NOLTA, IEICE
Paper

Better clock synchronization fromsimultaneous two skew estimations
Hisa-Aki Tanaka 1 a) , Youjie Ouyang 1 , Yoji Yabe 1 ,Isao Nishikawa 1 , and Kazuki Nakada 1 ,2
1

Graduate School of Informatics and Engineering, The University ofElectro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan2

The author is currently with Graduate School of Information Sciences,
Hiroshima City University, 3-4-1 Ozuka-Higashi, Asaminami-ku, Hiroshima
731-3194, Japana)htanaka@uec.ac.jp

Received December 6, 2015; Revised June 6, 2016; Published October 1, 2016
Abstract: An improvement for clock synchronization in wireless sensor networks (WSNs) ispresented, which is obtained by analyzing a temporal frequency variation observed in internal clock circuits. Clock synchronization is an essential building component in WSNs for
distributed sensing. Flooding time synchronization protocol (FTSP) is one of the highestprecision synchronization protocols for WSNs, which has been implemented on certain WSN
testbeds. We carry out systematic experiments of FTSP with a Mica2Dot testbed to understand how synchronization precision is aﬀected by a dynamic frequency variation in the clock
circuit with a button battery. Our observations clarify that the following two elements are
essential for better clock synchronization; (i) a short-term frequency variation in the clock circuit, and (ii) the resulting error in clock drift (i.e., skew) estimation from the linear regression
in FTSP. Based on these ﬁndings, we propose a simplistic improvement for robust and more
precise clock synchronization, utilizing two sets of simultaneous estimations of skew between
sender and receiver nodes. Through systematic experiments and analysis, we conﬁrm this improvement realizes a higher synchronization precision in a stable network environment, while
it maintains robustness of time synchronization even in a worst case of unstable networks.
Key Words: clock synchronization, crystal oscillators, wireless sensor network, skew estimation, FTSP

1. Introduction and motivation of this study
Recent advances in electronics and wireless communication technology have made sensing and communicating devices smaller, cheaper, and more low-power than before. Such resource-limited devices(sensor nodes) construct wireless sensor networks (WSNs) for a wide range of distributed sensing
purpose; indoor, outdoor, and even in-body monitoring applications. In such WSNs, precise clock
synchronization often becomes essential because clock synchronization is a basis for consistent distributed sensing and control. An interesting application is shown in an early study [1] for instance.

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Nonlinear Theory and Its Applications, IEICE, vol. 7, no. 4, pp. 548–556c
IEICE2016

DOI: 10.1587/nolta.7.548

Several distributed algorithms for clock synchronization have been proposed so far [2–4]. Moreover,a large survey on synchronization protocols in WSNs is now available [5]. Among them, ﬂooding
time synchronization protocol (FTSP) [6] and PulseSync [7] are one of the standard energy-eﬃcientand high-precision synchronization algorithms for WSNs. Whereas ad-hoc mobile networks with adense network topology are assumed in the IEEE 802.11 timing synchronization function (TSF) [4],both FTSP and PulseSync construct an adaptive tree-like network of sensor nodes, in which synchronization messages [6] (i.e., time stamping packets) are periodically sent from the root node down tomultiple receiver nodes, as exempliﬁed in Fig. 1. As a result, undesirable frequent collisions [8] ofsynchronization messages (i.e., timing beacons [4]) are avoided. From these synchronization messages
each receiver node eﬀectively estimates its clock skew (i.e., the speed of clock drift, deﬁned in Section2) by using a linear regression algorithm in FTSP. A high-precision time synchronization is thenrealized even for resource-limited sensor nodes such as Mica2Dot motes [9].

Fig. 1.

Tree-like network topology in FTSP.

