Efficient processing of double differenced updates in a Kalman filter

• US 9,341,482 B2
• Filed: 09/25/2014
• Issued: 05/17/2016
• Est. Priority Date: 09/25/2014
• Status: Active Grant

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Inventors: Fax, J. Alexander
• Primary Examiner(s): Jabr, Fadey
• Assistant Examiner(s): Troost, Aaron L
• Application Number:
  US14/496,920
• Publication Number:
  US 20160091314A1
• Time in Patent Office: 600 Days
• Field of Search: 701/400
• US Class Current: 1/1
• CPC Class Codes: G01S 19/36 relating to the receiver frond end
• CPC Class Codes: G01S 19/393 Trajectory determination or predictive tracking, e.g. Kalman filtering
• CPC Class Codes: G01S 19/43 using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry

Abstract

Systems and methods are provided for sequentially updating a Kalman filter in a navigation system. Respective signals from a plurality of transmitters containing range-finding data are received at a plurality of antennas. For each of the plurality of transmitters, a single differenced observable is calculated between a given pair of the plurality of antennas. A common bias, stored as a state in a Kalman filter, is subtracted from the calculated single differenced observable for each of the plurality of transmitters to provide respective double differenced residual values. A plurality of states stored in the Kalman filter are updated using the double differenced residual values.

Claims

1. A method for providing sequential updates to a Kalman filter in a navigation system comprising:

receiving respective signals from a plurality of transmitters containing range-finding data at a plurality of antennas;

calculating, for each of the plurality of transmitters, a single differenced observable between a given pair of the plurality of antennas;

subtracting a common bias, stored as a state in a Kalman filter, from the calculated single differenced observable for each of the plurality of transmitters to provide respective double differenced residual values; and

updating a plurality of states stored in the Kalman filter using the double differenced residual values.

2. The method of claim 1, further comprising resetting a value associated within the common bias state within a covariance matrix associated with the Kalman filter to a default value.

3. The method of claim 1, wherein subtracting the common bias comprises applying an observation matrix to the stored plurality of states such that a resulting product includes the sum of the stored states and the common bias and subtracting the resulting product from the calculated single differenced observables.

4. The method of claim 1, further comprising replacing a value of the common bias state with a calculated value after updating the plurality of states stored in the Kalman filter.

5. The method of claim 4, further comprising calculating the calculated value at a receiver associated with one of the plurality of antennas.

6. A navigation system comprising:

a plurality of antennas configured to receive signals from a plurality of transmitters;

a signal processor configured to calculate, for each of the plurality of transmitters, a single differenced observable between a given pair of the plurality of antennas; and

a Kalman filter configured to track a position of at least one of the plurality of antennas, the Kalman filter storing and sequentially updating at least a plurality of position states and at least one state representing a common bias across the plurality of transmitters, wherein sequentially updating the plurality of position states comprises subtracting a value of the common bias state from the single differenced observables and updating the Kalman filter with a resulting difference.

7. The navigation system of claim 6, the Kalman filter storing an observation covariance matrix, the observation covariance matrix having no off-diagonal terms.

8. The navigation system of claim 6, further comprising a system control configured to replace the value of the common bias state with a value calculated at the signal processor after updating the plurality of states stored in the Kalman filter.

9. The navigation system of claim 6, further comprising a system control configured to reset a value associated within the common bias state within an observation covariance matrix associated with the Kalman filter to a default value.

10. The navigation system of claim 6, the Kalman filter comprising an observation matrix configured such that when applied to the stored plurality of states, a resulting product includes the sum of the stored states and the common bias.

11. The navigation system of claim 6, wherein at least one of the plurality of antennas is located on an aircraft and at least one of the plurality of antennas is located on an air-to-air refueling platform.

12. The navigation system of claim 6, wherein at least one of the plurality of antennas is located on an aircraft and at least one of the plurality of antennas is located on an aircraft carrier.

13. A non-transitory computer readable medium storing executable instructions for sequentially updating a position associated with an antenna, the executable instructions comprising:

a signal processor configured to calculate, for each of a plurality of transmitters, a single differenced observable between the antenna and at least one remote antenna; and

a Kalman filter configured to track the position of the antenna, the Kalman filter storing and sequentially updating at least a plurality of position states and at least one state representing a common bias across the plurality of transmitters, wherein sequentially updating the plurality of position states comprises subtracting a value of the common bias state from the single differenced observables and updating the Kalman filter with a resulting difference.

14. The navigation system of claim 13, the Kalman filter storing an observation covariance matrix, the observation covariance matrix having no off-diagonal terms.

15. The navigation system of claim 13, further comprising a system control configured to replace the value of the common bias state with a value calculated at the signal processor after updating the plurality of states stored in the Kalman filter.

16. The navigation system of claim 13, further comprising a system control configured to reset a value associated within the common bias state within an observation covariance matrix associated with the Kalman filter to a default value.

17. The navigation system of claim 13, the Kalman filter comprising an observation matrix configured such that when applied to the stored plurality of states, a resulting product includes the sum of the stored states and the common bias.