Sensor Networks, Aeroacoustics, and Signal Processing

Transcription

1 Sensor Networks, Aeroacoustics, and Signal Processing Part II: Aeroacoustic Sensor Networks Brian M. Sadler Richard J. Kozick 17 May May 004 ICASSP Tutorial II-1

2 Heterogeneous Network of Acoustic One mic. Sensors Sensor array Source Issues: Centralized versus distributed processing Minimize comms., energy Triangulation, TDOA? Effects of acoustic prop. (Node localization, sensor layout & density, Classification, tracking) Central Node? 10 s to 100 s of m range 17 May 004 ICASSP Tutorial II-

3 Acoustic Source & Propagation Source Turbulence scatters wavefronts DSP Signal at sensor (mic.) Source: Loud Spectral lines One sensor: Detection Doppler estimation Harmonic signature FREQUENCY (Hz) SPECTROGRAM OF SENSOR 1 (db) TIME (sec) 17 May 004 ICASSP Tutorial II-3

4 More Sophisticated Node: Sensor Array 1 m aperture or (much) less DSP Issues: Array size/baseline Coherence decreases with larger spacing AOA estimation accuracy with turbulent scattering What can we do with a hockey-puck sensor? Small, covert, easily deployable Performance? 17 May 004 ICASSP Tutorial II-4

5 Why Acoustics? Advantages: Mature sensor technology (microphones) Low data bandwidth: ~[30, 50] Hz Sophisticated, real-time signal proc. Loud sources, difficult to hide: vehicles, aircraft, ballistics Challenges: Ultra-wideband regime: 157% fractional BW λ in [1.3, 11] m Small array baselines Propagation: turbulence, weather, (multipath) Minimize network communications We bound the space of useful system design and performance [Kozick004a] Distinct from RF arrays with respect to SNR, range, frequency, bandwidth, observation time, propagation conditions (weather), sensor layout, source motion/track evaluate performance of algorithms (simulated & measured data) 17 May 004 ICASSP Tutorial II-5

6 Brief History of Acoustics in Military [Namorato000] Trumpeting down walls of Jericho Chinese, Roman (B.C.) Civil War: Generals used guns to signal attacks World War 1: Science of acoustics developed Air & underwater acoustic systems World War : Mine actuating, submarine detection Many developments Army Research Laboratory, present [Srour1995] Hardware and software for detection, localization, tracking, and classification Extensive field testing in various environments with many vehicle types 17 May 004 ICASSP Tutorial II-6

7 Remainder of Tutorial A little more background: Source characteristics Sound propagation through turbulent atmosphere Detection of sources (Saturation, Ω) Array processing Coherence loss from turbulence (Coherence, γ) Array size: sensors source AOA Array of arrays source localization Distributed processing? Data to transmit? Triangulation/TDOA Minimize comms. Experimentally validated models 17 May 004 ICASSP Tutorial II-7

8 Source Characteristics Ground vehicles (tanks, trucks), aircraft (rotary, jet), commercial vehicles, elephant herds 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 Distinct from underwater 17 May 004 ICASSP Tutorial II-8

9 High SNR TIME (sec) +/- 350 m from Closest Point of Approach (CPA) 17 May 004 ICASSP Tutorial II-9

10 Frequency FREQUENCY (Hz) SPECTROGRAM OF SENSOR 1 (db) Harmonic lines Time +/- 85 m from CPA TIME (sec) FREQ. (Hz) Gvc1007: FUNDAMENTAL FREQUENCY ESTIMATE Doppler shift: Hz 3 87 Hz CPA = 5 m 15 km/hr BLOCK FROM CPA 17 May 004 ICASSP Tutorial II-10

11 Overview of Propagation Issues Long propagation time: 1 s per 330 m Additive noise: Thermal, Gaussian (also wind and directional interference) Scattering from random inhomogeneities (turbulence) temporal & spatial correl. Random fluctuations in amplitude: Ω Spatial coherence loss (>1 sensor): γ Transmission loss: Attenuation by spherical spreading and other factors 17 May 004 ICASSP Tutorial II-11