Incidentally, recent studies [10–12] have investigated an intrinsic characteristics of the clock circuit(i.e., the crystal oscillator) in a dynamic environment. They have demonstrated that the clock skew isdynamically compensated according to the working temperature. In the present study, as opposed tosuch previous work [10–12], we focus on an intrinsic dynamic characteristics of the clock circuit undera static working temperature and humidity. We then clarify yet another mechanism that degrades thesynchronization precision in FTSP even under a static working environment. The main contributionsof this paper is twofold. First, we analyze the underlying mechanism of our experimental resultsfor FTSP on Mica2Dot motes, which clariﬁes that the following two elements play essential roles forbetter clock synchronization; (i) a short-term frequency modulation in the clock circuit, and (ii) the
associated error in clock skew estimation from the linear regression in FTSP. Second, based on these
insights, we propose a simplistic improvement of FTSP by utilizing two simultaneous estimations of
the clock skew. With this improvement, the synchronization precision is observed to increase by afactor of more than several times than the original FTSP, while robustness of time synchronization
is maintained even under a nonstatic, unstable network environment. We note that our improvement
can be useful even in a dynamic environment, since this can be incorporated into the results for suchan environment [10–12].
The remainder of this paper is organized as follows. In Section 2, we review FTSP to explain
how receiver nodes synchronize to the root node. In Section 3, we analyze an underlying mechanism
for the synchronization precision degradation. In Section 4, we propose an eﬀective improvement of
FTSP, and provide systematic performance evaluations through comparative experiments. Finally,
the discussion and conclusions are presented in Section 5.

2. Synchronization mechanism in FTSPIn FTSP, the root node provides a real global time which serves as the standard time in the network.
This global time can be obtained from GPS or other reliable sources. On the other hand, all otherreceiver nodes independently maintain the following two sets of times; (i) their own local times,
clocked by the crystal oscillators in each node, and (ii) their virtual global times. The virtual global
time in each receiver node is estimated from its local time by referencing synchronization messages
from a sender node. In the estimation of the virtual global time, delays in synchronization message
transmissions and clock drift between sender and receiver nodes are involved. The compensation ofdelays is successfully handled through a detailed analysis of message transmissions for Mica2 motes [6].
Compensation of the rate of clock drift (i.e., skew), on the other hand, is carried out by using linear549

regression for intrinsic frequency mismatch of clocks in sender and receiver nodes, and for temporal
instability of clocks, simultaneously.
Clock drift is estimated in FTSP in the following way. The original FTSP employs a linear regression(LR) in a time window of previous eight synchronization messages (SMs). These SMs are periodicallysent at each synchronization point (SP) in a ﬁxed resynchronization period denoted by T , as shownin Fig. 2. In usual, the value of T is set to 30 seconds [6]. At each SP, the receiver node obtains
the combination of the sender’s time stamp (carried on SMs) and the corresponding local time in
the receiver node at message reception; the sender’s time stamp is given as a virtual global time
estimated in the sender node (or can be the absolute global time if the sender is the root node) at
message transmission. Hence, if the time oﬀset (TO) between the sender’s (virtual) global time (SGT)and the receiver’s present local time (PLT) is correctly estimated, a receiver node knows the sender’sglobal time from its local time.

Fig. 2.

Schematic of skew estimation in FTSP.

In the estimation scheme described above, FTSP implicitly sets the following two assumptions; (i)the skew is a constant, and it is estimated from the increasing (or decreasing) rate of the LR line L
in Fig. 2, which best interpolates a set of past (eight) time oﬀsets, and (ii) by using the average ofthese past oﬀsets, delays in message transmissions can be compensated. Therefore, FTSP estimates
the receiver’s global time (RGT) as shown in Fig. 2 :RGT = present local time (PLT) + estimated time oﬀset= PLT + oﬀset average (OA) + skew × (PLT − local time average (LTA)).

