System and method for determining the location of emitters having well-behaved timing features

• US 7,342,536 B2
• Filed: 09/12/2005
• Issued: 03/11/2008
• Est. Priority Date: 09/12/2005
• Status: Expired due to Fees

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Johnson, J. Andrew
• Primary Examiner(s): Phan; Dao
• Application Number:
  US11/224,576
• Publication Number:
  US 20070075900A1
• Time in Patent Office: 911 Days
• Field of Search: 342/386, 342442-443, 342/457, 342463-465, 342/451, 455/456.1, 455/456.2, 455/456.3, 702/196
• US Class Current: 342/442
• CPC Class Codes: G01S 5/0244 Accuracy or reliability of position solution or of measurements contributing thereto
• CPC Class Codes: G01S 5/06 Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements G01S5/12 takes precedence
• CPC Class Codes: G01S 7/021 Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals

Abstract

A method, system, and computer program product are provided for determining the location of an emitter. A first subset of a plurality of parameters comprising a signal model associated with the emitter is selected. Values are estimated for the selected first subset of the plurality of parameters from a plurality of time of arrival measurements associated with the emitter and the signal model. Estimated values are generated for the plurality of parameters according to the estimated values for the selected first subset of the plurality of parameters, a plurality of time of arrival measurements, and the signal model.

Claims

1. A method for determining the location of an emitter, comprising:

selecting a first subset of a plurality of parameters comprising a signal model associated with the emitter;

estimating values for the selected first subset of the plurality of parameters from a plurality of time of arrival measurements associated with the emitter and the signal model, the estimation of the selected first subset of the plurality of parameters comprising;

defining a fitness surface from the selected first subset of the plurality of parameters and the signal model;

locating local extrema on the fitness surface;

refining the location of the local extrema to determine at least one candidate solution for the estimated values for the first subset of the plurality of parameters; and

selecting the candidate solution having the best fitness; and

generating estimated values for the plurality of parameters according to the estimated values for the selected first subset of the plurality of parameters, a plurality of time of arrival measurements, and the signal model.

2. The method of claim 1, the method further comprising:

defining a Fisher Information Matrix associated with the step of generating estimated values for the plurality of parameters;

defining a scaling matrix in which the diagonal elements have values equal to the reciprocal of the square root of the corresponding values in the Fisher Information Matrix;

producing a scaled representation of the Fisher Information Matrix using the scaling matrix; and

inverting the scaled representation of the Fisher Information Matrix to produce a Cramer-Rao Lower Bound for the step of estimating the plurality of parameters.

3. The method of claim 1, wherein the step of locating local extrema on the fitness surface includes performing a grid search of the fitness surface, the grid search having a predetermined range for each of the plurality of parameters.

4. The method of claim 3, wherein the step of generating estimated values for the plurality of parameters includes performing a grid search of a fitness surface defined by the plurality of parameters, the grid search encompassing a range of values for the plurality of parameters determined at least in part from the estimated values for the selected first subset of the plurality of parameters.

5. The method of claim 1, wherein the step of locating local extrema on the fitness surface includes the step of calculating a fitness parameter for each of a plurality of grid points in the fitness surface defined by the first subset of the plurality of parameters.

6. The method of claim 5, wherein the step of calculating a fitness parameter includes calculating the root mean square error between the plurality of time of arrival measurements and a set of time of arrival measurements calculated using a set of parameters associated with a given grid point on the fitness surface.

7. The method of claim 5, wherein the step of calculating a fitness parameter includes the step of determining the greatest common denominator of the plurality of time of arrival measurements, wherein the plurality of time of arrival measurements are adjusted according to a set of parameters associated with a given grid point.

8. The method of claim 1, the step of refining the local extrema includes the step of iteratively calculating a plurality of parameter updates for the estimated parameters in accordance with Newton'"'"'s method.

9. The method of claim 8, wherein the step of iteratively calculating a plurality of parameter updates includes calculating the inverse of an update matrix, derived from the Jacobian of the signal model, via the following steps:

defining a scaling matrix in which the diagonal elements have values equal to the square root of the corresponding values in the update matrix;

producing a scaled representation of the update matrix using the scaling matrix;

inverting the scaled representation of the update matrix; and

multiplying the scaling matrix by the scaled representation to obtain a first product and multiplying the first product by the scaling matrix to obtain the inverse of the update matrix.

10. The method of claim 1, wherein the step of estimating values for the selected first subset of the plurality of parameters comprises the following steps:

selecting a second subset of the plurality of parameters, the second subset being smaller than the first subset;

estimating values for the selected second subset of the plurality of parameters from a plurality of time of arrival measurements associated with the emitter and the signal model; and

generating estimated values for the first subset of the plurality of parameters according to the estimated values for the selected second subset of the plurality of parameters.

11. The method of claim 10, wherein the selected second subset of the plurality of parameters comprises a bearing parameter that indicates the direction of the emitter.

12. The method of claim 11, wherein the selected first subset of the plurality of parameters comprises at least one Cartesian coordinate associated with the location of the emitter.

13. A computer program product, operative in a data processing system and implemented on a computer readable medium, for determining the location of an emitter having well-behaved timing features from a plurality of time of arrival measurements associated with the emitter comprising:

a parameter selector that selects a first subset of a plurality of parameters comprising a signal model associated with the emitter;

a parameter estimator that estimates values for the selected first subset of the plurality of parameters from the plurality of time of arrival measurements and the signal model; and

a parameter evaluator that evaluates the estimated parameter values and directs the parameter selector to select a second, larger subset of the plurality of parameters if an error value associated with the estimation of the first subset meets a threshold value and directs the parameter evaluator to estimate the parameters using at least one additional time of arrival measurement if the error value does not meet a threshold value.

14. The computer program product of claim 13, wherein the computer program product is implemented as part of a mobile receiver.

15. The computer program product of claim 14, wherein the plurality, of parameters comprising the signal model includes an acceleration sensitivity coefficient that models the effect of acceleration on a time reference associated with the mobile receiver as a linear coefficient to the velocity of the mobile receiver.

16. A method for determining the location of an emitter, comprising:

estimating a plurality of parameters for a signal model associated with the emitter from a plurality of time of arrival measurements associated with the emitter and the signal model;

defining a Fisher Information Matrix associated with the step of estimating the plurality of parameters;

defining a scaling matrix in which the diagonal elements have values equal to the square root of the corresponding values in the Fisher Information Matrix;

producing a scaled representation of the Fisher Information Matrix using the scaling matrix; and

inverting the scaled representation of the Fisher Information Matrix.

17. The method of claim 16, wherein the step of estimating the plurality of parameters comprises the steps of:

selecting a first subset of the plurality of parameters;

estimating values for the selected first subset of the plurality of parameters from the plurality of time of arrival measurements; and

estimating values for a second, larger subset of the plurality of parameters according to the estimated values for the selected first subset of the plurality of parameters.

18. The method of claim 16, wherein the step of producing a scaled representation of the Fisher Information Matrix comprises the steps of determining the product of the scaling matrix and the Fisher Information matrix to produce a first product and determining the product of the first product and the scaling matrix, such that the diagonal elements of the scaled representation have a value of unity.

19. The method of claim 16, further comprising the step of multiplying the scaling matrix by the scaled representation to obtain a second product and multiplying the second product by the scaling matrix to obtain the Cramer-Rao lower bound.