1 12 April 2004 SPIE 2004 Algorithms and Performance of Small Baseline Acoustic Sensor Arrays Brian M. Sadler, Army Research Lab Richard J. Kozick, Bucknell University Sandra L. Collier, Army Research Lab Acknowledgments: D.K. Wilson and T. Pham 12 April 2004

2 12 April 2004 SPIE 2004 Motivation Frequency range for aeroacoustics: Freq. in [30, 250] Hz  in [1.3, 11] m Large array  better AOA accuracy Small array: –Cheaper, disposable(?) –Easier to deploy, more covert –What performance is achievable? Effects of turbulence –Saturation,  –Signal coherence, 

3 12 April 2004 SPIE 2004 SenTech HE01 acoustic sensor (Pictures from Prado & Succi, SPIE AeroSense 2002) Example of a Small-Aperture Sensor

4 12 April 2004 SPIE 2004 Outline Brief review of source characteristics (ground vehicles, aircraft) Physics-based statistical model for turbulence (saturation=  coherence=  AOA estimation accuracy: –Cramer-Rao bounds (CRBs) –Performance of practical algorithms (achieve CRB?) Questions: –What is the achievable accuracy with small-baseline acoustic arrays? –When is the ideal plane wave model valid (i.e., turbulence is negligible)? Useful for system design

5 12 April 2004 SPIE 2004 Source Characteristics Ground vehicles (tanks, trucks), aircraft (rotary, jet), commercial vehicles  LOUD Main contributors to source sound: –Rotating machinery: Engines, aircraft blades –Tires and “tread slap” (spectral lines) –Vibrating surfaces Internal combustion engines: Sum-of-harmonics due to cylinder firing Turbine engines: Broadband “whine” Key features: Spectral lines and high SNR

6 12 April 2004 SPIE /- 125 m from CPA TIME (sec) Hz

7 12 April 2004 SPIE 2004 Signal Model at One Sensor Sinusoidal signal emitted by moving source: Phenomena that determine the signal at the sensor: 1.Propagation delay (and Doppler) 2.Additive noise (thermal, wind, interference) 3.Transmission loss (TL) 4.Scattering by turbulence (random)

8 12 April 2004 SPIE 2004 Transmission Loss Energy is diminished from S ref (at 1 m from source) to value S at sensor: –Spherical spreading –Refraction (wind & temp. gradients) –Ground interactions –Molecular absorption We model S as a deterministic parameter:  Average signal energy Low Pass Filter Numerical solution

9 12 April 2004 SPIE /- 125 m from CPA Frequency dependent Transmission Loss

10 12 April 2004 SPIE 2004 No Scattering Sensor signal with transmission loss,propagation delay, and AWG noise: Complex envelope at frequency f o –Spectrum at f o shifted to 0 Hz –FFT amplitude at f o

11 12 April 2004 SPIE 2004 With Scattering A fraction of the signal energy is scattered from a pure sinusoid into a zero-mean, narrowband, Gaussian random process Saturation parameter,  in [0, 1] –Varies w/ source range, frequency, and meteorological conditions (sunny, windy) –Based on physical modeling of sound propagation through random, inhomogeneous medium [add ref] Easier to see scattering effect with a picture:

12 12 April 2004 SPIE 2004 AWGN, 2N o -B/2B/2 0 (1-  )S BvBv SS -B/2B/2 0 (1-  )S BvBv SS Important quantities: –Saturation,  (analogous to Rayleigh/Rician fading in comms.) –Processing bandwidth, B, and observation time, T –SNR = S / (2 No B) –Scattering bandwidth, B v (correlation time ~ 1/B v ) –Number of independent samples ~ T/B v  often small Scattering (  > 0) causes signal energy fluctuations Weak Scattering:  ~ 0Strong Scattering:  ~ 1 Freq. Power Spectral Density (PSD)

13 12 April 2004 SPIE 2004 Probability Distributions Complex amplitude has complex Gaussian PDF with non-zero mean: Energy has non-central  -squared PDF with 2 d.o.f. has Rice PDF