(1)

However, if the actual skew temporally increases or decreases in some nodes, the estimation (1) of
RGT should involve a certain amount of estimation error. In fact, such a temporal variation of skew isa major factor of the synchronization error (SE) as observed in Section 3. To evaluate the amount ofsuch SEs, here we assume that a skew increases at a constant speed in a short period. We then denoteAthe time oﬀset of node A’s clock (i.e., SGT) w.r.t. node B’s clock (i.e., RGT) as θB(t), in which t isAAA(t)/dt [10, 12].
the local time in node B [10, 12]. Similarly, the skew αB (t) is deﬁned as αB (t) ≡ dθB
Then, we consider the situation where the skew increases (or decreases) at a constant speed Δskew.
Namely,AdαB(t)= Δskew ≡ C.
(2)
dt
As shown in Fig. 2 the synchronization error (SE) is deﬁned as SE ≡ SGT − RGT. SGT and RGT at
a local time t1 (of node B) are respectively given by their deﬁnitions : t0 +T (=t1 )A
SGT(t1 ) ≈ t1 + OA +αB(t) dt,(3a)

RGT(t1 ) =t0At1 + OA + αB(t0 ) · (t1 − t0 ),

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(3b)

in which t0 and t1 respectively correspond to LTA and PLT in Fig. 2. Subtracting Eq. (3b) from
Eq. (3a), we obtain SE at t1 , asSE(t1 ) ≈

 t1
t0
 t1

A
A
αB
(t) dt − αB(t0 ) · (t1 − t0 ) =

 t1
t0

C
C
=
C · (t − t0 ) dt = (t1 − t0 )2 =
2
2
t0

A
A
αB
(t) − αB(t0 ) dt



n−1
T
2

2

,

(4)

A
A
since αB(t) = αB(t0 ) + C · (t − t0 ) from Eq. (2) and t1 − t0 = (n−1)
2 T , where n is the number of data
samples (from SMs) used in the linear regression, as shown in Fig. 2. This formula (4) turns out tobe informative in analyzing SE in Section 3.

3. Analysis of synchronization error
To see how skew and SE behave in a real world environment, we observe and analyze them, ﬁrstly in astable and static network environment (i.e., Experiment 1 ), and then in an unstable, transient network
environment due to root lost and root reelection (i.e., Experiment 2 ); for both environments in a
Mica2Dot testbed, we carry out systematic experiments using Mica2Dot motes which are shipped withtwo clock oscillators; a 32KHz crystal oscillator1 and a more ﬁne-grained 4MHz crystal oscillator. Here,we employ this 4MHz oscillator as the clock, because this 4MHz oscillator is used in the experiments
in [6] as well as in the experiments of RBS [2] and TPSN [3].
As explained in Section 2, skew estimation plays an essential role in FTSP. Therefore, ﬁrstly, weobserve temporal variations of skew in the following experiment.
Experiment 1: Eight sensor nodes (Mica2Dot motes) form a single-hop network in the highperformance incubator (Type KCL-2000A, Eyela Co.), in which external radio waves are naturally
shielded, as shown in Figs. 3(a) and 3(b). Until the battery becomes empty in some node of the network, temporal variations of the estimated skews are recorded in all nodes; one of typical data froma randomly chosen node is shown in Fig. 4(a). To exclude undesired changes in the environments,
temperature and humidity is maintained exactly at 25◦ C and 30%RH throughout the experiment.
In this experiment, we ﬁnd the estimated skew alternatively increases and decreases at almost
constant rates as shown in Fig. 4(a). At ﬁrst, we suspected that this is caused by a possible failurein this particular node. Then, we repeated the same experiments by using other motes, but all
experiments lead to similar observations. Next, we carried out a control experiment to Experiment 1,
in which all button batteries on Mica2Dot motes are replaced with a common stable voltage source(PMM35-1.2DU, KIKUSUI), to exclude a possible voltage instability from the button battery. In thiscontrol experiment, as we expect, almost no temporal variation is observed in the estimated skew for
all the nodes, and such an observed constant skew is of the same order to the time-averaged skew inthe same node with a button battery. (Data is not shown due to space limit.) Therefore, the observed
temporal variation of skew can be attributed to some internal mechanism of the battery and/or theclock circuit. In any case this temporal skew variation should aﬀect SE for each node.
Then, to examine the relationship between SE and the window size of linear regression in FTSP, werepeated Experiment 1 by increasing the resynchronization period T from its original 30 [s] upto 300[s]. For each value of T , ﬁve trials are carried out for 30T [s]. The time-averaged SE in one randomly
chosen node, which is further averaged over ﬁve trials, is shown in Fig. 4(b). A quadratic increase of
SE is observed w.r.t. T . This observation is consistent to the result of SE  T 2 in Eq. (4)2 under aconstant rate of skew variations.
Based on the above observations, in the following experiment we further investigate a more direct
relationship between temporal variations of skew and the resulting SEs.
Experiment 2: Eight Mica2Dot motes form a single-hop network for about two hours. The initialroot node is removed from the network at 2451 seconds later from the beginning of the experiment.
1
2

