Estimation algorithms and location techniques

• US 20040034465A1
• Filed: 04/20/2003
• Published: 02/19/2004
• Est. Priority Date: 04/20/2002
• Status: Active Grant

• Current Assignee: Scientific Food Solutions, LLC
• Original Assignee: John Louis Spiesberger
• Inventors: Spiesberger, John Louis
• Granted Patent: US 7,219,032 B2
• Time in Patent Office: Days
• US Class Current: 701/200
• CPC Class Codes: G01S 5/02 using radio waves using satellite radio beacon systems for determining position G01S19/00
• CPC Class Codes: G01V 1/28 Processing seismic data, e.g. for interpretation or for event detection G01V1/48 takes precedence
• CPC Class Codes: G01V 2200/14 Quality control
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

Robust methods are developed to provide bounds and probability distributions for the locations of objects as well as for associated variables that affect the accuracy of the location such as the positions of stations, the measurements, and errors in the speed of signal propagation. Realistic prior probability distributions of pertinent variables are permitted for the locations of stations, the speed of signal propagation, and errors in measurements. Bounds and probability distributions can be obtained without making any assumption of linearity. The sequential methods used for location are applicable in other applications in which a function of the probability distribution is desired for variables that are related to measurements.

Claims

1. A method to estimate at least one function of a probability distribution of at least one variable, where the variables consist of values of a primary function and arguments of said primary function, and where at least one said argument is a datum, and the data are separated into at least two groups and processed sequentially, comprising the steps of:

(a) assigning prior bounds for said datum, said arguments, and said primary function;

(b) assigning prior probability distributions within said prior bounds for all said arguments of said primary function;

(c) generating realizations of said primary function from realizations of said arguments using a Monte-Carlo technique;

(d) determining at least one posterior bound among said realizations of said primary function and said arguments;

(e) stopping the sequential processing when there are less than a minimum number of acceptable said realizations of said primary function within its said prior bounds;

(f) stopping said sequential processing when at least one said posterior bound is inconsistent with at least one said prior bound;

(g) determining at least one final bound after said data are sequentially processed;

whereby at least one said function of said probability distribution of at least one said variable is estimated, where said variables consist of said values of said primary function and said arguments of said primary function, and where at least one said argument is said datum, and said data are separated into at least two said groups and processed sequentially.

2. The method of claim 1 further including transitioning at least one said posterior bound between the sequential steps using a model.

3. The method of claim 1 further including forming at least one said function of said probability distribution other than said bound.

4. The method of claim 1 further including forming at least one said function of said probability distribution other than said posterior bound.

5. The method of claim 1 wherein said primary function is the location of a primary point determined from at least one difference in travel time between said primary point and two stations.

6. The method of claim 2 wherein said primary function is the location of a primary point determined from at least one difference in travel time between said primary point and two stations.

7. The method of claim 3 wherein said primary function is the location of a primary point estimated from at least one difference in travel time between said primary point and two stations.

8. The method of claim 4 wherein said primary function is the location of a primary point estimated from at least one difference in travel time between said primary point and two stations.

9. The method of claim 1 wherein said primary function is the location of a primary point estimated from at least one sum in travel time between said primary point and two stations.

10. The method of claim 2 wherein said primary function is the location of a primary point estimated from at least one sum in travel time between said primary point and two stations.

11. The method of claim 3 wherein said primary function is the location of a primary point estimated from at least one sum in travel time between said primary point and two stations.

12. The method of claim 4 wherein said primary function is the location of a primary point estimated from at least one sum in travel time between said primary point and two stations.

13. The method of claim 9 further including using directional data of signal from at least one station.

14. The method of claim 10 further including using directional data of signal from at least one station.

15. The method of claim 11 further including using directional data of signal from at least one station.

16. The method of claim 12 further including using directional data of signal from at least one station.

17. The method of claim a1 wherein said primary function is the location of a primary point determined from at least one travel time between said primary point and one station.

