Methods for nanosecond-scale time synchronization over a network

A method for calculating time bias between a pair of nodes in a network comprising, at a first node in the pair of nodes:

• transmitting a coordination signal to a second node in the pair of nodes, the coordination signal indicating a second time to transmit a second synchronization signal;
• 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;
• receiving the first self-receive signal;
• calculating a time-of-arrival of the first self-receive signal according to the first clock;
• receiving the second synchronization signal, the second synchronization signal transmitted by the second node according at the second time according to a second clock of the second node;
• calculating a time-of-arrival of the second synchronization signal according to the first clock;
• receiving a time-of-arrival of the first synchronization signal from the second node, the time-of-arrival of the first synchronization signal calculated by the second node according to the second clock;
• receiving a time-of-arrival of a second self-receive signal from the second node, the second self-receive signal back-coupled by the second node upon transmission of the second synchronization signal, the time-of-arrival of the second self-receive signal calculated according to the second clock;
• and
• calculating a first time bias between the first clock and the second clock and a first propagation delay between the first node and the second node based on the time-of-arrival of the first self-receive signal, the time-of-arrival of the first synchronization signal, the time-of-arrival of the second self-receive signal, and the time-of-arrival of the second synchronization signal.

A method for calculating time bias between a pair of nodes in a network, including:

• at a first node in the pair of nodes, during a first synchronization slot:
• 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;
• receiving the first self-receive signal;
• calculating a time-of-arrival of the first self-receive signal according to the first clock;
• receiving a second synchronization signal from the second node;
• and
• calculating a time-of-arrival of the second synchronization signal according to the first clock;
• at the second node, during the first synchronization slot:
• 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;
• receiving the second self-receive signal;
• calculating a time-of-arrival of the second self-receive signal according to the second clock;
• receiving the first synchronization signal from the first node;
• and
• calculating a time-of-arrival of the first synchronization signal according to the second clock;
• and
• calculating a time bias and a propagation delay between the pair of nodes based on the time-of-arrival of the first self-receive signal and the time-of-arrival of the second synchronization signal, the time-of-arrival of the second self-receive signal and the time-of-arrival of the first synchronization signal at the second node.