Direct determination of rigid body motion using data collected from independent accelerometers

1. A method of direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, the method comprising:

(a) receiving, in a computer system having an application module for direct determination of angular and translation velocity at a particular location on a rigid body installed thereon, the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

(b) forming initial direction cosine matrices for said each of the accelerometers and for the rigid body using the respective orientations in the computer system;

(c) initializing current solution time in the computer system;

(d) transforming measured accelerations to the global reference frame in the computer system;

(e) calculating global velocity by integrating the transformed global accelerations in the computer system;

(f) calculating current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix in the computer system;

(g) creating a first set of redundant vector equations for the angular velocity in the computer system;

(h) obtaining the angular velocity by solving the first set of redundant equations using a first solution technique in the computer system;

(i) creating a second set of redundant vector equations for the translational velocity in the computer system;

(j) obtaining the translational velocity by solving the second set of redundant equations using a second technique in the computer system;

(k) updating the current solution time in the computer system; and

repeating (d) to (k) until the current time is greater than pre-defined total solution time, wherein both the angular velocity and the translational velocity are displayed to a monitor coupled to the computer system.

2. The method of claim 1 , further comprising optionally filtering out high frequency noises of the measured accelerations.

3. The method of claim 1 , the orientation of each of the independent accelerometers is represented by an accelerometer reference frame and the orientation of the rigid body is represented by a local reference frame.

4. The method of claim 1 , wherein number of the accelerometers is N, wherein N is a positive integer greater or equal to 2.

5. The method of claim 4 , wherein number of the first set of redundant vector equations is (N×(N−1)/2).

6. The method of claim 4 , wherein number of the second set of redundant vector equations is N.

7. The method of claim 1 , wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

8. The method of claim 1 , wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.

9. The method of claim 1 , wherein the particular location is the center of mass of the rigid body.

10. The method of claim 1 , wherein the first technique includes, but is not limited to, least squares fitting and selective Gaussian elimination.

11. The method of claim 1 , wherein the second technique includes, but is not limited to, average value and minimization of the rotational term.

12. The method of claim 1 , wherein the first and the second techniques are predefined and used consistently throughout the entire direct determination.

13. The method of claim 1 , wherein the first and the second techniques are dynamically decided at each solution cycle.

14. A computer program product including a computer usable medium having computer readable code embodied in the medium for causing an application module to execute on a computer for direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, the computer program product comprising:

computer readable code for receiving the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

computer readable code for forming initial direction cosine matrices in the global reference frame for said each of the accelerometers and for the rigid body using the respective orientations;

computer readable code for initializing current solution time;

computer readable code for transforming measured accelerations to the global reference frame;

computer readable code for calculating global velocity by integrating the transformed global accelerations;

computer readable code for calculating current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix;

computer readable code for creating a first set of redundant vector equations for the angular velocity;

computer readable code for obtaining the angular velocity by solving the first set of redundant equations using a first solution technique;

computer readable code for creating a second set of redundant vector equations for the translational velocity; and

computer readable code for obtaining the translational velocity by solving the second set of redundant equations using a second technique.

15. The computer program product of claim 14 , wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

16. The computer program product of claim 14 , wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.

17. A apparatus for direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, said apparatus comprising:

a physical computing system comprising an I/O interface, a communication interface, a main memory, a secondary memory and at least one processor coupled to the main memory, the secondary memory, the I/O interface, and the communication interface, wherein said main memory contains executable instructions which when executed by the at least one processor cause the processor to:

(a) receive the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

(b) form initial direction cosine matrices in the global reference frame for said each of the accelerometers and for the rigid body using the respective orientations;

(c) initialize current solution time;

(d) transform measured accelerations to the global reference frame;

(e) calculate global velocity by integrating the transformed global accelerations;

calculate current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix;

(g) create a first set of redundant vector equations for the angular velocity;

(h) obtain the angular velocity by solving the first set of redundant equations using a first solution technique;

(i) create a second set of redundant vector equations for the translational velocity;

(j) obtain the translational velocity by solving the second set of redundant equations using a second technique;

(k) update the current solution time; and

repeating (d) to (k) until the current time is greater than pre-defined total solution time.

18. The apparatus of claim 17 , wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

19. The apparatus of claim 17 , wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.