Assured-integrity monitored-extrapolation navigation apparatus

• US 5,583,774 A
• Filed: 06/16/1994
• Issued: 12/10/1996
• Est. Priority Date: 06/16/1994
• Status: Expired due to Term

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Litton Systems Incorporated (Northrop Grumman Corporation)
• Inventors: Diesel, John W.
• Primary Examiner(s): Teska, Kevin J.
• Assistant Examiner(s): Walder, Jr., Stephen J.
• Application Number:
  US08/260,520
• Time in Patent Office: 908 Days
• Field of Search: 364/443, 364/449, 364/459, 73/178 R, 342/352, 342/356, 342/357, 342/451, 342/457
• US Class Current: 701/200
• CPC Class Codes: G01C 21/165 combined with non-inertial navigation instruments
• CPC Class Codes: G01S 1/026 of associated receivers
• CPC Class Codes: G01S 19/49 whereby the further system is an inertial position system, e.g. loosely-coupled

Abstract

The assured-integrity monitored-extrapolation (AIME) navigation apparatus selectively utilizes measurements provided by ancillary sources at periodic intervals in determining the state of the platform on which the apparatus is mounted. The measurements have attributes which are measures of quality, quality being a measure of the usefulness of the measurement in accurately estimating the state of a platform. The AIME apparatus makes its selection of measurements for state determination on the basis of estimates of the values of these quality attributes. The determination of the quality of a time sequence of measured values of a particular quantity requires an evaluation time for its accomplishment. The AIME apparatus therefore determines the platform'"'"'s state in two phases. It obtains highly-accurate determinations of the states of the platform at times prior to present time minus the evaluation time by using the quality measures available at these times and using only those measurements that are determined to be of high quality in the determination of state at these times. The platform state at present time is then obtained by extrapolation of the highly-accurate state at time minus the evaluation time using measurements whose quality is more uncertain.

Claims

1. A navigation apparatus comprising a digital processor and a memory that utilizes a first subset and a second subset of a set of measured quantities which do not vary by amounts that are improbable or impossible, the set of measured quantities being provided at periodic time intervals delta-time by an external source for determining the state of a platform on which the apparatus is mounted, the set of measured quantities being presumptively useful in determining platform state, the number of members of the first subset being equal to or greater than zero but less than the total number of members of the set of measured quantities, the members of the set of measured quantities not included in the first subset being subject to selection for the second subset by the apparatus in accordance with a predetermined set of selection rules.

2. The navigation apparatus of claim 1 wherein the measured quantities subject to selection for the second subset have one or more attributes, the apparatus utilizing estimates of the attributes in selecting the members of the second subset.

3. The navigation apparatus of claim 2 wherein the one or more attributes of a measured quantity subject to selection for the second subset are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

4. The navigation apparatus of claim 2 wherein the estimates of the attributes are provided by an external source.

5. The navigation apparatus of claim 2 wherein the estimates of the attributes are determined by the apparatus from the measured quantities.

6. The navigation apparatus of claim 5 wherein the measured quantities for a time period extending from present time minus a predetermined time to present time are used in the determination of the estimates of the attributes.

7. The navigation apparatus of claim 5 wherein the estimates of the attributes and the state of the platform are determined by a minimal mean-square-error process.

8. The navigation apparatus of claim 7 wherein the minimal mean-square-error process is a Kalman filter.

9. The navigation apparatus of claim 8 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, an average differential observation vector being obtained by averaging the differential observation vector over T delta-time time intervals, an average differential state vector being obtained by averaging the differential state vector over T delta-time time intervals, an average observation matrix being obtained by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T, the Kalman filter extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix, the Kalman filter transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix, the Kalman filter obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix.

10. The navigation apparatus of claim 9 wherein values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix are calculated and retained in the memory for at least KT delta-time intervals, K being an integer.

11. The navigation apparatus of claim 10 wherein the calculated values retained in memory are used in the determination of the estimates of the attributes.

12. The navigation apparatus of claim 11 wherein the estimates of the attributes and the state of the platform are determined by a minimal mean-square-error process.

13. The navigation apparatus of claim 12 wherein the minimal mean-square-error process is a Kalman filter.

14. The navigation apparatus of claim 1 wherein a predetermined first set of selection rules pertain to state determinations prior to a time equal to present time minus a predetermined time interval and a predetermined second set of selection rules pertain to state determinations from present time minus the predetermined time interval to present time.

