Methods for time synchronization and localization in a mesh network

A method comprising:

• during a first time period:
• at a first node:
• transmitting a first synchronization signal comprising a first modulated maximum length sequence;
• and
• accessing a first phase reference associated with the first synchronization signal;
• and
• at a second node:
• receiving the first synchronization signal;
• based on the first modulated maximum length sequence, calculating a first cross-correlation of the first synchronization signal;
• and
• based on the first cross-correlation, extracting the first phase-of-arrival;
• during a second time period:
• at the second node:
• transmitting a second synchronization signal comprising a second modulated maximum length sequence;
• and
• accessing a second phase reference associated with the second synchronization signal;
• and
• at the first node:
• receiving the second synchronization signal;
• based on the second modulated maximum length sequence, calculating a second cross-correlation of the second synchronization signal;
• and
• based on the second cross-correlation, extracting the second phase-of-arrival;
• and
• calculating a propagation delay between the first node and the second node based on:
• the first phase reference;
• the second phase reference;
• the first phase-of-arrival;
• and
• the second phase-of-arrival.

A method comprising:

• during a first time period:
• at a first node:
• transmitting a first synchronization signal;
• and
• accessing a first phase reference for each carrier frequency in a first set of carrier frequencies, the first set of carrier frequencies characterizing the first synchronization signal;
• and
• at a second node, accessing a first phase-of-arrival for each carrier frequency in the first set of carrier frequencies;
• during a second time period:
• at the second node:
• transmitting a second synchronization signal;
• and
• accessing a second phase reference for each carrier frequency in a second set of carrier frequencies, the second set of carrier frequencies characterizing the second synchronization signal;
• and
• at the first node, accessing a second phase-of-arrival for each carrier frequency in the second set of carrier frequencies;
• and
• calculating a time bias between the first node and the second node based on:
• the first phase reference for each carrier frequency in the first set of carrier frequencies;
• the first phase-of-arrival for each carrier frequency in the first set of carrier frequencies;
• the second phase reference for each carrier frequency in the second set of carrier frequencies;
• and
• the second phase-of-arrival for each carrier frequency in the second set of carrier frequencies.

A method comprising:

• during a first time period:
• at a first node:
• transmitting a first synchronization signal;
• and
• accessing a first reference phase of a first local reference copy of the first synchronization signal;
• and
• at a second node, accessing a first phase of the first synchronization signal received at the second node;
• during a second time period:
• at the second node:
• transmitting a second synchronization signal;
• and
• accessing a second reference phase of a second local reference copy of the second synchronization signal;
• and
• at the first node, accessing a second phase of the second synchronization signal received at the first node;
• and
• calculating a time bias between a first internal clock of the first node and a second internal clock of the second node based on:
• the first reference phase of the first local reference copy;
• the first phase of the first synchronization signal at the second node;
• the second reference phase of the second local reference copy;
• and
• the second phase of the second synchronization signal at the first node.