Energy at Sensor
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Saturation vs. Frequency Range
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Model for Sensor Samples

• Gaussian randomprocess with non-zero mean
• Sample at rate Fs B, spacing Ts 1/B
• Observe for T sec, so N BT samples with
• Independent AWGN
• Correlated scattered signal (Ts lt 1/ Bv)

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Model for Sensor Samples

• Vector of samplesis complex Gaussian

Mean
Covariance ofscattered samples
AWGN
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Cramer-Rao Bound (CRB)

• CRB is a lower bound on the variance of unbiased
  estimates of fd
• Schultheiss Weinstein JASA, 1979 provided
  CRBs for special cases
• W 1 (fully saturated, random signal)
• W 0 (no scattering, deterministic signal)
• We evaluate CRB for 0 lt W lt 1 with discrete-time
  (sampled) model

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Fully Saturated W 1
No Scattering W 0
S
S
2No
-fd
0
-fd
0
-B/2
B/2
-B/2
B/2
Bv
Schultheiss Weinstein JASA, 1979
High SNR S/(2 No B), Large (Bv T)
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Example 1 Vary Bv W

• SNR 28.5 dB
• B 7 Hz
• T 1 sec
• Bv from 0.1 Hz to 2.0 Hz
• True fd -0.2 Hz

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(Bv T) is not large
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Example 2 Vary T W

• SNR 28.5 dB
• B 7 Hz
• Bv 1 Hz
• T from 0.5 sec to 10 sec
• True fd -0.2 Hz

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(Bv T) is large
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Example 3 Vary SNR W

• T 1 sec
• B 7 Hz
• Bv 1 Hz
• SNR from -1.5 dB to 38.5 dB
• True fd -0.2 Hz

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SNRfloor
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(Bv T) is not large
No SNRfloor
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CRBs with Saturation Model

• Value of harmonics for Doppler est.?
• Fundamental frequency 15 Hz
• Process harmonics 3, 6, 9, 12 ? 45, 90, 135, and
  180 Hz
• Range 5 to 320 m
• SNR (Range)-2

T1 s, B10 Hz, Bv0.1 Hz
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W 5 m 10 m 20 m 40 m 80 m 160 m 320 m
45 Hz .004 .008 .02 .03 .06 .12 .23
90 Hz .02 .03 .06 .12 .23 .41 .65
135 Hz .04 .07 .13 .25 .44 .69 .90
180 Hz .06 .12 .23 .41 .65 .88 .98
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CRB 5 m 10 m 20 m 40 m 80 m 160 m 320 m
45 Hz .006 .009 .01 .02 .04 .07 .13
90 Hz .01 .01 .02 .03 .05 .09 .19
135 Hz .01 .02 .03 .04 .05 .09 .20
180 Hz .02 .02 .03 .04 .05 .09 .21
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Differential Doppler Estimation
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Differential Doppler Estimation
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Continuing Work

• ACIDS database, exploiting gt1 harmonic
• Extend CRBs from differential Doppler to source
  localization with gt 5 sensors
• Use CRBs to test the value of using differential
  Doppler with bearings for localization
• Include coherence losses due to scattering in the
  bearing results
• Frequency estimates may already be available at
  the nodes
• Use Doppler to help data association?

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Bearings Doppler
Sensor 2 fd,2
Sensor 1 fd,1
y
Source Path
Sensor 3 fd,3
Sensor 5 fd,5
Sensor 4 fd,4
x