2003 MSS BA C-8 1 Acoustic Source Estimation with Doppler Processing Richard J. Kozick Bucknell University Brian M. Sadler Army Research Laboratory

2003 MSS BA C-8 2 Why Doppler? x y Source Path Sensor 1 f d,1 Sensor 5 f d,5 Sensor 2 f d,2 Sensor 3 f d,3 Sensor 4 f d,4

2003 MSS BA C-8 3 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-8 4 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-8 5 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)

2003 MSS BA C-8 6 Transmission Loss Energy is diminished from S ref (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-8 7 Propagation Delay & Doppler Source Path: (x s (t), y s (t)) Sensor at (x 1, y 1 ) toto t o + T

2003 MSS BA C-8 8 No Scattering Sensor signal with transmission loss,propagation delay, and additive noise: Complex envelope at frequency f o (i.e., spectrum at f o shifted to 0 Hz):

2003 MSS BA C-8 9 No Scattering Complex envelope at frequency f o : Pure sinusoid in additive noise Doppler frequency shift is proportional to the source frequency, f o

2003 MSS BA C-8 10 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)

2003 MSS BA C-8 11 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:

2003 MSS BA C-8 12 Power Spectrum (PSD) Freq. PSD AWGN, 2N o -B/2B/2 0 (1-  )S -f d B v = Bandwidth of scattered component Area =  S B = Processing bandwidth -f d = Doppler freq. shift SNR = S / (2 N o B)

2003 MSS BA C N o -B/2B/2 0 (1-  )S -f d BvBv SS -B/2B/2 0 (1-  )S -f d BvBv SS Strong Scattering:  ~ 1 Study estimation of Doppler, f d, w/ respect to –Saturation,  (analogous to Rayleigh/Rician fading) –Processing bandwidth, B, and observation time, T –SNR = S / (2 No B) –Scattering bandwidth, B v (correlation time ~ 1/B v ) Scattering (  > 0) causes signal energy fluctuations; may have low signal energy if (B v T) is small Weak Scattering:  ~ 0

2003 MSS BA C-8 14 PDF of Signal Energy at Sensor

2003 MSS BA C-8 15 Saturation vs. Frequency & Range

2003 MSS BA C-8 16 Model for Sensor Samples Gaussian random process with non- zero mean Sample at rate F s = B, spacing T s =1/B Observe for T sec, so N = BT samples with –Independent AWGN –Correlated scattered signal (T s < 1/ B v ) 2N o -B/2B/2 0 (1-  )S -f d BvBv SS

2003 MSS BA C-8 17 Model for Sensor Samples Vector of samples is complex Gaussian: 2N o -B/2B/2 0 (1-  )S -f d BvBv SS Mean Covariance of scattered samples AWGN

2003 MSS BA C-8 18 Cramer-Rao Bound (CRB) CRB is a lower bound on the variance of unbiased estimates of f d 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 N o -B/2B/2 0 S -f d -B/2B/2 0 -f d BvBv S Fully Saturated:  = 1No Scattering:  = 0 High SNR = S/(2 N o B), Large (B v T) Schultheiss & Weinstein [JASA, 1979]

2003 MSS BA C-8 20 Example 1: Vary B v &  SNR = 28.5 dB B = 7 Hz T = 1 sec B v from 0.1 Hz to 2.0 Hz True f d = -0.2 Hz 2N o -B/2B/2 0 (1-  )S -f d BvBv SS

2003 MSS BA C-8 21 (Bv T) is not large

2003 MSS BA C-8 22

2003 MSS BA C-8 23 Example 2: Vary T &  SNR = 28.5 dB B = 7 Hz B v = 1 Hz T from 0.5 sec to 10 sec True f d = -0.2 Hz 2N o -B/2B/2 0 (1-  )S -f d BvBv SS

2003 MSS BA C-8 24 (Bv T) is large

2003 MSS BA C-8 25

2003 MSS BA C-8 26 Example 3: Vary SNR &  T = 1 sec B = 7 Hz B v = 1 Hz SNR from -1.5 dB to 38.5 dB True f d = -0.2 Hz 2N o -B/2B/2 0 (1-  )S -f d BvBv SS

2003 MSS BA C-8 27 SNR floor

2003 MSS BA C-8 28 (Bv T) is not large No SNR floor

2003 MSS BA C-8 29 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 T=1 s, B=10 Hz, Bv=0.1 Hz

2003 MSS BA C-8 30  5 m10 m20 m40 m80 m160 m 320 m 45 Hz Hz Hz Hz

2003 MSS BA C-8 31 CRB 5 m10 m20 m40 m80 m160 m 320 m 45 Hz Hz Hz Hz

2003 MSS BA C-8 32 Differential Doppler Estimation

2003 MSS BA C-8 33 Differential Doppler Estimation

2003 MSS BA C-8 34

2003 MSS BA C-8 35 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-8 36 Bearings & Doppler x y Source Path Sensor 1 f d,1 Sensor 5 f d,5 Sensor 2 f d,2 Sensor 3 f d,3 Sensor 4 f d,4