Method and apparatus for determining parameters for a parametric expression characterizing the phase of an acquired signal

• US 7,446,705 B1
• Filed: 10/24/2007
• Issued: 11/04/2008
• Est. Priority Date: 10/24/2007
• Status: Active Grant

• Current Assignee: Wisconsin Alumni Research Foundation (University of Wisconsin System)
• Original Assignee: Wisconsin Alumni Research Foundation (University of Wisconsin System)
• Inventors: Feigl, Kurt L., Thurber, Clifford H.
• Primary Examiner(s): PHAN, DAO LINDA
• Application Number:
  US11/877,779
• Time in Patent Office: 377 Days
• Field of Search: 342/357.02, 342/357.06, 342/357.09, 342/357.12, 342/357.13, 342/357.15, 701/207, 701/213, 701/215
• US Class Current: 342/357.27
• CPC Class Codes: G01S 13/9023 combined with interferometric techniques
• CPC Class Codes: G01S 13/9064 Inverse SAR [ISAR]
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
• CPC Class Codes: G01S 2013/466 by Trilateration, i.e. two antennas or two sensors determine separately the distance to a target, whereby with the knowledge of the baseline length, i.e. the distance between the antennas or sensors, the position data of the target is determined

Abstract

A method and apparatus have been developed to model wrapped phase data directly. An average statistical cost measures the misfit between the observed phase value modeled phase value. A set of acceptable values for the parameters in a parametric expression characterizing the wrapped phase is found by searching for an average statistical cost below a threshold. In the context of interferometry, the parameter values can then be used to determine the impact of a geophysical event on a geographic area. In the context of a global navigation satellite system (GNSS), such as the Global Positioning System (GPS), the values can be used to determine the position of a GNSS receiver.

Claims

1. A method comprising:

(a) acquiring a plurality of signals, each having a phase component of observed phase value characterized by a parametric model expression, the parametric model expression defined by a set of parameters of unknown value;

(b) establishing a set of values for the parameters;

(c) determining a modeled phase value for each of the phase components by evaluating the parametric expression with the set of values;

(d) determining a statistical cost for the set of parameter values as a function of a difference between the observed phase value and the modeled phase value of each of the phase components averaged over the plurality of signals;

(e) repeating (b)-(d) until finding an average statistical cost that is less than a predetermined threshold; and

(f) conveying those values for the parameters corresponding to the parametric expression that provides the desired value of average statistical cost.

2. The method of claim 1 further comprising receiving a user input associated with the signal and establishing an initial set of values for the set of parameters from the user input.

3. The method of claim 2 wherein the plurality of signals is transmitted by the Global Navigation Satellite System (GNSS) and received by a GNSS receiver of unknown position and the set of parameters defines the position of the GNSS receiver.

4. The method of claim 3 wherein the set of parameters includes the latitude coordinate, longitude coordinate, elevation, and time of day.

5. The method of claim 3 wherein the phase component is the carrier phase of the GNSS signal.

6. The method of claim 1 wherein (a) includes acquiring the signal from an interferogram defined from a first image and a second image acquired of a common geographic area and wherein the set of parameters defines geophysical characteristics of the geographic area.

7. The method of claim 6 wherein (f) includes generating a modeled interferogram from a set of values for the parameters corresponding to an acceptable value of average statistical cost.

8. The method of claim 6 wherein (f) includes generating an unwrapped interferogram.

9. The method of claim 6 wherein (a) includes acquiring a plurality of signals from a plurality of images.

10. The method of claim 6 wherein the first image is acquired of a geographic region at a first moment in time and the second image is acquired of the geographic region at a second moment in time, and further comprising displaying a map showing differences in the geographic region associated with a geophysical event occurring between the first moment in time and the second moment in time.

11. The method of claim 10 wherein the geophysical event includes a seismic, volcanic, glacial, landslide, flooding, atmospheric, or meteorological event proximate to the geographic region.

12. The method of claim 10 wherein the geophysical event includes a ground disturbance associated with extraction, injection, or explosion of material proximate to the geographic region.

