Abstract: A method includes, at a first node: transmitting a first synchronization signal at a first time according to a first clock of the first node; back-coupling the first synchronization signal to generate a first self-receive signal; calculating a time-of-arrival of the first self-receive signal according to the first clock; and calculating a time-of-arrival of the second synchronization signal according to the first clock. The method also includes, at the second node: transmitting the second synchronization signal at a second time according to a second clock of the second node; back-coupling the second synchronization signal to generate a second self-receive signal; calculating a time-of-arrival of the second self-receive signal according to the second clock; and calculating a time-of-arrival of the first synchronization signal according to the second clock. The method S100 further includes calculating a time bias and a propagation delay between the pair of nodes based on the time-of-arrivals.

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 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 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 system for generating a self-receive signal including: a signal generator; a signal processor including an analog-to-digital converter; and an antenna. The system also includes a passive coupling device including: an antenna port electromagnetically coupled to the antenna; a transmit port electromagnetically coupled to the signal generator; and a receive port electromagnetically coupled to the signal processor. The system additionally includes an impedance matching network: electromagnetically interposed between the antenna port and the antenna; and configured to shift an impedance of the antenna to a load impedance different from a characteristic impedance of the passive coupling device.

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.

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, at a first node: transmitting a first synchronization signal at a first time according to a first clock of the first node; back-coupling the first synchronization signal to generate a first self-receive signal; calculating a time-of-arrival of the first self-receive signal according to the first clock; and calculating a time-of-arrival of the second synchronization signal according to the first clock. The method also includes, at the second node: transmitting the second synchronization signal at a second time according to a second clock of the second node; back-coupling the second synchronization signal to generate a second self-receive signal; calculating a time-of-arrival of the second self-receive signal according to the second clock; and calculating a time-of-arrival of the first synchronization signal according to the second clock. The method S100 further includes calculating a time bias and a propagation delay between the pair of nodes based on the time-of-arrivals.

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 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 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.