Accuracy-Driven Synchronization Protocol

Transcription

1 The Second International Conference on Sensor Technologies and Applications Accuracy-Driven Synchronization Protocol Fabrizio Sellone 1, Hussein Khaleel 1, Marco Urso 1, Mirko Franceschinis 2, Marina Mondin 1 1 Politecnico di Torino, C.so Duca degli Abruzzi, 10129, Torino (Italy) 2 Istituto Superiore Mario Boella, Via P.C. Boggio, 10129, Torino (Italy) 1 {name.surname}@polito.it, 2 {surname}@ismb.it Abstract Sensor nodes are small-size, low-cost embedded systems capable of local processing and RF communication. In a sensor network, nodes need to organize their operations to perform distributed sensing tasks, and need therefore to be time synchronized to a common reference. In this paper we present a time-synchronization approach for Wireless Sensor Networks (WSNs), denoted as Accuracy- Driven Synchronization Protocol (ADSP). ADSP is based on the always-on model of time synchronization, and offers customizable accuracy level, using a novel method to reduce the transmit-to-receive time delay. The time reference is provided by a master node frequently broadcasting packets that the nodes use to synchronize themselves, and then to improve their synchronization. Nodes imate their own clock characteristics with respect to the master node, thus keeping themselves synchronized even when the master node is not transmitting. The one-way broadcast scheme adopted by ADSP guarantees extremely low energy consumption. 1. Introduction Recent technology advances have been supporting the development and success of WSN technology [1], [2], consisting of small-scale, low-cost devices, operating at very low power levels. A sensor node generally consists of sensing, processing and RF units. Sensor nodes are randomly deployed in a certain area, forming a sensor network. Sensor networks are able to operate in an unattended manner and require no infrastructure. This concept has in fact triggered many new research topics and applications. The combination of localprocessing, RF communication and autonomous operation has a wide variety of applications, especially in inhospitable areas. Of course, these advantages are obtained at the cost of many rrictions, primarily the limited power availability, the dense nature of these networks, as well as the challenge represented by the complicated self-organization algorithms. While autonomous sensor nodes are capable of local processing and RF communication, nodes in a sensor network are able to selforganize their effort, to efficiently share a common medium and to perform various distributed sensing and processing tasks. To make this possible, a common time reference must be available. Time synchronization is an important component in distributed systems such as WSNs, for the correct ordering and time-stamping of collected data or other events, although different applications require different degrees of accuracy [4]. Time synchronization protocols and technologies have been developed for traditional networks, and have been largely successful, such as NTP [8] and GPS [9], that provided global network synchronization for various purposes. However, conventional synchronization schemes have focused on achieving the b possible accuracy, without energy, CPU, or memory constraints, making previous solutions not suitable for WSNs. In addition, several sensor networks applications require synchronization accuracy in the microsecond scale, such as distributed beam forming and object tracking, which is a strong requirement in terms of time synchronization Related work Among the several time synchronization protocols specifically proposed for sensor networks, two are briefly discussed here, pointing out relevant issues for comparison. The Reference Broadcast Synchronization (RBS) method [5] is based on the concept of receiver-to-receiver synchronization. A reference node broadcasts a beacon message to its neighbors, then the receiving nodes exchange the arrival time of the beacon as a reference to compare the phase between their clocks. The difference operation completely cancels out the sender uncertainties, allowing an average synchronization error of microseconds. The Timing-Synchronization Protocol for Sensor Networks (TPSN) [6] is based on traditional sender-to-receiver synchronization. Two nodes perform a two-way message exchange in order to calculate their clocks relative phase. This reduces the complete send-to-receive uncertainties by a factor of two, allowing an average synchronization error of 16.9 microseconds, roughly two times better than RBS, requiring however a more complicated two-phase scheme. These algorithms achieve fine synchronization accuracy, though, but they show a strong impact on energy consumption, which is a major concern in WSNs. RBS requires a broadcast operation, followed by two peerto-peer message exchanges. TPSN requires a two-way message exchange between a pair of nodes. In addition, these algorithms require the nodes to re-synchronize whenever they have information to share. This can rapidly deplete the node energy, especially reference ones Contribution Here we present the so-called Accuracy-Driven Synchronization Protocol, a time-synchronization solution designed for WSNs. This protocol is based on the sender-toreceiver synchronization. It uses one-way broadcast transmissions instead of peer-to-peer message exchange. In this algorithm all the nodes imate the reference time, which is provided by the master node by frequently broadcasting timamps, which are used by the individual nodes to /08 $ IEEE DOI /SENSORCOMM