12 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 Low Pass Molecular absorption [Embleton1996] We model S as a deterministic parameter: Average signal energy height (m) Filter northing (km) Numerical Solution [Wilson00] easting (km) Transmission Loss (db) +/- 15 m from CPA 17 May 004 ICASSP Tutorial II-1

13 Measured Aeroacoustic Data 17 May 004 ICASSP Tutorial II-13

14 Measured SNR vs. Range & Frequency db Time Aspect dependence SNR ~ 50 db at CPA Fluctuations due to turbulence 17 May 004 ICASSP Tutorial II-14

15 Outline Detection of sources Saturation, Ω Detection performance Array processing Coherence loss from turbulence, γ Array size: sensors Source AOA Array of arrays: Source localization Triangulation/TDOA, minimize comms. Sinusoidal signal emitted by moving source: s ref ( π f + χ ) ( t) = Sref cos ot 1. Propagation delay, τ. Additive noise 3. Transmission loss 4. Turbulent scattering Signal at the sensor: z ( t) = s( t τ ) + w( t) 17 May 004 ICASSP Tutorial II-15

16 Sensor Signal: No Scattering Sensor signal with transmission loss,propagation delay, and AWG noise: z( t) = s( t τ ) + w( t), to t to + T s( t) = S cos( πf ot + χ ), τ = propagation time Complex envelope at frequency f o Spectrum at f o shifted to 0 Hz FFT amplitude at f o ~ z ( t) = S exp j( χ ω τ ) = S exp [ o ] [ jθ ] + w ~ ( t) + w~ ( t) 17 May 004 ICASSP Tutorial II-16

17 Sensor Signal: With Scattering A fraction, Ω, of the signal energy is scattered from a pure sinusoid into a zero-mean, narrowband, Gaussian random process, v ~ ( t ) : ~ z ( t) = ~ ( θ + ~ ( t ( 1 Ω) S exp[ jθ ] + ΩS v t) exp[ j ] w ) Saturation parameter, Ω in [0, 1] [Norris001, Wilson00a] Varies w/ source range, frequency, and meteorological conditions (sunny, windy) Based on physical modeling of sound propagation through random, inhomogeneous medium Easier to see scattering effect with a picture: 17 May 004 ICASSP Tutorial II-17

18 Weak Scattering: Ω ~ 0 Strong Scattering: Ω ~ 1 Area = ΩS (1- Ω)S Power Spectral Density (PSD) ΩS AWGN, N o -B/ B/ 0 B v Freq. 0 (1- Ω)S -B/ B/ B v Study detection of source, w/ respect to Saturation, Ω (analogous to Rayleigh/Rician fading in comms.) Processing bandwidth, B, and observation time, T SNR = S / ( No B) Scattering bandwidth, B v < 1 Hz (correlation time ~ 1/B v > 1 sec) Number of independent samples ~ (T B v ) often small Scattering (Ω > 0) causes signal energy fluctuations 17 May 004 ICASSP Tutorial II-18

19 Probability Distributions Complex amplitude has complex Gaussian PDF with non-zero mean: ( ( ) ) jθ e 1- Ω S, ΩS + ~ z ~ CN σ Energy P = has non-central χ-squared PDF with d.o.f. has Rice PDF P ~ z PROBABILITY DENSITY (Experimental validation in [Daigle1983, Bass1991, Norris001]) jθ ( e ( 1- Ω) S, ΩS + ) ~ z ~ CN σ PDF OF RECEIVED ENERGY (S=1, SNR = 30 db) Ω = ENERGY, 10 log 10 (P) (db) 17 May 004 ICASSP Tutorial II-19

20 Saturation vs. Frequency & Range Saturation depends on [Ostashev000]: d Weather conditions (sunny/cloudy), but varies little with wind speed Source frequency ω and range d o Ω = 1 exp µ o = ( ω) range of = κ 1 source (m), ( µ d ) o 7 7 ω π ω π ( weather) ω,, ω = frequency (rad/sec) Theoretical forms mostly sunny, mostly cloudy ω [30,500] Hz π 17 May 004 ICASSP Tutorial II-0 Constants from numerical evaluation of particular conditions

