Determining angular acceleration

1. A system comprising:

a first inertial measurement unit and a second inertial measurement unit, wherein the second internal measurement unit is disposed at a fixed position with respect to the first inertial measurement unit; and

one or more processors configured to perform a method comprising:

receiving first inertial data via the first inertial measurement unit;

receiving second inertial data via the second inertial measurement unit;

calculating an angular acceleration based on the first inertial data and based further on the second inertial data;

estimating a position of a wearable head device based on the angular acceleration, wherein:

the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and

the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device, and wherein each of the first state and the second state comprises respective position data and respective velocity data; and

presenting virtual content based on the position of the wearable head device.

2. The system of claim 1 , wherein the calculating the pre-integration term comprises determining a single relative motion constraint based on the first inertial data.

3. The system of claim 1 , wherein the position is estimated further based on the pre-integration term.

4. The system of claim 1 , wherein the method further comprises performing simultaneous localization and mapping via the pre-integration term.

5. The system of claim 1 , wherein the method further comprises determining a relative motion constraint between the first state and the second state based on the pre-integration term.

6. The system of claim 1 , wherein each of the first state and the second state comprises a keyrig pose.

7. The system of claim 1 , wherein each of the first state and the second state comprises a representation of a quaternion.

8. The system of claim 1 , wherein a position of the virtual content is determined based on the position of the wearable head device.

9. The system of claim 1 , wherein the estimating the position of the wearable head device is further based on bias data associated with the first inertial measurement unit.

10. The system of claim 1 , wherein the method further comprises:

predicting a second position of the wearable head device based on the angular acceleration and based further on the position of the wearable head device; and

updating presentation of the virtual content based on the second position of the wearable head device.

11. A method comprising:

receiving first inertial data via a first inertial measurement unit;

receiving second inertial data via a second inertial measurement unit, wherein the second internal measurement unit is disposed at a fixed position with respect to the first inertial measurement unit;

calculating an angular acceleration based on the first inertial data and based further on the second inertial data;

estimating a position of a wearable head device based on the angular acceleration,

wherein:

the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and

the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device, and wherein each of the first state and the second state comprises respective position data and respective velocity data; and presenting virtual content based on the position of the wearable head device.

12. The method of claim 11 , wherein the calculating the pre-integration term comprises determining a single relative motion constraint based on the first inertial data.

13. The method of claim 11 , wherein the position is estimated further based on the pre-integration term.

14. The method of claim 11 , further comprising performing simultaneous localization and mapping via the pre-integration term.

15. The method of claim 11 , further comprising determining a relative motion constraint between the first state and the second state based on the pre-integration term.

16. The method of claim 11 , wherein each of the first state and the second state comprises a keyrig pose.

17. The method of claim 11 , wherein each of the first state and the second state comprises a representation of a quaternion.

18. The method of claim 11 , wherein a position of the virtual content is determined based on the position of the wearable head device.

19. The method of claim 11 , wherein the estimating the position of the wearable head device is further based on bias data associated with the first inertial measurement unit.

20. A non-transitory computer-readable medium storing one or more instructions, which, when executed by one or more processors of an electronic device, cause the one or more processors to perform a method comprising:

receiving first inertial data via a first inertial measurement unit;

receiving second inertial data via a second inertial measurement unit, wherein the second internal measurement unit is disposed at a fixed position with respect to the first inertial measurement unit;

calculating an angular acceleration based on the first inertial data and based further on the second inertial data;

estimating a position of a wearable head device based on the angular acceleration, wherein:

the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and

the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device, and wherein each of the first state and the second state comprises respective position data and respective velocity data; and

presenting virtual content based on the position of the wearable head device.