IPC분류정보
국가/구분 |
United States(US) Patent
등록
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국제특허분류(IPC7판) |
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출원번호 |
US-0898629
(2010-10-05)
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등록번호 |
US-8416133
(2013-04-09)
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발명자
/ 주소 |
- Hatch, Ronald R.
- Dai, Liwen L.
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출원인 / 주소 |
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대리인 / 주소 |
Morgan, Lewis & Bockius LLP
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인용정보 |
피인용 횟수 :
1 인용 특허 :
4 |
초록
▼
A system and method for compensating for faulty satellite navigation measurements. A plurality of measurements in a system is received for a measurement epoch. A Kalman filter is used to calculate a state of the system for the measurement epoch based on the plurality of measurements, wherein the sta
A system and method for compensating for faulty satellite navigation measurements. A plurality of measurements in a system is received for a measurement epoch. A Kalman filter is used to calculate a state of the system for the measurement epoch based on the plurality of measurements, wherein the state of the system for the measurement epoch is calculated using a first closed-form update equation. A faulty measurement is detected in the plurality of measurements for the measurement epoch and a revised state of the system for the measurement epoch that compensates for the faulty measurement is calculated, using the calculated state of the system for the measurement epoch as an input to the revised state calculation, and using a revised closed-form update equation comprising the first closed-form update equation modified with respect to the faulty measurement.
대표청구항
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1. A computer-implemented method, comprising: at a computer system including one or more processors and memory storing one or more programs, the one or more processors executing the one or more programs to perform the operations of: receiving a plurality of measurements in a system for a measurement
1. A computer-implemented method, comprising: at a computer system including one or more processors and memory storing one or more programs, the one or more processors executing the one or more programs to perform the operations of: receiving a plurality of measurements in a system for a measurement epoch;using a Kalman filter to calculate a state of the system for the measurement epoch based on the plurality of measurements, wherein the state of the system for the measurement epoch is calculated using a first closed-form update equation;detecting a faulty measurement in the plurality of measurements for the measurement epoch; andcalculating a revised state of the system for the measurement epoch that compensates for the faulty measurement, using the calculated state of the system for the measurement epoch as an input to the revised state calculation, and using a revised closed-form update equation comprising the first closed-form update equation modified with respect to the faulty measurement. 2. The method of claim 1, wherein detecting the faulty measurement in the plurality of measurements for the measurement epoch includes: for each measurement in the plurality of measurements, calculating an outlier bias for the measurement;determining whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determining that the measurement is a faulty measurement. 3. The method of claim 2, wherein calculating the revised state of the system for the measurement epoch that compensates for the faulty measurement includes: determining whether the outlier bias for the faulty measurement is above a second threshold, wherein the second threshold is greater than the first threshold; andif the outlier bias is greater than the second threshold, removing the effect of the faulty measurement from the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using the negative of a value of a covariance for the faulty measurement, where the covariance for the faulty measurement is determined from a covariance matrix corresponding to the calculated state of the system;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the calculated state of the system. 4. The method of claim 3, including: revising a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculating a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the covariance matrix associated with the calculated state of the system. 5. The method of claim 3, wherein the second threshold is a minimum detectable error threshold. 6. The method of claim 3, wherein if the outlier bias is between the first threshold and the second threshold, the method includes reducing the effect of the faulty measurement on the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using a fraction of the value of the covariance for the faulty measurement;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the calculated state of the system. 7. The method of claim 6, including: revising a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculating a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the covariance matrix associated with the calculated state of the system. 8. The method of claim 2, wherein if the outlier bias is below the first threshold, the method includes determining that the measurement is not a faulty measurement. 9. The method of claim 1, wherein the system is a satellite navigation receiver, wherein the plurality of measurements comprise measurements of signals received from a plurality of global navigation satellites, and wherein the state of the satellite navigation receiver includes a position of the satellite navigation receiver, a velocity of the satellite navigation receiver, and a time. 10. The method of claim 9, including: receiving correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andadjusting the state of the satellite navigation receiver based on the correction signals. 