 # Time Synchronization in Wireless Sensor Networks

Gyula Simon (University of Pannonia, Hungary) and Gergely Vakulya (University of Pannonia, Hungary)
DOI: 10.4018/978-1-60960-732-6.ch021

## Abstract

Time synchronization services are often required to support coordinated operation of the nodes in sensor networking applications, potentially containing hundreds or thousands of elements. The synchronization service must provide application-specific performance (in terms of accuracy and overhead), and must be scalable and robust. For the design of suitable algorithms, the error sources of both the applied synchronization models and the physical devices must be understood and taken into account. In this chapter, various time synchronization models will be introduced, and their potential accuracy and complexity will be shown. The error sources of real devices and communication channels will also be analyzed. Based on the models, several synchronization primitives will be reviewed, and complex synchronization algorithms will be introduced and analyzed.
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## Time And Clocks

### Clock Models

A clock can be modeled by the following equation:

Where C(t) is the local time shown by the clock at time instant t, f is the instantaneous frequency of the clock’s time base and is the nominal time-base frequency. A clock is called accurate if C(t)=t. The difference between the clock value and the real time C(t)−t is called clock offset.

Digital clocks use hardware (usually quartz) oscillators as time bases, and digital counters to approximate the integrator. Ideally, the counter c(t) is incremented by one in every second, so the local time of a digital clock is

where c(t0)=0.

The frequency of the clock is , which should ideally be exactly one, while the real time-base frequency is , which ideally should be equal to . The frequency of real clocks somewhat differs from the nominal frequency. This phenomenon is called drift and defined as

or in terms of the time-base frequency

If the drift value is -1 then the clock is stopped, for values smaller than -1 the clock is going backwards. Thus a reasonable assumption for real clocks is for all t.

If the drift is known to be bounded by

then bounds for measured time differences can be calculated. If two events occur at ta and tb, and the corresponding measured local time instants are C(ta) and C(tb), respectively, where ta < tb then, taking into account the drift of the clock, the following bound can be calculated for the time difference:

Since digital clocks change their values at discrete time instants, an important property called time resolution must be introduced. Time resolution is the smallest time difference the clock can represent, which is obviously . Thus, a higher clock frequency provides higher resolution.

Drift in clocks using quartz oscillators results from several sources, the most important ones being manufacturing inaccuracies, temperature changes and ageing. The drift of commonly used, inexpensive quartz oscillators is around 10-100 ppm (parts per million). This means that in case of a 10ppm crystal, the clock will drift 1 second in 100.000 seconds, i.e. almost 28 hours. The time resolution of a clock using a 32 kHz crystal is 30.5 microseconds, while if a 4MHz crystal is used then the resolution is 0.25 microseconds.

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