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Timestamp-free synchronization and ranging

Timestamp-free synchronization and ranging

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Bernhard Etzlinger

Description
Assume a round-trip packet exchange between two wireless nodes, where the nodes are asynchronous in frequency and phase. Traditionally, the clocks are modeled as affine function. The round-trip time (RTT), i.e., the difference between receive time at the end of a round and transmit time at the beginning of a round, is constant over the packet rounds:

RTT measurements with ideal clocks

From the round-trip time measurements one is not able to jointly determine the frequency and phase offset among the nodes and the propagation delay of the packet exchange.

However, in the above sketch we used the traditional affine clock model to account for asynchronity. In reality, clocks are value discrete function, counting one interval at every rising clock edge of the driving oscillator. Our approach is to model this imperfection and to derive a analytical waveform for the round-trip time:

RTT measurements with real clocks

We discovered that this waveform is unique among every pair of nodes. By estimating the waveform parameters we are able to determine clock frequency and phase offset, and the propagation delay without any exchange of timing information.