Global positioning system (GPS) self-calibrating lever arm function

1. A method to calibrate at least one lever arm ( 20 ) between at least one respective global positioning position (GPS) antenna/receiver ( 50 ) and a communicatively coupled inertial navigation system ( 70 ), the method comprising:

receiving signals from the at least one GPS antenna/receiver ( 50 ) at the inertial navigation system communicatively coupled to a Kalman filter ( 90 ); and

estimating, in the Kalman filter, at least one fixed lever arm component while accounting for a bending motion of the lever arm ( 20 ) based on the received signals by implementing an expanded state transition matrix and an expanded noise covariance matrix; and

calibrating the at least one lever arm based on estimating the at least one fixed lever arm component.

2. The method of claim 1 , wherein estimating, in the Kalman filter, the at least one fixed lever arm component while accounting for the bending motion of the lever arm comprises:

implementing the expanded state transition matrix including at least one expanded state-matrix diagonal element associated with at least one fixed lever arm and associated with at least one bent lever arm;

implementing the expanded noise covariance matrix including at least one expanded noise-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm; and

estimating the at least one lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix.

3. The method of claim 2 , wherein the at least one GPS antenna/receiver is a single GPS antenna/receiver, and wherein the at least one lever arm is a single lever arm,

wherein implementing the expanded state transition matrix including the at least one expanded state-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm comprises:

implementing the expanded state transition matrix including a single expanded state-matrix diagonal element associated with a single fixed lever arm and associated with a single bent lever arm.

4. The method of claim 3 , wherein implementing the expanded noise covariance matrix including the at least one expanded noise-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm comprises:

implementing the expanded noise transition matrix including a single expanded noise-matrix diagonal element associated with the single fixed lever arm and associated with the single bent lever arm, and

wherein estimating the at least one lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix comprises:

estimating the single lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix.

5. The method of claim 3 , further comprising:

positioning the inertial navigation system in a first position on a vehicle; and

positioning the single GPS antenna/receiver in a second position on the vehicle, wherein the single lever arm is the difference between the first position and the second position.

6. The method of claim 2 , wherein the at least one GPS antenna/receiver comprises a first GPS antenna/receiver and a second GPS antenna/receiver, wherein the at least one lever arm comprises a first lever arm and a second lever arm, and

wherein implementing the expanded state transition matrix including the at least one expanded state-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm comprises:

implementing the expanded state transition matrix, wherein the expanded state transition matrix includes: a first-expanded state-matrix diagonal element associated with a first fixed lever arm and associated with a first bent lever arm; and a second-expanded state-matrix diagonal element associated with a second fixed lever arm and associated with a second bent lever arm.

7. The method of claim 6 , wherein implementing the expanded noise covariance matrix including the at least one expanded noise-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm comprises:

implementing the expanded noise covariance matrix, wherein the expanded noise covariance matrix includes: a first-expanded noise-matrix diagonal element associated with the first fixed lever arm and associated with the first bent lever arm; and a second-expanded noise-matrix diagonal element associated with the second fixed lever arm and associated with the second bent lever arm.

8. The method of claim 7 , wherein the estimating at least one lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix comprises:

estimating a first lever arm; and

estimating a second lever arm.

9. The method of claim 6 , further comprising:

positioning the inertial navigation system in a first position on a vehicle;

positioning the first GPS antenna/receiver in a second position on the vehicle, wherein the first lever arm is the difference between the first position and the second position; and

positioning the second GPS antenna/receiver in a third position on the vehicle, wherein the second lever arm is the difference between the first position and the third position.

10. A system with a respective global positioning system (GPS) self-calibrating lever arm function, the system comprising:

an inertial navigation system in a first position on a vehicle;

at least one global positioning system (GPS) antenna/receiver on the vehicle, wherein at least one lever arm is the at least one respective difference between the first position and an at least one position of the respective at least one GPS antenna/receiver; and

a Kalman filter executable by a processor communicatively coupled to the inertial navigation system to: estimate at least one fixed lever arm component while accounting for a bending motion of the lever arm based on signals received at the inertial navigation system from the at least one GPS antenna/receiver by implementing an expanded state transition matrix and an expanded noise covariance matrix; and calibrate at least one lever arm based on the at least one fixed lever arm component estimate.

