ACES: Adaptive Clock Estimation and Synchronization Using Kalman Filtering Benjamin R. Hamilton Xiaoli Ma School of ECE School of ECE Georgia Institute of Technology Georgia Institute of Technology Atlanta, GA 30332, USA Atlanta, GA 30332, USA [email protected] [email protected] Qi Zhao Jun Xu AT&T Labs - Research College of Computing 180 Park Ave. Georgia Institute of Technology Florham Park, NJ 07932, USA Atlanta, GA 30332, USA [email protected] [email protected] ABSTRACT Keywords Clock synchronization across a network is essential for a Kalman filter, clock synchronization, clock offset, clock skew, large number of applications ranging from wired network resource-constrained network measurements to data fusion in sensor networks. Earlier techniques are either limited to undesirable accuracy or rely on specific hardware characteristics that may not be avail- 1. INTRODUCTION able for certain systems. In this work, we examine the The availability of an accurately synchronized clock en- clock synchronization problem in resource-constrained net- ables and enhances a wide range of applications in distributed works such as wireless sensor networks where nodes have environments that facilitate pervasive computing and com- limited energy and bandwidth, and also lack the high ac- munications. For example, Internet measurements, which curacy oscillators or programmable network interfaces some rely on either passively monitoring network events (e.g., previous protocols depend on. This paper derives a gen- packet loss) or actively probing network conditions (e.g., eral model for clock offset and skew and demonstrates its end-to-end delay and loss rate), implicitly require a com- applicability. We design efficient algorithms based on this mon notion of time among all participating measurement model to achieve high synchronization accuracy given lim- points. Another example lies in Wireless Sensor Networks ited resources. These algorithms apply the Kalman filter to (WSNs). Sensor network applications need a common no- track the clock offset and skew, and adaptively adjust the tion of time for precise data integration and sensor reading synchronization interval so that the desired error bounds fusion. Clock synchronization is also essential in network are achieved. We demonstrate the performance advantages and communications protocols such as TDMA medium ac- of our schemes through extensive simulations obeying real- cess scheduling, power mode energy saving, and scheduling world constraints. for directional antenna reception. Many clock synchronization techniques for the Internet have been proposed over the past few decades, among which the most popular and widely used is Network Time Protocol Categories and Subject Descriptors (NTP). The development and evolution of NTP is described C.2.4 [Computer-Communication Networks]: Distributed Mills’ classic papers [13,14]. Several techniques [6,12,18,25] Systems; I.6.5 [Simulation and Modeling]: Model Devel- have been proposed to improve its synchronization accuracy opment with local hardware enhancement or specially designed net- work infrastructure when NTP is not able to satisfy the requirements of demanding applications. Additionally, in General Terms applications that do not require real-time synchronization, several other techniques are proposed to estimate and re- Design, Measurement, Theory move clock offset and skew offline in captured data sets such as a packet delay trace [16, 27]. In the Internet, each node is either a router or a host which is wired to a constant power source and has one or Permission to make digital or hard copies of all or part of this work for more stable and powerful CPU’s. In contrast, some other personal or classroom use is granted without fee provided that copies are networks have only very limited resources such as scarce en- not made or distributed for profit or commercial advantage and that copies ergy, unstable processors, and unreliable and low communi- bear this notice and the full citation on the first page. To copy otherwise, to cation bandwidth, which we refer to as“resource-constrained republish, to post on servers or to redistribute to lists, requires prior specific networks”. The unique characteristics of these resource- permission and/or a fee. MobiCom’08, September 14–19, 2008, San Francisco, California, USA. constrained networks make it difficult to directly apply the Copyright 2008 ACM 978-1-60558-096-8/08/09 ...$5.00. aforementioned network clock synchronization approaches. 152 our method only expends energy when it is needed to im- prove synchronization. Our Kalman filter provides a gen- eral framework to achieve the optimal performance-overhead tradeoffs. Note that our clock synchronization scheme establishes local clock models and a Kalman filter based tracking al- gorithm, which does not require any particular message ex- change mode. Therefore, our scheme can be easily adapted into both receiver-to-receiver [4, 15, 17, 23] and sender-to- receiver modes [5, 11, 21, 22, 28]. The rest of the paper is organized as follows. We first summarize the related work in Section 2. Section 3 describes Figure 1: Block diagram of this work the general models we develop to model a clock in detail. In Section 4 we present and analyze our algorithms to track clock skew and offset. In Section 5 we demonstrate the need They need a more energy- and communication-efficient way, for dynamic adjustment of the synchronization period and a challenge we are going to address in this work. present our rate adaptation algorithm. We conclude the WSN is a representative example of resource-constrained paper in Section 6. networks. In a WSN, the vast majority of sensors are battery- powered so that a desirable clock synchronization scheme must preserve energy to prolong the battery life. Pottie et 2. RELATED WORK al. [20] shows that transmitting 1 bit over 100 meters re- Clock synchronization mechanisms ensure that physically quires 3 joules, which can be used for executing 3 million dispersed processors have a common knowledge of time. This instructions. Therefore a successful clock synchronization topic is well studied in wired networks such as the global scheme must minimize the amount of message exchange and Internet. The most common and widely used mechanism at the same time maintain high synchronization accuracy. is NTP [13, 14], which uses NTP packets containing times- Scarcity of power on sensor nodes however is not the only tamp information exchanged between NTP server and the resource constraint. Due to its small size and low cost, the host across a network to perform time synchronization. NTP clock readings in a sensor are derived from oscillators with is designed to provide clock offset accuracy bounded by the only limited stability (due to phase noise, thermal noise, ag- round-trip time (RTT) between the server and the client. ing, etc). Consequently, clocks on sensors are easily affected However, NTP provides insufficient accuracy and robust- by temperature variations, vibration and interference and ness for many demanding applications. A few techniques can significantly deviate from the reference sources [19, 26]. have been proposed to improve measurement accuracy or The situation could become even worse under catastrophic clock stability. In [12] the synchronization is offloaded into conditions such as earthquake, battlefield, and forrest fire. a programmable network interface card. This card would In this work, we design energy- and bandwidth-efficient autonomously perform synchronization by sending periodic clock estimation and synchronization techniques that can messages and perform timestamping when packets arrive. work with low precision oscillators under resource-constrained In [18, 25], the methods of using a clock based on the more environments such as sensor networks. The main flow of this accurate CPU oscillator were proposed. This method relies paper is summarized in Figure 1. on the high reliability of the processor oscillator and the First, we decompose the clock uncertainty into multiple availability of a TimeStamp Counter (TSC) register. The independent components and use these components to con- Precision Time Protocol [6] was drafted into the IEEE 1588 struct general models for a real clock. None of the previous standard for synchronization of network measurement and synchronization protocols take into account all these com- control systems. It uses a specially designed network in- ponents. The proposed models are also general enough to frastructure to achieve high synchronization accuracy. Un- subsume all of the existing models. fortunately, all these improvements rely on some specific Second, a Kalman filter is designed to track the clock un- hardware enhancements which may not be available in a certainty based on the aforementioned models. In fact, most resource-constrained environment. of the prior protocols fail when the clock has some time- Since some passive network monitoring tasks do not re- varying drift performance. To our best knowledge, we are quire real-time synchronization, a few algorithms have emerged the first who try to model the random drift of the clock for synchronizing data captures. In [16] a linear-programming using Kalman filter which tracks the variation of the clock based algorithm for estimating and removing the skew and drift and thus enhances the synchronization performance. offset of a dataset was proposed. Convex hulls were used Furthermore, we derive the theoretical steady-state Mean in [27] to estimate the clock skew and