Hybrid method for time-of-arrival-based ranging

1. A method comprising:

accessing a ranging signal transmitted from a transmitter and received by a receiver, the ranging signal transmitted by a transmitter the ranging signal comprising:

a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies;

generating a time-based representation of the ranging signal;

calculating a first time-of-arrival estimate based on the time-based representation of the ranging signal;

calculating a set of phase differences of sub-signal pairs in a subset of multiplexed sub-signals of the set of multiplexed sub-signals;

calculating a second time-of-arrival estimate based on the set of phase differences of sub-signal pairs;

characterizing a hybrid time-of-arrival estimate based on a combination of the first time-of-arrival estimate and the second time-of-arrival estimate; and

calculating a distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate.

2. The method of claim 1 :

wherein calculating the first time-of-arrival estimate comprises calculating a time-based time-of-arrival estimate based on the time-based representation; and

wherein calculating the second time-of-arrival estimate comprises calculating a phase-based time-of-arrival estimate based on the set of phase differences of sub-signal pairs in the subset of multiplexed sub-signals.

3. The method of claim 1 :

wherein capturing the time-based representation of the ranging signal comprises capturing a series of time-domain digital samples representing the ranging signal; and

wherein calculating the first time-of-arrival estimate comprises calculating the first time-of-arrival estimate based on the series of time-domain digital samples.

4. The method of claim 3 :

further comprising:

calculating a first uncertainty of the time-based time-of-arrival estimate based a sampling frequency associated with the receiver; and

calculating a second uncertainty of the phase-based time-of-arrival estimate based on a variability measure characteristic of a phase difference of each sub-signal pair in the subset of multiplexed sub-signals; and

wherein characterizing the hybrid time-of-arrival estimate based on a combination of the first time-of-arrival estimate and the second time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted combination of the time-based time-of-arrival estimate and the phase-based time-of-arrival estimate based on the first uncertainty and the second uncertainty.

5. The method of claim 4 :

wherein calculating the first uncertainty comprises calculating a time-based uncertainty of the time-based time-of-arrival estimate based the sampling frequency associated with the receiver; and

wherein calculating the second uncertainty comprises calculating a phase-based uncertainty of the phase-based time-of-arrival estimate based on the variability measure characteristic of the phase difference of each sub-signal pair in the subset of multiplexed sub-signals.

6. The method of claim 1 , wherein calculating the second time-of-arrival estimate comprises:

identifying the subset of multiplexed sub-signals based on a threshold frequency difference, the threshold frequency based on a threshold propagation time of the ranging signal from a transmitter to a receiver;

for each sub-signal pair in the subset of multiplexed sub-signals, calculating a sub-signal pair time-of-arrival estimate based on the phase difference of the sub-signal pair;

calculating a central tendency metric descriptive of the sub-signal pair time-of-arrival estimates for the sub-signal pairs in the subset of multiplexed signals; and

calculating the second time-of-arrival estimate based on the central tendency metric.

7. The method of claim 1 :

further comprising:

detecting a set of multipath components characteristic of the ranging signal;

calculating a third time-of-arrival estimate based on the set of multipath components characteristic of the ranging signal; and

calculating a multipath metric characteristic of a power ratio between a line-of-sight component and non-line-of-sight components in the set of multipath components characteristic of the ranging signal; and

wherein characterizing the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate based on a combination of the time-based time-of-arrival estimate, the second time-of-arrival estimate, and the third time-of-arrival estimate.

8. The method of claim 7 :

wherein detecting the set of multipath components characteristic of the ranging signal comprises detecting the set of multipath components characteristic of the ranging signal based on a signal classification function;

wherein calculating the third time-of-arrival estimate comprises calculating a phase-amplitude-based time-of-arrival estimate based on the set of multipath components characteristic of the ranging signal; and

wherein calculating the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted combination of the first time of-arrival estimate, the second time-of-arrival estimate, and the third time-of-arrival estimate based on the first uncertainty, the second uncertainty, and the multipath metric.

9. The method of claim 7 :

wherein calculating the multipath metric characteristic comprises calculating a K-factor characteristic of a power ratio between a first arriving component and subsequent components in the set of multipath components characteristic of the ranging signal; and

wherein calculating the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted combination of the first time of-arrival estimate, the second time-of-arrival estimate, and the third time-of-arrival estimate based on the first uncertainty, the second uncertainty, and the K-factor.

10. The method of claim 1 , wherein calculating the distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate comprises:

accessing a time of departure of the ranging signal from the transmitter;

accessing a time bias between the transmitter and the receiver; and

calculating a hybrid range estimate for the distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate, the time of departure of the ranging signal, and the time bias.

11. A method comprising:

accessing a ranging signal transmitted from a transmitter and received by a receiver, the ranging signal transmitted by a transmitter the ranging signal comprising:

a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies;

capturing a time-based representation of the ranging signal;

calculating a time-based time-of-arrival estimate based on the series of time-based samples;

detecting a set of multipath components characteristic of the ranging signal;

calculating a phase-amplitude-based time-of-arrival estimate based on the set of multipath components characteristic of the ranging signal;

characterizing a hybrid time-of-arrival estimate based on a combination of the time-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate; and

calculating a distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate.