The experiments in [11] are carried out with a citizen CMR200T oscillator running at 32KHz in TelosB motes.
Note C in Eq. (4) is naturally time-averaged during this observation.

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Fig. 3. Experimental setup. (a) A single-hop network in a Mica2Dot testbed.
(b) All experiments are carried out at a constant temperature and humidity inthe incubator.

Fig. 4. Short-term skew variations observed in Experiment 1. (a) Temporalvariation in an estimated skew in one node. (b) Averaged synchronization
errors in one node for several diﬀerent resynchronization periods. The curve
represents the quadratic function of T ﬁtting data points ×.

Fig. 5. Temporal skew variation and the associated synchronization error(SE). (a) Data from node A. (b) Data from node B. (c) Data from node C.

Then, the newly reelected root node is removed at 4830 seconds later from the beginning. Temperatureand humidity is maintained exactly at 25◦ C and 30%RH throughout the experiment.
Figures 5(a), (b), and (c) respectively shows a temporal variation of the estimated skew and theassociated SE in three randomly chosen receiver nodes; node A, node B, and node C. We note thatfour other receiver nodes show a similar temporal variation of the skew. In Fig. 5, we observe theskew keeps decreasing at an almost constant rate respectively in node A, B, and C, for about 2,400[s] between two events of root removal at 2451 seconds and 4830 seconds respectively, and the rate ofskew variation is altered before and after the root removal and reelection.
More precisely, we observe that node A, node B, and node C respectively shows about 0.02 × 10−4 ,0.02 × 10−4 , and 0.05 × 10−5 decrease in skew during a time laps of 210 [s], at around the local
time = 3500 seconds. By using the data and Eq. (4), we can roughly predict the resulting SEs innode A; SE(t = 3500) = 12 (0.02 × 10−4 /210) (210/2)2 = 52.5 [μs], since C = 0.02 × 10−4 /210 andt1 − t0 = 210/2 in Eq. (4). In the same way, SEs in node B and node C are respectively obtained as
52.5 [μs] and 13.1 [μs]. Note that these predictions show a fair agreement to the observed SEs in Fig. 5.
We also note that ﬁne ﬂuctuations of SEs in Fig. 5 are smaller than the associated time-averaged SEs,
and this validates the meaning of the time-averaged SEs shown in Fig. 4(b).
From the above analysis of temporal skew variations observed in Experiment 1 and Experiment 2,
we infer that the estimated skew and the associated time oﬀsets are inﬂuenced by the time window552

size as follows3 . Firstly, the instantaneous skew is the time derivative of the time oﬀsets curve (i.e.,
Eq. (2)). And, as shown in Fig. 2, data sets of time oﬀsets should be on a concave curve (or a convex
curve) if the skew continues to increase (or decrease). Therefore, as illustrated in Fig. 6, smaller
SEs are expected for less number of data points (i.e., shorter time window size) in linear regression(i.e., Eq. (4)), on average, in the environment of Experiment 1 and Experiment 2. This prediction is
veriﬁed in control experiments for a stable static network environment in Section 4.

