Method and system for estimating ionospheric delay using a single frequency or dual frequency GPS signal

• US 6,781,542 B2
• Filed: 01/13/2003
• Issued: 08/24/2004
• Est. Priority Date: 01/13/2003
• Status: Active Grant

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Klotz, Harold A. Jr., Hoven, Randall M.
• Primary Examiner(s): Issing, Gregory C.
• Assistant Examiner(s): Mull, Fred H
• Application Number:
  US10/341,080
• Publication Number:
  US 20040135721A1
• Time in Patent Office: 589 Days
• Field of Search: 342/357-1-3
• US Class Current: 342/357.59
• CPC Class Codes: G01S 19/215 issues related to spoofing
• CPC Class Codes: G01S 19/32 Multimode operation in a single same satellite system, e.g. GPS L1/L2

Abstract

A global positioning system comprising: (a) a GPS receiver configured to (1) receive a plurality of signals from a plurality of visible GPS satellites, and (2) produce a plurality of pseudorange measurements from the received signals, the pseudorange measurements being indicative of the GPS receiver'"'"'s position and having an amount of ionospheric delay error contained therein, (b) a processor configured to estimate the amount of ionospheric delay in the pseudorange measurements by (1) estimating an amount of global ionospheric delay attributable collectively to the plurality of visible GPS satellites, and (2) estimating a plurality of amounts of local ionospheric delays, each local ionospheric delay being attributable to a different visible GPS satellite. Preferably the processor implements the ionospheric delay estimations using a modified Kalman filter.

Claims

1. A method for estimating ionospheric delays present in pseudorange measurements produced by a global positioning system (GPS) receiver configured to track a plurality of GPS satellites, the method comprising:

at a Processor that receives pseudorange measurements from a single GPS receiver, (1) estimating an amount of global ionospheric delay in the pseudorange measurements attributable to all of the tracked GPS satellites; and

(2) for each tracked GPS satellite, estimating an amount of local ionospheric delay in the pseudorange measurements attributable thereto.

2. The method of claim 1 wherein the global ionospheric delay estimating step comprises estimating, at the processor, the global ionospheric delay amount as a function of a single GPS frequency L₁ or L₂.

3. The method of claim 2 wherein the local ionospheric delay estimating step comprises estimating, at the processor, each of the local ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

4. The method of claim 1 wherein the local ionospheric delay estimating step comprises estimating, at the processor, each of the local ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

5. The method of claim 1 wherein the GPS receiver is in motion.

6. A method for estimating ionospheric delays present in pseudorange measurements produced by a global positioning system (GPS) receiver configured to track a plurality of GPS satellites, the method comprising:

estimating an amount of global ionospheric delay attributable to all of the tracked GPS satellites as a function of a single GPS frequency L₁ or L₂; and

for each tracked GPS satellite, estimating an amount of local ionospheric delay attributable thereto.

7. The method of claim 6 wherein the local ionospheric delay estimating step comprises estimating each of the local ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

8. The method of claim 6 further comprising performing each of the recited steps for a GPS receiver that is in motion.

9. A method for estimating ionospheric delays present in pseudorange measurements produced by a global positioning system (GPS) receiver configured to track a plurality of GPS satellites, the method comprising:

estimating an amount of global ionospheric delay attributable to all of the tracked GPS satellites; and

for each tracked GPS satellite, estimating an amount of local ionospheric delay attributable thereto;

wherein the local ionospheric delay estimating step comprises estimating each of the local ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

10. The method of claim 9 further comprising performing each of the recited steps for a GPS receiver that is in motion.

11. A global positioning system comprising:

a global positioning system (GPS) receiver configured to (1) receive a plurality of signals from a plurality of visible GPS satellites, and (2) produce a plurality of pseudorange measurements from the received signals, the pseudorange measurements being indicative of the GPS receiver'"'"'s position and having an amount of ionospheric delay error contained therein;

a processor configured to estimate the amount of ionospheric delay in the pseudorange measurements by (1) estimating an amount of global ionospheric delay attributable collectively to the plurality of visible GPS satellites, and (2) estimating a plurality of amounts of local ionospheric delays, each local ionospheric delay being attributable to a different visible GPS satellite.

12. The system of claim 11 wherein the processor uses a modified Kalman filter in estimating the ionospheric delay amounts.

