System and method for tracking a wearable device

A first device comprising:

• one or more receiving antennas, each receiving antenna configured to receive radar signals;
• one or more processors configured to perform a method comprising, at the first device:
• while in a first mode, transmitting a first signal and receiving a second signal, the second signal comprising a reflection of the first signal by a second device;
• determining, based on the received second signal, a position of the second device relative to the first device;
• transitioning from the first mode to a second mode, wherein transitioning from the first mode to the second mode comprises discontinuing transmitting the first signal;
• while in the second mode, forgoing transmitting the first signal, and further while in the second mode, receiving a third signal from the second device, wherein the third signal is not provided by the second device in response to a signal from the first device;
• and
• determining, based on the third signal, an orientation of the second device relative to the first device,
• wherein:
• the second device comprises one or more transmitting antennas,
• the third signal corresponds to an antenna of the one or more transmitting antennas,
• determining the position of the second device relative to the first device comprises determining a translation matrix relating a position of the second device to a position of the first device, and
• determining the orientation of the second device relative to the first device comprises determining a ratio of a signal power of the third signal to an expected maximum signal power of the antenna to which the third signal corresponds.

A wearable system comprising:

• a first device comprising one or more receiving antennas, each receiving antenna configured to receive radar signals, and one or more processors;
• a second device comprising one or more transmitting antennas, each receiving antenna configured to transmit radar signals;
• wherein the one or more processors of the first device are configured to perform a method comprising, at the first device:
• while in a first mode, transmitting a first signal and receiving a second signal, the second signal comprising a reflection of the first signal by a second device;
• determining, based on the received second signal, a position of the second device relative to the first device;
• transitioning from the first mode to a second mode, wherein transitioning from the first mode to the second mode comprises discontinuing transmitting the first signal;
• while in the second mode, forgoing transmitting the first signal, and further while in the second mode, receiving a third signal from the second device, wherein the third signal is not provided by the second device in response to a signal from the first device;
• and
• determining, based on the third signal, an orientation of the second device relative to the first device,
• wherein:
• the third signal corresponds to an antenna of the one or more transmitting antennas,
• determining the position of the second device relative to the first device comprises determining a translation matrix relating a position of the second device to a position of the first device, and
• determining the orientation of the second device relative to the first device comprises determining a ratio of a signal power of the third signal to an expected maximum signal power of the antenna to which the third signal corresponds.