13. The method of claim 6 wherein the first image is acquired of a geographic region from a first point of view and the second image is acquired of the geographic region from a second point of view, and wherein displaying the map includes showing the topographic elevation in the geographic region.

14. A Global Navigation Satellite System (GNSS) device comprising an antenna, a receiver, a display, and a processor, the processor adapted to execute a set of instructions that cause the processor to:

(a) measure a carrier phase for each of a plurality of GNSS signals acquired by the receiver;

(b) access a stored parametric expression for the carrier phase, the parametric expression defined by a set of parameters;

(c) establish a set of values for the parameters from a combination of user input values and stored values;

(d) calculate a modeled phase for the carrier phase for each of the plurality of GNSS signals from the parametric expression;

(e) calculate a statistical cost of the set of parameter values as a function of the difference between the measured value and the modeled value for each phase component, averaged over the over the plurality of GNSS signals;

(f) repeat (b)-(e) until finding an average statistical cost that is less than a predetermined threshold; and

(g) present, on the display of the GNSS device, the set of parameter values corresponding to the acceptable value of average statistical cost.

15. The GNSS device of claim 14 wherein the set of parameters describes the position of the GNSS device.

16. The GNSS device of claim 14 further comprising a user interface that allows a user to input approximate values for the set of parameters.

17. The GNSS device of claim 16 wherein the processor is further caused to receive a user input and determine initial values for the set of parameters of the parametric expression from the user input.

18. A computer-readable storage medium having a set of instructions stored thereon that when executed by a processor causes the processor to:

(a) determine a phase component for each of a plurality of recorded signals received by a GNSS receiver;

(b) access a stored parametric expression characterizing the phase components, the parametric expression defined by a set of parameters;

(c) establish values for the set of parameters from a combination of user input values and stored values;

(d) calculate a modeled value for each of the phase components from the parametric expression;

(e) calculate an average statistical cost of the set of parameter values as a function of the difference between recorded values and modeled values of each of the phase components averaged over the plurality of signals;

(f) repeat (b)-(e) until finding an acceptable average statistical cost; and

(g) convey the set of parameter values corresponding to the acceptable average statistical cost.

19. The computer readable storage medium of claim 18 wherein the plurality of signals includes GNSS signals.

20. The computer readable storage medium of claim 18 wherein the processor adjusts the values for the set of parameters until the average statistical cost is acceptable.

21. The computer readable storage medium of claim 18 wherein the processor is caused to determine a specific position of the GNSS receiver with an accuracy of better than 1 meter.

22. A computer readable storage medium having a set of instructions stored thereon that when executed by a processor causes the processor to:

(a) acquire a first image and a second image of a geographic area;

(b) generate an interferogram from the first image and the second image;

(c) select a subset of the interferogram;

(d) measure a phase of each pixel of the subset;

(e) determine a parametric expression that characterizes the phase of each pixel of the subset;

(f) determine a statistical cost for parameters of the parametric expression as a function of the phase averaged over the pixels of the subset of pixels;

(g) repeat (e)-(f) until finding an average statistical cost that is less than a predetermined threshold; and

at least one of;

(h) convey those values for the parameters corresponding to the parametric expression that provides an average statistical cost that is less than the threshold;

(i) generate a modeled interferogram from those values for the parameters corresponding to the parametric expression that provides an average statistical cost that is less than the threshold value; and

(j) unwrap the observed interferogram by using the modeled interferogram generated in (i).

23. The computer readable storage medium of claim 22 wherein the first image is acquired of a geographic region at a first moment in time and the second image is acquired of the geographic region at a second moment in time, and further comprising displaying a map showing changes in the geographic region associated with a geophysical event occurring between the first moment in time and the second moment in time.

24. The computer readable storage medium of claim 22 wherein the first image is acquired of a geographic region in one geometric configuration and the second image is acquired of the geographic region in a second geometric configuration, and wherein the processor is further caused to display a map of topographic elevation in the geographic region.