Time Synchronization for Wireless Sensor Networks - Adaptive Signal Processing in Wireless Communications - page 398

Calculate the optimal
number of samples in
model parameters
estimation

Calculate
prediction
error

Adjust the frequency
of getting new
timing message

Model parameters
estimation

FIgure 13.8 Flowchart of RATS run at the node receiving time-stamped messages from

another node.

in memory) and estimates the model parameters. Then, node B computes the predic-
tion error. Finally, using the calculated prediction error, node B adjusts the frequency
of getting a new timing message from node A: If the prediction error is larger than the
upper limit threshold E u , then the timing message rate is not frequent enough from node
A, and therefore τ should be decreased. On the other hand, if the prediction error is
smaller than the lower limit threshold E l , then there are fewer timing messages, and thus
τ should be increased. Multiplicative increase and decrease strategies are used to enable
fast convergence and quick response to the changing environment. After getting a new
data point according to the new value of τ, the above process is repeated.

13.5.2 RBS-Based Adaptive Clock Synchronization

With the RBS setting, [39] extends the deterministic RBS protocol (discussed in sec-
tion 13.4.1) to an adaptive probabilistic synchronization algorithm, allowing trade-offs
between synchronization accuracy and resource requirement. It is based on the observa-
tion that if the relative clock skew error between two nodes ε, after applying RBS with
one broadcast message, is a Gaussian RV with zero mean and variance σ 2 , then the prob-
ability of error-free synchronization with N broadcast messages is given by

 

N ε

σ

< ( ) =

    ,

Pr |εε 2 erf

max

(13. 37)

max

 

where ε max stands for the maximum specified (allowable) clock offset for communica-
tions, and

∫

x

− ( )

2

erfx ()  12 / π⋅ exp t / 2 t .

0

From the above equation, it is clear that the performance criterion is a probabilistic
measure since there is always a possibility that the clock offset is greater than some limit
ε max . However, one can reduce this probability to an arbitrarily small value by increasing
N , the number of broadcasting messages in one round of RBS.
After application of RBS, we can bound the clock skew error with certain probability.
However, since clocks from different nodes would drift apart as time passes, we need to