Method and apparatus for estimation of center of gravity using accelerometers

• US 9,568,320 B2
• Filed: 05/05/2015
• Issued: 02/14/2017
• Est. Priority Date: 05/05/2015
• Status: Expired due to Fees

• Current Assignee: King Fahd University of Petroleum & Minerals (Government of Saudi Arabia)
• Original Assignee: King Fahd University of Petroleum & Minerals (Government of Saudi Arabia)
• Inventors: Al-Rawashdeh, Yazan Mohammad, Al-Malki, Mohammad Fahd, Elshafei, Moustafa Elshafei Ahmed
• Primary Examiner(s): Trivedi, Atul
• Application Number:
  US14/704,650
• Publication Number:
  US 20160327394A1
• Time in Patent Office: 651 Days
• Field of Search: 701/504
• US Class Current: 1/1
• CPC Class Codes: G01C 21/185 for gravity
• CPC Class Codes: G01M 1/127 during the flight

Abstract

A system and associated methodology determine navigation parameters of a vehicle under varying center of gravity position and varying unknown gravitational forces. The system uses high precision accelerometers arranged in a plurality of configurations.

Claims

1. A method for determining navigation parameters of a vehicle, the method comprising:

receiving measurements from accelerometers;

calculating, using processing circuitry, differential accelerometers measurements as a function of the measurements from the accelerometers;

calculating, using the processing circuitry, an angular acceleration as a function of the differential accelerometers measurements under varying center of gravity position and unknown varying gravitational force with anomaly;

calculating, using the processing circuitry, the square of the magnitude of an angular velocity as a function of the differential accelerometers measurements; and

calculating, using the processing circuitry, the navigation parameters by determining the angular velocity using a Kalman filter as a function of the angular acceleration and the square of the magnitude of the angular velocity, wherein the calculation of the navigation parameters is fully operated in a passive navigation system.

2. The method of claim 1, wherein the navigation parameters includes an inertial position, a velocity, an acceleration, an angular velocity, an angular acceleration, attitude, a position of a center of gravity and its rate of change, gravity tensor, and a gravitational acceleration.

3. The method of claim 2, wherein the angular velocity estimation is isolated from gravity tensor estimation via a constrained filtering technique.

4. The method of claim 2, wherein calculating the gravity tensor includes applying:

5. The method of claim 2, wherein the calculating of the navigation parameters uses one or more of the following models

{right arrow over (m)}_i(k)={right arrow over (a)}_ri−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_i+{right arrow over (g)}_b0={{right arrow over ({umlaut over (S)})}−

{right arrow over ({umlaut over (R)})}_G−

∫

₀^tΓ

^a{right arrow over (V)}_bdt}−

2[Ω

]{right arrow over ({dot over (R)})}_G−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_G,

{right arrow over (m)}_i(k)={right arrow over (a)}_ri−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_i+{right arrow over (g)}_b0={{right arrow over ({umlaut over (S)})}−

{right arrow over ({umlaut over (R)})}_G−

Γ

^a{right arrow over (S)}}−

2[Ω

]{right arrow over ({dot over (R)})}_G−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_G,

{right arrow over (m)}_i(k)={right arrow over (a)}_ri−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_i+{right arrow over (g)}_b0={{right arrow over ({umlaut over (S)})}−

∫

₀^tΓ

^a{right arrow over (V)}_bdt}−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_G, and

{right arrow over (m)}_i(k)={right arrow over (a)}_ri−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_i+{right arrow over (g)}_b0={{right arrow over ({umlaut over (S)})}−

Γ

^a{right arrow over (S)}}−

([{dot over (Ω

)}]+[Ω

×

]){right arrow over (R)}_G

where

{right arrow over (a)}_ri;

is an acceleration measurement at the center of the i^th ring,

[Ω

];

is a skew matrix of an angular velocity vector,

{right arrow over (g)}_b0;

is an initial gravity vector at time (t₀),

{right arrow over (A)}_b;

is an inertial acceleration of the vehicle measured at a center of gravity of a body frame of the vehicle,

{right arrow over ({umlaut over (R)})}_G and {right arrow over ({dot over (R)})}_G;

are the acceleration and the velocity of the center of gravity respectively

{right arrow over (R)}_G;

is the position of the center of gravity,

Γ

^a;

is a gravity gradient measured in the body frame,

{right arrow over (V)}_b;

is an inertial velocity of the vehicle,

{right arrow over (S)};

is an inertial position of the vehicle,

[{dot over (Ω

)}] is expressed as

6. The method of claim 2, wherein calculating the gravitational acceleration includes applying:

{right arrow over (g)}₁(t)=∫

₀^tDCM^TΓ

^a{right arrow over (V)}_bdt

where the DCM is the directional cosine matrix, Γ

^a is a gravity gradient, and {right arrow over (V)}_b is an inertial velocity of the vehicle measured in the body frame of the vehicle.

7. The method of claim 2, wherein the accelerometers are arranged in one or more distributed diamond configurations.

8. The method of claim 7, wherein the processing circuitry is embedded in the one or more distributed diamond configurations.

9. The method of claim 2, wherein the navigation parameters are represented using different navigation frames.

10. The method of claim 2, wherein the calculating of the navigation parameters is operated in combination with aided navigation systems.

11. The method of claim 1, wherein the vehicle is one of an air vehicle, an underwater vehicle, an underground vehicle, or a space vehicle.

12. The method of claim 1, further comprising:

computing a gravity tensor of the vehicle; and

sending the gravity tensor to a host application to provide computer guidance to avoid obstacles.

13. The method of claim 1, wherein the accelerometers are arranged in two or more rings.

14. The method of claim 13, wherein calculating the angular acceleration includes applying:

15. The method of claim 1, wherein the accelerometers are arranged in a diamond configuration.

16. The method of claim 15, wherein calculating the angular acceleration includes applying:

17. The method of claim 1, wherein the Kalman filter is a norm constrained Kalman filter.

18. The method of claim 1, wherein the measurements are received from eighteen or more accelerometers.

19. A system for determining navigation parameters of a vehicle, the system comprising:

processing circuitry configured to

receive measurements from accelerometers,

calculate differential accelerometers measurements based on the measurements,

calculate an angular acceleration based on the differential accelerometers

measurements under varying center of gravity position and unknown varying gravitational force with anomaly,

calculate the square of the magnitude of an angular velocity as a function of the differential accelerometers measurements, and

calculate the navigation parameters by determining the angular velocity using a Kalman filter as a function of the angular acceleration and the square of the magnitude of the angular velocity, wherein the calculation of the navigation parameters is fully operated in a passive navigation system.

20. An inertial navigation unit comprising:

six or more accelerometers; and

processing circuitry configured to

receive measurements from the six or more accelerometers,

calculate differential accelerometers measurements based on the measurements,

calculate an angular acceleration based on the differential accelerometers measurements under varying center of gravity position and unknown varying gravitational force with anomaly,

calculate the square of the magnitude of an angular velocity as a function of the differential accelerometers measurements, and

calculate the navigation parameters by determining the angular velocity using a Kalman filter as a function of the angular acceleration and the square of the magnitude of the angular velocity wherein the calculation of the navigation parameters is fully operated in a passive navigation system.