15. The navigation apparatus of claim 14 wherein the state of the platform is determined by a first minimal mean-square-error process prior to present time minus the predetermined time interval and by a second minimal mean-square-error process from present time minus the predetermined time interval to present time.

16. The navigation apparatus of claim 15 wherein the first minimal mean-square-error process is a first Kalman filter and the second minimal mean-square-error process is a second Kalman filter, the state vector and the covariance matrix obtained by the first Kalman filter at present time minus the predetermined time interval being inputs to the second Kalman filter.

17. The navigation apparatus of claim 16 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, an average differential observation vector being obtained by averaging the differential observation vector over T delta-time time intervals, an average differential state vector being obtained by averaging the differential state vector over T delta-time time intervals, an average observation matrix being obtained by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T, the Kalman filter extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix, the Kalman filter transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix, the Kalman filter obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix, the first and second Kalman filters using the same calculated T-transition matrices and average observation matrices.

18. The navigation apparatus of claim 17 wherein values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix are calculated and retained in the memory for at least KT delta-time intervals, K being an integer.

19. The navigation apparatus of claim 18 wherein the calculated values retained in memory are used in the determination of the state of the platform.

20. The navigation apparatus of claim 19 wherein the estimates of the state of the platform are determined by a minimal mean-square-error process.

21. The navigation apparatus of claim 20 wherein the minimal mean-square-error process is a Kalman filter.

22. The navigation apparatus of claim 1 wherein the state of the platform is determined by a minimal mean-square-error process.

23. The navigation apparatus of claim 22 wherein the minimal mean-square-error process is a Kalman filter.

24. The navigation apparatus of claim 23 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, an average differential observation vector being obtained by averaging the differential observation vector over T delta-time time intervals, an average differential state vector being obtained by averaging the differential state vector over T delta-time time intervals, an average observation matrix being obtained by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T, the Kalman filter extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix, the Kalman filter transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix, the Kalman filter obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix.

25. The navigation apparatus of claim 24 wherein values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix are calculated and retained in the memory for at least KT delta-time intervals, K being an integer.

26. The navigation apparatus of claim 25 wherein the calculated values retained in memory are used in the determination of the state of the platform.

27. The navigation apparatus of claim 26 wherein the estimates of the state of the platform are determined by a minimal mean-square-error process.

28. The navigation apparatus of claim 27 wherein the minimal mean-square-error process is a Kalman filter.

29. The navigation apparatus of claim 1 wherein the measured quantities subject to selection for the second subset are the measured ranges to a plurality of earth satellites.

30. The navigation apparatus of claim 29 wherein the measured quantities have one or more attributes, the apparatus utilizing estimates of one or more of the attributes in selecting the members of the second subset.

31. The navigation apparatus of claim 30 wherein the one or more attributes of a measured quantity are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

32. The navigation apparatus of claim 31 wherein the range to each satellite includes a range bias error RBE, the behavior of the RBE for each satellite as a function of time being representable by the expression [RBE₀ +RBE₁.(TIME-TIME₀)] where TIME denotes time and RBE₀ and RBE₁ are equal to RBE and the time rate of change of RBE respectively at TIME equal to TIME₀, the quantities RBE₀, var_-- RBE₀, RBE₁, and var_-- RBE₁ constituting quality attributes, var_-- RBE₀ and var_-- RBE₁ being the variances of RBE₀ and RBE₁ respectively, smaller magnitudes of RBE₀, var_-- RBE₀, RBE₁, and var_-- RBE₁ being associated with a higher quality.

33. The navigation apparatus of claim 32 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold.

34. The navigation apparatus of claim 32 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold and RBE₀ does not exceed a second threshold.

35. The navigation apparatus of claim 32 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold, RBE₀ does not exceed a second threshold, and RBE₁ does not exceed a third threshold.

36. The navigation apparatus of claim 1 wherein the set of measured quantities includes at least one satellite measured quantity and at least one measured quantity from a second source, the satellite measured quantities comprising the range and range rate for a plurality of earth satellites, the satellite measured quantities as functions of time being associated with noise spectral densities that are functions of frequency, the second-source measured quantities comprising the position, velocity, and acceleration of the platform, the second-source measured quantities as functions of time being associated with noise spectral densities that are functions of frequency, the noise spectral density for satellite measured quantities being greater than that for second-source measured quantities at high frequencies, the noise spectral density for satellite measured quantities being less than that for second-source measured quantities at low frequencies, the second-source measured quantities included in the set of measured quantities being in the first subset, the satellite measured quantities included in the set of measured quantities being subject to selection for the second subset.