13. The system of claim 12 wherein the processor is further configured to estimate the ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

14. The system of claim 13 wherein the processor is further configured to initially set the global ionospheric delay amount equal to a predetermined value and subsequently modify that initial value as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

15. The system of claim 14 wherein the processor is further configured to initially set each of the local ionospheric delay amounts equal to a predetermined value and subsequently modify those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

16. The system of claim 15 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

17. The system of claim 13 wherein the processor is further configured to initially set each of the local ionospheric delay amounts equal to a predetermined value and subsequently modify those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

18. The system of claim 17 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

19. The system of claim 12 wherein the processor is further configured to estimate the ionospheric delay amounts as a function of a both GPS frequencies L₁ and L₂ simultaneously.

20. The system of claim 11 wherein the GPS receiver is in motion.

21. A method of generating global position system (GPS) ionospheric delay estimates, the method comprising:

augmenting a GPS Kalman filter with (1) a state representing a global ionospheric delay attributable to a plurality of GPS satellites and (2) a plurality of states representing local ionospheric delays, each local ionospheric delay being attributable to a particular GPS satellite;

receiving a plurality of pseudorange measurements from a GPS receiver, the pseudorange measurements having an amount of ionospheric delay included therein; and

processing the received pseudorange measurements with the augmented Kalman filter to thereby generate estimates of the amount of ionospheric delay present in the received pseudorange measurements.

22. The method of claim 21 wherein the global ionospheric delay state depends upon a single GPS frequency, L₁ or L₂.

23. The method of claim 22 wherein the local ionospheric delay states depend upon a single GPS frequency, L₁ or L₂.

24. The method of claim 23 further comprising:

providing a measurement sensitivity matrix H for the augmented Kalman filter, wherein H comprises a predetermined number of rows m corresponding to the maximum number of GPS satellites tracked by the filter at any one time, each row corresponding to a particular GPS satellite tracked by the filter and comprising a predetermined number n+m+1 elements, wherein (1) elements 1 through n are baseline H elements, (2) element n+1 is an obliquity factor multiplied by a GPS frequency coefficient, and (3) elements n+2 through n+m+1 comprise a local iono vector, wherein each element is equal to zero except for an element associated with the GPS satellite corresponding to the row, which is equal to a local iono scalar.

25. The method of claim 24 wherein the local iono scalar is the obliquity factor multiplied by the GPS frequency coefficient.

26. A system for estimating global position using signals received from a plurality of global positioning system (GPS) satellites, the system comprising:

a GPS receiver for receiving GPS signals from a plurality of GPS satellites and producing a pseudorange position estimate therefrom that is representative of the global position of the GPS receiver, the pseudorange estimate having no correction for ionospheric delay;

a processor for receiving and refining the pseudorange estimate, the processor comprising a Kalman filter configured to correct for ionospheric delay in the pseudorange estimate, the Kalman filter comprising a state representing a global ionospheric delay estimate and a plurality of states representing local ionospheric delay estimates for individual GPS satellites.

27. The system of claim 26 wherein the global Kalman filter state is a function of a single GPS frequency, L₁ or L₂.

28. The system of claim 27 wherein the GPS satellites transmit GPS signals on two frequencies, L₁ and L₂, wherein both of those frequencies are jammed by a jamming device, the system further comprising an antijammer for unjamming one of the two frequencies.

29. The system of claim 28 wherein the antijammer unjams only one of the two frequencies.

30. The system of claim 26 wherein the GPS receiver is in motion.

31. A method of generating the amount of ionospheric delay present in global positioning system (GPS) pseudorange measurements, the method comprising:

at a processor associated with a single GPS receiver, (a) receiving a plurality of pseudorange measurements from the single GPS receiver configured to receive signals from a plurality of visible GPS satellites, the pseudorange measurements being indicative of the GPS receiver'"'"'s position and having an amount of ionospheric delay error contained therein; and

(b)

estimating the amount of ionospheric delay in the pseudorange measurements by (1) estimating an amount of global ionospheric delay attributable collectively to the plurality of visible GPS satellites, and (2) estimating a plurality of amounts of local ionospheric delays, each local ionospheric delay being attributable to a different visible GPS satellite.

32. The method of claim 31 wherein the estimating step estimates the ionospheric delay amounts using a modified Kalman filter.