11. The method of claim 1, wherein the system is a plurality of global navigation satellites, wherein the plurality of measurements comprise measurements of signals received from the plurality of global navigation satellites, and wherein the state of the plurality of global navigation satellites includes a position of each global navigation satellite in the plurality of global navigation satellites, a velocity of each global navigation satellite in the plurality of global navigation satellites, and a time reported by each global navigation satellite in the plurality of global navigation satellites. 12. The method of claim 11, including: using the revised state of the plurality of global navigation satellites to calculate correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andtransmitting the correction signals to one or more satellite navigation receivers. 13. The method of claim 1, wherein the system includes a power distribution network comprising one or more power plants and one or more power grids, wherein the plurality of measurements is received from a plurality of sensors for a power distribution network, and wherein the calculated state of the system comprises a calculated state of the power distribution network and includes a magnitude, frequency, and phase relationship of the one or more power plants, fuel flow to power generators of the one or more power plants, and an amount of power drawn by the power grid. 14. The method of claim 1, wherein the system is a weather system, wherein the plurality of measurements is received from a plurality of meteorological sensors distributed across a plurality of geographic locations in the weather system, and wherein the state of the weather system includes air temperature and wind speed at the plurality of geographic locations. 15. The method of claim 1, wherein the system is a radar system, wherein the plurality of measurements includes radar signals reflected from plurality of radar targets, and wherein the state of the radar system includes a distance to each radar target, a velocity of each radar target, and a time. 16. A computer system, comprising: one or more processors;memory; andone or more programs stored in the memory, the one or more programs comprising instructions to: receive a plurality of measurements in a system for a measurement epoch;use a Kalman filter to calculate a state of the system for the measurement epoch based on the plurality of measurements, wherein the state of the system for the measurement epoch is calculated using a first closed-form update equation;detect a faulty measurement in the plurality of measurements for the measurement epoch; andcalculate a revised state of the system for the measurement epoch that compensates for the faulty measurement, using the calculated state of the system for the measurement epoch as an input to the revised state calculation, and using a revised closed-form update equation comprising the first closed-form update equation modified with respect to the faulty measurement. 17. The computer system of claim 16, wherein the instructions to detect the faulty measurement in the plurality of measurements for the measurement epoch include instructions to: for each measurement in the plurality of measurements, calculate an outlier bias for the measurement;determine whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determine that the measurement is a faulty measurement. 18. The computer system of claim 17, wherein the instructions to calculate the revised state of the system for the measurement epoch that compensates for the faulty measurement include instructions to: determine whether the outlier bias for the faulty measurement is above a second threshold, wherein the second threshold is greater than the first threshold; andif the outlier bias is greater than the second threshold, remove the effect of the faulty measurement from the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using the negative of a value of a covariance for the faulty measurement, where the covariance for the faulty measurement is determined from a covariance matrix corresponding to the calculated state of the system;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the calculated state of the system. 19. The computer system of claim 18, including instructions to: revise a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculate a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the covariance matrix associated with the calculated state of the system. 20. The computer system of claim 18, wherein the second threshold is a minimum detectable error threshold. 21. The computer system of claim 18, wherein if the outlier bias is between the first threshold and the second threshold, the one or more programs include instructions to reduce the effect of the faulty measurement on the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using a fraction of the value of the covariance for the faulty measurement;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the calculated state of the system. 22. The computer system of claim 21, including instructions to: revise a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculate a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the covariance matrix associated with the calculated state of the system. 23. The computer system of claim 17, wherein if the outlier bias is below the first threshold, the one or more programs include instructions to determine that the measurement is not a faulty measurement. 24. The computer system of claim 16, wherein the system is a satellite navigation receiver, wherein the plurality of measurements comprise measurements of signals received from a plurality of global navigation satellites, and wherein the state of the satellite navigation receiver includes a position of the satellite navigation receiver, a velocity of the satellite navigation receiver, and a time. 25. The computer system of claim 24, including instructions to: receive correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andadjust the state of the satellite navigation receiver based on the correction signals. 