37. The navigation apparatus of claim 1 wherein the set of measured quantities includes at least one satellite measured quantity and at least one inertial reference system measured quantity, the satellite measured quantities comprising the range and range rate for a plurality of earth satellites, the inertial reference system measured quantities comprising the position, velocity, and acceleration of the inertial reference system, the inertial reference system measured quantities included in the set of measured quantities being in the first subset, the satellite measured quantities included in the set of measured quantities being subject to selection for the second subset.

38. The navigation apparatus of claim 37 wherein the measured quantities subject to selection for the second subset have one or more attributes, the apparatus utilizing estimates of one or more of the attributes in selecting the members of the second subset.

39. The navigation apparatus of claim 38 wherein the one or more attributes of a measured quantity subject to selection for the second subset are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

40. The navigation apparatus of claim 39 wherein the range to each satellite includes a range bias error RBE, the behavior of the RBE for each satellite as a function of time being representable by the expression [RBE₀ +RBE₁.(TIME-TIME₀)] where TIME denotes time and RBE₀ and RBE₁ are equal to RBE and the time rate of change of RBE respectively at TIME equal to TIME₀, the quantities RBE₀, var_-- RBE₀, RBE₁, and var_-- RBE₁ constituting quality attributes, var_-- RBE₀ and var_-- RBE₁ being the variances of RBE₀ and RBE₁ respectively, smaller magnitudes of RBE₀, var_-- RBE₀, RBE₁, and var_-- RBE₁ being associated with a higher quality.

41. The navigation apparatus of claim 40 wherein the quantities RBE₀, var_-- RBE0, RBE₁, and var_-- RBE₁ for a specified satellite are determined by solving the navigation problem with a Kalman filter, the input values for var_-- RBE₀ and var_-- RBE₁ for the specified satellite that are supplied to the Kalman filter being sufficiently large that the estimated errors in RBE₀ and RBE₁ and the estimated values of var_-- RBE₀ and var_-- RBE₁ obtained by the Kalman filter for the specified satellite are essentially determined by the other satellites.

42. The navigation apparatus of claim 40 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold.

43. The navigation apparatus of claim 40 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold and RBE₀ does not exceed a second threshold.

44. The navigation apparatus of claim 40 wherein the predetermined set of selection rules are that a range measurement is selected if var_-- RBE₀ does not exceed a first threshold, RBE₀ does not exceed a second threshold, and RBE₁ does not exceed a third threshold.

45. The navigation apparatus of claim 39 wherein the quality of a target satellite'"'"'s measured quantities is determined by solving the satellite-inertial navigation problem with a Kalman filter, the input values for the variances of the target satellite'"'"'s measured quantities being large enough to assure that the estimates of the measured quantities and the variances of the measured quantities for the target satellite are essentially determined by the other satellites, the quality of the target satellite'"'"'s measured quantities being determined by the degree to which estimates of the target satellite'"'"'s measured quantities and the variances of the measured quantities approach those of the other satellites.

46. The navigation apparatus of claim 39 wherein the measured quantities for a time period extending from present time minus a predetermined time to present time are used in the determination of the estimates of the attributes.

47. The navigation apparatus of claim 46 wherein the estimates of the attributes and the state of the platform are determined by a minimal mean-square-error process.

48. The navigation apparatus of claim 47 wherein the minimal mean-square-error process is a Kalman filter process.

49. The navigation apparatus of claim 48 wherein the Kalman filter error states for the platform include one or more of the group consisting of position errors, velocity errors, navigation axis misalignment errors, gyro bias errors, acceleration bias errors, barometric altitude bias error, and barometric altitude bias rate error.

50. The navigation apparatus of claim 48 wherein the Kalman filter error states for the satellite system include one or more of the group consisting of receiver clock bias error, receiver clock bias rate error, range bias error, and range bias rate error.

51. The navigation apparatus of claim 48 wherein the residuals in the Kalman filter solution pertaining to satellite measured quantities are attributes of those quantities.

