Post on 19-Dec-2015
2003 MSS BA C-81
Acoustic Source Estimation with Acoustic Source Estimation with Doppler ProcessingDoppler Processing
Richard J. KozickRichard J. Kozick
Bucknell UniversityBucknell University
Brian M. SadlerBrian M. Sadler
Army Research LaboratoryArmy Research Laboratory
2003 MSS BA C-82
Why Doppler?
x
y
SourcePath
Sensor 1fd,1
Sensor 5fd,5
Sensor 2fd,2
Sensor 3fd,3
Sensor 4fd,4
2003 MSS BA C-83
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
2003 MSS BA C-84
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
2003 MSS BA C-85
Signal Observed at One Sensor
• Sinusoidal signal emitted by moving source:
• Phenomena that determine the signal at the sensor:
1. Transmission loss
2. Propagation delay (and Doppler)
3. Additive noise (thermal, wind, interference)
4. Scattering by turbulence (random)
tfSts o2cos)( refref
2003 MSS BA C-86
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 parameter:Average signal energy remains constant
2003 MSS BA C-87
Propagation Delay & Doppler ososs
ososs
ttyyty
ttxxtx
,
,
)(
)(
oooro tttv
ct
c
tdt 18if
1)(
)()(
:n timePropagatio
2/121,
21, :Distance yyxxtd ososo
ososso
oss
o
osor tytxy
td
yyx
td
xxtv sincos
: velocityRadial
1,1,
Source Path: (xs(t), ys(t))
Sensor at (x1, y1)
toto + T
ot
otd
2003 MSS BA C-88
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):
oor
o
o
oo
ttc
tvtt
tfSts
Tttttwttstz
)()(
2cos)(
),()()(
2003 MSS BA C-89
No Scattering
• Complex envelope at frequency fo:
• Pure sinusoid in additive noise
• Doppler frequency shift is proportional to the source frequency, fo
shiftfrequency Doppler
)(~2expexp
)(~2expexp)(~
oor
d
od
ooor
oo
fc
tvf
twttfjjS
twttfc
tvjtjStz
2003 MSS BA C-810
Signal Observed at One Sensor
• Sinusoidal signal emitted by moving source:
• Phenomena that determine the signal at the sensor:
1. Transmission loss
2. Propagation delay (and Doppler)
3. Additive noise (thermal, wind, interference)
4. Scattering by turbulence (random)
tfSts o2cos)( refref
2003 MSS BA C-811
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, in [0, 1]– Varies w/ source range, frequency, and meteorological
conditions (sunny, cloudy)
• Easier to see with a picture:
)(~2expexp)(~
2expexp1)(~
twttfjjtvS
ttfjjStz
od
od
2003 MSS BA C-812
Power Spectrum (PSD)
Freq.
PSD
AWGN, 2No
-B/2 B/20
(1- )S
-fd
Bv = Bandwidth of scattered component
Area= S
B = Processing bandwidth
-fd = Doppler freq. shift
SNR = S / (2 No B)
2003 MSS BA C-813
2No
-B/2 B/20
(1- )S
-fd
Bv
S
-B/2 B/20
(1- )S
-fd
Bv
S
Strong Scattering: ~ 1
• Study estimation of Doppler, fd, w/ respect to– Saturation, (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 ( > 0) causes signal energy fluctuations;may have low signal energy if (Bv T) is small
Weak Scattering: ~ 0
2003 MSS BA C-814
PDF of Signal Energy at Sensor
-20 -15 -10 -5 0 5 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
ENERGY, 10 log10
(P) (dB)
PR
OB
AB
ILIT
Y D
EN
SIT
YPDF OF RECEIVED ENERGY (S=1, SNR = 30 dB)
= 0.02
0.04
0.08
0.20
0.50
1.00
2003 MSS BA C-815
Saturation vs. Frequency & Range
50 100 150 200 250
40
60
80
100
120
140
160
180
200F
RE
QU
EN
CY
(H
z)
RANGE (m)
SATURATION () CONTOURS, MOSTLY SUNNY
= 0.02
0.05
0.1
0.2
0.3
0.9
0.4
0.5
0.6
0.7
0.8
2003 MSS BA C-816
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 < 1/ Bv)
2No
-B/2 B/20
(1- )S
-fd
Bv
S
2003 MSS BA C-817
Model for Sensor Samples
• Vector of samplesis complex Gaussian:
2No
-B/2 B/20
(1- )S
-fd
Bv
S
BfNj
Bfj
d
d
/)1(2exp
/2exp
1
a
IaaRaz BNSSe
TNz
Tz
z
oH
vj
s
s 2,-1CN~
1~
)(~)0(~
~~
Mean Covariance ofscattered samples
AWGN
2003 MSS BA C-818
