Abstract: 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.

Abstract: A method including accessing a network graph including: a set of transceiver nodes representing a set of transceivers operating in a mesh network of transceivers; a set of transmitter nodes representing a set of transmitters communicating with the mesh network of transceivers; and a set of edges, each connecting a pair of nodes in the set of nodes. The method also includes: identifying a subgraph of the network graph associated with a node in the set of nodes, the node representing a transceiver; accessing a network state of the subgraph comprising a set of edge values for each edge in the subgraph; calculating a probability of failure of the transceiver based on the network state of the subgraph; and in response to detecting the probability of failure of the transceiver exceeding a threshold likelihood, triggering a corrective action at the transceiver.

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, at a first node: transmitting a first calibration signal at a first time-of-departure measured by the first node; and transmitting a second calibration signal at a second time-of-departure measured by the first node. The method also includes, at a second node: receiving the first calibration signal at a first time-of-arrival measured by the second node; and receiving the second calibration signal at a second time-of-arrival measured by the second node. The method further includes: defining a first calibration point and a second calibration point in a set of calibration points, each calibration point comprising a time-of-departure and a time-of-arrival of each calibration signal; calculating a regression on the set of calibration points; and calculating a frequency offset between the first node and the second node based on the first regression.

Abstract: 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.

Abstract: A method including accessing a network graph including: a set of transceiver nodes representing a set of transceivers operating in a mesh network of transceivers; a set of transmitter nodes representing a set of transmitters communicating with the mesh network of transceivers; and a set of edges, each connecting a pair of nodes in the set of nodes. The method also includes: identifying a subgraph of the network graph associated with a node in the set of nodes, the node representing a transceiver; accessing a network state of the subgraph comprising a set of edge values for each edge in the subgraph; calculating a probability of failure of the transceiver based on the network state of the subgraph; and in response to detecting the probability of failure of the transceiver exceeding a threshold likelihood, triggering a corrective action at the transceiver.

Abstract: A method of determining a reference clock in a mesh network includes receiving multiple signals, correlating the multiple signals with a local signal generated by the first node to determine a coarse set of time differences, refining the coarse set of time differences using a phase of a carrier signal of the multiple signals to produce a refined set of time differences, and using the refined set of time differences to define a reference clock.

Abstract: 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.

Abstract: 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.

Abstract: A method for detecting times-of-arrival of signals comprising, at a receiving node: during a time slot, receiving a signal comprising a carrier signal characterized by a carrier frequency and modulated by a template signal defining a code sequence characterized by a transmitter chip period; demodulating the signal according to a local oscillator frequency to generate a received baseband signal, the local oscillator frequency and the carrier frequency defining a desynchronization ratio characterized by a denominator greater than a threshold denominator; sampling the received baseband signal at the transmitter chip period to generate a set of digital samples; generating a reconstructed baseband signal based on the set of digital samples; calculating a cross-correlation function comprising a cross-correlation of the reconstructed baseband signal and the template signal; and calculating, on the fine time grid, a time-of-arrival of the signal based on the cross-correlation function.

Abstract: A method including, at each node in each pair of nodes in a network: transmitting an outbound synchronization signal; generating a self-receive signal based on the outbound synchronization signal; detecting the self-receive signal at a self-receive TOA; detecting an inbound synchronization signal; based on the pair of self-receive TOAs and the pair of synchronization TOAs, for each pair of nodes in the network: calculating a pairwise time offset and distance; for each node in the network: based on the set of pairwise distances, calculating a location and a time bias of the node. The method also includes: at each node in the network, detecting a localization signal, transmitted by a device, at a localization TOA; and calculating a location of the device based on, for each node in the network, the localization signal detected at the node, and the time bias and the relative location of the node.

Abstract: A method includes: scheduling transmission of a first synchronization signal by a first node; and scheduling transmission of a second synchronization signal by a second node. The method also includes, after transmission of the first synchronization signal: receiving, from the first node, a first phase reference associated with the first synchronization signal; and receiving, from the second node, a first phase-of-arrival of the first synchronization signal at the second node. The method additionally includes, after transmission of the second synchronization signal: receiving, from the second node, a second phase reference associated with the second synchronization signal; and receiving, from the first node, a second phase-of-arrival of the second synchronization signal at the first node.

Abstract: 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.

Abstract: A method for detecting times-of-arrival of signals comprising, at a receiving node: during a time slot, receiving a signal comprising a carrier signal characterized by a carrier frequency and modulated by a template signal defining a code sequence characterized by a transmitter chip period; demodulating the signal according to a local oscillator frequency to generate a received baseband signal, the local oscillator frequency and the carrier frequency defining a desynchronization ratio characterized by a denominator greater than a threshold denominator; sampling the received baseband signal at the transmitter chip period to generate a set of digital samples; generating a reconstructed baseband signal based on the set of digital samples; calculating a cross-correlation function comprising a cross-correlation of the reconstructed baseband signal and the template signal; and calculating, on the fine time grid, a time-of-arrival of the signal based on the cross-correlation function.

Abstract: A method including, at each node in each pair of nodes in a network: transmitting an outbound synchronization signal; generating a self-receive signal based on the outbound synchronization signal; detecting the self-receive signal at a self-receive TOA; detecting an inbound synchronization signal; based on the pair of self-receive TOAs and the pair of synchronization TOAs, for each pair of nodes in the network: calculating a pairwise time offset and distance; for each node in the network: based on the set of pairwise distances, calculating a location and a time bias of the node. The method also includes: at each node in the network, detecting a localization signal, transmitted by a device, at a localization TOA; and calculating a location of the device based on, for each node in the network, the localization signal detected at the node, and the time bias and the relative location of the node.

Abstract: A method includes: scheduling transmission of a first synchronization signal by a first node; and scheduling transmission of a second synchronization signal by a second node. The method also includes, after transmission of the first synchronization signal: receiving, from the first node, a first phase reference associated with the first synchronization signal; and receiving, from the second node, a first phase-of-arrival of the first synchronization signal at the second node. The method additionally includes, after transmission of the second synchronization signal: receiving, from the second node, a second phase reference associated with the second synchronization signal; and receiving, from the first node, a second phase-of-arrival of the second synchronization signal at the first node.

Abstract: A method includes, at a first node: transmitting a first calibration signal at a first time-of-departure measured by the first node; and transmitting a second calibration signal at a second time-of-departure measured by the first node. The method also includes, at a second node: receiving the first calibration signal at a first time-of-arrival measured by the second node; and receiving the second calibration signal at a second time-of-arrival measured by the second node. The method further includes: defining a first calibration point and a second calibration point in a set of calibration points, each calibration point comprising a time-of-departure and a time-of-arrival of each calibration signal; calculating a regression on the set of calibration points; and calculating a frequency offset between the first node and the second node based on the first regression.

Abstract: 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.

Abstract: 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.

Abstract: A system for generating a self-receive signal includes: a signal generator; a first signal processor; a second signal processor; and an antenna. The system also includes a first passive coupling device: defining a first input port electromagnetically coupled to the signal generator; defining a first transmitted port; defining a first coupled port electromagnetically coupled to the first signal processor; and characterized by a first phase balance between the first transmitted port and the first coupled port. The system further includes a second passive coupling device: defining a second input port electromagnetically coupled to the antenna; defining a second transmitted port electromagnetically coupled to the first transmitted port; defining a second coupled port electromagnetically coupled to the second signal processor; and characterized by a second phase balance between the second transmitted port and the second coupled port substantially similar to the first phase balance.