System and method for linear prediction

• US 20060265214A1
• Filed: 08/01/2006
• Published: 11/23/2006
• Est. Priority Date: 10/13/2000
• Status: Active Grant

• Current Assignee: Leidos, Inc. (Leidos Holdings, Inc.)
• Original Assignee: Science Applications International Corporation
• Inventors: Goldstein, Jay Scott, Witzgall, Hanna Elizabeth
• Granted Patent: US 7,426,463 B2
• Time in Patent Office: Days
• US Class Current: 704/219
• CPC Class Codes: G06F 2218/22 Source localisation; Inverse modelling
• CPC Class Codes: G10L 19/04 using predictive techniques
• CPC Class Codes: G10L 25/12 the extracted parameters being prediction coefficients

Abstract

In a digital signal processor (DSP), input data is configured as a data matrix comprising data samples collected from an input signal. A weight vector is applied to the matrix, where the weight vector comprises three parts including (a) a rank reduction transformation produced by decomposition of data samples in a multistage Wiener filter having a plurality of stages, each stage comprising projection onto two subspaces. Each subsequent stage comprises projecting data transformed by the preceding second subspace onto each of a first subspace comprising a normalized cross-correlation vector at the previous stage and a second subspace comprising the null space of the normalized cross-correlation vector of the current stage, to form a reduced rank data matrix. Part (b) of the weight vector comprises minimizing mean squared error in the reduced rank data space. The output is a linear estimate of input data.

Claims

1. A method for training a linear prediction filter for prediction of information, comprising:

providing reference data;

collecting observed data containing the reference data;

identifying a reduced order Krylov subspace between the observed data and the reference data; and

maximizing mutual data between the observed data and the reference data in the subspace to define at least one autoregressive weight for use in the linear prediction filter.

2. The method of claim 1, wherein the step of identifying a reduced order Krylov subspace comprises applying a multi-stage Wiener filter to the observed data.

3. The method of claim 1, wherein the observed data comprises data from a plurality of elements in an array so that each element provides a data point in a snapshot.

4. The method of claim 3, wherein the observed data arrive at the array at a plurality of different angles.

5. The method of claim 3, wherein the subspace has a rank smaller than the number of elements in the array.

6. The method of claim 1, wherein the information comprises frequency spectrum information.

7. The method of claim 1, wherein the subspace has a rank smaller than the quantity of observed data points in a snapshot.

8. The method of claim 1, wherein collecting observed data comprises collecting a plurality of snapshots of at least one signal.

9. The method of claim 8, wherein the plurality of snapshots comprises time series data.

10. The method of claim 1, further comprising generating an error vector using the subspace.

11. The method of claim 10, wherein the error vector is generated by performing a Gram-Schmidt transformation in the subspace.

12. The method of claim 1, wherein the autoregressive weight is defined by minimizing the mean squared error between the observed data and the reference data.

46. The method of claim 4, wherein the information comprises at least one angle of arrival.

73. The method of claim 1, wherein the information comprises time of arrival information.

13. A method for linear prediction of information determinable from at least one input signal comprising a plurality of data points, the method comprising:

providing a plurality of reference data points;

training a filter by collecting p observed data points from the at least one input signal corresponding to p reference data points, wherein p reference data points comprise a portion of the plurality of reference data points, wherein the training further comprises;

processing the p observed data points through the filter to identify a reduced order Krylov subspace between the observed data points and the reference data points; and

defining a weight for minimizing the mean squared error between a predicted p+1 observed data point and a p+1 reference data point; and

applying the weight to filter the at least one input signal.

14. The method of claim 13, wherein the step of processing the p observed data points comprises applying a multi-stage Wiener filter to the observed data.

15. The method of claim 13, wherein the at least one input signal comprises a plurality of signals received at a multi-element detector array so that each element of the array provides a data point in a snapshot.

16. The method of claim 15, wherein the plurality of signals arrive at the array at a plurality of different angles and the information comprises at least one angle of arrival.

17. The method of claim 15, wherein the subspace has a rank smaller than the number of elements in the multi-element detector array.

18. The method of claim 13, wherein the information comprises frequency spectrum information.

19. The method of claim 15, wherein the subspace has a rank smaller than the quantity of data points in a snapshot.

20. The method of claim 13, wherein collecting p observed data points comprises collecting a plurality of snapshots of at least one input signal.

21. The method of claim 20, wherein the plurality of snapshots comprises time series data.

74. The method of claim 13, wherein the information comprises time of arrival information.

22. A method for linear prediction of information determinable from at least one received signal containing a plurality of data points received at a detector, the method comprising:

defining a reference data matrix comprising data points collected from at least one reference signal;

defining a received data matrix comprising data points collected from the at least one received signal;

calculating a weight vector by;

(a) performing a rank reduction transformation to create a reduced rank data matrix produced by decomposition of the received data matrix in a multi-stage Wiener filter; and

(b) minimizing the mean squared error in the reduced rank data matrix;

and

applying the weight vector to the received data matrix.