21 SATURATION, Ω m 00 m 100 m 50 m d o = 10 m MOSTLY SUNNY Turbulence effects are small only for very short range and low frequency SATURATION, Ω km 5 km km 1 km MOSTLY SUNNY 1 SATURATION, Ω m 00 m MOSTLY CLOUDY d o = 10 m FREQUENCY (Hz) MOSTLY CLOUDY 1 Saturation varies over entire range [0, 1] for typical range & freq. values SATURATION, Ω km 1 km 10 km 5 km FREQUENCY (Hz) 17 May 004 ICASSP Tutorial II m 50 m Fully scattered

22 Detection Performance PROBABILITY OF DETECTION, P FA = 0.01 P D Ω = 0 Ω = 0.1 Ω = 0.3 Ω = 1 No scattering Full scattering P D = probability of detection P FA = probability of false alarm 0.4 PROBABILITY OF DETECTION, P FA = SNR (db) P D Scattering begins to limit performance SNR = 30 db SNR = 5 db P D SNR = 0 db SNR = 15 db SNR = 10 db SATURATION, Ω 17 May 004 ICASSP Tutorial II-

23 Detection Performance with Range SNR = 50 db at 10 m range SNR ~ 1/(range) P D PROB. OF DETECTION WITH SNR α 1/RANGE Lower frequencies detected at larger ranges CLOUDY, 40 Hz SUNNY, 40 Hz CLOUDY, 00 Hz SUNNY, 00 Hz SATURATION VARIATION WITH WEATHER AND FREQUENCY RANGE (m) SATURATION, Ω Hz 40 Hz CLOUDY, 40 Hz SUNNY, 40 Hz CLOUDY, 00 Hz SUNNY, 00 Hz RANGE (m) km Saturation increases with Range Frequency Temperature (sunny) 17 May 004 ICASSP Tutorial II-3

24 Detection Extensions Sensor networks: Detection queuing (wake-up) of more sophisticated sensors Multiple snapshots & frequencies Source motion & nonstationarities Coherence time of scattering Physical models for cross-freq coherence and coherence time are in preliminary stage [Norris001, Havelock1998] Multiple sensors with different SNR and Ω Distributed detection, what to communicate? Required sensor density for reliable detection Source localization based on energy level at the sensors [Pham003] 17 May 004 ICASSP Tutorial II-4

25 Outline Detection of sources Saturation, Ω Detection performance Array processing Coherence loss from turbulence, γ Array size: sensors Source AOA Array of arrays: Source localization Triangulation/TDOA, minimize comms. Coherence, γ, depends on Sensor separation, ρ Source frequency, ω Source range, d o Weather conditions: sunny/cloudy, wind speed 17 May 004 ICASSP Tutorial II-5

26 Signal Model for Two Sensors θ = AOA ρ= sensor spacing < λ/ ~ z = ~ z ~ CN ( jφ ), ( ( 1- Ω), ( Ω ) ( ) + σ ) jχ H e S a S Γ o aa I ~ 1 z 1 a = exp θ = φ = AOA phase = arcsin = ( ω / c o ( φ c ( ωρ )) o ) ρ sinθ Ω = Saturation [0,1] 1 γ Γ =, = Coherence 1 γ γ [0,1] Turbulence effects Perfect plane wave: Ω = 0 or 1 γ = 1 17 May 004 ICASSP Tutorial II-6

27 Model for Coherence, γ Assume AOA θ = 0, θ freq. in [30, 500] Hz Recall saturation model: Ω = 1 exp [ κ ( weather ) ω d ] 1 o Coherence model [Ostashev000]: γ = 0 γ 1 κ exp [ ( ) ] 5/3 κ weather ω ρ d ( 1 Ω) T v ( weather) = + co To 3 co Temperature fluctuations Ω C d o = range ρ= sensor spacing 17 May 004 ICASSP Tutorial II-7 o C, ρ << L eff γ 0 with freq., sensor spacing, and range Velocity fluctuations (wind)

