GPS-alternative method to perform asynchronous positioning of networked nodes
A new asynchronous localization method for a network of nodes and transmitters, the position of at least one of the nodes and/or transmitters being known, involves receiving a first signal directly from a first transmitter at a first node of a first node pair, receiving the first signal relayed from a second node of the first node pair at the first node, and determining the delay at the first node between the direct and relayed first signal by comparing the direct and relayed first signals. This may be repeated with the first node acting as relay to determine the delay at the second node. Time difference of arrival and/or time of flight between first and second nodes may be determined using the determined delay at the first and/or second node and/or known node locations. The process is repeated for additional transmitters/node pairs until sufficient information is determined for desired applications.
1. 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;
(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;
wherein at least one of the first and second nodes in the first pair of nodes has an unknown location;
repeating steps (a) through (g) for one or more additional ones of the transmitters and/or one or more additional pairs of the nodes having at least one node of unknown position, and/or 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;
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.
2. The method of claim 1 , wherein the first transmitter is a source of acoustic energy or non-RF electromagnetic energy.
3. The method of claim 1 , wherein each of the nodes is configured to multiplex three transceiver functions: receiving a signal directly from one of the transmitters, transmitting a relay of the signal received directly from the one transmitter to one or more other nodes, and receiving from others of the nodes one or more relays of the signal received directly from the one transmitter by the others of the nodes.
4. The method of claim 1 , further comprising determining the position of N nodes in D dimensions, wherein positions of the transmitters are known and the number of transmitters Q is greater than or equal to (N(2D+1−N))/([2(N−1)]).
5. The method of claim 4 , wherein N is at least four, D is three, and Q is only two.
6. The method of claim 1 , wherein the one or more transmitters consist of at least three transmitters with known three-dimensional locations and the nodes comprise a single node having a known location, further comprising determining the three-dimensional location of all other nodes in the network.
7. The method of claim 1 , wherein the one or more transmitters consist of at least two transmitters with known two-dimensional locations and the nodes comprise a single node having a known location, further comprising determining the two-dimensional location of all other nodes in the network.
8. The method of claim 7 , wherein one of the transmitters is a radar target passively transmitting a reflected signal.
9. The method of claim 1 , further comprising using additional sensor information and/or prior knowledge to increase fidelity of positioning and/or reduce the number of transmitters required for positioning.
10. The method of claim 9 , wherein the additional sensor information comprises angle-of-arrival of transmitter signals, velocity and orientation via Inertial Measurement Unit (IMU), incomplete but useable GPS measurements, direction of magnetic north via compass, orientation to celestial objects (e.g. sun, moon, stars) with date/time known, and/or polarization of the sky due to Rayleigh scattering within the atmosphere, and the prior knowledge comprises Geographic Information Systems information, Digital Terrain Elevation Data, Land Cover Land Use information, reconnaissance information, a physical model of node kinematics, transmitter locations and waveforms, a priori rough estimate of location of operation, and/or weather forecasts.
11. The method of claim 1 , wherein the one or more transmitters transmit signals of opportunity.
12. The method of claim 11 , wherein the signals of opportunity are wireless signals that are emitted for purposes other than navigation but may be intercepted and used for navigation.
13. The method of claim 11 , wherein the signals of opportunity originate from one or more sources of propagating energy that are not purposefully directed towards any of the nodes in the network of nodes.
14. The method of claim 1 , wherein each of the nodes in the first pair of nodes is a handheld receiver.
15. The method of claim 1 , wherein each of the nodes in the first pair of nodes is non-stationary.
16. The method of claim 1 , wherein each of the nodes in the first pair of nodes is capable of being physically moved from a first location to a second location by a user.
17. The method of claim 1 , wherein at least one node in the network of nodes is a different physical device than the one or more transmitters.
18. 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.
19. The method of claim 18 , further comprising determining a D-dimensional position of each of the transmitters, wherein the nodes consist of at least D+1 nodes of known location.
20. The method of claim 18 , wherein the nodes comprise at least four nodes of known location, further comprising determining a three-dimensional position of all the transmitters.
21. The method of claim 18 , wherein the nodes comprise at least three nodes of known location, further comprising determining a two-dimensional position of all the nodes in the network using the time of flight determinations.
22. 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 T 1 of the first node's clock to the second node, determining a state T 12 of the second node's clock when the state T 1 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 T 12 to determine a state T 2 of the second node's clock when the state of the first node's clock was T 1 , subtracting T 1 from T 2 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.