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Motivation

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. Motivation.

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Motivation

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  1. Algorithms and Performance of Small Baseline Acoustic Sensor Arrays Brian M. Sadler, Army Research LabRichard J. Kozick, Bucknell UniversitySandra L. Collier , Army Research Lab Acknowledgments: D.K. Wilson and T. Pham12 April 2004 SPIE 2004

  2. Motivation • Frequency range for aeroacoustics:Freq. in [30, 250] Hz  l 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, W • Signal coherence, g SPIE 2004

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

  4. Outline • Brief review of source characteristics (ground vehicles, aircraft) • Physics-based statistical model for turbulence (saturation=W, coherence=g) • 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 SPIE 2004

  5. 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 SPIE 2004

  6. Hz TIME (sec) +/- 125 m from CPA SPIE 2004

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

  8. Transmission Loss • Energy is diminished from Sref (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 Numerical solution Low Pass Filter SPIE 2004

  9. Frequency dependent Transmission Loss +/- 125 m from CPA SPIE 2004

  10. No Scattering • Sensor signal with transmission loss,propagation delay, and AWG noise: • Complex envelope at frequency fo • Spectrum at fo shifted to 0 Hz • FFT amplitude at fo SPIE 2004

  11. With Scattering • A fraction of the signal energy is scattered from a pure sinusoid into a zero-mean, narrowband, Gaussian random process • Saturation parameter, W 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: SPIE 2004

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

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

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

  15. Turbulence effects are small only for very short range and low frequency Saturation variesover entire range[0, 1] for typicalvalues Fully scattered SPIE 2004

  16. q = AOA • = sensor spacing < l/2 Model forTwo Sensors Turbulence effects Perfect plane wave:W = 0 or 1g = 1 SPIE 2004

  17. q do = range • = sensor spacing Model for Coherence, g • Assume AOA q = 0, freq. in [30, 500] Hz • Recall saturation model: • Coherence model [Ostashev & Wilson 2000]: g 0 with freq., sensorspacing, and range Temperaturefluctuations Velocityfluctuations SPIE 2004

  18. Velocityfluctuations Temperaturefluctuations Depends on wind leveland sunny/cloudy SPIE 2004

  19. Coherence, g, forsensor spacingr = 12 inches g > 0.99 for range < 100 mIs this “good”? Curves moveup w/ less wind,down w/ more wind SPIE 2004

  20. Impact on AOA Estimation • How does the turbulence (W, g) affect AOA estimation accuracy? • Cramer-Rao lower bound (CRB), simulated RMSE • Achievable accuracy with small arrays? Larger sensorspacing, r: DESIRABLE BAD! SPIE 2004

  21. Special Cases • No scattering (ideal plane wave model): • High SNR, with scattering: SNR-limitedperformance Coherence-limitedperformance If SNR = 30 dB, then g < 0.9989995 limits performance! SPIE 2004

  22. Phase CRB with Scattering Coherence loss g < 1 is significantwhen saturationW > 0.1 Idealplanewave SPIE 2004

  23. CRB on AOA Estimation SNR = 30 dB for all ranges Sensor spacing r = 12 in. Coherence-limited at larger ranges Increasingrange (fixed SNR) Aperture-limitedat low frequency Ideal plane wave modelis accurate for very shortranges ~ 10 m SPIE 2004

  24. Cloudy and Less Wind SNR = 30 dB for all ranges Sensor spacing r = 12 in. Atmospheric conditionshave a large impact onAOA CRBs Aperture-limitedat low frequency Plane wave model isaccurate to 100 m range SPIE 2004

  25. Small Sensor Spacing: r = 3 in.SNR = 40 dB, Range = 50 m Phase difference estimator: Also evaluated maximum likelihood (ML) estimator. AOA estimators break away from CRB approx.when W > 0.1 Saturation W issignificant for most offrequency range Turbulence prevents performance gain from larger aperture Coherence is high: g > 0.999 Aperture-limited SPIE 2004

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

  27. Turbulence Conditions for Three-Harmonic Example Strongscattering Coherence is close to 1, butstill limits performance. SPIE 2004

  28. 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 W > 0.1) • Small array (3 in. and 6 in.) AOA performance: • AOA accuracy < 5o at 20 m range, ~>10o at 100 m • Similar results for circular arrays with >2 sensors(SNR gain) SPIE 2004

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