Passive sonar classification using time-frequency domain ... - Penn State

Waveguide invariant analysis for modeling time‐frequency striations in a range‐dependent environment. Alexander Sell Graduate Program in Acoustics Penn State University Work supported by ONR Undersea Signal Processing

Overview • • • • • •

Modal Interference Patterns Spectral striation patterns Waveguide Invariant formulations Application to CALOPS dataset Performance Improvements Conclusions

Modal Interference λnm

2π = krn − krm

1 2 2 = krn ω − ωn c 2D 1 n prop = + λ 2 The number of propagating modes is proportional to the water depth. 3 Mode 2 Mode 2

Mode Mode 4 4

The closer the interfering modes are in frequency, the longer the interference Length.

Accounting for Range Dependence

Mode 4 Mode 2 Mode 2

Mode 4

4

Interference from two modes propagating over constant bathymetry and sloped bathymetry Constant water column depth

Linearly decreasing water column depth

5

Time [minutes]

What do these interference patterns look like?

Frequency [Hz]

A better way to understand striations • Modal interference can be understood in terms of phase and group speed. 1 1 1 − = S pm − S pn = v pm v pn f 0 λ nm  1 1  − = ωc   ωc ( S gm − S gn= )  vgm vgn 

1 r0 Ω c

• At fixed frequency, the separation of our striations is based on phase speed. • At fixed range, the separation of our striations is based on group speed.

The Waveguide Invariant Parameter • Phase and group speed differences describe the horizontal and vertical spacing of our striations. • We develop the invariant parameter

β= −

∂S p ∂S g

• The invariant parameter is not the slope of our spectral striations, but contains information necessary to describe them.

What assumptions must we make? • To excite enough modes to create a striation pattern, our source must radiate a broadband signal • In order for the invariant to be useful in range and depth classification, our waveguide must be range and depth dependent. • Further, we must know the bathymetry and sound speed profile between source and receiver

10

Depth (meters)

Beamformed signal from 125 element horizontal line array located 9 nm east of Port of the Everglades, FL.

11

Time [minutes]

Model Spectrogram

Frequency [Hz]

Accounting for Range Dependence • Recall

1 1 1 − = S pm − S pn = v pm v pn f 0 λ nm  1 1  − = ωc   ωc ( S gm − S gn= )  vgm vgn 

1 r0 Ω c

• To get a range dependent invariant, we must average the depth dependent group speeds at points between the source and receiver ∂S

n p

( recr )

r

1 n , S (r ) ≡ ∫ S g ( x)dx β (r) = − r0 ∂ S gn (r ) n g

These equations were taken from a 1999 paper by Gerald D’Spain and W. A. Kuperman

15

Depth (meters)

Time varying bathymetry between “APL Turquoise” and receiver

16

Relationship between striation slope and the invariant parameter For changing source water column depth, but constant source/receiver range we have

 β (t )  ω (t ) = ω0   β  0 

− β recv

For constant source water column depth, but changing source/receiver range we have

 r (t )  ω (t ) = ω0    r0 

β (t )

To account for changes in both parameters, we have

 r (t )  ω (t ) = ω0    r0 

β (t )

 β (t )     β0 

− β recv

These equations were taken from a 1999 paper by Gerald D’Spain and W. A. Kuperman

17

Applying the Invariant with starting frequencies of 70, 105, and 140 Hz

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How can we improve this? • We still need to include range varying bathymetry, but we also need to – Include contributions from all propagating modes – Weight the modal contributions based upon source and receiver depth – Include a depth varying sound speed profile

We now have the RaDWID Eβ ( r )

1 2 Lωmid ∑ βlm (r ) / β Blm [ FC2 + FS2 ] 2 lm

βl ,m ( r ) = −

FC

S pl ( recr ) − S pm ( recr ) r

(

)

1 S gl ( x ) − S gm ( x ) dx ∫ r0

C (γ + ) + C (γ − )

= FS S (γ + ) + S (γ − )

γ±

1/2

  1 ωmid rmid ∫ S gl ( x ) − S gm ( x ) dx / ( βπ )  r0   r

ωmid Q= (ωmax − ωmin )

(

)

 1 −1   2 Q ± ( β − βlm (r )) 

This formulation was an adaptation of a range independent waveguide invariant distribution by Dan Rouseff and Robert Spindel

Advantages of RaDWID • Includes the following: – Source depth/receiver depth (modal weighting) – Bathymetry between source and receiver – Sound speed profile between source and receiver – Output is a distribution, which makes for efficient inclusion of the above parameters into Bayesian localization framework

RaDWID for APL Turquoise

Applying RaDWID to Modeled Spectrogram of Ship Track

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Improving RaDWID Performance • RaDWID is sensitive to changes in environmental parameters. – Source location (range and depth) – Bathymetry along propagation path – Sound speed profile along propagation path

• Better understanding of parameter (environmental) uncertainty will help us sharpen the peaks of the distribution.

Invariant Distribution for Massachusetts downward refracting profile D = 70, RD = 65

0 10

Normalized E

5

30

4

40

3 50 2 1

60

0

70 0

0.5

1

1.5

2 Beta

2.5

3

3.5

4

source depth [m]

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Conclusions • The RaDWID is a synthesis of two waveguide invariant models. • RaDWID connects spectral striations with acoustically important environmental parameters. • We need to better understand environmental uncertainty to improve performance.

References and Acknowledgements A. B. Baggeroer, “Estimation of the Distribution of the Interference Invariant with Seismic Streamers,” AIP Conference Proceedings, vol. 621, pp 151-170, 2001. G. L. D’Spain and W. A. Kuperman, “Application of waveguide invariants to analysis of spectrograms from shallow water environments that vary in range and azimuth,” J. Acoust. Soc. Am., vol. 106, no. 5, pp 2454-2468, 1999. C. W. Jemmott, “Model-based recursive Bayesian state estimation for single hydrophone passive sonar localization,” PhD. Thesis, The Pennsylvania State University, 2010. D. Rouseff and R. C. Spindel, “Modeling the Waveguide Invariant as a Distribution,” AIP Conference Proceedings, vol. 621, pp 137-150, 2001.

[Work supported by ONR Undersea Signal Processing]