28 γ = 0 γ 1 κ exp [ ( ) ] 5/3 κ weather ω ρ d ( 1 Ω) T v ( weather) = + co To 3 co Temperature fluctuations Ω C o C, ρ << L eff Velocity fluctuations (wind) (From [Kozick004a], based on [Ostashev000, Wilson000]) Depends on wind level and sunny/cloudy 17 May 004 ICASSP Tutorial II-8

29 Assumptions for Model Validity [Kozick004a] Line of sight propagation (no multipath) appropriate for flat, open terrain AWGN is independent from sensor to sensor ignores wind noise, directional interference Scattered process is complex, circular, Gaussian [Daigle1983, Bass1991, Norris001] Wavefronts arrive at array aperture with near-normal incidence Sensor spacing, ρ, resides in the inertial subrange of the turbulence: smallest turbulent eddies << ρ << largest turbulent eddies = L eff γ = exp exp [ ( ) ] 5/3 κ weather ω ρ d ( 1 Ω) Ω [ ( ) ] 5/3 κ weather ω ρ do ( 1 Ω) for ρ >> Leff o 0 for ρ >> L eff 17 May 004 ICASSP Tutorial II-9

30 COHERENCE, γ COHERENCE, γ Coherence, γ, versus frequency and range for sensor spacing ρ = 1 inches COHERENCE, γ COHERENCE, γ MOSTLY SUNNY, MODERATE WIND MOSTLY SUNNY, MODERATE WIND 17 May 004 ICASSP Tutorial II m 00 m km MOSTLY CLOUDY, MODERATE 0.6WIND d o = 10 m 50 m m m FREQUENCY (Hz) m MOSTLY CLOUDY, MODERATE WIND 5 km 10 km FREQUENCY (Hz) 1 km km 5 km d o = 10 m 50 m 100 m 1 km km γ> 0.99 for range < 100 m. Is this good? Curves shift up w/ less wind, down w/ more wind

31 Outline Detection of sources Saturation, Ω Detection performance Array processing Coherence loss from turbulence, γ Array size: sensors Source AOA Array of arrays: Source localization Freq. in [30, 50] Hz λ in [1.3, 11] m Angle of arrival (AOA) accuracy w.r.t. Array aperture size Turbulence (Ω, γ) Small aperture: Easier to deploy More covert Better coherence How small can we go? Triangulation/TDOA, minimize comms. SenTech HE01 acoustic sensor [Prado00] 17 May 004 ICASSP Tutorial II-31

32 Impact on AOA Estimation How does the turbulence (Ω, γ) affect AOA estimation accuracy? [Sadler004] 1 a = exp( ) jφ θ = AOA = arcsin Cramer-Rao lower bound (CRB), simulated RMSE Achievable accuracy with small arrays? φ = phase ( φ ( ωρ )) c o Larger sensor spacing, ρ: CRB J φφ ( ) ( ) CRB( ˆ) ˆ 1, CRB ˆ φ φ = θ = J φφ DESIRABLE 1- Ω = SNR 1+ Ω SNR + SNR Ω Ω πρ λ [ ( )] + Ω SNR 1-γ ( 1- Ω 1-γ ) [ ( )] -1 + Ω SNR 1-γ + SNR 17 May 004 ICASSP Tutorial II-3 c o 1 φ ρω BAD!

33 Special Cases of CRB No scattering (ideal plane wave model): J φφ = SNR SNR-limited performance High SNR, with scattering: J φφ = Ω + Ω 1-1+ γ Ω 1-γ 1- Ω SNR 1- ( γ ) 1- Ω + Ω for SNR >> 1 and ( 1-γ ) ( 1-γ ) γ < 1 Coherencelimited performance SNR If SNR = 30 db, then γ < limits performance! 17 May 004 ICASSP Tutorial II-33

34 Phase CRB with Scattering ( Ω, γ) 3 SNR = 30 db sqrt [CRB(φ)] (rad) Coherence loss γ < 1 is significant when saturation Ω > 0.1 Ideal plane wave Ω = COHERENCE, γ 17 May 004 ICASSP Tutorial II-34