26. The computer system of claim 16, wherein the system is a plurality of global navigation satellites, wherein the plurality of measurements comprise measurements of signals received from the plurality of global navigation satellites, and wherein the state of the plurality of global navigation satellites includes a position of each global navigation satellite in the plurality of global navigation satellites, a velocity of each global navigation satellite in the plurality of global navigation satellites, and a time reported by each global navigation satellite in the plurality of global navigation satellites. 27. The computer system of claim 26, including instructions to: use the revised state of the plurality of global navigation satellites to calculate correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andtransmit the correction signals to one or more satellite navigation receivers. 28. The computer system of claim 16, wherein the system includes a power distribution network comprising one or more power plants and one or more power grids, wherein the plurality of measurements is received from a plurality of sensors for a power distribution network, and wherein the calculated state of the system comprises a state of the power distribution network and includes a magnitude, frequency, and phase relationship of the one or more power plants, fuel flow to power generators of the one or more power plants, and an amount of power drawn by the power grid. 29. The computer system of claim 16, wherein the system is a weather system, wherein the plurality of measurements is received from a plurality of meteorological sensors distributed across a plurality of geographic locations in the weather system, and wherein the state of the weather system includes air temperature and wind speed at the plurality of geographic locations. 30. The computer system of claim 16, wherein the system is a radar system, wherein the plurality of measurements includes radar signals reflected from plurality of radar targets, and wherein the state of the radar system includes a distance to each radar target, a velocity of each radar target, and a time. 31. A non-transitory computer readable storage medium storing one or more programs configured for execution by a computer, the one or more programs comprising instructions to: receive a plurality of measurements in a system for a measurement epoch;use a Kalman filter to calculate a state of the system for the measurement epoch based on the plurality of measurements, wherein the state of the system for the measurement epoch is calculated using a first closed-form update equation;detect a faulty measurement in the plurality of measurements for the measurement epoch; andcalculate a revised state of the system for the measurement epoch that compensates for the faulty measurement, using the calculated state of the system for the measurement epoch as an input to the revised state calculation, and using a revised closed-form update equation comprising the first closed-form update equation modified with respect to the faulty measurement. 32. The computer readable storage medium of claim 31, wherein the instructions to detect the faulty measurement in the plurality of measurements for the measurement epoch include instructions to: for each measurement in the plurality of measurements, calculate an outlier bias for the measurement;determine whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determine that the measurement is a faulty measurement. 33. The computer readable storage medium of claim 32, wherein the instructions to calculate the revised state of the system for the measurement epoch that compensates for the faulty measurement include instructions to: determine whether the outlier bias for the faulty measurement is above a second threshold, wherein the second threshold is greater than the first threshold; andif the outlier bias is greater than the second threshold, remove the effect of the faulty measurement from the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using the negative of a value of a covariance for the faulty measurement, where the covariance for the faulty measurement is determined from a covariance matrix corresponding to the calculated state of the system;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the calculated state of the system. 34. The computer readable storage medium of claim 33, including instructions to: revise a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculate a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to remove the effect of the faulty measurement from the covariance matrix associated with the calculated state of the system. 35. The computer readable storage medium of claim 33, wherein the second threshold is a minimum detectable error threshold. 36. The computer readable storage medium of claim 33, wherein if the outlier bias is between the first threshold and the second threshold, the one or more programs include instructions to reduce the effect of the faulty measurement on the calculated state of the system by: calculating a revised Kalman gain corresponding to the faulty measurement using a fraction of the value of the covariance for the faulty measurement;revising the first closed-form update equation based on the revised Kalman gain to produce a revised first closed-form update equation, andcalculating the revised state of the system by applying the revised first closed-form update equation to the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the calculated state of the system. 