EXTENDED RANGE INTERFEROMETRIC METHODS AND SYSTEMS

• US 20110208481A1
• Filed: 02/17/2011
• Published: 08/25/2011
• Est. Priority Date: 02/19/2010
• Status: Abandoned Application

• Current Assignee: Navintex Inc.
• Original Assignee: Navintex Inc.
• Inventors: Slastion, Vladimir
• Application Number:
  US13/029,857
• Publication Number:
  US 20110208481A1
• Time in Patent Office: Days
• US Class Current: 702/189
• CPC Class Codes: G01S 3/48 the waves arriving at the antennas being continuous or intermittent and the phase difference of signals derived therefrom being measured
• CPC Class Codes: G01S 3/74 Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals systems in which the directions of different signals are determined sequentially and displayed simultaneously G01S3/04, G01S3/14

Abstract

An interferometer estimates at least one interferometric parameter of one or more signals emitted from a source. The interferometer includes at least one phase measurement module for measuring phase differences between the source signals received at different signal receiving sensors. At least one coarse estimate of a sought parameter used to represent the at least one interferometric parameter is generated by processing the one or more signals received from the source. At least one fine estimate of the sought parameter is also generated by processing the at least one coarse sought parameter using the plurality of phase measurements received from the at least one phase measurement module. The at least one fine sought parameter represents the at least one interferometric parameter with greater accuracy than the at least one coarse sought parameter and over an extended range of values in which the sought parameter is not unambiguously determinable using only the plurality of phase measurements.

Claims

1. An interferometer for estimating at least one interferometric parameter of one or more signals received from a source, the interferometer comprising:

at least one phase measurement module configured to determine a plurality of phase measurements of the one or more signals received from a source;

at least one coarse sought parameter estimator configured to determine at least one coarse sought parameter representing the at least one interferometric parameter by processing the one or more signals received from the source;

a fine sought parameter estimator configured to process the at least one coarse sought parameter received from the at least one coarse sought parameter estimator, using the plurality of phase measurements received from the at least one phase measurement module, to determine at least one fine sought parameter representing the at least one interferometric parameter with greater accuracy than the at least one coarse sought parameter.

2. The interferometer of claim 1, wherein the fine sought parameter estimator comprises:

a combined estimator configured to determine at least one partial sought parameter, representing the interferometric parameter over a narrower range of values than the at least one coarse sought parameter, and at least one noise parameter associated with the plurality of phase measurements by processing the plurality of phase measurements received from the at least one phase measurement module; and

at least one partial sought parameter extender configured to calculate the at least one fine sought parameter using the at least one partial sought parameter received from the combined estimator and the at least one coarse sought parameter received from the at least one coarse sought parameter estimator.

3. The interferometer of claim 2, wherein the combined estimator is configured to estimate a vector Θ

of M partial sought parameters and the at least one noise parameter by processing a vector φ

of N phase measurements received into the combined estimator, where N is greater than M, each element of the vector φ

of phase measurements defined within one phase cycle, and the vector φ

of phase measurements is related to the vector Θ

of partial sought parameters by;

a vector of N integer numbers k of phase cycles missed in the N phase measurements φ

, a vector n of N phase errors associated with the N phase measurements φ

, and a matrix A with dimensions N×

M comprising M column vectors a_i that are N-dimensional linearly independent vectors of relatively prime numbers.

4. The interferometer of claim 3, wherein the vector φ

of phase measurements is related to the vector Θ

of partial sought parameters according to;

φ

=AΘ

−

k+n.

5. The interferometer of claim 4, wherein one or more of the at least one partial sought parameter extenders is configured to calculate a corresponding fine sought parameter Θ

_F according to;

Θ

_F=Θ

*_C+Θ

_P,

where Θ

_P represents a corresponding partial sought parameter received from the combined estimator, and Θ

*_C is calculated by processing a corresponding coarse sought parameter Θ

_C, received from the coarse sought parameter estimator, according to;

6. The interferometer of claim 4, wherein the combined estimator comprises:

a first phase measurements converter configured to calculate an M-dimensional vector ψ

by processing the vector cp of phase measurements, received from the at least one phase measurement module, according to;

ψ

=Vφ

,

where V is a matrix with dimensions M×

N that is predefined for the matrix A;

a second phase measurements converter configured to calculate an (N−

M) dimensional vector δ

by processing the vector φ

of phase measurements, received from the at least one phase measurement module, according to;

δ

=Uφ

,

where U is a matrix with dimensions (N−

M)×

N that is predefined for the matrix A; and

a noise parameters calculator configured to process the vector δ

received from the second phase measurements converter to calculate an (N−

M) dimensional vector v of noise parameters according to;

v=rrni{δ

},

where rrni{ . . . } is a procedure for calculating residuals of rounding each element of the vector inside the braces { . . . } to nearest integers.