14 12 April 2004 SPIE 2004 Saturation vs. Frequency & Range Saturation depends on [Ostashev & Wilson]: –Weather conditions (sunny/cloudy), but varies little with wind speed –Source frequency  and range d o Theoretical form Constants from numerical evaluation of particular conditions

15 12 April 2004 SPIE 2004 Turbulence effects are small only for very short range and low frequency Fully scattered Saturation varies over entire range [0, 1] for typical values

16 12 April 2004 SPIE 2004 Model for Two Sensors  sensor spacing   AOA Turbulence effects Perfect plane wave:  = 0 or 1  = 1

17 12 April 2004 SPIE 2004 Model for Coherence,  Assume AOA  = 0, freq. in [30, 500] Hz Recall saturation model: Coherence model [Ostashev & Wilson 2000]:  sensor spacing  d o = range Velocity fluctuations Temperature fluctuations   0 with freq., sensor spacing, and range

18 12 April 2004 SPIE 2004 Velocity fluctuations Temperature fluctuations Depends on wind level and sunny/cloudy

19 12 April 2004 SPIE 2004 Coherence, , for sensor spacing  = 12 inches  > 0.99 for range < 100 m Is this “good”? Curves move up w/ less wind, down w/ more wind

20 12 April 2004 SPIE 2004 Impact on AOA Estimation How does the turbulence ( ,  ) affect AOA estimation accuracy? –Cramer-Rao lower bound (CRB), simulated RMSE –Achievable accuracy with small arrays? Larger sensor spacing,  : DESIRABLE BAD!

21 12 April 2004 SPIE 2004 Special Cases No scattering (ideal plane wave model): High SNR, with scattering: SNR-limited performance Coherence- limited performance If SNR = 30 dB, then  < limits performance!

22 12 April 2004 SPIE 2004 Phase CRB with Scattering Ideal plane wave Coherence loss  0.1

23 12 April 2004 SPIE 2004 CRB on AOA Estimation SNR = 30 dB for all ranges Sensor spacing  = 12 in. Increasing range (fixed SNR) Aperture-limited at low frequency Ideal plane wave model is accurate for very short ranges ~ 10 m Coherence- limited at larger ranges

24 12 April 2004 SPIE 2004 Cloudy and Less Wind SNR = 30 dB for all ranges Sensor spacing  = 12 in. Aperture-limited at low frequency Atmospheric conditions have a large impact on AOA CRBs Plane wave model is accurate to 100 m range

25 12 April 2004 SPIE 2004 Small Sensor Spacing:  = 3 in. SNR = 40 dB, Range = 50 m Coherence is high:  > Saturation  is significant for most of frequency range AOA estimators break away from CRB approx. when  > 0.1 Aperture- limited Phase difference estimator: Also evaluated maximum likelihood (ML) estimator. Turbulence prevents performance gain from larger aperture

26 12 April 2004 SPIE 2004 AOA Estimation for Harmonic Source Equal-strength harmonics at 50, 100, 150 Hz SNR = 40 dB at 20 m range, SNR ~ 1/(range) 2 (simple TL) Sensor spacing  = 3 in. and 6 in. Mostly sunny, moderate wind  = 6 in.  = 3 in. RMSE CRB Achievable AOA accuracy ~ 10’s of degrees for source at 100 m with a small array

27 12 April 2004 SPIE 2004 Turbulence Conditions for Three-Harmonic Example Coherence is close to 1, but still limits performance. Strong scattering

28 12 April 2004 SPIE 2004 Summary of AOA with Small Arrays CRB analysis of AOA estimation –Ideal plane wave model is overly optimistic for longer source ranges *Breakdown point depends on weather cond. –Important to consider turbulence effects –Shows interplay of frequency, range, SNR, array size, and propagation conditions (temp., wind) on performance Performance of phase-difference AOA algorithm is worse than the CRB in turbulence (saturation  > 0.1) Small array (3 in. and 6 in.) AOA performance: –AOA accuracy 10 o at 100 m Similar results for circular arrays with >2 sensors (SNR gain)