33. The method of claim 32 wherein the estimating step further comprises estimating the ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

34. The method of claim 33 wherein the step of estimating the global ionospheric delay amount comprises initially setting the global ionospheric delay amount equal to a predetermined value and subsequently modifying that initial value as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

35. The method of claim 34 wherein the step of estimating the local ionospheric delay amounts comprises initially setting each of the local ionospheric delay amounts equal to a predetermined value and subsequently modify those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

36. The method of claim 35 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

37. The method of claim 33 wherein the step of estimating the local ionospheric delay amounts comprises initially setting each of the local ionospheric delay amounts equal to a predetermined value and subsequently modifying those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

38. The method of claim 37 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

39. The method of claim 32 wherein the estimating step comprises estimating the ionospheric delay amounts as a function of a both GPS frequencies L₁ and L₂ simultaneously.

40. A method of generating the amount of ionospheric delay present in GPS pseudorange measurements, the method comprising:

receiving a plurality of pseudorange measurements from a global positioning system (GPS) receiver configured to receive signals from a plurality of visible GPS satellites, the pseudorange measurements being indicative of the GPS receiver'"'"'s position and having an amount of ionospheric delay error contained therein; and

using a modified Kalman filter, estimating the amount of ionospheric delay in the pseudorange measurements by (1) estimating an amount of global ionospheric delay attributable collectively to the plurality of visible GPS satellites, and (2) estimating a plurality of amounts of local ionospheric delays, each local ionospheric delay being attributable to a different visible GPS satellite.

41. The method of claim 40 wherein the estimating step further comprises estimating the ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

42. The method of claim 41 wherein the step of estimating the global ionospheric delay amount comprises initially setting the global ionospheric delay amount equal to a predetermined value and subsequently modifying that initial value as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

43. The method of claim 42 wherein the step of estimating the local ionospheric delay amounts comprises initially setting each of the local ionospheric delay amounts equal to a predetermined value and subsequently modifying those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

44. The method of claim 43 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

45. The method of claim 41 wherein the step of estimating the local ionospheric delay amounts comprises initially setting each of the local ionospheric delay amounts equal to a predetermined value and subsequently modifying those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

46. The method of claim 45 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

47. The method of claim 40 wherein the estimating step comprises estimating the ionospheric delay amounts as a function of a both GPS frequencies L₁ and L₂ simultaneously.

48. A global positioning system comprising:

a global positioning system (GPS) receiver configured to (1) receive a plurality of signals from a plurality of visible GPS satellites, (2) produce a plurality of pseudorange measurements from the received signals, the pseudorange measurements being indicative of the GPS receiver'"'"'s position, (3) estimate an amount of ionospheric delay error in the pseudorange measurements, and (4) correct the pseudorange measurements using the estimated ionospheric delay error;

a processor configured to (1) receive the corrected pseudorange measurements and the estimated ionospheric delay error amounts from the GPS receiver, (2) add the received estimated ionospheric delay error amounts to the corrected pseudorange measurements to thereby create uncorrected pseudorange measurements, and (3) estimate anew the amount of ionospheric delay in the uncorrected pseudorange measurements by (a) estimating an amount of global ionospheric delay attributable collectively to the plurality of visible GPS satellites, and (b) estimating a plurality of amounts of local ionospheric delays, each local ionospheric delay being attributable to a different visible GPS satellite.

49. The system of claim 48 wherein the processor uses a modified Kalman filter in estimating the ionospheric delay amounts.

50. The system of claim 49 wherein the processor is further configured to estimate the ionospheric delay amounts as a function of a single GPS frequency L₁ or L₂.

51. The system of claim 50 wherein the processor is further configured to initially set the global ionospheric delay amount equal to a predetermined value and subsequently modify that initial value as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

52. The system of claim 51 wherein the processor is further configured to initially set each of the local ionospheric delay amounts equal to a predetermined value and subsequently modify those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

53. The system of claim 52 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

54. The system of claim 50 wherein the processor is further configured to initially set each of the local ionospheric delay amounts equal to a predetermined value and subsequently modify those initial values as a function of an obliquity factor and a scalar, the scalar being dependent upon the single GPS frequency.

55. The system of claim 54 wherein each of the initial values for the local ionospheric delay amounts are equal to each other.

56. The system of claim 49 wherein the processor is further configured to estimate the ionospheric delay amounts as a function of a both GPS frequencies L₁ and L₂ simultaneously.