7. The interferometer of claim 6, wherein the combined estimator further comprises a partial sought parameters estimator configured to determine the vector Θ

of partial sought parameters by processing the vector ψ

, received from the first phase measurements converter, according to;

Θ

=rrni{ψ

},

wherein the vector Θ

of partial sought parameters and the at least one noise parameter are outputs of the combined estimator.

8. The interferometer of claim 7, wherein the vector v of noise parameters is an output of the combined estimator.

9. The interferometer of claim 7, wherein the combined estimator further comprises a common noise parameter estimator configured to calculate a common noise parameter a according to:

10. The interferometer of claim 7, wherein the combined estimator further comprises a discrete noise parameter estimator having the vector v of noise parameters received from the noise parameters calculator and (N−

M)×

Z threshold values γ

_ij as inputs, the discrete noise parameter estimator configured to calculate;

11. The interferometer of claim 7, wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the at least one noise parameter received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

12. The interferometer of claim 6, wherein the combined estimator further comprises a partial sought parameters estimator configured to determine the vector Θ

of partial sought parameters according to;

Θ

=rrni{Hξ

},

where H is a matrix with dimensions M×

N that is predefined for the matrix A and for a covariance matrix B that characterizes the vector n of phase errors, and ξ

is an N-dimensional vector combination of the vector v of noise parameters received from the noise parameters calculator, and the vector ψ

received from the first phase measurements converter, according to;

13. The interferometer of claim 12, wherein the at least one noise parameter is an output of the combined estimator.

14. The interferometer of claim 13, wherein the vector v of noise parameters is an output of the combined estimator.

15. The interferometer of claim 13, wherein the combined estimator further comprises a common noise parameter estimator configured to calculate a common noise parameter α

according to;

16. The interferometer of claim 13, wherein the combined estimator further comprises a discrete noise parameter estimator having the vector v of noise parameters received from the noise parameters calculator and (N−

M)×

Z threshold values γ

_ij as inputs, the discrete noise parameter estimator configured to calculate;

17. The interferometer of claim 13, wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the at least one noise parameter received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

18. The interferometer of claim 6, wherein the combined estimator further comprises:

a noise parameters converter configured to process the vector v of noise parameters received from the noise parameters calculator to calculate an (N−

M)-dimensional vector η

according to;

η

=Pv,

where P is a matrix with dimensions (N−

M)×

(N−

M) that is predefined for the matrix A and for a covariance matrix B that characterizes the vector n of phase errors;

a region shift calculator configured to process the vector η

received from the noise parameters converter to calculate an (N−

M)-dimensional vector χ

* according to;

19. The interferometer of claim 18, wherein the at least one noise parameter is an output of the combined estimator.

20. The interferometer of claim 19, wherein the vector v of noise parameters is an output of the combined estimator.

21. The interferometer of claim 19, wherein the combined estimator further comprises a common noise parameter estimator configured to calculate a common noise parameter α

according to;

22. The interferometer of claim 19, wherein the combined estimator further comprises a discrete noise parameter estimator having the vector v of noise parameters received from the noise parameters calculator and (N−

M)×

Z threshold values γ

_ij as inputs, the discrete noise parameter estimator configured to calculate;

23. The interferometer of claim 19, wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the at least one noise parameter received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

24. The interferometer of claim 6, wherein the combined estimator further comprises:

a noise parameters converter configured to process the vector v of noise parameters received from the noise parameters calculator to calculate an (N−

M)-dimensional vector η

according to;

η

=Pv,

where P is a matrix with dimensions (N−

M)×

(N−

M) that is predefined for the matrix A and for a covariance matrix B that characterizes the vector n of phase errors;

a region shift calculator configured to process the vector η

received from the noise parameters converter to calculate an (N−

M)-dimensional vector χ

* according to;

25. The interferometer of claim 24, wherein the at least one noise parameter is an output of the combined estimator.

26. The interferometer of claim 25, wherein the vector v of noise parameters is an output of the combined estimator.

27. The interferometer of claim 25, wherein the combined estimator further comprises a common noise parameter estimator configured to calculate a common noise parameter a according to:

28. The interferometer of claim 25, wherein the combined estimator further comprises a discrete noise parameter estimator having the vector v of noise parameters received from the noise parameters calculator and (N−

M)×

Z threshold values γ

_ij as inputs, the discrete noise parameter estimator configured to calculate;

29. The interferometer of claim 25, wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the at least one noise parameter received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

30. The interferometer of claim 6, wherein the combined estimator further comprises:

a discrete noise parameter estimator having the vector v of noise parameters received from the noise parameters calculator and (N−

M)×

Z threshold values γ

_ij as inputs, the discrete noise parameter estimator configured to calculate;

31. The interferometer of claim 30, wherein the adaptive estimator is configured to determine the vector Θ

of partial sought parameters;

if q is below or equal to a first threshold, according to;

Θ

=rrni{ψ

};

if q is above the first threshold and below or equal to a second threshold greater than the first threshold, according to;

