GPS-alternative method to perform asynchronous positioning of networked nodes

An asynchronous localization method, comprising:

• in a network of nodes and one or more transmitters, including a first pair of nodes and a first transmitter, the position of at least one of the nodes in the first pair of nodes and/or the first transmitter being known as a default state of the network, for the first pair of nodes and the first transmitter:
• (a) receiving a first signal directly from the first transmitter at a first node of the first pair of nodes,
• (b) receiving the first signal relayed from a second node of the first pair of nodes at the first node;
• (c) determining the delay at the first node between the direct first signal and the relayed first signal by comparing the direct and relayed first signals;
• (d) determining at least one of the time difference of arrival and time of flight between the first and second nodes of the first node pair, in part using the determined delay at the first node, and wherein positions of the first and second nodes are known, determining time of flight between the first and second nodes based on their known positions, wherein determining at least one of the time difference of arrival and time of flight between the first and second nodes of the first node pair comprises determining the time difference of arrival between the first and second nodes using the delay at the first node and the determined time of flight between the first and second nodes;
• repeating steps (a) through (d) for one or more additional pairs of the nodes having known positions and determining time of flight between the one or more additional pairs of the nodes having known positions based on their known positions, and/or repeating for one or more additional pairs of the nodes having at least one node of unknown position steps (a) through (d) and further steps of (e) receiving a second signal directly from the first transmitter at the second node of the first pair of nodes, (f) receiving the second signal relayed from the first node of the first pair of nodes at the second node, (g) determining the delay at the second node between the direct second signal and the relayed second signal by comparing the direct and relayed second signals, and (h) determining the time difference of arrival and time of flight between the first and second nodes using the delay at the first node and the delay at the second node;
• generating a first set of values for the time difference of arrival and a second set of values for the time of flight;
• and
• calculating, using the first set of values and the second set of values, a position of a desired node and/or transmitter,
• wherein both the network of nodes and the one or more transmitters are unsynchronized.

An asynchronous localization method, comprising:

• in a network of nodes and one or more transmitters, including a first pair of nodes and a first transmitter, the position of at least one of the nodes in the first pair of nodes and/or the first transmitter being known, the position of at least one of the first and second nodes in the first pair of nodes being unknown, for the first pair of nodes and the first transmitter:
• (a) receiving a first signal directly from the first transmitter at a first node of the first pair of nodes;
• (b) receiving the first signal relayed from a second node of the first pair of nodes at the first node;
• (c) determining the delay at the first node between the direct first signal and the relayed first signal by comparing the direct and relayed first signals;
• (d) determining at least one of the time difference of arrival and time of flight between the first and second nodes of the first node pair, in part using the determined delay at the first node;
• wherein determining at least one of the time difference of arrival and time of flight between the first and second nodes of the first node pair comprises determining the time of flight between the first and second nodes, further comprising communicating a state T1 of the first node's clock to the second node, determining a state T12 of the second node's clock when the state T1 of the first node's clock is received at the second node, subtracting the determined time of flight between the first node and the second node from T12 to determine a state T2 of the second node's clock when the state of the first node's clock was T1, subtracting T1 from T2 to determine an offset between the two nodes' clocks, and applying the offset to synchronize the clocks of the first node and the second node.