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

capturing a series of time-domain samples representing the ranging signal;

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

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

for each sub-signal pair in a subset of multiplexed sub-signals of the set of multiplexed sub-signals, extracting a phase difference of the sub-signal pair;

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

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

calculating a hybrid time-of-arrival estimate as a weighted combination of the time-based time-of-arrival estimate, the phase-based time-of-arrival estimate, based on the time-based uncertainty and the phase-based uncertainty.

2. The method of claim 1 , wherein receiving the ranging signal from the transmitter comprises receiving a frequency-hopping spread spectrum signal comprising the set of multiplexed sub-signals, each multiplexed sub-signal characterized by the frequency in the set of frequencies.

3. The method of claim 1 , wherein receiving the ranging signal from the transmitter comprises receiving an orthogonal-frequency-division-multiplexed signal comprising the set of multiplexed sub-signals, each multiplexed sub-signal characterized by the frequency in the set of frequencies.

4. The method of claim 1 , wherein calculating the time-based time-of-arrival estimate based on the series of time-domain samples comprises:

accessing a template signal corresponding to the ranging signal;

correlating the template signal with the series of time-domain samples to identify a correlation peak; and

calculating the time-based time-of-arrival estimate based on the correlation peak.

5. The method of claim 1 , wherein calculating the phase-based time-of-arrival estimate comprises:

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 phase-based time-of-arrival estimate based on a measure of central tendency of the sub-signal pair time-of-arrival estimate for each sub-signal pair in the subset of multiplexed signals; and

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

6. The method of claim 1 , further comprising:

estimating a time-based time-of-flight estimate of the ranging signal based on the time-based time-of-arrival estimate; and

identifying the subset of multiplexed sub-signals in the set of multiplexed sub-signals, the subset of multiplexed sub-signals characterized by a subset of frequencies in the set of frequencies, each frequency in the subset of frequencies defining a total phase accumulation of less than 2π radians for a duration of the time-based time-of-flight estimate.

7. The method of claim 6 , wherein calculating the phase-based time-of-arrival estimate comprises:

generating a frequency-versus-phase-difference plot based on the subset of frequencies and the phase difference of each sub-signal pair in the subset of multiplexed sub-signals; and

calculating the phase-based time-of-arrival estimate based on a linear regression of the frequency-versus-phase-difference plot.

8. The method of claim 1 :

further comprising:

executing a multiple signal classification algorithm to detect a set of multipath components of the ranging signal;

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

calculating a K-factor based on a power ratio of an earliest-arriving component to all other components in the set of multipath components; 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 K-factor.

9. The method of claim 1 , further comprising:

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

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

calculating a hybrid range estimate for a 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 relative time bias between the transmitter and the receiver.

10. A method comprising:

accessing a ranging signal transmitted from a transmitter and received by a receiver, 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 series of time-domain samples representing the ranging signal;

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

calculating a time-based uncertainty based on the sampling frequency of the receiver;

executing a multiple signal classification algorithm to detect a set of multipath components of the ranging signal;

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

calculating a K-factor based on a power ratio of an earliest-arriving component to all other components in the set of multipath components; and

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 K-factor.

11. The method of claim 10 :

further comprising:

for each sub-signal pair in a subset of multiplexed sub-signals of the set of multiplexed sub-signals, extracting a phase difference of the sub-signal pair;

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

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

12. The method of claim 10 , wherein executing the multiple signal classification algorithm to detect the set of multipath components of the ranging signal comprises:

generating a received ranging signal vector based on a series of digital samples representing each sub-signal in the set of sub-signals;

calculating an autocorrelation matrix of the received ranging signal vector;

for each frequency in the set of frequencies, calculating an eigenvector of the autocorrelation matrix and a corresponding eigenvalue of the autocorrelation matrix;

sorting the eigenvector for each frequency in the set of frequencies based on the corresponding eigenvalue for each frequency in the set of frequencies to identify a noise subspace of eigenvectors and a signal subspace of eigenvectors;

evaluating an estimation function over a range of possible times-of-arrival based on the noise subspace of eigenvectors and a steering vector; and

identifying peaks of the estimation function as the set of multipath components of the ranging signal, each multipath component in the set of multipath components corresponding to a multipath time-of-arrival.

13. The method of claim 12 , wherein calculating the phase-amplitude-based time-of-arrival estimate based on the set of multipath components of the ranging signal comprises selecting an earliest multipath component in the set of multipath components based on the multipath time-of-arrival of each multipath component.

14. A method comprising:

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

for each sub-signal pair in a subset of multiplexed sub-signals of the set of multiplexed sub-signals, extracting a phase difference of the sub-signal;

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

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

executing a multiple signal classification algorithm to detect a set of multipath components of the ranging signal;

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

calculating a K-factor based on a power ratio of an earliest-arriving component to all other components in the set of multipath components; and

calculating a 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 K-factor.

15. The method of claim 14 :

further comprising:

capturing a series of time-domain samples representing the ranging signal;

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

calculating a time-based uncertainty based on the sampling frequency of the receiver; 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 K-factor.

16. The method of claim 14 , further comprising:

estimating a time-of-flight estimate of the ranging signal; and

identifying the subset of multiplexed sub-signals in the set of multiplexed sub-signals, the subset of multiplexed sub-signals characterized by a subset of frequencies in the set of frequencies, each frequency in the subset of frequencies defining a total phase accumulation of less than 2π radians for a duration of the time-of-flight estimate.

17. The method of claim 16 , wherein calculating the phase-based time-of-arrival estimate comprises:

generating a frequency-versus-phase-difference plot based on the subset of frequencies and the phase difference of each sub-signal pair in the subset of multiplexed sub-signals; and

calculating the phase-based time-of-arrival estimate based on a linear regression of the frequency-versus-phase-difference plot.

18. The method of claim 14 , executed by a remote computational device in communication with the receiver.

19. The method of claim 14 , executed by the receiver.

20. The method of claim 14 :

wherein accessing the ranging signal comprises, at the receiver, receiving the ranging signal transmitted by the transmitter and received by the receiver;

wherein extracting the phase difference of each sub-signal pair in the subset of multiplexed sub-signals comprises, at the receiver, for each sub-signal pair in the subset of multiplexed sub-signals of the set of multiplexed sub-signals, extracting the phase difference of the sub-signal pair;

wherein calculating the phase-based time-of-arrival estimate comprises, at the receiver, calculating the phase-based time-of-arrival estimate based on the phase difference of each sub-signal pair in the subset of multiplexed sub-signals;

wherein calculating the phase-based uncertainty of the phase-based time-of-arrival comprises, at the receiver, calculating the phase-based uncertainty of the phase-based time-of-arrival estimate based on the variability measure based on the phase difference of each sub-signal pair in the subset of multiplexed sub-signals;

wherein executing the multiple signal classification algorithm comprises, at a remote computational device, executing the multiple signal classification algorithm to detect the set of multipath components of the ranging signal;

wherein calculating the phase-amplitude-based time-of-arrival estimate comprises, at the remote computational device, calculating the phase-amplitude-based time-of-arrival estimate based on the set of multipath components of the ranging signal;

wherein calculating the K-factor comprising, at the remote computational device, calculating the K-factor based on the power ratio of the earliest-arriving component to all other components in the set of multipath components; and

wherein calculating the hybrid time-of-arrival estimate comprises, at the remote computational device, 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 K-factor.