Fig. 6. Time oﬀsets resulting from a constantly decreasing skew. The symbols •, ◦, and  respectively represent data points, the estimated time oﬀset
from eight data points, and the one from two data points.

In contrast to the static network environment considered above, in a harsh, dynamical network
environment a failure in a node or a link is inevitable. One of the worst case scenarios of such a
failure in FTSP is a lost of the root node and the resulting root node reelection. As observed in Fig. 5of Experiment 2, right after root removal a large SE lasts for about several hundreds seconds. To
ensure the quality of synchronization within a certain level, we analyze such large SEs in detail byvarying the number of time oﬀsets in linear regressions, in the next Section.

4. Design of improved FTSP and its performance evaluation
Based on the analysis of SE in Section 3, we now propose a simplistic improvement of FTSP in a
Mica2Dot testbed. We evaluate its performance through systematic experiments in a stable network
environment as well as in an unstable network environment due to root reelection.
First, to verify the prediction in Section 3, we investigate the relation between SE and the numberof time oﬀsets (i.e., data samples) in linear regression (LR), in the following experiment.
Experiment 3: Twenty Mica2Dot motes form a single-hop network for 30 minutes. For each trial, thenumber of time oﬀsets in LR is set to 2, 4, 6, 8, and 10, respectively. For the fairness in the conditions,the same motes and new button batteries are used. Temperature and humidity is maintained exactly
at 25◦ C and 30%RH throughout the experiment. In this Experiment 3, we measured (i) skew variations
and the associated SEs for each time oﬀsets number, and (ii) SEs for our improved FTSP, both ofwhich are obtained in the stable as well as in the unstable network environment as in Experiment 1
and Experiment 2.
Firstly, we compare temporal skew variations for diﬀerent time oﬀsets numbers (i.e., numbers ofdata samples) in detail. Figure 7 illustrates typical skew variations in Experiment 3 ; two data setsare respectively obtained for the case of eight time oﬀsets (× in Fig. 7), and for the case of two time
oﬀsets (+ in Fig. 7). In both cases, right after the root removal at the local time (LT) = 1190 seconds,
the observed skew becomes constant until another root is newly elected at LT = 1360 seconds. This isbecause in FTSP the value of skew estimation remains unchanged until a new root is reelected. After
this root reelection, skew estimation starts again by joining previous time oﬀsets (before root lost)to the current time oﬀsets (after root reelection). This transient state lasts until the previous time
oﬀsets are completely lost from the moving time window of LR; it lasts for about 30 × (8 − 1) = 210[s] in the eight oﬀsets case, and for about 30 × (2 − 1) = 30 [s] in the two oﬀsets case, as observedin Fig. 7. During these transients, larger instantaneous skew variations emerge as the number oftime oﬀsets becomes smaller; we observe big jumps in the estimated skew for the minimum two time
oﬀsets case (+) in Fig. 7. This induces large SE (not shown here, but similar to Fig. 5) according to3
In this particular testbed, the time oﬀsets data itself was not directly available from the motes. Therefore, we observe
the time oﬀsets indirectly from the skew estimations available in each mote.

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Fig. 7. Temporal skew variations due to root removal and root reelection.
Data points × and + respectively show the case of eight time oﬀsets and thecase of two time oﬀsets.

Fig. 8. Comparisons of synchronization errors from the original FTSP and
the improved FTSP. (a) Average synchronization error in a stable network
environment. (b) Maximum synchronization error in an unstable network environment.

