Apparatus, system, and method for mitigating systematic distance errors in radar-based triangulation calculations

1. A wearable device comprising:

at least one processing device;

a set of radar devices configured to:

transmit radar signals to at least one transponder that modifies the radar signals by shifting the radar signals by a certain amount of frequency to enable the processing device to accurately measure distances between the set of radar devices and the transponder even when the transponder is located within a minimum distance threshold of the set of radar devices, wherein the minimum distance threshold is outside a detection range of the set of radar devices; and

receive the radar signals returned from the transponder; and

an error-mitigation device configured to provide, to the processing device, data for mitigating position errors in triangulation calculations involving the radar signals.

2. The wearable device of claim 1 , wherein the processing device is communicatively coupled to the set of radar devices and the error-mitigation device, wherein the processing device:

calculates, based at least in part on roundtrip flight times of the radar signals and the data, distance measurements that represent the distances between the set of radar devices and the transponder; and

triangulates, based at least in part on the distance measurements, a three-dimensional location of the transponder relative to the wearable device.

3. The wearable device of claim 2 , wherein:

the set of radar devices comprises:

a first radar device;

a second radar device; and

a third radar device; and

the error-mitigation device comprises a fourth radar device that:

transmits a radar signal to the transponder; and

receives the radar signal returned from the transponder.

4. The wearable device of claim 3 , wherein the processing device calculates the distance measurements between the set of radar devices and the transponder based at least in part on:

the roundtrip flight times of the radar signals; and

a roundtrip flight time of the radar signal transmitted and received by the fourth radar device.

5. The wearable device of claim 2 , wherein the error-mitigation device comprises an additional transponder that receives, from a signal generator, an oscillating signal that is delayed by a known time delay.

6. The wearable device of claim 5 , wherein the error-mitigation device further comprises a fiber optic cable communicatively coupled between the additional transponder and the signal generator, wherein the fiber optic cable is tuned to delay the oscillating signal by the known time delay as the oscillating signal traverses from the signal generator to the additional transponder.

7. The wearable device of claim 5 , wherein the processing device:

determining a systematic distance error that affects the distance measurements based at least in part on:

the oscillating signal; and

the known time delay;

correcting the distance measurements by subtracting the system distance error from the distance measurements; and

triangulating the three-dimensional location of the transponder based at least in part on the corrected distance measurements.

8. The wearable device of claim 2 , wherein the set of radar devices are secured to the wearable device such that at least some of the radar devices are non-colinear with one another on the wearable device.

9. The wearable device of claim 2 , wherein the set of radar devices comprise:

a first radar device that is situated, on the wearable device, proximate to a left ear of a user;

a second radar device that is situated, on the wearable device, proximate to a right ear of the user; and

a third radar device that is situated, on the wearable device, proximate to a top of the user's head.

10. The wearable device of claim 2 , wherein:

the transponder is secured to a wearable accessory worn by a specific body part of the user; and

the processing device determines, based at least in part on the distance measurements, a change in position of the specific body part of the user.

11. The wearable device of claim 2 , wherein:

the processing device compensates for the certain amount of frequency when calculating the distances between the transponder and the radar devices.

12. The wearable device of claim 2 , wherein:

the set of radar devices generate the radar signals according to at least one frequency model that is linear with time; and

the processing device calculates the distance measurements by:

determining beat frequencies of the radar signals; and

multiplying the beat frequencies by a range conversion factor.

13. The wearable device of claim 2 , wherein the processing device generates an input command for an artificial reality system that accounts for the distances between the set of radar devices and the transponder.

14. The wearable device of claim 13 , wherein the processing device facilitates modifying at least one virtual component of the artificial reality system in accordance with the input command to account for the distances between the set of radar devices and the transponder.

15. An artificial reality system comprising:

a wearable device dimensioned to be worn by a user;

at least one processing device;

a set of radar devices secured to the wearable device, wherein the set of radar devices:

transmit radar signals to at least one transponder that modifies the radar signals by shifting the radar signals by a certain amount of frequency to enable the processing device to accurately measure distances between the set of radar devices and the transponder even when the transponder is located within a minimum distance threshold of the set of radar devices, wherein the minimum distance threshold is outside a detection range of the set of radar devices; and

receive the radar signals returned from the transponder;

an error-mitigation device secured to the wearable device, wherein the error-mitigation device provides, to the processing device, data for mitigating position errors in triangulation calculations involving the radar signals; and

wherein the processing device:

calculates, based at least in part on roundtrip flight times of the radar signals and the data, distance measurements that represent distances between the set of radar devices and the transponder; and

triangulates, based at least in part on the distance measurements, a three-dimensional location of the transponder relative to the wearable device.

16. The artificial reality system of claim 15 , wherein:

the set of radar devices comprises:

a first radar device;

a second radar device; and

a third radar device; and

the error-mitigation device comprises a fourth radar device that:

transmits a radar signal to the transponder; and

receives the radar signal returned from the transponder.

17. The artificial reality system of claim 16 , wherein the processing device calculates the distance measurements between the set of radar devices and the transponder based at least in part on:

the roundtrip flight times of the radar signals; and

a roundtrip flight time of the radar signal transmitted and received by the fourth radar device.

18. The artificial reality system of claim 15 , wherein the error-mitigation device comprises an additional transponder that receives, from a signal generator, an oscillating signal that is delayed by a known time delay.

19. The artificial reality system of claim 18 , wherein the error-mitigation device further comprises a fiber optic cable communicatively coupled between the additional transponder and the signal generator, wherein the fiber optic cable is tuned to delay the oscillating signal by the known time delay as the oscillating signal traverses from the signal generator to the additional transponder.

20. A method comprising:

transmitting, by a set of radar devices secured to a wearable device worn by a user of an artificial reality system, radar signals to at least one transponder that modifies the radar signals by shifting the radar signals by a certain amount of frequency to enable at least one processing device to accurately measure distances between the set of radar devices and the transponder even when the transponder is located within a minimum distance threshold of the set of radar devices, wherein the minimum distance threshold is outside a detection range of the set of radar devices;

receiving, by the set of radar devices, the radar signals returned from the transponder;

obtaining, by the processing device from an error-mitigation device secured to the wearable device, data for mitigating position errors in triangulation calculations involving the radar signals;

calculating, by the processing device based at least in part on roundtrip flight times of the radar signals and the data, distance measurements that represent distances between the set of radar devices and the transponder; and

triangulating, by the processing device based at least in part on the distance measurements, a three-dimensional location of the transponder relative to the wearable device.