18. A method in hyperbolic location for estimating a function of a probability distribution of at least one primary point and a function of a probability distribution of at least one other variable comprising the steps of:

(a) estimating data between at least one said primary point and a constellation of stations;

(b) establishing prior bounds for the variables;

(c) implementing a Monte-Carlo technique to generate candidate realizations of location on hyperbolic surfaces for said primary point within said prior bounds from all other said variables;

(d) stopping when there are less than a minimum number of said realizations of said primary points within their said prior bounds;

(e) estimating said function of said probability distribution for said primary point and at least one said function of said probability distribution of said other variable;

whereby said function of said probability distribution of at least one said primary point and said function of said probability distribution of at least one other said variable is estimated for said hyperbolic location.

19. The method of claim b1 further including using at least one database to establish at least one spatial bound for the location of at least one said primary point.

20. A method for analytically estimating at least one location of at least one primary point using isodiachronic location comprising the steps of:

(a) estimating differences in travel time from at least one said primary point and a constellation of stations;

(b) estimating speeds of a signal between said primary point and each said station where at least one said speed is different than others;

(c) obtaining the analytical solution for said isodiachronic location of said primary point;

(d) stopping if there is no said solution for said location of said primary point;

whereby at least one said location for at least said primary point is estimated analytically using said isodiachronic location.

21. The method of claim c1 further including iterating said analytical solution for convergence when effects of advection significantly alter at least one said difference in travel time.

22. A method of obtaining at least one function of a probability distribution for location of at least one primary point using isodiachronic location comprising the steps of:

(a) estimating differences in travel time from at least number of stations in a constellation;

(b) establishing prior bounds for said location of said primary point and for all arguments of a primary function for said location of said primary point;

(c) assigning probability distributions to said arguments;

(d) generating realizations of said arguments to compute realizations of said primary function for said location within its said prior bounds using a Monte-Carlo technique;

(e) forming said function of said probability distribution for said primary point from said realizations;

(f) stopping when there are less than an acceptable number of said realizations of said primary point;

whereby at least one said function of said probability distribution for said location of at least one said primary point using said isodiachronic location is estimated.

23. The method of claim 22 further including obtaining at least one bound for location of at least one said primary point from at least one database of synthesized travel time differences.

24. The method of claim 22 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

25. The method of claim 23 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

26. The method of claim 22 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds said number in said constellation.

27. The method of claim 23 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds said number in said constellation.

28. A method for analytically estimating a location of at least one primary point using isosigmachronic location comprising the steps of:

(a) estimating sums of travel times for a constellation of stations and said primary point;

(b) estimating speeds of a signal between said primary point and each said station where at least one said speed is different than others;

(c) utilizing at least one said analytical solution for said location of said primary point;

(d) stopping if there is no said solution for said location of said primary point;

whereby said location of said primary point is estimated with at least one said analytical solution using said isosigmachronic location.

29. The method of claim 28 further including iterating at least one said analytical solution for convergence when effects of advection significantly alter at least one of said sums of travel times.

30. A method of obtaining at least one function of a probability distribution for a location of at least one primary point using isosigmachronic location comprising the steps of:

(a) estimating sums of travel times from at least one constellation and said primary point;

(b) establishing prior bounds for said location of said primary point and for all arguments of a primary function for said location of said primary point;

(c) assigning probability distributions to said arguments;

(d) generating realizations of said arguments to compute realizations of said primary function for said location within its said prior bounds using a Monte-Carlo technique;

(e) forming said function of said probability distribution for said primary point from said realizations;

(f) stopping when there are less than an acceptable number of said realizations of said primary point;

whereby at least one said function of said probability distribution for said location of at least one said primary point using said isosigmachronic location is estimated.

31. The method of claim 30 further including obtaining at least one bound for location of said primary point from at least one database of synthesized sums of travel times.

