Method for real time matched field processing

• US 20080181056A1
• Filed: 01/30/2007
• Published: 07/31/2008
• Est. Priority Date: 01/30/2007
• Status: Active Grant

• Current Assignee: Government of the United States of America
• Original Assignee: Government of the United States of America
• Inventors: Bernecky, W. Robert
• Granted Patent: US 7,800,978 B2
• Time in Patent Office: Days
• US Class Current: 367/21
• CPC Class Codes: G01S 3/8006 Multi-channel systems specially adapted for direction-finding, i.e. having a single aerial system capable of giving simultaneous indications of the directions of different signals

Abstract

A method for utilizing a matched field-processing algorithm employing a number of sensors wherein the sensor output is the measured acoustic data as the first input and is translated to a frequency by applying a Fourier transform to a set of time samples as a data vector output. A replica vector is the second data input as a predicted quantity which is computed by an acoustic model with an assumed acoustic location. The output is an ambiguity surface ranging between zero and one with the highest values indicating the likely position of an acoustic location. The matched field response is generalized by averaging the response over multiple frequencies. A response for an array may be computed by forming beams and then combining them by multiplying each by an eigenray factor before summing. The computation of the response may be further defined by voxel interpolation.

Claims

1. A method for real time matched field processing, said method comprising the steps of:

measuring acoustic data from at least one sensor of a sonar array of sensors;

providing a first data input from said measuring step;

translating the first data input to a frequency domain with a Fourier transform to a set of continuous time samples from said at least one sensor;

defining a data vector from the frequency domain;

determining at least one replica vector representing a predicted value of the at least one sensor output for a specific frequency;

averaging multiple replica data sets of the at least one replica vector to the first data input;

determining a closest matched data set to the first data input from said averaging step; and

outputting an ambiguity surface as a set of numbers in a range between zero and one with a highest value corresponding to a position of an acoustic source.

2. The method in accordance with claim 1, said method comprising the further step of replacing the data vector with a co-variance matrix from a time average of successive moments in time of the data vector.

3. The method in accordance with claim 2, said method comprising the further steps of:

determining a broadband matched field response over multiple frequencies by the equation;

$B=\frac{1}{W}<br><br>\underset{w=1}{\overset{w}{\sum <br><br>}}<br><br><br><br>\frac{d^H<br><br>\mathrm{Rd}}{<br><br>d^H<br><br>d<br><br><br><br>\mathrm{tr}<br><br>\left(R\right)};<br><br>\mathrm{and}$

rewriting said matched field averaging response as

$B=\frac{1}{W}<br><br>\underset{t=1}{\overset{T}{\sum <br><br>}}<br><br><br><br>\underset{w=1}{\overset{w}{\sum <br><br>}}<br><br><br><br>\frac{{<br><br>d^H<br><br>x_t<br><br>}^2}{<br><br>d^H<br><br>d<br><br><br><br>\mathrm{tr}<br><br>\left(R\right)};<br><br>$

wherein B is the broadband response, w is the frequency, d is the replica vector and R is the co-variance matrix.

4. The method in accordance with claim 3, wherein said method employs ray theory by computing an acoustic model with the equation:

$d_n=\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>{\mathrm{\alpha <br><br>}}_{p,n}<br><br>\exp <br><br>\left[-\left({\mathrm{j\omega <br><br>\tau <br><br>}}_{p,n}+{\mathrm{j\phi <br><br>}}_{p,n}\right)\right]$

wherein d_n is a sum of P eigenrays, has an amplitude α

p,n, an additive phase shift φ

p,n and phase ω

τ

_p,n with total travel time from the acoustic source to the at least one sensor; and

