Abstract: A method includes: receiving a ranging signal from the transmitter including a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies; calculating a sample-based time-of-arrival estimate based on the series of time-domain samples of the ranging signal; calculating a sample-based uncertainty of the sample-based time-of-arrival; 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; and calculating a hybrid time-of-arrival estimate as a weighted combination of the sample-based time-of-arrival estimate, the phase-based time-of-arrival estimate, based on the sample-based uncertainty and the phase-based uncertainty.

Abstract: A method includes: receiving a ranging signal from the transmitter including a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies; calculating a sample-based time-of-arrival estimate based on the series of time-domain samples of the ranging signal; calculating a sample-based uncertainty of the sample-based time-of-arrival; 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; and calculating a hybrid time-of-arrival estimate as a weighted combination of the sample-based time-of-arrival estimate, the phase-based time-of-arrival estimate, based on the sample-based uncertainty and the phase-based uncertainty.

Abstract: A method includes: receiving a ranging signal from the transmitter including a set of multiplexed sub-signals, each multiplexed sub-signal characterized by a frequency in a set of frequencies; calculating a sample-based time-of-arrival estimate based on the series of time-domain samples of the ranging signal; calculating a sample-based uncertainty of the sample-based time-of-arrival; 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; and calculating a hybrid time-of-arrival estimate as a weighted combination of the sample-based time-of-arrival estimate, the phase-based time-of-arrival estimate, based on the sample-based uncertainty and the phase-based uncertainty.