52. The navigation apparatus of claim 48 wherein the satellite measured quantities selected for the second subset are used to estimate the satellite-inertial navigation system state and the error states associated therewith at present time minus the predetermined time interval, the selection of the satellite measured quantities being based on the estimates of their attributes exceeding a predetermined first quality level.

53. The navigation apparatus of claim 52 wherein the satellite measured quantities selected for the second subset are used to estimate the satellite-inertial navigation system state and the error states associated therewith at present time, the selection of the satellite measured quantities being based on the estimates of their attributes exceeding a predetermined second quality level, the inputs to the Kalman filter being the outputs of the Kalman filter at present time minus the predetermined time interval, the second quality level being lower than the first quality level.

54. The navigation apparatus of claim 52 wherein the inertial navigation system, having been calibrated by the Kalman filter at present time minus the predetermined time interval, operates independently when the estimates of the attributes of the satellite measured quantities all fail to exceed the predetermined first quality level.

55. The navigation apparatus of claim 48 wherein the difference between estimates of the range bias error at present time minus the predetermined time and at present time for each satellite is a quality attribute for the measured quantities associated with that satellite, the difference being called the drift rate, the lower the drift rate, the higher the quality.

56. The navigation apparatus of claim 46 wherein the values of at least one satellite measured quantity are retained in memory for a predetermined time and then discarded, the predetermined time being longer than the correlation time of the noise in the satellite measured quantity.

57. The navigation apparatus of claim 46 wherein weighted sums of the values of at least one satellite measured quantity are computed at T delta-time intervals, retained in memory for a predetermined time, and then discarded, T being a predetermined integer, the predetermined time being longer than the correlation time of the noise in the satellite measured quantity.

58. A method that utilizes a first subset and a second subset of a set of measured quantities which do not vary by amounts that are improbable or impossible, the set of measured quantities being provided at periodic time intervals delta-time by an external source for determining the state of a platform, the measured quantities being presumptively useful in determining platform state, the number of members of the first subset being equal to or greater than zero but less than the total number of members of the set of measured quantities, the members of the set of measured quantities not included in the first subset being subject to selection for the second subset in accordance with a predetermined set of selection rules, the method comprising the steps:

selecting the measured quantities in the second subset;

determining the state of the platform.

59. The method of claim 58 wherein the measured quantities subject to selection for the second subset have one or more attributes and estimates of one or more of the attributes are utilized in selecting the members of the second subset.

60. The method of claim 59 wherein the one or more attributes of a measured quantity subject to selection for the second subset are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

61. The method of claim 59 wherein the estimates of the attributes are provided by an external source.

62. The method of claim 59 further comprising the step:

determining the estimates of the attributes from the measured quantities.

63. The method of claim 62 wherein the estimates of the attributes and the state of the platform are determined by a minimal mean-square-error process.

64. The method of claim 63 wherein the minimal mean-square-error process is a Kalman filter process.

65. The method of claim 64 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, the step of determining the state of the platform comprising the steps:

obtaining an average differential observation vector by averaging the differential observation vector over T delta-time time intervals;

obtaining an average differential state vector by averaging the differential state vector over T delta-time time intervals;

obtaining an average observation matrix by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T;

extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix;

transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix;

obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix.

66. The method of claim 65 further comprising the steps:

calculating the values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix at T delta-time intervals;

retaining the calculated values for at least KT delta-time intervals, K being an integer.

67. The method of claim 58 wherein a first predetermined set of selection rules pertain to state determinations prior to a time equal to present time minus a predetermined time interval and a second predetermined set of selection rules pertain to state determinations from present time minus the predetermined time interval to present time.

68. The method of claim 67 wherein the state determining step comprises the steps:

determining the platform state by a first minimal mean-square-error process prior to present time minus the predetermined time interval;

determining the platform state by a second minimal mean-square-error process from present time minus the predetermined time interval to present time.

69. The method of claim 68 wherein the first minimal mean-square-error process is a first Kalman filter process and the second minimal mean-square-error process is a second Kalman filter process, the method further comprising the step:

using the state vector and the covariance matrix obtained by the first Kalman filter process at present time minus the predetermined time interval as inputs to the second Kalman filter process.

70. The method of claim 58 wherein the state of the platform is determined by a minimal mean-square-error process.

71. The method of claim 70 wherein the minimal mean-square-error process is a Kalman filter process.

72. The method of claim 71 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, the step of determining the state of the platform comprising the steps:

obtaining an average differential observation vector by averaging the differential observation vector over T delta-time time intervals;

obtaining an average differential state vector by averaging the differential state vector over T delta-time time intervals;

obtaining an average observation matrix by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T;

extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix;

transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix;

obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix.

