Method and system for remote sound speed measurement

1. A method of estimating a sound speed, the method comprising:

transmitting an acoustic signal from a first location through a water column;

receiving a first scattered signal at a second location, the first scattered signal comprising a plurality of echoes of the acoustic signal reflected by a scattering layer in the water column;

receiving a second scattered signal at a third location, the second scattered signal comprising a plurality of echoes of the acoustic signal reflected by the scattering layer;

receiving a third scattered signal at a fourth location, the third scattered signal comprising a plurality of echoes of the acoustic signal reflected by the scattering layer;

estimating a travel time based on at least one of the first, second, or third scattered signals;

generating a cross-correlation signal comprising a product of echoes of at least two of the first, second, and third scattered signals having an approximate bistatic geometry;

estimating a travel time difference based on at least the cross-correlation signal; and

estimating a sound speed based on the estimated travel time and the estimated travel time difference.

2. The method of claim 1 , wherein at least two of the first, second, third, and fourth locations are the same location.

3. The method of claim 1 , wherein estimating a sound speed comprises determining the square root of an inverse of a quantity consisting of the estimated travel time multiplied by the estimated travel time difference.

4. The method of claim 1 , further comprising estimating a depth associated with the sound speed.

5. The method of claim 4 , wherein estimating the depth comprises multiplying the estimated sound speed by half of an actual or inferred vertical travel time.

6. The method of claim 4 , further comprising estimating a sound speed profile based on the estimated sound speed and the estimated depth.

7. The method of claim 6 , wherein the estimated sound speed profile is based on a plurality of estimated sound speeds, and a respective plurality of estimated depths.

8. The method of claim 1 , wherein at least one of transmitting the acoustic signal transmitting, receiving a first scattered signal, receiving a second scattered signal, or receiving a third scattered signal comprises using an array of transducers.

9. The method of claim 1 , wherein estimating a travel time comprises at least one of estimating a propagation time of a signal between the first location, the scattering layer, and the second, third, or fourth location.

10. The method of claim 1 , wherein estimating a travel time comprises:

determining a time interval between i) a first time when the acoustic signal is transmitted and ii) a second time when at least one of the first, second, or third scattered signal is received.

11. The method of claim 1 , wherein estimating a travel time comprises:

determining a first time interval between i) a first time when the acoustic signal is transmitted and ii) a second time when the first scattered signal is received;

determining a second time interval between i) the first time and ii) a third time when the second scattered signal is received;

determining a third time interval between i) the first time and ii) a fourth time when the third scattered signal is received; and

averaging the first, second, and third time intervals to generate an estimate of travel time.

12. The method of claim 1 , wherein the cross-correlation signal comprises a four-fold complex product comprising the first, second, and third scattered signals and a complex conjugate of at least one of the first, second, and third scattered signals.

13. The method of claim 1 , further comprising receiving a fourth scattered signal at a fifth location.

14. The method of claim 13 , wherein the cross-correlation signal comprises a four-fold complex product of the first, second, third, and fourth scattered signals, wherein two of the signals are conjugated.

15. A method of estimating a sound speed profile, the method comprising:

transmitting a first acoustic signal from a first location towards a plurality of reflectors comprising at least a first scattering layer at a first depth in a water column and a second scattering layer at a second depth in the water column;

transmitting a second acoustic signal from a second location towards the plurality of reflectors;

receiving a first scattered signal at a third location from the plurality of reflectors, the first scattered signal comprising a plurality of echoes of the acoustic signal reflected by the first and second scattering layers;

receiving a second scattered signal at a fourth location from the plurality of reflectors, the second scattered signal comprising a plurality of echoes of the acoustic signal reflected by the first and second scattering layers;

estimating at least a first and second travel time based on at least one of the first or second scattered signals;

generating a cross-correlation signal comprising a cross-correlation of the first scattered signal and the second scattered signal having an approximate bistatic geometry;

estimating at least first and second travel time differences based on the cross-correlation signal;

estimating the first and second depths;

estimating a sound speed to the first and second depths; and

estimating a sound speed profile based on the estimated depths and estimated sound speeds.

16. A system for estimating a sound speed, the system comprising:

a plurality of transducers configured to i) transmit a first acoustic signal from a first location, ii) receive a first scattered signal at a second location, iii) receive a second scattered signal at a third location, and iv) receive a third scattered signal at a fourth location, the scattered signals each comprising a plurality of echoes of the acoustic signal reflected by a scattering layer in a water column; and

a microprocessor configured to i) estimate a travel time based on at least one of the first, second, or third scattered signals, ii) generate a cross-correlation signal comprising a product of at least two of the first, second, and third scattered signals having an approximate bistatic geometry, iii) estimate a travel time difference based on at least the cross-correlation signal, and iv) estimate a sound speed based on at least the estimated travel time and the estimated travel time difference.

17. The system of claim 16 , wherein the microprocessor is configured to estimate the travel time based on determining the temporal location of a peak in the cross-correlation signal.

18. A system for estimating a sound speed, the system comprising:

a plurality of transducers configured to i) transmit a first acoustic signal from a first location, ii) receive a first scattered signal at a second location, iii) receive a second scattered signal at a third location, and iv) receive a third scattered signal at a fourth location, the scattered signals each comprising a plurality of echoes of the acoustic signal reflected by a scattering layer; and

a microprocessor configured to i) estimate a travel time based on at least one of the first, second, or third scattered signals, ii) generate a cross-correlation signal comprising a product of at least two of the first, second, and third scattered signals, wherein the cross-correlation is 50% or less, iii) estimate a travel time difference based on at least the cross-correlation signal, and iv) estimate a sound speed based on at least the estimated travel time and the estimated travel time difference.

19. A system for estimating a sound speed, the system comprising:

means for transmitting an acoustic signal through a water column from a first location;

means for receiving a first scattered signal at a second location, the first scattered signal comprising a plurality of echoes of the acoustic signal reflected by a scattering layer in the water column;

means for receiving a second scattered signal at a third location, the second scattered signal comprising a plurality of echoes of the acoustic signal reflected by the scattering layer;

means for receiving a third scattered signal at a fourth location, the third scattered signal comprising a plurality of echoes of the acoustic signal reflected by the scattering layer;

means for estimating a travel time based on at least one of the first, second, or third scattered signals;

means for generating a cross-correlation signal comprising a product of at least two of the first, second, and third scattered signals in accordance with the bistatic invariance principle;

means for estimating a travel time difference based on at least the cross-correlation signal; and

means for estimating a sound speed based on the estimated travel time and the estimated travel time difference.

20. A non-transitory computer-readable storage medium having instructions stored thereon which, when executed by a processor, causes a method of estimating a sound speed to be performed, the method comprising:

estimating a travel time based on at least one of a first scattered signal, a second scattered signal, or a third scattered signal, wherein each of the first, second, and third scattered signals comprises a plurality of echoes of an acoustic signal reflected by a scattering layer in a water column;

generating a cross-correlation signal comprising a product of a least two of the first, second, and third scattered signals in accordance with the bistatic invariance principle;

estimating a travel time difference based on at least the cross-correlation signal; and

estimating a sound speed based on the estimated travel time and the estimated travel time difference.