approximately as

$\begin{array}{c}{d}_n\approx <br><br><br><br>\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>{\mathrm{\alpha <br><br>}}_{p,0}<br><br>\exp <br><br>\left[-\left(\mathrm{j\omega <br><br>}<br><br>\left({\mathrm{\tau <br><br>}}_{p,0}+\mathrm{\Delta <br><br>}<br><br><br><br>{\mathrm{\tau <br><br>}}_{p,n}\right)+{\mathrm{j\varphi <br><br>}}_{p,0}\right)\right]\\ =<br><br>\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>\underset{\underset{d_{p,0}=e_p}{\mathrm{<br><br>}}}{{\mathrm{\alpha <br><br>}}_{p,0}<br><br>\exp <br><br>\left[-\left({\mathrm{j\omega <br><br>\tau <br><br>}}_{p,0}+{\mathrm{j\varphi <br><br>}}_{p,0}\right)\right]}<br><br>\underset{\underset{s_{p,n}}{\mathrm{<br><br>}}}{\exp <br><br>\left[-\mathrm{j\omega <br><br>\Delta <br><br>}<br><br><br><br>{\mathrm{\tau <br><br>}}_{p,n}\right]};<br><br>\end{array}$

wherein s_p,n is a relative phase shift that is applied to d_{p, 0} to adjust for additional travel time between sensors of the sonar array of sensors.

5. The method in accordance with claim 4, said method further comprising the steps of:

assembling d_n into the replica vector d; and

forming the steering vector s_p for each eigenray p by the equation;

$d=\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>d_{p,0}<br><br>s_p=\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>e_p<br><br>s_p,$

wherein the steering vector is an N×

1 vector of phase shifts −

exp[−

jω

Δ

τ

_p,n] as Δ

τ

_{p, n} being the travel time of an acoustic wave along the eigenray from an array origin to the at least one sensor.

6. The method in accordance with claim 3, said method further comprising the step of computing:

$d^H<br><br>x={\left(\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>e_p<br><br>s_p\right)}^H<br><br>x=\underset{p=1}{\overset{P}{\sum <br><br>}}<br><br><br><br>e_p^{*}<br><br>\underset{\underset{b_p}{\mathrm{<br><br>}}}{\left(s_p^H<br><br>x\right)};<br><br>$

wherein b_p is a complex beamformer output resulting from application of the steering vector from eigenray p to the frequency domain sensor x.

7. The method in accordance with claim 6, said method further comprising the steps of computing:

$B=\frac{1}{W}<br><br>\underset{w=1}{\overset{W}{\sum <br><br>}}<br><br><br><br>\frac{1}{\mathrm{tr}<br><br>\left(R_w\right)}<br><br>\underset{t=1}{\overset{T}{\sum <br><br>}}<br><br><br><br>\frac{{<br><br>e_w^H<br><br>b_{w,t}<br><br>}^2}{<br><br>e_w^H<br><br>e_w<br><br>};<br><br>$

forming P beams; and

combining the P beams by multiplying each by a complex eigenray factor; and

summing the beams.

8. The method in accordance with claim 7, said method further comprising the step of computing an eigenray factor for an origin of the sensor array.

9. The method in accordance with claim 7, said method further comprising the step of applying voxel interpolation to the matched field response.

10. The method in accordance with claim 9, said voxel interpolation step comprising the steps of:

determining a sample voxel as a three-dimensional region in space;

designating subvoxels in relation to the sample voxel as polar coordinates as a distance from an origin of the sample voxel and an angle from the horizontal;

computing the eigenrays between a source at the origin voxel and a destination at an acoustic center of the sonar array;

retaining the eigenray having the most energy;

forming a beam for each of the P eigenrays that is steered exactly at a conical angle coinciding with an arrival angle of the eigenray being considered;

attenuating and phase shifting the individual beams;

determining a real time matched algorithm output response by the equation

$B=\frac{1}{W}<br><br>\underset{w=1}{\overset{W}{\sum <br><br>}}<br><br><br><br>\frac{1}{\mathrm{tr}<br><br>\left(R_w\right)}<br><br>\underset{t=1}{\overset{T}{\sum <br><br>}}<br><br><br><br>\frac{{<br><br>e_w^H<br><br>b_{w,t}<br><br>}^2}{<br><br>e_w^H<br><br>e_w<br><br>};<br><br>$

and

repeating for each of the subvoxels in the voxel.

11. The method in accordance with claim 10 wherein the eigenrays generated by an acoustic model of the voxel origin are each defined by travel time, attenuation, additive phase, arrival angle and departure angle.

12. The method in accordance with claim 11 wherein eigenrays offset from an original departure point are determinable to compute a real time matched algorithm output response for each of the subvoxels in the region comprising the voxel.