32. The method of claim 30 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

33. The method of claim 31 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

34. The method of claim 30 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds number in said constellation.

35. The method of claim 31 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds number in said constellation.

36. A method of obtaining at least one function of a probability distribution for a location of at least one primary point using ellipsoidal location comprising the steps of:

(a) estimating sums of travel times from at least one constellation and said primary point;

(b) establishing prior bounds for said location of said primary point and for all arguments of a primary function for said primary point;

(c) assigning probability distributions to said arguments;

(d) generating realizations of said arguments to compute realizations of said primary function for said location within its said prior bounds using a Monte-Carlo technique and within each realization, speeds of signal propagation are identical;

(e) forming said function of said probability distribution for said primary point from said realizations;

(f) stopping when there are less than an acceptable number of said realizations of said primary point;

whereby at least one said function of said probability distribution for said location of at least one said primary point using said ellipsoidal location is estimated.

37. The method of claim 36 further including obtaining at least one bound for location of at least one said primary point from at least one database of synthesized sums of travel times.

38. The method of claim 36 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

39. The method of claim 37 further including forming a function of a probability distribution of at least one said argument from its posterior realizations.

40. The method of claim 36 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds number in said constellation.

41. The method of claim 37 further including using Sequential Bound Estimation to estimate at least one function of a probability distribution of at least one variable from at least one of its posterior realizations when the number of said stations exceeds number in said constellation.

42. A method for estimating at least one function of a probability distribution of a location of at least one primary point using ellipsoidal geometry comprising the steps of:

(a) estimating travel time of signal and estimate of incoming signal direction at a station;

(b) establishing prior bounds for all variables functionally affecting location of said primary point;

(c) assigning probability distributions between said prior bounds for all said variables except said location of said primary point;

(d) generate realizations with Monte-Carlo technique of said location of said primary point using analytical solution for the ellipsoidal location and retaining said locations within prior bounds;

(e) stop if there are fewer than a minimum number of acceptable said realizations of said primary point;

(f) estimate at least one posterior bound of said primary point from said realizations;

whereby at least one said function of said probability distribution of said location of at least one said primary point using said ellipsoidal geometry is estimated.

43. The method of claim 42 further including estimating at least one function of a probability distribution of at least one said variable besides that representing said location of said primary point.

44. The method of claim 42 further including assimilating at least one more travel time and directional set of data from any station using Sequential Bound Estimation.

45. The method of claim 43 further including assimilating at least one more travel time and directional set of data from any station using Sequential Bound Estimation.

46. The method of claim 42 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

47. The method of claim 43 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

48. The method of claim 44 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

49. The method of claim 45 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

50. A method for estimating at least one function of a probability distribution of a location of at least one primary point using isosigmachronic geometry comprising the steps of:

(a) estimating travel time of signal and estimate of incoming signal direction at a station;

(b) establishing prior bounds for all variables functionally affecting location of said primary point;

(c) assigning probability distributions between said prior bounds for all said variables except said location of said primary point;

(d) generate realizations with Monte-Carlo technique of said location of said primary point using analytical solution for the isosigmachronic location and retaining said locations within prior bounds;

(e) stop if there are fewer than a minimum number of acceptable said realizations of said primary point;

(f) estimate at least one posterior bound of said primary point from said realizations;

whereby at least one said function of said probability distribution of said location of said primary point using said isosigmachronic geometry is estimated.

51. The method of claim 50 further including estimating at least one function of a probability distribution of at least one said variable besides that representing said location of said primary point.

52. The method of claim 50 further including assimilating at least one more travel time and directional set of data from any station using Sequential Bound Estimation.

53. The method of claim 51 further including assimilating at least one more travel time and directional set of data from any station using Sequential Bound Estimation.

54. The method of claim 50 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

55. The method of claim 51 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

56. The method of claim 52 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.

57. The method of claim 53 wherein a two-dimensional geometry is established to approximate said location of at least one said primary point on a horizontal plane.