Real-time time-difference-of-arrival (TDOA) estimation via multi-input cognitive signal processor
Described is a multi-input cognitive signal processor (CSP) for estimating time-difference-of-arrival (TDOA) of incoming signals. The multi-input CSP receives a mixture of input signals from an antenna a and an antenna b. The multi-input CSP predicts and temporally de-noises input signals a and b received from antennas a and b, respectively, using an input corresponding to each input signal, resulting in de-noised state vectors for input signals a and b. Using the de-noised state vectors for input signals a and b, cross-predicting and spatially de-noising the other of the de-noised state vectors for input signals a and b. TDOA values of signal pulses to each of antennas a and b are estimated and converted into estimated angles of arrival for each signal pulse.
1. A system for estimating time-difference-of-arrival (TDOA) of incoming signals, the system comprising:
a multi-input cognitive signal processor (CSP) and a non-transitory computer-readable medium having executable instructions encoded thereon such that when executed, the multi-input CSP performs operations of:
receiving a mixture of input signals from an antenna a and an antenna b;
predicting and temporally de-noising an input signal a received from antenna a using a first input of the multi-input CSP, resulting in a de-noised state vector for input signal a;
predicting and temporally de-noising an input signal b received from antenna b using a second input of the multi-input CSP, resulting in a de-noised state vector for input signal b;
using the de-noised state vectors for one of input signals a and b, cross-predicting and spatially de-noising the other of the de-noised state vectors for input signals a and b; and
estimating TDOA values of signal pulses to each of antennas a and b.
2. The system as set forth in claim 1 , wherein the multi-input CSP further perform an operation of converting the TDOA values into estimated angles of arrival for each signal pulse.
3. The system as set forth in claim 2 , wherein the estimated angles of arrival are used to geolocate at least one mobile communication device.
4. The system as set forth in claim 2 , wherein the estimated angles of arrival are used to detect at least one of a direction and a location of at least one radio frequency emitting device.
5. The system as set forth in claim 1 , where in predicting and temporally de-noising each of input signals a and b, the multi-input CSP further performs operations of:
linearly mapping one of input signals a and b into a reservoir computer (RC);
generating a high-dimensional state-space representation of the mixture of input signals from antennas a and b;
generating a delay embedded state signal from a reservoir state of one of input signals a and b; and
temporally de-noising the reservoir state, resulting in the de-noised state vector for one of input signals a and b.
6. The system as set forth in claim 1 , where in cross-predicting the de-noised state vector for input signal b by the de-noised state vector for input signal a, each element of the de-noised state vector for input signal a is sent into a length-L delay embedding and then combined in a weighted sum with a set of output filter coefficients related to input signal a to obtain a spatially de-noised state vector for input signal b.
7. The system as set forth in claim 6 , wherein the set of output filter coefficients related to input signal a is adapted via gradient descent using a cross-prediction error function that is a difference between the de-noised state vector for input signal a and the de-noised state vector for input signal b.
8. The system as set forth in claim 6 , where in estimating TDOA values between a pulse arriving antenna a and antenna b, the multi-input CSP further performs an operation of comparing the set of output filter coefficients related to input signal a, C n1 ab , . . . C n(L+1) ab , to a set of output filter coefficients related to input signal b, C n1 ba , . . . C n(L+1) ba , wherein filter coefficients for antenna a that exceed a predetermined threshold correspond to a positive pulse delay τ ab =l, and filter coefficients for antenna b that exceed the predetermined threshold correspond to a negative pulse delay τ ab =−l, and wherein n denotes a particular state number, l denotes an estimated delay between two antennas, L denotes a maximum delay between the two antennas, and C denotes a set of output filter coefficients.
9. The system as set forth in claim 8 , wherein for each pulse delay τ ab , an angle of arrival θ ab for the signal pulse relative to antenna a is calculated as
θ
ab
=
sin
-
1
c
τ
ab
d
,
where a denotes a distance between antenna a and antenna b, and c is the speed of light.
10. A computer implemented method for estimating time-difference-of-arrival (TDOA) of incoming signals, the method comprising an act of:
causing a multi-input cognitive signal processor (CSP) to execute instructions encoded on a non-transitory computer-readable medium, such that upon execution, the multi-input CSP performs operations of:
receiving a mixture of input signals from an antenna a and an antenna b;
predicting and temporally de-noising an input signal a received from antenna a using a first input of the multi-input CSP, resulting in a de-noised state vector for input signal a;
predicting and temporally de-noising an input signal b received from antenna b using a second input of the multi-input CSP, resulting in a de-noised state vector for input signal b;
using the de-noised state vectors for one of input signals a and b, cross-predicting and spatially de-noising the other of the de-noised state vectors for input signals a and b; and
estimating TDOA values of signal pulses to each of antennas a and b.
11. The method as set forth in claim 10 , wherein the multi-input CSP further performs an operation of converting the TDOA values into estimated angles of arrival for each signal pulse.