35 CRB on AOA Estimation SNR = 30 db for all ranges MOSTLY SUNNY, STRONG WIND 10 km Sensor spacing ρ = 1 in. sqrt [CRB(θ)] (deg) d o = 10 m Aperture-limited at low frequency FREQUENCY (Hz) 17 May 004 ICASSP Tutorial II-35 5 km Increasing range (fixed SNR) Coherencelimited at larger ranges km 1 km 500 m 100 m Ideal plane wave model is accurate for very short ranges ~ 10 m

36 Cloudy and Less Wind SNR = 30 db for all ranges Sensor spacing ρ = 1 in. sqrt [CRB(θ)] (deg) d o = 10 m MOSTLY CLOUDY, LIGHT WIND Aperture-limited at low frequency Atmospheric conditions have a large impact on AOA CRBs FREQUENCY (Hz) 10 km 5 km km 1 km Plane wave model is accurate to 100 m range 500 m 100 m 17 May 004 ICASSP Tutorial II-36

37 Coherence vs. Sensor Spacing SOURCE FREQ. = 100 Hz, RANGE = 00 m, SNR = 30 db Light wind COHERENCE, γ Omega = 0.80, SUNNY Omega = 0.43, CLOUDY Strong wind MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, MODERATE WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, MODERATE WIND MOSTLY CLOUDY, STRONG WIND SENSOR SPACING, ρ (in.) γ = 0 for ρ ~ 1,000 in = 5 m 17 May 004 ICASSP Tutorial II-37

38 CRB on AOA vs. Sensor Spacing sqrt [CRB(θ)] (deg) SOURCE FREQ. = 100 Hz, RANGE = 00 m, SNR = 30 db MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, STRONG WIND IDEAL PLANE WAVE (Ω = 0, γ = 1) ρ = 5 inches SENSOR SPACING, ρ (in.) 17 May 004 ICASSP Tutorial II-38

39 Coherence vs. Sensor Spacing SOURCE FREQ. = 100 Hz, RANGE = 1,000 m, SNR = 0 db COHERENCE, γ Omega = 1.00, SUNNY Omega = 0.94, CLOUDY MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, MODERATE WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, MODERATE WIND MOSTLY CLOUDY, STRONG WIND SENSOR SPACING, ρ (in.) 17 May 004 ICASSP Tutorial II-39

40 sqrt [CRB(θ)] (deg) CRB on AOA vs. Sensor Spacing SOURCE FREQ. = 100 Hz, RANGE = 1,000 m, SNR = 0 db MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, STRONG WIND IDEAL PLANE WAVE (Ω = 0, γ = 1) Coherence losses degrade AOA perf. for ρ > 8 feet Ideal plane wave model is optimistic (poor weather) 5 (First noted in [Wilson1998], [Wilson1999]) SENSOR SPACING, ρ (in.) Plane wave is OK for good weather 17 May 004 ICASSP Tutorial II-40 λ/

41 CRB Achievability COHERENCE, γ SATURATION, Ω Phase difference estimator: Phase : ˆ φpd = z z1 AOA : ˆ θ PD SNR = 40 db, ρ = 3 in, RANGE = 50 m FREQUENCY (Hz) Coherence is high: γ > co = arcsin ˆ φ ωρ Saturation Ω is significant for most of frequency range PD RMSE & sqrt[crb] ON AOA, θ (deg) Scenario: Small Sensor Spacing: ρ = 3 in., SNR = 40 db, Range = 50 m SNR = 40 db, ρ = 3 in, RANGE = 50 m AOA estimators break away from CRB approx. when Ω > 0.1 PD ESTIMATE ML ESTIMATE CRB Turbulence prevents performance gain from larger aperture FREQUENCY (Hz) May 004 ICASSP Tutorial II-41 0 Aperturelimited FREQUENCY (Hz)