37. The computer readable storage medium of claim 36, including instructions to: revise a second closed-form update equation based on the revised Kalman gain to produce a revised second closed-form update equation, andcalculate a revised covariance matrix associated with the revised state of the system by applying the revised second closed-form update equation to a covariance matrix associated with the calculated state of the system for the measurement epoch to reduce the effect of the faulty measurement on the covariance matrix associated with the calculated state of the system. 38. The computer readable storage medium of claim 32, wherein if the outlier bias is below the first threshold, the one or more programs include instructions to determine that the measurement is not a faulty measurement. 39. The computer readable storage medium of claim 31, wherein the system is a satellite navigation receiver, wherein the plurality of measurements comprise measurements of signals received from a plurality of global navigation satellites, and wherein the state of the satellite navigation receiver includes a position of the satellite navigation receiver, a velocity of the satellite navigation receiver, and a time. 40. The computer readable storage medium of claim 39, including instructions to: receive correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andadjust the state of the satellite navigation receiver based on the correction signals. 41. The computer readable storage medium of claim 31, wherein the system is a plurality of global navigation satellites, wherein the plurality of measurements comprise measurements of signals received from the plurality of global navigation satellites, and wherein the state of the plurality of global navigation satellites includes a position of each global navigation satellite in the plurality of global navigation satellites, a velocity of each global navigation satellite in the plurality of global navigation satellites, and a time reported by each global navigation satellite in the plurality of global navigation satellites. 42. The computer readable storage medium of claim 41, including instructions to: use the revised state of the plurality of global navigation satellites to calculate correction signals that compensate for errors in predicted orbits and clocks of the plurality of global navigation satellites; andtransmit the correction signals to one or more satellite navigation receivers. 43. The computer readable storage medium of claim 31, wherein the system includes a power distribution network comprising one or more power plants and one or more power grids, wherein the plurality of measurements is received from a plurality of sensors for a power distribution network, and wherein the calculated state of the system comprises a state of the power distribution network and includes a magnitude, frequency, and phase relationship of the one or more power plants, fuel flow to power generators of the one or more power plants, and an amount of power drawn by the power grid. 44. The computer readable storage medium of claim 31, wherein the system is a weather system, wherein the plurality of measurements is received from a plurality of meteorological sensors distributed across a plurality of geographic locations in the weather system, and wherein the state of the weather system includes air temperature and wind speed at the plurality of geographic locations. 45. The computer readable storage medium of claim 31, wherein the system is a radar system, wherein the plurality of measurements includes radar signals reflected from plurality of radar targets, and wherein the state of the radar system includes a distance to each radar target, a velocity of each radar target, and a time. 46. The method of claim 1, furthering including: calculating a plurality of residuals corresponding to a subset of the plurality of measurements using the calculated state of the system;calculating a metric for the plurality of residuals; andfor each respective measurement of two or more measurements in the subset of the plurality of measurements, calculating an outlier bias for the respective measurement in the two or more measurements corresponding to a respective residual using the respective residual and the metric for the plurality of residuals;determining whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determining that the measurement is a faulty measurement. 47. The computer system of claim 17, wherein the instructions to calculate the outlier bias for the measurement further include instructions to: calculate a plurality of residuals corresponding to a subset of the plurality of measurements using the calculated state of the system;calculate a metric for the plurality of residuals; andfor each respective measurement of two or more measurements in the subset of the plurality of measurements, calculate an outlier bias for the respective measurement in the two or more measurements corresponding to a respective residual using the respective residual and the metric for the plurality of residuals;determine whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determine that the measurement is a faulty measurement. 48. The computer readable storage medium of claim 32, wherein the instructions to calculate the outlier bias for the measurement further include instructions to: calculate a plurality of residuals corresponding to a subset of the plurality of measurements using the calculated state of the system;calculate a metric for the plurality of residuals; andfor each respective measurement of two or more measurements in the subset of the plurality of measurements, calculate an outlier bias for the respective measurement in the two or more measurements corresponding to a respective residual using the respective residual and the metric for the plurality of residuals;determine whether the outlier bias for the measurement is greater than a first threshold; andif the outlier bias for the measurement is greater than the first threshold, determine that the measurement is a faulty measurement.
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