12. The method of claim 11 :

wherein detecting a set of multipath components characteristic of the ranging signal comprises detecting a set of multipath components characteristic of the ranging signal based on a multiple signal classification function;

further comprising, calculating a time-based uncertainty based on a sampling frequency associated with the receiver;

wherein detecting the set of multipath components characteristic of the ranging signal comprises:

calculating a multipath metric characteristic representing a ratio between a first arriving component and other components in the set of multipath components; and

wherein characterizing the hybrid time-of-arrival estimate comprises calculating a hybrid time-of-arrival estimate as a weighted combination of the time-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate based on the time-based uncertainty and the multipath metric characteristic.

13. The method of claim 12 :

further comprising:

calculating a set of phase differences for sub-signal pairs corresponding to subcarrier frequency pairs in a subset of multiplexed sub-signals of the set of multiplexed sub-signals;

calculating a phase-based time-of-arrival estimate based on the set of phase differences for the sub-signal pairs; and

calculating a phase-based uncertainty of the phase-based time-of-arrival estimate based on a distribution associated with the set of phase differences of sub-signal pairs; and

wherein calculating the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as the weighted combination of the time-based time-of-arrival estimate, the phase-based time-of-arrival estimate, and the phase-amplitude-based time-of-arrival estimate based on the time-based uncertainty, the phase-based uncertainty, and the multipath metric characteristic.

14. The method of claim 13 :

further comprising:

calculating a first weight for the time-based time-of-arrival estimate based on the time-based uncertainty;

calculating a second weight for the phase-based time-of-arrival estimate based on the phase-based uncertainty; and

calculating a third weight for the phase-amplitude-based time-of-arrival estimate based on the multipath metric; and

wherein calculating the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as the weighted average of the time-based time-of-arrival estimate, the phase-based time-of-arrival estimate, and the phase-amplitude-based time-of-arrival estimate based on the first weight, the second weight, and the third weight.

15. A method comprising:

accessing a ranging signal transmitted from a transmitter and received by a receiver, the ranging signal transmitted by a transmitter the ranging signal comprising:

a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies;

capturing a time-based representation of the ranging signal;

calculating a set of phase differences for sub-signal pairs in a subset of multiplexed sub-signals of the set of multiplexed sub-signals;

calculating a phase-based time-of-arrival estimate based on the set of phase differences of sub-signal pairs in the subset of multiplexed sub-signals;

detecting a set of multipath components characteristic of the ranging signal based on a multiple signal classification function;

calculating a phase-amplitude-based time-of-arrival estimate based on the set of multipath components characteristic of the ranging signal;

characterizing a hybrid time-of-arrival estimate based on a combination of the phase-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate; and

calculating a distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate.

16. The method of claim 15 :

further comprising:

calculating a phase-based uncertainty of the phase-based time-of-arrival estimate based on a distribution associated with a phase difference of each sub-signal pair in the subset of multiplexed sub-signals; and

wherein calculating the phase-amplitude-based time-of-arrival estimate comprises calculating a multipath metric characteristic of a power ratio between a line-of-sight component and non-line-of-sight components in the set of multipath components characteristic of the ranging signal; and

wherein characterizing a hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted combination of the phase-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate based on the phase-based uncertainty and the multipath metric.

17. The method of claim 16 :

further comprising:

in response to detecting the multipath metric exceeding a multipath metric threshold:

assigning a first weight to the phase-based time-of-arrival estimate; and

assigning a second weight to the phase-amplitude-based time-of-arrival estimate; and

in response to detecting the multipath metric falling below the multipath metric threshold:

assigning the first weight to the phase-amplitude-based time-of-arrival estimate; and

assigning the second weight to the phase-based time-of-arrival estimate; and

wherein characterizing the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted combination of the phase-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate based on the first weight and the second weight.

18. The method of claim 15 :

further comprising:

assigning a first weight to the phase-based time-of-arrival estimate;

assigning a second weight to the phase-amplitude-based time-of-arrival estimate;

in response to detecting a multipath metric falling below a multipath metric threshold, decreasing the first weight relative to the second weight; and

in response to detecting a multipath metric exceeding the multipath metric threshold, increasing the first weight relative to the second weight; and

wherein characterizing the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate as a weighted average of the phase-based time-of-arrival estimate and the phase-amplitude-based time-of-arrival estimate based on the first weight and the second weight.

19. The method of claim 15 , wherein calculating the distance between the transmitter and the receiver comprises:

accessing a time of departure of the ranging signal from the transmitter;

accessing a time bias between the transmitter and the receiver; and

calculating a hybrid range estimate for the distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate, the time of departure of the ranging signal, and the time bias.

20. The method of claim 19 , further comprising:

accessing a set of ranging signals transmitted from a set of transmitters and received by a receiver, the set of transmitters characteristic of a known location;

calculating a set of hybrid time-of-arrival estimates for the set of ranging signals;

calculating a set of distances between the receiver and a corresponding transmitter in the set of transmitters; and

executing a multilateration function on the set of distances to localize the receiver relative to the set of transmitters.