42 AOA Estimation for Harmonic Source Equal-strength harmonics at 50, 100, 150 Hz SNR = 40 db at 0 m range, SNR ~ 1/(range) (simple TL) Sensor spacing ρ = 3 in. and 6 in. AOA (deg) COMBINED AOA ESTIMATES AT FREQS. 50, 100, 150 Hz RMSE, ρ = 6 in sqrt[crb], ρ = 6 in RMSE, ρ = 3 in sqrt[crb], ρ = 3 in RMSE ρ = 3 in. ρ = 6 in. Mostly sunny, moderate wind 5 CRB One snapshot RANGE (m) Achievable AOA accuracy ~ 10 s of degrees for this case 17 May 004 ICASSP Tutorial II-4

43 Turbulence Conditions for Three-Harmonic Example Strong scattering Coherence is ~ 1, but still limits performance. 17 May 004 ICASSP Tutorial II-43

44 Summary of AOA Estimation 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 (Ω > 0.1) with one snapshot Similar results obtained for circular arrays with > sensors [Sadler004] 17 May 004 ICASSP Tutorial II-44

45 Outline Detection of sources Saturation, Ω Detection performance Array processing Coherence loss from turbulence, γ Array size: sensors Source AOA Array of arrays: Source localization y Issues: Comm. bandwidth Distributed processing Exploit long baselines? Time sync. among arrays Model assumptions: Individual arrays: * Perfect coherence * Far-field Between arrays: * Partial coherence * Different power spectra * Near-field Triangulation/TDOA, minimize comms. ARRAY 1 (x_1, y_1) SOURCE (x_s, y_s) ARRAY H (x_h, y_h) ARRAY (x_, y_) x FUSION CENTER 17 May 004 ICASSP Tutorial II-45

46 AOA Three Localization Schemes AOA AOA & TDOA AOA & TDOA AOA Source Source Transmit raw data from one sensor to other nodes AOA Source Transmit AOAs Transmit raw data from all sensors Transmit AOAs & TDOAs Fusion Node Noncoherent triangulation of AOAs Fusion Node Optimum, coherent processing Fusion Node Triangulation of AOAs and TDOAs 1) Triangulate AOAs: ) Fully centralized 3) AOAs & TDOAs: Comms.: Low Distributed processing Coarse time sync. Comms.: High Centralized processing Fine time sync. req d Near-field w.r.t. arrays Comms.: Medium Distributed processing Fine time sync. req d Alt.: Each array xmits raw data from 1 sensor 17 May 004 ICASSP Tutorial II-46

47 Localization Cramer-Rao Bounds [Kozick004b] 1. Triangulation of AOAs Minimal comms.. Fully centralized Maximum comms. 3. #1 + time delay estimation (TDE) Raw data from 1 sensor CRB ELLIPSES FOR COHERENCE 0, 0.5, 1.0 (JOINT PROCESSING) Schemes & 3 have same CRB! Results are coherence sensitive: coherence improves CRB over AOA triangulation Are the CRBs achievable? Y AXIS (m) TARGET ARRAY AOA triangulation CRB ELLIPSES FOR COHERENCE 0, 0.5, 1.0 (BEARING + TD EST.) Parameters: 3 arrays, 7 elements, 8 ft. diam. Narrowband (49.5 to 50.5 Hz) SNR = 16 db at each sensor 0.5 sec. observation time X AXIS (m) X AXIS (m) 17 May 004 ICASSP Tutorial II-47 Y AXIS (m)

48 Ziv-Zakai Bound on TDE Threshold coherence to attain CRB: Function(SNR, % BW, TB product, coherence) Extends [WeissWeinstein83] to TDE with partially-coherent signals TB product Fract BW SNR 17 May 004 ICASSP Tutorial II-48

49 Threshold Coherence Simulation RMS TDE (WIDEBAND): f o = 100 Hz, f = 30 Hz RMS TDE (NARROWBAND):, f o = 40 Hz, f = Hz 10 1 SIMULATION CRB DELAY (sec) 10 3 DELAY (sec) THRESHOLD COHERENCE = COHERENCE THRESHOLD COHERENCE > COHERENCE Breakaway from CRB is accurately predicted by threshold coherence value 17 May 004 ICASSP Tutorial II-49

