1. 2004 MSS AC C-05 24 August 2004 1 Acoustic Sensor Arrays with Small Baseline Richard J. Kozick, Bucknell University Brian M. Sadler, Army Research Lab Sandra L. Collier, Army Research Lab Acknowledgments: D.K. Wilson and T. Pham 24 August 2004

2. 2004 MSS AC C-05 24 August 2004 2 Motivation Freq. in [30, 250] Hz  in [1.3, 11] m Angle of arrival (AOA) accuracy w.r.t. –Array aperture size –Turbulence ( ,  ) Small aperture: –Cheaper, disposable –Easier to deploy –More covert –Better coherence –How small can we go? SenTech HE01 acoustic sensor [Prado2002]

3. 2004 MSS AC C-05 24 August 2004 3 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)? Implications for system design

4. 2004 MSS AC C-05 24 August 2004 4 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

5. 2004 MSS AC C-05 24 August 2004 5 Signal Model at One Sensor Sinusoidal signal emitted by moving source: Signal at the sensor: 1.Propagation delay,  2.Additive noise 3.Transmission loss 4.Turbulent scattering

6. 2004 MSS AC C-05 24 August 2004 6 Transmission Loss Energy is diminished from S ref (at 1 m from source) to 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 [Wilson2002] +/- 125 m from CPA [Embleton1996]

7. 2004 MSS AC C-05 24 August 2004 7 Sensor Signal: 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

8. 2004 MSS AC C-05 24 August 2004 8 Sensor Signal: 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 Illustration in the frequency domain: [Norris2001, Wilson2002a]

9. 2004 MSS AC C-05 24 August 2004 9 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 1 sec) –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)

10. 2004 MSS AC C-05 24 August 2004 10 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 (Experimental validation in [Daigle1983, Bass1991, Norris2001])

11. 2004 MSS AC C-05 24 August 2004 11 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

12. 2004 MSS AC C-05 24 August 2004 12 Turbulence effects are small only for very short range and low frequency Fully scattered Saturation varies over entire range [0, 1] for typical values

13. 2004 MSS AC C-05 24 August 2004 13 Signal Model for Two Sensors  sensor spacing   AOA Turbulence effects Perfect plane wave:  = 0 or 1  = 1

14. 2004 MSS AC C-05 24 August 2004 14 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

15. 2004 MSS AC C-05 24 August 2004 15 Velocity fluctuations Temperature fluctuations Depends on wind level and sunny/cloudy

16. 2004 MSS AC C-05 24 August 2004 16  > 0.99 for range < 100 m Is this “good”? Curves move up w/ less wind, down w/ more wind Coherence, , versus frequency and range for sensor spacing  = 12 inches

17. 2004 MSS AC C-05 24 August 2004 17 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!

18. 2004 MSS AC C-05 24 August 2004 18 Special Cases of CRB No scattering (ideal plane wave model): High SNR, with scattering: SNR-limited performance Coherence- limited performance If SNR = 30 dB, then  < 0.9989995 limits performance!

19. 2004 MSS AC C-05 24 August 2004 19 Phase CRB with Scattering ( ,  ) Ideal plane wave Coherence loss  0.1

20. 2004 MSS AC C-05 24 August 2004 20 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

21. 2004 MSS AC C-05 24 August 2004 21 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

22. 2004 MSS AC C-05 24 August 2004 22 CRB Achievability Coherence is high:  > 0.999 Saturation  is significant for most of frequency range AOA estimators break away from CRB approx. when  > 0.1 Aperture- limited Phase difference estimator: Turbulence prevents performance gain from larger aperture Scenario: Small Sensor Spacing:  = 3 in., SNR = 40 dB, Range = 50 m

23. 2004 MSS AC C-05 24 August 2004 23 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 One snapshot  = 6 in.  = 3 in. RMSE CRB Achievable AOA accuracy ~ 10’s of degrees for this case

24. 2004 MSS AC C-05 24 August 2004 24 Turbulence Conditions for Three-Harmonic Example Coherence is close to 1, but still limits performance. Strong scattering

25. 2004 MSS AC C-05 24 August 2004 25 Summary of AOA with Small Arrays CRB analysis of AOA estimation –Tradeoff: larger aperture vs. coherence loss –Ideal plane wave model is overly optimistic for longer source ranges –Performance varies significantly with weather cond. –Important to consider turbulence effects AOA algorithms do not achieve the CRB in turbulence (  > 0.1) with one snapshot Similar results obtained for circular arrays with > 2 sensors (SNR gain)  Continuing study