23. The method of claim 22, wherein the at least one received signal comprises a plurality of signals received at a multi-element detector array so that each element of the array provides a data point in a snapshot.

24. The method of claim 23, wherein the plurality of signals arrive at the multi-element detector array at a plurality of different angles and the information comprises angle of arrival.

25. The method of claim 24, wherein the reduced rank data matrix has a rank smaller than the number of elements in the multi-element detector array.

26. The method of claim 22, wherein the information comprises frequency spectrum information.

27. The method of claim 23 wherein the reduced rank data matrix has a rank smaller than the quantity of data points in the snapshot.

28. The method of claim 22, wherein the step of defining a reference data matrix comprises collecting a plurality of snapshots of the at least one reference signal.

29. The method of claim 28, wherein the plurality of snapshots comprises time series data.

30. The method of claim 22, wherein the step of defining a received data matrix comprises collecting a plurality of snapshots of the at least one received signal.

31. The method of claim 30, wherein the plurality of snapshots comprises time series data.

32. The method of claim 23, further comprising generating an error vector using the reduced rank data matrix.

33. The method of claim 32, wherein generating an error vector comprises performing a Gram-Schmidt transformation on the reduced rank data matrix.

34. The method of claim 22, wherein the information is an estimate of the frequency spectrum of the at least one received signal.

75. The method of claim 22, wherein the information comprises time of arrival information.

35. A system for linear prediction of information determinable from at least one received signal comprising a plurality of data points, the system comprising:

a linear prediction filter for processing the plurality of data points, the linear prediction filter comprising a multi-stage Wiener filter for projecting a full rank data matrix formed from the plurality of data points into a subspace having a reduced rank to form a reduced rank data matrix and minimizing the mean squared prediction error in the reduced rank matrix, and for applying a weight vector to the at least one received signal to generate a predicted signal.

36. The system of claim 35, further comprising a receiver for receiving the at least one received signal, the receiver comprising a plurality of elements in an array, each element generating a data point in a snapshot.

37. The system of claim 35, wherein the information comprises estimated spectrum information.

38. The system of claim 35, wherein the at least one received signal comprises a plurality of signals impinging at a plurality of angles on a detector array comprising a plurality of elements, and wherein the information comprises angle of arrival.

39. The system of claim 35 wherein the filter is incorporated in a digital signal processor.

76. The system of claim 35, wherein the information comprises time of arrival information.

40. A method for spectrum estimation of at least one received signal, the method comprising:

providing reference data points;

collecting a plurality of snapshots of the at least one received signal, each snapshot comprising a plurality of received data points corresponding to the reference data points;

defining a received data matrix comprising the plurality of snapshots;

identifying a reduced order Krylov subspace between the received data points and the reference data points;

maximizing mutual data points between the observed data points and the reference data points in the subspace to define an autoregressive weight; and

using the autoregressive weight to calculate an estimated spectrum.

41. The method of claim 40, wherein the autoregressive weight is defined by minimizing the mean squared error between the observed data points and the reference data points.

42. The method of claim 40, wherein the at least one received signal comprises a plurality of signals arriving at an array at a plurality of different angles and the estimated spectrum includes an angle of arrival for each of the plurality of received signals.

43. A system for spectrum estimation of at least one received signal comprising a plurality of received data points received at a detector, the system comprising:

a filter for processing the plurality of received data points, the filter comprising a multi-stage Wiener filter for projecting a full rank data matrix formed from the plurality of received data points and a plurality of known data points into a subspace having a reduced rank to form a reduced rank data matrix and determining a weight for minimizing the mean squared error in the reduced rank data space; and

a processor for calculating an estimated spectrum using the weight.

44. The system of claim 43, the detector comprising a plurality of elements in an array, each element generating a data point of the plurality of received data points.

45. The system of claim 43, wherein the filter and the processor are incorporated in a digital signal processor.

47. A computer program product for training a linear prediction filter for prediction of information, the computer program product comprising:

at least one computer readable medium;

a providing module resident on the medium and operable to provide reference data;

a collection module resident on the medium and operable to collect observed data containing the reference data;

an identification module resident on the medium and operable to identify a reduced order Krylov subspace between observed data containing the information and the reference data characteristic of the information; and

a maximization module resident on the medium and operable to maximize mutual data between the observed data and the reference data in the reduced order data space.

48. The computer program product of claim 47, wherein the identification module applies a multi-stage Wiener filter to the observed data to identify the subspace.