57. A system for estimating the amount of ionospheric delay present in a pseudorange measurement, the system comprising:

a global positioning system (GPS) receiver configured to track a plurality of GPS satellites and generate pseudorange measurements Z corresponding to the tracked GPS satellites, the pseudorange measurements Z being indicative of the GPS receiver'"'"'s position and having an amount of ionospheric delay error present therein;

a processor configured to estimate the amount of ionospheric delay present in the pseudorange measurements Z, the processor comprising a Kalman filter, the Kalman filter comprising;

(1) a state vector X comprising n baselines states, one state corresponding to a global ionospheric delay estimate, and m states corresponding to local ionospheric delay estimates, wherein m is a predetermined value and corresponds to a number of GPS satellites tracked by the GPS receiver, (2) a measurement sensitivity matrix H comprising m rows, each row being associated with a particular GPS satellite tracked by the GPS receiver and comprising n baseline coefficients, one global ionospheric delay coefficient, and m local ionospheric delay coefficients, each local ionospheric delay coefficient corresponding to a particular GPS satellite tracked by the GPS receiver and being equal to zero except for the local ionospheric delay coefficient corresponding to the GPS satellite associated with that particular row of H, (3) an n+m+1 by n+m+1 covariance estimate matrix P comprising an n by n baseline covariance estimate matrix P_BASELINE with elements p_1,1 through p_n,n being diagonal elements of P_BASELINE, wherein diagonal element p_n+1,n+1 is set equal to a global ionospheric delay covariance σ

_G², wherein diagonal elements p_n+2,n+2 through p_n+m+1,n+m+1 are set equal to σ

_L², and wherein all off-diagonal elements outside P_BASELINE are set equal to zero, (4) an n+m+1 by n+m+1 state transition matrix Φ

comprising an n by n baseline state transition matrix Φ

_BASELINE with elements Φ

_1,1 through Φ

_n,n being diagonal elements of Φ

_BASELINE, wherein diagonal elements p_n+1,n+1 through p_n+m+1,n+m+1 are set equal to ρ

, wherein all off-diagonal elements outside Φ

_BASELINE are set equal to zero, wherein ρ

=e<sup>−

T/τ</sup>

, wherein T represents a filter propagation time having a predetermined value, and wherein τ

represents a time constant having a predetermined value, (5) an n+m+1 by n+m+1 process noise matrix Q comprising an n by n baseline state transition matrix Q_BASELINE with elements Q_1,1 through Q_n,n being diagonal elements of Q_BASELINE, wherein diagonal element p_n+1,n+1 is set equal to σ

_G²(1−

ρ

²), wherein diagonal elements p_n+2,n+2 through p_n+m+1,n+m+1 are set equal to σ

_L²(1−

ρ

²), and wherein all off-diagonal elements outside Q_BASELINE are set equal to zero, (6) a measurement noise covariance matrix R, and (7) wherein the Kalman filter operates by (a) propagating the state vector to measurement time according to the formula X=Φ

X, (b) propagating the covariance estimate matrix to measurement time according to the formula P=Φ

PΦ

^T+Q, (c) calculating a Kalman filter gain K according to the formula K=PH^T[HPH^T+R]<sup>−

1</sup>, (d) updating the state vector according to the formula X=X=K[Z−

HX], and (e) updating the covariance estimate matrix according to the formula P=[I−

KH]P, wherein I is an identity matrix.

58. The system of claim 57 wherein the global ionospheric delay coefficient in H is α

β

, wherein a is an obliquity factor and β

is a frequency scalar dependent upon a single GPS frequency L₁ or L₂.

59. The system of claim 58 wherein the global ionospheric delay state x_n+1 is initialized to a value of 5 meters.

60. The system of claim 59 wherein the local ionospheric delay states x_n+2 through x_n+m+1 are each initialized to predetermined values of zero.

61. The system of claim 60 wherein the global ionospheric covariance estimate is initialized to a predetermined value of 25 meters².

62. The system of claim 60 wherein the local ionospheric covariance estimates p_n+2 through p_n+m+1 are each initialized to predetermined values of σ

_L²=4 meters².

63. The system of claim 58 wherein the global ionospheric delay state x_n+1 is initialized to a value that is a predetermined function of year, time of day, latitude, and longitude.

64. A device for estimating global position, the device comprising:

a single frequency GPS receiver configured to (1) track a plurality of GPS satellites, (2) produce a plurality of pseudorange measurements corresponding to the tracked GPS satellites, the pseudorange measurements having an amount of ionospheric delay error present therein, (3) estimate an amount of global ionospheric delay attributable to all of the tracked GPS satellites, (4) for each tracked GPS satellite, estimate an amount of local ionospheric delay attributable thereto, and (5) correct the pseudorange measurements using both the global ionospheric delay estimate and the plurality of local ionospheric delay estimates, the corrected pseudorange measurements being indicative of the global position of the GPS receiver.

65. The device of claim 64 wherein the GPS receiver is in motion.