Hybrid method for time-of-arrival-based ranging

1 . A method comprising:

accessing a ranging signal transmitted from a transmitter and received at a receiver, the ranging signal comprising a set of multiplexed sub-signals characterized by 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 the set of multiplexed sub-signals;

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

characterizing a hybrid time-of-arrival estimate of the ranging signal based on a combination of the first time-of-arrival estimate and the second time-of-arrival estimate.

2 . The method of claim 1 :

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

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a combination of:

the first time-of-arrival estimate;

the second time-of-arrival estimate; and

the third time-of-arrival estimate.

3 . The method of claim 2 :

further comprising calculating a multipath metric characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on:

the first time-of-arrival estimate;

the second time-of-arrival estimate;

the third time-of-arrival estimate; and

the multipath metric.

4 . The method of claim 1 :

further comprising:

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

calculating a multipath value characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

in response to the multipath value falling below a threshold multipath value, decreasing a second weight, assigned to the second time-of-arrival estimate, relative to a third weight assigned to the third time-of-arrival estimate; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a weighted combination of:

the first time-of-arrival estimate according to a first weight;

the second time-of-arrival estimate according to the second weight; and

the third time-of-arrival estimate according to the third weight.

5 . The method of claim 1 :

further comprising:

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

calculating a multipath value characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

in response to the multipath value exceeding a threshold multipath value, increasing a second weight, assigned to the second time-of-arrival estimate, relative to a third weight assigned to the third time-of-arrival estimate; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a weighted combination of:

the first time-of-arrival estimate according to a first weight;

the second time-of-arrival estimate according to the second weight; and

the third time-of-arrival estimate according to the third weight.

6 . The method of claim 1 , wherein calculating the set of phase differences comprises:

identifying a subset of multiplexed sub-signals in the set of multiplexed sub-signals based on a threshold propagation time of the ranging signal; and

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

7 . The method of claim 6 :

wherein calculating the set of phase differences comprises:

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

calculating a central tendency metric descriptive of the set of sub-signal pair time-of-arrival estimates; and

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

8 . The method of claim 1 :

further comprising:

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

calculating a second uncertainty of the second time-of-arrival estimate based on a variability measure characteristic of phase differences of sub-signal pairs in the set of multiplexed sub-signals; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on:

the first time-of-arrival estimate;

the second time-of-arrival estimate;

the first uncertainty; and

the second uncertainty.

9 . The method of claim 8 :

further comprising:

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

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

wherein characterizing the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate based on a weighted combination of:

the first time-of-arrival estimate according to the first weight; and

the second time of arrival estimate according to the second weight.

10 . The method of claim 1 , further comprising calculating a distance between the transmitter and the receiver based on the hybrid time-of-arrival estimate.

11 . The method of claim 10 , wherein calculating the distance between the transmitter and the receiver comprises:

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

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

12 . The method of claim 1 :

wherein accessing the ranging signal comprises accessing a set of ranging signals transmitted from a set of transmitters and received at the receiver, the set of ranging signals comprising the ranging signal;

wherein characterizing the hybrid time-of-arrival estimate comprises calculating a set of hybrid time-of-arrival estimates for the set of ranging signals, the set of hybrid time-of-arrival estimates comprising the hybrid time-of-arrival estimate; and

further comprising:

calculating a set of distances between the receiver and the set of transmitters; and

localizing the receiver relative to the set of transmitters based on the set of distances.

13 . A method comprising:

accessing a ranging signal transmitted from a transmitter and received at a receiver, the ranging signal comprising a set of multiplexed sub-signals characterized by 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;

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

calculating a second time-of-arrival estimate based on the set of multipath components; and

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.

14 . The method of claim 13 :

further comprising:

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

calculating a multipath metric characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on:

the first time-of-arrival estimate;

the second time-of-arrival estimate;

the first uncertainty; and

the multipath metric.

15 . The method of claim 13 :

further comprising:

calculating a multipath value characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

assigning a first weight, to the first time-of-arrival estimate, relative to a second weight assigned to the second time-of-arrival estimate based on the multipath value; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a weighted combination of:

the first time-of-arrival estimate according to a first weight; and

the second time-of-arrival estimate according to the second weight.

16 . The method of claim 13 :

further comprising:

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

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

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a combination of:

the first time-of-arrival estimate;

the second time-of-arrival estimate; and

the third time-of-arrival estimate; and

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

17 . The method of claim 16 , wherein characterizing the hybrid time-of-arrival estimate comprises calculating the hybrid time-of-arrival estimate based on a weighted average of:

the first time-of-arrival estimate;

the second time-of-arrival estimate; and

the third time-of-arrival estimate.

18 . A method comprising:

accessing a ranging signal transmitted from a transmitter and received at a receiver, the ranging signal comprising a set of multiplexed sub-signals characterized by a set of frequencies;

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

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

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

characterizing a hybrid time-of-arrival estimate of the ranging signal based on a combination of the first time-of-arrival estimate and the second time-of-arrival estimate.

19 . The method of claim 18 :

further comprising:

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

calculating a multipath metric characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on:

the first time-of-arrival estimate;

the second time-of-arrival estimate;

the first uncertainty; and

the multipath metric.

20 . The method of claim 18 :

further comprising:

calculating a multipath value characteristic of a power ratio between a first-arriving component and subsequent components in the set of multipath components; and

assigning a first weight, to the first time-of-arrival estimate, relative to a second weight assigned to the second time-of-arrival estimate based on the multipath value; and

wherein characterizing the hybrid time-of-arrival estimate comprises characterizing the hybrid time-of-arrival estimate based on a weighted combination of:

the first time-of-arrival estimate according to a first weight; and

the second time-of-arrival estimate according to the second weight.