Θ

=rrni{Hξ

},

where H is a matrix with dimensions M×

N that is predefined for the matrix A and for a covariance matrix B that characterizes the vector n of phase errors, and ξ

is an N-dimensional vector combination of v and ψ

according to;

32. The interferometer of claim 31, wherein the discrete noise parameter q is an output of the combined estimator, and wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the discrete noise parameter q received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

33. The interferometer of claim 30, wherein the adaptive estimator is configured to determine the vector Θ

of partial sought parameters;

if q is below or equal to a first threshold, according to;

Θ

=rrni{ψ

};

if q is above the first threshold and below or equal to a second threshold greater than the first threshold, according to;

Θ

=rrni{Hξ

},

where H is a matrix with dimensions M×

N that is predefined for the matrix A and for a covariance matrix B that characterizes the vector n of phase errors, and ξ

is an N-dimensional vector combination of v and ψ

according to;

34. The interferometer of claim 33, wherein the discrete noise parameter q is an output of the combined estimator, and wherein the fine sought parameter estimator further comprises a postprocessor configured to generate at least one postprocessed fine sought parameter by processing the at least one fine sought parameter received from the at least one partial sought parameter extender, using the discrete noise parameter q received from the combined estimator, to improve an estimate of the at least one interferometric parameter.

35. The interferometer of claim 2, wherein the combined estimator is configured to:

compare the at least one noise parameter with at least one threshold; and

based on a result of the comparison, determine the at least one partial sought parameter by processing the plurality of phase measurements.

36. The interferometer of claim 1, wherein the fine sought parameter estimator comprises:

a combined estimator configured to determine a vector Θ

of M partial sought parameters, representing the at least one interferometric parameter over a narrower range of values than the at least one coarse sought parameter, by processing a vector φ

of N phase measurements received into the combined estimator, where N is greater than M, each element of the vector φ

of phase measurements defined within one phase cycle, and the vector φ

of phase measurements is related to the vector Θ

of partial sought parameters according to;

φ

=AΘ

−

k+n,

where k represents a vector of N integer numbers of phase cycles missed in the N phase measurements φ

, n represents a vector of N phase errors associated with the N phase measurements φ

, and A represents a matrix with dimensions N×

M comprising M column vectors a_i that are N-dimensional linearly independent vectors of relatively prime numbers, the combined estimator comprising;

a phase measurements converter configured to calculate an M-dimensional vector ψ

by processing the vector φ

of phase measurements, received from the at least one phase measurement module, according to;

ψ

=Vφ

,

 

where V is a matrix with dimensions M×

N that is predefined for the matrix A; and

a partial sought parameters estimator configured to process the vector p received from the phase measurements converter to determine the vector Θ

of partial sought parameters according to;

Θ

=rrni{ψ

},

 

wherein the vector Θ

of partial sought parameters is an output of the combined estimator; and

at least one partial sought parameter extender configured to calculate the at least one fine sought parameter using the at least one partial sought parameter received from the combined estimator and the at least one coarse sought parameter received from the at least one coarse sought parameter estimator.

37. The interferometer of claim 36, wherein one or more of the at least one partial sought parameter extender is configured to calculate a corresponding fine sought parameter Θ

_F according to;

Θ

_F=Θ

*_C+Θ

_P,

where Θ

_P represents a corresponding partial sought parameter received from the combined estimator, and Θ

*_C is calculated by processing a corresponding coarse sought parameter Θ

_C, received from the coarse sought parameter estimator, according to;

38. A fine sought parameter estimator for use in an interferometer to estimate at least one interferometric parameter, the fine sought parameter estimator comprising a processor configured to:

receive a vector φ

of N phase measurements and a vector Θ

_C of M coarse sought parameters;

estimate a vector Θ

of M partial sought parameters by processing the vector φ

of phase measurements, where N is greater than M, each element of the vector φ

of phase measurements defined within one phase cycle, and the vector φ

of phase measurements related to the vector Θ

of partial sought parameters by;

a vector of N integer numbers k of phase cycles missed in the N phase measurements φ

, a vector n of N phase errors associated with the N phase measurements φ

, and a matrix A with dimensions N×

M comprising M column vectors a_i that are N-dimensional linearly independent vectors of relatively prime numbers; and

process the vector Θ

of M partial sought parameters and the vector Θ

_C of M coarse sought parameters to generate a vector Θ

_F of M fine sought parameters representing the at least one interferometric parameter with greater accuracy than the vector Θ

_C of M coarse sought parameters and over a greater range of values than the vector Θ

of M partial sought parameters.

39. A method of estimating at least one interferometric parameter of one or more signals from a source, the method comprising:

determining a plurality of phase measurements of the one or more signals received from a source;

determining at least one coarse sought parameter representing the at least one interferometric parameter by processing the one or more signals received from the source; and

processing the at least one coarse sought parameter using the plurality of phase measurements to determine at least one fine sought parameter representing the at least one interferometric parameter with greater accuracy than the at least one coarse sought parameter.