50 Threshold Coherence 1 ω 0 = π 100 rad/sec, T = 1 sec 1 G s / G w 0.9 G s / G w = 0 db G s / G w = 10 db 0.8 THRESHOLD COHERENCE, γ s G s / G w THRESHOLD COHERENCE, γ s FRAC. BW = 0.1 FRAC. BW = 0.5 FRAC. BW = 0.5 FRAC. BW = BANDWIDTH (Hz), ω / ( π) TIME BANDWIDTH Narrowband source requires perfect coherence Doubling fractional BW time-bw product reduced by factor of ~ 10 f 0 = 50 Hz, f = 5 Hz T>100 s 17 May 004 ICASSP Tutorial II-50

51 TDE Experiment Harmonic Source GROUND VEHICLE PATH AND ARRAY LOCATIONS MEAN SHORT TIME SPECTRAL COHERENCE, ARRAYS 1 & 3 Moderate coherence, small bandwidth NORTH (m) VEHICLE PATH 10 SEC SEGMENT ARRAY 1 ARRAY 3 ARRAY 4 ARRAY 5 4 COHERENCE γ EAST (m) FREQUENCY (Hz) 1 CROSS CORRELATION: ARRAYS 1 AND 3 1 CROSS CORRELATION: ARRAY1, SENSORS 1,5 1 MEAN SHORT TIME SPECTRAL COHERENCE, ARRAY 1, SENSORS 1 & LAG (SEC) GENERALIZED CROSS CORRELATION: ARRAYS 1 AND COHERENCE γ TDE works within an array (sensor spacing < 8 feet) LAG (SEC) TDE is not possible between arrays LAG (SEC) FREQUENCY (Hz) 17 May 004 ICASSP Tutorial II-51

52 TDE Experiment Wideband Source 17 May 004 ICASSP Tutorial II-5

53 TDE Experiment Wideband Source Measured coherence exceeds threshold coherence ~ 0.8 for this case Accurate localization from TDEs 17 May 004 ICASSP Tutorial II-53

54 Summary of Array of Arrays Threshold coherence analysis tells conditions when joint, coherent processing improves localization accuracy Pairwise TDE between arrays captures localization information reduced comms. Incoherent triangulation of AOAs is optimum for narrowband, harmonic sources y ARRAY 1 (x_1, y_1) SOURCE (x_s, y_s) ARRAY H (x_h, y_h) ARRAY (x_, y_) x FUSION CENTER 17 May 004 ICASSP Tutorial II-54

55 Odds & Ends Other Sensing Approaches Infrasonics: f < 30 Hz, λ > 11 m [Bedard000] Over the horizon propagation via ducting from temperature gradients Wind noise is very high Propagation models may be lacking Fuse acoustics with other low-bw sensor modalities Seismic has proven useful for heavy, loud vehicles and aircraft (also footsteps) Vector magnetic sensors are emerging 17 May 004 ICASSP Tutorial II-55

56 Odds & Ends Other Processing Doppler estimation: [Kozick004c] Localize based on differential Doppler from multiple sensors (combine with AOAs?) Not sensitive to coherence Simple, and exploits spectral lines in source We have analyzed CRBs and algorithms Tracking of moving sources [see Biblio.] Classification based on harmonic ampls. [see Biblio.] Harmonic amplitudes fluctuate Exploit aspect angle differences of sources? 17 May 004 ICASSP Tutorial II-56

57 Summary Source characteristics: Spectral lines, ultra-wideband, high SNR Propagation: dominated by turbulent scattering Amplitude & phase fluctuations (saturation, Ω) Spatial coherence loss (coherence, γ) Depends on freq., range, weather, sensor spacing Signal processing: Coherence losses limit AOA and TDE performance Ideal plane wave is overly optimistic Implications for detection and array aperture size Sensor network: comms. & distributed processing Source Central Node? Provided a detailed case-study of a particular sensor network. 17 May 004 ICASSP Tutorial II-57