Eq. (1). Namely, in an unstable network, LR with minimum two oﬀsets no longer produces a betterskew estimation compared with the original eight oﬀsets LR, and this is consistent to the insight from
Fig. 6.
Next, we consider how time oﬀsets number inﬂuences the amount of SE on average. Figures 8(a)and 8(b) show the SEs for several numbers of time oﬀsets, obtained in Experiment 3, respectively forstable networks and for unstable networks involving root reelection. Figure 8(a) shows a result of ﬁve
trials in Experiment 3 for the stable network environment. Each data point (×) represents the timeaveraged SE over 30 minutes. On the other hand, Fig. 8(b) shows a result of ten trials in Experiment
3 for the unstable network environment. Each data point represents the instantaneous, maximum SE
observed in each trial. Note we have already observed this sort of large instantaneous SEs of a few
milliseconds in Fig. 7. From these data, we observe; (i) for stable networks, the time-averaged SE issmaller for a less time oﬀsets number in LR, and (ii) in contrast, the maximum, instantaneous SE issmaller for a larger time oﬀsets number, for unstable networks involving root reelection. Note, theseobservations are consistent to the result shown in Fig. 4(b) and the observations in Fig. 7.
From these observations, we obtain a reasonable idea of simple improvement for better clock
synchronization; FTSP (with Mica2Dot) is improved by using simultaneous two skew estimations.
Namely, the minimum two time oﬀsets in LR are used for reducing SEs on average in a stable environment. And, at the same time eight (or ten) time oﬀsets are used for suppressing large, instantaneousSEs in an unstable environment, which are less than around 0.5 [ms] as observed in Fig. 8(b). As theresults, from these independent two estimates of skew, our improved FTSP should provide less thanaround 0.5 [ms] SEs within around 30 [s] transients in the worst case scenario mentioned above (asfar as the network instability does not occur so frequently).
This improvement in the skew estimation algorithm is realized on each receiver node. We illustrate
the algorithm in Mica2Dot motes in Fig. 9. The algorithm of Fig. 9 involves two branches; in theﬁrst branch ‘myrootID == rootID’ means the sender node (to this particular receiver node) is the554

Fig. 9.

Outline of the proposed algorithm for skew estimation.

same as before. Namely, it checks whether the network is the same as before (i.e., stable). On theother hand, in the second branch ‘myrootID > rootID’ means the network is NOT the same as before(i.e., unstable). We note that these branches eﬀectively take care of all kinds of temporal link lostand discommunication between nodes, including the worst case of root reelection. In addition, toevaluate the performance of our improvement, we conducted systematic experiments under the same
conditions in Experiment 3. In Figs. 8(a) and 8(b) the average SE and the maximum SE from ourimproved FTSP are shown for the stable network case, and for the unstable network case, respectively.
Both results verify that the improved FTSP outperforms the original FTSP in its synchronization
precision. Finally, we note the power consumption in the improved FTSP is nearly the same to theone in the original FTSP, because we observe the battery life time is nearly the same for both cases
throughout the experiments.

5. Conclusion
Systematic control experiments identiﬁed and clariﬁed yet another mechanism, in which synchronization error is generated from temporal frequency (skew) variations in Mica2Dot motes. Based on thisinsight, a simplistic improvement of FTSP is proposed, which is easily implemented with small computational and communication costs. Its eﬀectiveness is conﬁrmed through comparative experiments.
Although our ﬁndings and improvement have been obtained in a particular testbed with Mica2Dot
motes, its essential idea can be useful for any other environments if skew is estimated from linear regression. One candidate on this line is a smaller and cheaper (injection-locked) CMOS ring oscillator
as a GHz clock circuit which should exhibit a certain amount of temporal frequency variation [13, 14].
In addition to this, as mentioned in Section 1, recent results in [10–12] have enabled temperatureaware clock skew estimations by utilizing the information of temperature dependence of the oscillator
frequency. These self-calibration methods should be naturally incorporated into our proposed scheme.
Therefore, our scheme here can possibly be useful in dynamic environments of working temperature
if the temperature dependence of the oscillator frequency is available. More experiments including
multi-hop networks and/or using other kind of clock oscillators would lead to further improvementsof clock synchronization and their applications.

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