Abstract: A method includes accessing a network graph including: a set of nodes, each representing a transceiver; and a set of edges, each edge connecting two nodes and representing a communication channel between a pair of transceivers. The method also includes: accessing a network state comprising a set of edge values for the set of edges; and identifying a set of triangle graphs in the network graph. The method further includes, for each triangle graph in the network graph: calculating a component diagnostic score based on a subset of edge values; and for each node in the triangle graph, updating a cumulative diagnostic score for the node based on the component diagnostic score. The method additionally includes, in response to detecting a cumulative diagnostic score for a node exceeding a threshold cumulative diagnostic score, triggering a corrective action at a transceiver represented by the node.

Abstract: A method includes accessing a network graph including: a set of nodes, each representing a transceiver; and a set of edges, each edge connecting two nodes and representing a communication channel between a pair of transceivers. The method also includes: accessing a network state comprising a set of edge values for the set of edges; and identifying a set of triangle graphs in the network graph. The method further includes, for each triangle graph in the network graph: calculating a component diagnostic score based on a subset of edge values; and for each node in the triangle graph, updating a cumulative diagnostic score for the node based on the component diagnostic score. The method additionally includes, in response to detecting a cumulative diagnostic score for a node exceeding a threshold cumulative diagnostic score, triggering a corrective action at a transceiver represented by the 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 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 accessing a network graph including: a set of nodes, each representing a transceiver; and a set of edges, each edge connecting two nodes and representing a communication channel between a pair of transceivers. The method also includes: accessing a network state comprising a set of edge values for the set of edges; and identifying a set of triangle graphs in the network graph. The method further includes, for each triangle graph in the network graph: calculating a component diagnostic score based on a subset of edge values; and for each node in the triangle graph, updating a cumulative diagnostic score for the node based on the component diagnostic score. The method additionally includes, in response to detecting a cumulative diagnostic score for a node exceeding a threshold cumulative diagnostic score, triggering a corrective action at a transceiver represented by the node.

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 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 accessing a network graph including: a set of nodes, each representing a transceiver; and a set of edges, each edge connecting two nodes and representing a communication channel between a pair of transceivers. The method also includes: accessing a network state comprising a set of edge values for the set of edges; and identifying a set of triangle graphs in the network graph. The method further includes, for each triangle graph in the network graph: calculating a component diagnostic score based on a subset of edge values; and for each node in the triangle graph, updating a cumulative diagnostic score for the node based on the component diagnostic score. The method additionally includes, in response to detecting a cumulative diagnostic score for a node exceeding a threshold cumulative diagnostic score, triggering a corrective action at a transceiver represented by 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 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 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 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 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 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 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 technique for simplifying structure data for representing an environment. Polyhedrons can make up structure data used in an application such as modeling, visualization, and navigation. Consequently, the operations that are performed on the data often involve determining, for each polyhedron that defines a structure such as a building, whether the polyhedron obstructs a line-of-sight line between a first point in space being considered in the application and a second point. In order to determine whether a polyhedron obstructs a line-of-sight line, a data-processing system operating on the structure data must determine whether any walls of the polyhedron intersect the line. Thus, the more polyhedrons there are or the more vertices that are in each polyhedron, the more walls there are, and the more intersection checks are required, thereby adding to the computations. The disclosed technique reduces the number of walls by simplifying objects that make up the structure data.

Abstract: A technique for simplifying structure data for representing an environment. Polyhedrons can make up structure data used in an application such as modeling, visualization, and navigation. Consequently, the operations that are performed on the data often involve determining, for each polyhedron that defines a structure such as a building, whether the polyhedron obstructs a line-of-sight line between a first point in space being considered in the application and a second point. In order to determine whether a polyhedron obstructs a line-of-sight line, a data-processing system operating on the structure data must determine whether any walls of the polyhedron intersect the line. Thus, the more polyhedrons there are or the more vertices that are in each polyhedron, the more walls there are, and the more intersection checks are required, thereby adding to the computations. The disclosed technique reduces the number of walls by simplifying objects that make up the structure data.

Abstract: A technique for simplifying structure data for representing an environment. Polyhedrons can make up structure data used in an application such as modeling, visualization, and navigation. Consequently, the operations that are performed on the data often involve determining, for each polyhedron that defines a structure such as a building, whether the polyhedron obstructs a line-of-sight line between a first point in space being considered in the application and a second point. In order to determine whether a polyhedron obstructs a line-of-sight line, a data-processing system operating on the structure data must determine whether any walls of the polyhedron intersect the line. Thus, the more polyhedrons there are or the more vertices that are in each polyhedron, the more walls there are, and the more intersection checks are required, thereby adding to the computations. The disclosed technique reduces the number of walls by simplifying objects that make up the structure data.