Distributed position, navigation, and timing (pnt) chain

A method comprising:

• providing a first platform and a second platform each comprising one or more position or inertial sensors;
• one or more ranging sensors, including a first ranging sensor;
• and a controller to execute a de-centralized decentralized, collaborative navigation operation for a network of platforms;
• at the first platform,
• receiving a sensor measurement from the one or more inertial sensors and the one or more ranging sensors;
• receiving a message from a second platform of a plurality of platforms;
• determining at least one of position, velocity, and orientation values for the first platform using the received sensor measurement and the message;
• determining, via a distributed estimation algorithm, a first set of estimated states as a subgraph of a complete graph, wherein the subgraph corresponds to the first platform and a set of neighboring platforms, including a first neighboring platform, and wherein the complete graph corresponds to the plurality of platforms, wherein the message comprises a second set of estimated states of the second platform for a set of neighboring platforms of the second platform;
• and
• executing control operations to adjust at least one of position, velocity, navigation, steering, or a combination thereof of the first platform using the estimated states to maintain position or relative position or movement with, at least, the set of neighboring platforms.

A non-transitory computer readable medium having instructions stored thereon, wherein the instructions when executed by a controller of a platform cause the controller to:

• receive a message from a second platform of a plurality of platforms;
• determine at least one of position, velocity, and orientation values for the first platform using the received sensor measurement and the message;
• determine, via a distributed estimation algorithm, a first set of estimated states as a subgraph of a complete graph, wherein the subgraph corresponds to the first platform and a set of neighboring platforms, including a first neighboring platform, and wherein the complete graph corresponds to the plurality of platforms,
• wherein the message comprises a second set of estimated states of the second platform for a set of neighboring platforms of the second platform;
• and
• execute control operations to adjust at least one of position, velocity, navigation, steering, or a combination thereof of the first platform using the estimated states to maintain position or relative position or movement with, at least, the set of neighboring platforms.