ZaiNar, Inc.

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

A method includes: accessing propagation delay values associated with a signal transmitted from a target device and received at antenna elements of a set of nodes; defining combinations of antenna elements, each combination of antenna elements including an antenna element of each node in the set of nodes. For each combination of antenna elements, the method includes: accessing a group of propagation delay values corresponding to antenna elements in the combination of antenna elements; calculating a candidate position, in a set of candidate positions, occupied by the target device based on the group of propagation delay values. The method includes: isolating a subset of candidate positions, in the set of candidate positions, falling within a selected region in the reference coordinate system; and calculating an estimated position, in the reference coordinate system, occupied by the target device based on a combination of the subset of candidate positions.

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.

A method includes: accessing time-difference-of-arrival data associated with a signal transmitted by a transmitter and received by a pair of nodes in an environment; generating parameters of a mixture model based on the time-difference-of-arrival data and a neural network; generating a probability density function, in a set of probability density functions, representing a distribution of distances between the transmitter and the pair of nodes based on the parameters and the time-difference-of-arrival data; based on the set of probability density functions, generating a spatial probability density function representing likelihoods of positions of the transmitter within the environment; calculating a set of likelihoods of the transmitter positioned at a set grid of points representing the environment based on the spatial probability density function; and identifying a target grid point exhibiting highest likelihood in the set of likelihoods as an estimated position of the transmitter.

A method includes, generating a schedule for an asset tag group, the schedule defining: a multicast trigger time for transmission of a multicast trigger to the asset tag group; and for each asset tag in the asset tag group, a transmit time succeeding receipt of the multicast trigger and unique to the asset tag, and a wake window intersecting the transmit time and the receipt of the multiact trigger. The method also includes, at the node network: broadcasting the multicast trigger; and, at an asset tag in the asset tag group, entering a wake mode; receiving the multicast trigger; transmitting a ranging signal; and entering the sleep mode. The method further includes, at the node network: receiving ranging signals from the asset tag group; and deriving locations of the asset tags in the asset tag group based on the ranging signals received by the node network.

A method includes, generating a schedule for an asset tag, the schedule defining: a unicast trigger time for transmission of a unicast trigger to the asset tag; a transmit time succeeding receipt of the multicast trigger; and a wake window intersecting the transmit time and the receipt of the multiact trigger. The method also includes transmitting the schedule from a node network to the asset tag and configuring the asset tag based on the schedule. The method also includes, at the node network, broadcasting the unicast trigger and, at an asset tag: entering a wake mode; receiving the unicast trigger; transmitting a ranging signal; and entering the sleep mode. The method further includes, at the node network: deriving location of the asset tag based on instance of the ranging signal received by nodes in the node network.

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

A method for calculating a time-of-arrival of a multicarrier uplink signal includes: accessing a multicarrier reference signal including a subcarrier reference signal for each subcarrier frequency in a set of subcarrier frequencies; receiving the multicarrier uplink signal transmitted from a user device, the multicarrier uplink signal including a subcarrier uplink signal for each subcarrier frequency in the set of subcarrier frequencies; for each subcarrier frequency in the set of subcarrier frequencies, calculating a phase difference, in a set of phase differences, between the subcarrier reference signal for the subcarrier frequency and a subcarrier uplink signal for the subcarrier frequency; calculating a time-of-arrival of the multicarrier uplink signal at the transceiver based on the set of adjusted phase differences; and transmitting the time-of-arrival of the multicarrier uplink signal to a remote server.

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.

A radio-frequency system including: a self-complementary antenna characterized by an input impedance substantially independent of signal frequency across an operational frequency band; a passive coupling device characterized by a characteristic impedance and configured to couple the self-complementary antenna to a signal generator and a set of signal processors; a resistive matching network electrically connected between the self-complementary antenna and the passive coupling device configured to match the characteristic impedance of the passive coupling device to the input impedance of the self-complementary antenna; and a back-coupling line characterized by a substantially constant group delay across the operational frequency band configured to electromagnetically couple the signal generator to the set of signal processors.