11. The system of claim 10 , wherein the Kalman filter executable by the processor to estimate at least one fixed lever arm component while accounting for the bending motion of the lever arm is further configured to:

implement the expanded state transition matrix including at least one expanded state-matrix diagonal element associated with at least one fixed lever arm and associated with at least one bent lever arm;

implement the expanded noise covariance matrix including at least one expanded noise-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm; and

estimate the at least one lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix.

12. The system of claim 11 , wherein the at least one GPS antenna/receiver is a single GPS antenna/receiver, and wherein the Kalman filter is further configured, when executed by the processor, to:

implement the expanded state transition matrix including a single expanded state-matrix diagonal element associated with a single fixed lever arm and associated with a single bent lever arm;

implement the expanded noise covariance matrix including a single expanded noise-matrix diagonal element associated with the single fixed lever arm and associated with the single bent lever arm; and

estimate a single lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix.

13. The system of claim 12 , wherein the expanded state-matrix diagonal element associated with the single fixed lever arm and associated with the single bent lever arm comprises a 6-by-6 first-expanded state sub-matrix, and

wherein the expanded noise-matrix diagonal element associated with the single fixed lever arm and associated with the single bent lever arm comprises a 6-by-6 first-expanded noise sub-matrix.

14. The system of claim 11 , wherein the at least one lever arm includes a first lever arm and a second lever arm, and wherein the at least one GPS antenna/receiver further includes:

a first GPS antenna/receiver at a second position on the vehicle, wherein the first lever arm is the difference between the first position and the second position; and

a second GPS antenna/receiver at a third position on the vehicle, wherein the second lever arm is the difference between the first position and the third position, and

wherein the Kalman filter is further configured when executed by the processor to:

implement the expanded state transition matrix, wherein the expanded state transition matrix includes: a first expanded state-matrix diagonal element associated with a first fixed lever arm and associated with a first bent lever arm; and a second expanded state-matrix diagonal element associated with a second fixed lever arm and associated with a second bent lever arm;

implement the expanded noise covariance matrix, wherein the expanded noise covariance matrix includes: a first-expanded noise-matrix diagonal element associated with the first fixed lever arm and associated with the first bent lever arm; and a second-expanded noise-matrix diagonal element associated with the second fixed lever arm and associated with the second bent lever arm.

15. The system of claim 14 , wherein, based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix, the Kalman filter is further configured when executed by the processor to:

estimate a first lever arm in real-time; and

estimate a second lever arm in real-time.

16. The system of claim 14 , wherein the first expanded state-matrix diagonal element associated with the first fixed lever arm and associated with the first bent lever arm comprises a 6-by-6 first-expanded state sub-matrix, and wherein the second expanded state-matrix diagonal element associated with the second fixed lever arm and associated with the second bent lever arm comprises a 6-by-6 first-expanded state sub-matrix.

17. The system of claim 14 , wherein the first-expanded noise-matrix diagonal element associated with the first fixed lever arm and associated with the first bent lever arm comprises a 6-by-6 first-expanded noise sub-matrix, and wherein the second-expanded noise-matrix diagonal element associated with the second fixed lever arm and associated with the second bent lever arm comprises a 6-by-6 second-expanded noise sub-matrix.

18. The system of claim 10 , further comprising:

at least one inertial navigation sensor communicatively coupled to the processor.

19. A program product for implementing an inertial navigation system to calibrate a lever arm, the program product comprising a non-transitory processor-readable medium on which program instructions are embodied, wherein the program instructions are operable, when executed by at least one processor in the inertial navigation system, to cause the inertial navigation system to:

estimate at least one fixed lever arm component while accounting for the bending motion of the lever arm in the Kalman filter based on signals received from at least one GPS antenna/receiver at the inertial navigation system by implementing an expanded state transition matrix and an expanded noise covariance matrix; and

calibrate the lever arm based on the at least one fixed lever arm component estimate.

20. The program product of claim 19 , further comprising program instructions operable, when executed by at least one processor in an inertial navigation system including a single GPS antenna/receiver, to cause the inertial navigation system to:

implement the expanded state transition matrix including at least one expanded state-matrix diagonal element associated with at least one fixed lever arm and associated with at least one bent lever arm;

implement the expanded noise covariance matrix including at least one expanded noise-matrix diagonal element associated with the at least one fixed lever arm and associated with the at least one bent lever arm; and

estimate the lever arm in real-time based on the implementing of the expanded state transition matrix and the expanded noise covariance matrix.