73. The method of claim 72 further comprising the steps:

calculating the values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix at T delta-time intervals;

retaining the calculated values for at least KT delta-time intervals, K being an integer.

74. The method of claim 71 wherein, using Kalman filter terminology, a differential observation vector substitutes for the observation vector and a differential state vector substitutes for the state vector, the differential observation vector being the difference between the actual observation vector and the observation vector that would be obtained if the actual state of the platform were the same as the estimated state, the differential state vector being the difference between the actual state vector and the state vector that would be obtained if the actual state of the platform were the same as the estimated state, the step of determining the state of the platform comprising the steps:

obtaining an average differential observation vector by averaging the differential observation vector over T delta-time time intervals;

obtaining an average differential state vector by averaging the differential state vector over T delta-time time intervals;

obtaining an average observation matrix by averaging the product of the t-transition matrix and the observation matrix over T delta-time time intervals, the t-transition matrix being the matrix which extrapolates the differential state vector t delta-time intervals into the future, T being a predetermined integer greater than 1 and t being any integer from 1 to T;

extrapolating the differential state vector by T delta-time intervals by means of the T-transition matrix;

transforming the extrapolated differential state vector into the differential observation vector for the same time by means of the average observation matrix;

obtaining the associated covariance matrix and the filter gain matrix by means of the T-transition matrix and the average observation matrix.

75. The method of claim 74 further comprising the steps:

calculating the values of the average differential state vector, the average differential observation vector, the average observation matrix, and the T-transition matrix at T delta-time intervals;

retaining the calculated values for at least KT delta-time intervals, K being an integer.

76. The method of claim 58 wherein the measured quantities are the measured ranges to a plurality of earth satellites, none of the measured quantities being in the first subset.

77. The method of claim 76 wherein the measured quantities have one or more attributes and estimates of one or more of the attributes are utilized in selecting the members of the second subset.

78. The method of claim 77 wherein the one or more attributes of a measured quantity are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

79. The method of claim 78 wherein the range to each satellite includes a range bias error RBE, the behavior of the RBE for each satellite as a function of time being representable by the expression (RBE₀ +RBE₁.TIME) where RBE₀ and RBE₁ are constants and TIME denotes time, RBE₀, s.d.RBE₀, and RBE₁ constituting quality attributes, s.d.RBE₀ being the standard deviation of RBE₀, smaller magnitudes of RBE₀, s.d.RBE₀, and RBE₁ being associated with a higher quality.

80. The method of claim 79 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold.

81. The method of claim 79 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold and RBE₀ does not exceed a second threshold.

82. The method of claim 79 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold, RBE₀ does not exceed a second threshold, and RBE₁ does not exceed a third threshold.

83. The method of claim 58 wherein the set of measured quantities are the measured ranges to a plurality of earth satellites and the position, velocity, and acceleration of the platform measured by an inertial reference system, the position, velocity, and acceleration measurements by the inertial reference system being in the first subset, the measured ranges being subject to selection for the second subset.

84. The method of claim 83 wherein the measured quantities subject to selection for the second subset have one or more attributes and estimates of one or more of the attributes are utilized in selecting the members of the second subset.

85. The method of claim 84 wherein the one or more attributes of a measured quantity subject to selection for the second subset are measures of quality, quality being a measure of the usefulness of the measured quantity in accurately estimating the state of a platform.

86. The method of claim 85 wherein the range to each satellite includes a range bias error RBE, the behavior of the RBE for each satellite as a function of time being representable by the expression (RBE₀ +RBE₁.TIME) where RBE₀ and RBE₁ are constants and TIME denotes time, RBE₀, s.d.RBE₀, and RBE₁ constituting quality attributes, s.d.RBE₀ being the standard deviation of RBE₀, smaller magnitudes of RBE₀, s.d.RBE₀, and RBE₁ being associated with a higher quality.

87. The method of claim 86 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold.

88. The method of claim 86 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold and RBE₀ does not exceed a second threshold.

89. The method of claim 86 wherein the predetermined set of selection rules are that a range measurement is selected if s.d.RBE₀ does not exceed a first threshold, RBE₀ does not exceed a second threshold, and RBE₁ does not exceed a third threshold.