12. The method as set forth in claim 10 , where in predicting and temporally de-noising each of input signals a and b, the multi-input CSP further performs operations of:
linearly mapping one of input signals a and b into a reservoir computer (RC);
generating a high-dimensional state-space representation of the mixture of input signals from antennas a and b;
generating a delay embedded state signal from a reservoir state of one of input signals a and b; and
temporally de-noising the reservoir state, resulting in the de-noised state vector for one of input signals a and b.
13. The method as set forth in claim 10 , where in cross-predicting the de-noised state vector for input signal b by the de-noised state vector for input signal a, each element of the de-noised state vector for input signal a is sent into a length-L delay embedding and then combined in a weighted sum with a set of output filter coefficients related to input signal a to obtain a spatially de-noised state vector for input signal b.
14. The method as set forth in claim 13 , wherein the set of output filter coefficients related to input signal a is adapted via gradient descent using a cross-prediction error function that is a difference between the de-noised state vector for input signal a and the de-noised state vector for input signal b.
15. The method as set forth in claim 13 , where in estimating TDOA values between a pulse arriving antenna a and antenna b, the multi-input CSP further performs an operation of comparing the set of output filter coefficients related to input signal a, C n1 ab , . . . C n(L+1) ab to a set of output filter coefficients related to input signal b, C n1 ba , . . . C n(L+1) ba , wherein filter coefficients for antenna a that exceed a predetermined threshold correspond to a positive pulse delay τ ab =1, and filter coefficients for antenna b that exceed the predetermined threshold correspond to a negative pulse delay τ ab =−l, and wherein n denotes a particular state number, l denotes an estimated delay between two antennas, L denotes a maximum delay between the two antennas, and C denotes a set of output filter coefficients.
16. The method as set forth in claim 15 , wherein for each pulse delay τ ab , an angle of arrival θ ab for the signal pulse relative to antenna a is calculated as
θ
ab
=
sin
-
1
c
τ
ab
d
,
where d denotes a distance between antenna a and antenna b, and c is the speed of light.
17. A computer program product for estimating time-difference-of-arrival (TDOA) of incoming signals, the computer program product comprising:
computer-readable instructions stored on a non-transitory computer-readable medium that are executable by a computer having a multi-input cognitive signal processor (CSP) for causing the multi-input CSP to perform operations of:
receiving a mixture of input signals from an antenna a and an antenna b;
predicting and temporally de-noising an input signal a received from antenna a using a first input of the multi-input CSP, resulting in a de-noised state vector for input signal a;
predicting and temporally de-noising an input signal b received from antenna b using a second input of the multi-input CSP, resulting in a de-noised state vector for input signal b;
using the de-noised state vectors for one of input signals a and b, cross-predicting and spatially de-noising the other of the de-noised state vectors for input signals a and b; and
estimating time-difference-of-arrival (TDOA) values of signal pulses to each of antennas a and b.
18. The computer program product as set forth in claim 17 , wherein the multi-input CSP further performs an operation of converting the TDOA values into estimated angles of arrival for each signal pulse.
19. The computer program product as set forth in claim 17 , where in predicting and temporally de-noising each of input signals a and b, the multi-input CSP further performs operations of:
linearly mapping one of input signals a and b into a reservoir computer (RC);
generating a high-dimensional state-space representation of the mixture of input signals from antennas a and b;
generating a delay embedded state signal from a reservoir state of one of input signals a and b; and
temporally de-noising the reservoir state, resulting in the de-noised state vector for one of input signals a and b.
20. The computer program product as set forth in claim 17 , where in cross-predicting the de-noised state vector for input signal b by the de-noised state vector for input signal a, each element of the de-noised state vector for input signal a is sent into a length-L delay embedding and then combined in a weighted sum with a set of output filter coefficients related to input signal a to obtain a spatially de-noised state vector for input signal b.
21. The computer program product as set forth in claim 20 , wherein the set of output filter coefficients related to input signal a is adapted via gradient descent using a cross-prediction error function that is a difference between the de-noised state vector for input signal a and the de-noised state vector for input signal b.
22. The computer program product as set forth in claim 20 , where in estimating TDOA values between a pulse arriving antenna a and antenna b, the multi-input CSP further performs an operation of comparing the set of output filter coefficients related to input signal a, C n1 ab , . . . C n(L+1) ab to a set of output filter coefficients related to input signal b, C n1 ba , . . . C n(L+1) ba , wherein filter coefficients for antenna a that exceed a predetermined threshold correspond to a positive pulse delay τ ab =l, and filter coefficients for antenna b that exceed the predetermined threshold correspond to a negative pulse delay τ ab =−l, and wherein n denotes a particular state number, l denotes an estimated delay between two antennas, L denotes a maximum delay between the two antennas, and C denotes a set of output filter coefficients.
23. The computer program product as set forth in claim 22 , wherein for each pulse delay τ ab , an angle of arrival θ ab for the signal pulse relative to antenna a is calculated as
θ
ab
=
sin
-
1
c
τ
ab
d
,
where a denotes a distance between antenna a and antenna b, and c is the speed of light.