49. The computer program product of claim 47, wherein the collection module collects a snapshot of observed data points.

50. The computer program product of claim 49, wherein the subspace has a rank smaller than the quantity of observed data points in the snapshot.

51. The computer program product of claim 49, wherein the plurality of snapshots comprises time series data.

52. The computer program product of claim 47, further comprising a generation module resident on the medium and operable to generate an error vector in the subspace.

53. The computer program product of claim 52, wherein the generation module generates an error vector by performing a Gram-Schmidt transformation in the subspace.

54. The computer program product of claim 47, wherein the autoregressive weight is defined by minimizing the mean squared error between the observed data and the reference data.

77. The computer program product of claim 47, wherein the information comprises time of arrival information.

55. A computer program product for linear prediction of information determinable from at least one input signal comprising a plurality of data points, the computer program product comprising:

at least one computer readable medium;

a providing module resident on the medium and operable to provide a plurality of reference data points;

a training module resident on the medium and operable to train a filter by collecting p observed data points in a snapshot from the at least one input signal corresponding to p reference data points, wherein p reference data points comprise a portion of the plurality of reference data points, wherein the training module further comprises;

a processing module resident on the medium and operable to process the p observed data points through the filter to identify a reduced order Krylov subspace between the observed data points and the reference data points;

and

a defining module resident on the medium and operable to define a weight for minimizing the mean squared error between a predicted p+1 observed data point and a p+1 reference data point; and

an applying module resident on the medium and operable to apply the weight to filter the at least one input signal.

56. The computer program product of claim 55, wherein the processing module applies a multi-stage Wiener filter to the observed data.

57. The computer program product of claim 55, wherein the information comprises frequency spectrum information.

58. The computer program product of claim 55, wherein the subspace has a rank smaller than the quantity of observed data points in the snapshot.

59. The computer program product of claim 55, wherein the training module collects a plurality of snapshots of at least one input signal.

60. The computer program product of claim 59, wherein the plurality of snapshots comprises time series data.

78. The computer program product of claim 55, wherein the information comprises time of arrival information.

61. A computer program product for linear prediction of information determinable from at least one signal comprising a plurality of data points, the computer program product comprising:

at least one computer readable medium;

a processing module resident on the medium and operable to process the plurality of data points by using a multi-stage Wiener filter for projecting a full rank data matrix formed from the plurality of data points into a subspace having a reduced rank to form a reduced rank data matrix;

the processing module resident on the medium and operable to minimize the mean squared prediction error in the reduced rank matrix;

the processing module resident on the medium and operable to apply a weight vector to the at least one signal to generate a predicted signal.

62. The computer program product of claim 61, further comprising a receiving module resident on the medium and operable to receive the at least one signal, the receiving module comprising a plurality of elements in an array, each element generating a data point in a snapshot.

63. The computer program product of claim 61, wherein the information comprises estimated spectrum information.

64. The computer program product of claim 61, wherein the at least one signal comprises a plurality of signals impinging at a plurality of angles on elements of an array, and wherein the information comprises angle of arrival.

79. The computer program product of claim 61, wherein the information comprises time of arrival information.

65. A computer program product for spectrum estimation of at least one signal received at a detector, the computer program product comprising:

at least one computer readable medium;

a collecting module resident on the medium and operable to collect a plurality of data snapshots from the at least one received signal, each data snapshot comprising received data points;

a defining module resident on the medium and operable to define a data matrix comprising the plurality of data snapshots;

a processing module resident on the medium and operable to process a weight by;

(a) performing a rank reduction transformation to create a reduced rank data matrix produced by decomposition of the data matrix in a multi-stage Wiener filter; and

(b) minimizing the mean squared error in the reduced rank data matrix;

and

a calculating module resident on the medium and operable to use the weight to calculate a frequency spectrum.

66. The computer program product of claim 65, wherein the at least one received signal comprises a plurality of signals received by elements of an array.

67. The computer program product of claim 65, wherein the reduced rank matrix has a rank smaller than the number of elements in the array.

68. The computer program product of claim 66, wherein the plurality of signals arrive at the elements at a plurality of different angles.

69. The computer program product of claim 65, wherein the processing module generates an error vector by performing a Gram-Schmidt transformation on the reduced rank data matrix.

70. The computer program product of claim 65, wherein the reduced rank matrix has a rank smaller than the quantity of received data points in a snapshot.

71. A method for training a linear prediction filter for prediction of information, comprising:

providing reference data having known values;

collecting observed data containing the reference data;

identifying a reduced order Krylov subspace between the observed data and the reference data.

72. A method for training a linear prediction filter for prediction of information, comprising:

providing reference data having known values;

collecting observed data containing the reference data;

identifying a reduced order Krylov subspace between the observed data and the reference data; and

maximizing mutual data between the observed data and the reference data in the subspace.