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:– = 1 (fully saturated, random signal)– = 0 (no scattering, deterministic signal)
• We evaluate CRB for 0 < < 1 with discrete-time (sampled) model
2003 MSS BA C-819
2No
-B/2 B/20
S
-fd -B/2 B/20 -fd
Bv
S
Fully Saturated: = 1No Scattering: = 0 dv ffGS ~
S
N
Tf od 322
3ˆCRB
12
0
1 )(logˆCRB
dxxGdx
d
T
Bf vd
vvv B
fG
BfG 1~
1
High SNR = S/(2 No B), Large (Bv T)
Schultheiss & Weinstein [JASA, 1979]
2003 MSS BA C-820
Example 1: Vary Bv &
• SNR = 28.5 dB
• B = 7 Hz
• T = 1 sec
• Bv from 0.1 Hz to 2.0 Hz
• True fd = -0.2 Hz
2No
-B/2 B/20
(1- )S
-fd
Bv
S
2003 MSS BA C-821
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.05
0.1
0.15
0.2
0.25
0.3
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
Bv = 0.1
0.5
1.0
1.5
2.0
SAMPLEDSCHULTHEISS-WEINSTEIN
(Bv T)is notlarge
2003 MSS BA C-822
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10-2
10-1
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
SAMPLEDSCHULTHEISS-WEINSTEIN
2003 MSS BA C-823
Example 2: Vary T &
• SNR = 28.5 dB
• B = 7 Hz
• Bv = 1 Hz
• T from 0.5 sec to 10 sec
• True fd = -0.2 Hz
2No
-B/2 B/20
(1- )S
-fd
Bv
S
2003 MSS BA C-824
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
T = 0.5
1.0
1.5
2.0
5.010
SAMPLEDSCHULTHEISS-WEINSTEIN
(Bv T)is large
2003 MSS BA C-825
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
-4
10-3
10-2
10-1
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
SAMPLEDSCHULTHEISS-WEINSTEIN
2003 MSS BA C-826
Example 3: Vary SNR &
• T = 1 sec
• B = 7 Hz
• Bv = 1 Hz
• SNR from -1.5 dB to 38.5 dB
• True fd = -0.2 Hz
2No
-B/2 B/20
(1- )S
-fd
Bv
S
2003 MSS BA C-827
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
SNR = -1.5 dB
8.5 dB 18.5 dB
38.5 dB
SAMPLEDSCHULTHEISS-WEINSTEIN
SNRfloor
2003 MSS BA C-828
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
-3
10-2
10-1
SATURATION
sqrt
(CR
B)
(Hz)
CRB on fd
SAMPLEDSCHULTHEISS-WEINSTEIN (Bv T)
is notlarge
No SNRfloor
2003 MSS BA C-829
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
50 100 150 200 250
40
60
80
100
120
140
160
180
200
FR
EQ
UE
NC
Y (
Hz)
RANGE (m)
SATURATION () CONTOURS, MOSTLY SUNNY
= 0.02
0.05
0.1
0.2
0.3
0.9
0.4
0.5
0.6
0.7
0.8
T=1 s, B=10 Hz, Bv=0.1 Hz
2003 MSS BA C-830
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
2003 MSS BA C-831
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
2003 MSS BA C-832
Differential Doppler Estimation
7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100
9200
9300
9400
9500
9600
9700
9800
9900
EAST (m)
NO
RT
H (
m)
GROUND VEHICLE PATH AND ARRAY LOCATIONS
VEHICLE PATH10 SEC SEGMENTARRAY 1ARRAY 3ARRAY 4ARRAY 5
1
3
4
5
2003 MSS BA C-833
Differential Doppler Estimation
340 341 342 343 344 345 346 347 348 349-1.25
-1.2
-1.15
-1.1
-1.05
-1
-0.95
-0.9
TIME (sec)
FR
EQ
UE
NC
Y S
HIF
T (
Hz)
DIFFERENTIAL DOPPLER FREQUENCY SHIFT FOR ARRAYS 1 AND 3
SQRT(CRB) = 0.1 Hz
GPS GROUND TRUTHESTIMATESMEAN ESTIMATE
2003 MSS BA C-834
7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100
9200
9300
9400
9500
9600
9700
9800
9900
EAST (m)
NO
RT
H (
m)
GROUND VEHICLE PATH AND ARRAY LOCATIONS
VEHICLE PATH10 SEC SEGMENTARRAY 1ARRAY 3ARRAY 4ARRAY 5
1
3
4
5
340 341 342 343 344 345 346 347 348 349-1.25
-1.2
-1.15
-1.1
-1.05
-1
-0.95
-0.9
TIME (sec)
FR
EQ
UE
NC
Y S
HIF
T (
Hz)
DIFFERENTIAL DOPPLER FREQUENCY SHIFT FOR ARRAYS 1 AND 3
SQRT(CRB) = 0.1 Hz
GPS GROUND TRUTHESTIMATESMEAN ESTIMATE
2003 MSS BA C-835
Continuing Work
• ACIDS database, exploiting >1 harmonic
• Extend CRBs from differential Doppler to source localization with >= 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?
2003 MSS BA C-836
Bearings & Doppler
x
y
SourcePath
Sensor 1fd,1
Sensor 5fd,5
Sensor 2fd,2
Sensor 3fd,3
Sensor 4fd,4