2 determine their own clock characteristics with respect to the master node. Frequent broadcasts from the master node can be used by the nodes to improve/adjust their synchronization. During time intervals between the master node's broadcasts, each node can still imate the actual time, since it has information about its own clock. This provides network wide synchronization any time, any where, without the need to requ synchronization. This is a low-energy implementation of the always-on model. In general, the send-to-receive uncertainties are the main limitation of time synchronization. In ADSP, the accuracy of synchronization is adjustable, indeed we will show that the send-to-receive uncertainties can be reduced to several degrees based on the amount of node's resources provided for synchronization. The low energy consumption, and accuracy versus resources trade off, may add more convenience to the implementation of this approach on WSNs. A mathematical model derivation, as well as a computer MATLAB simulation are presented, achieving synchronization accuracy in the order of the microseconds. 2. Accuracy-Driven Synchronization Protocol further timamps from the master node can be used to enhance their imations. During time intervals between broadcasts (timamps) from the master node, each node can still imate the time since it has information about its own clock characteristics, and if the node needs to transmit some information, it can directly attach its imation of the master node time to the packet as the time of the event. Since the master node has the reference time that all other nodes synchronize to, then the value of a timamp is actually the current time of the master node. After the nodes imate their clocks, new timamps from the master node can improve synchronization accuracy. Nodes can store a certain number of previous timamps, along with their corresponding reception times, and by locally processing this data (as will be discussed in detail), the complete send-toreceive uncertainties can be reduced to different levels, corresponding to the number of stored samples. The main synchronization steps are schematically shown in Fig.1, and explained in detail in the next section Clock model Computing devices such as sensor nodes control their internal activities with clocks. A clock is operated by a hardware crystal oscillator. The oscillator generates an imation c t of the actual time t. The time synchronization problem arises from the fact that the frequency of an oscillator can vary randomly due to various environmental effects. As a consequence, the time n t of a generic node n can be modeled as follows: n t =a n t t b n, (1) where a n t is the clock drift of node n, representing the rate at which the clock runs, and b n is the clock offset, representing the time difference between the node's clock and a reference clock at time t = 0 [3]. In general, the clock drift can vary with time due to environmental conditions, but it is assumed to have a high short-term stability (constant) for the observed time window, then continuous frequency adjustments are performed using recent observations, as will be discussed in section Concepts and operation The idea of ADSP is that all the nodes imate the time of a master node. They do so by imating their own clock parameters, drift and offset, with the help of timamps from the master node. A wireless transmission is broadcast in nature, i.e. heard by all receivers in range, and can be used to synchronize them, saving energy, and increasing channel efficiency. The master node is required to broadcast timamps frequently, so, it can include a timamp in each of its transmitted packets while performing its ordinary tasks, giving the algorithm a background feature. Broadcasts of the master node don't require a reply from the recipients. After the nodes have imated their clock parameters, Figure 1. Scheme of the main synchronization steps. 3. Analysis of ADSP In this section, the mathematical model of ADSP is derived. The analysis is presented with the point-of-view of a node in the network. Node's drift a n and offset b n are denoted without subscripts as a and b respectively. Furthermore, we suppose that a and b vary slowly enough to be considered constant in this analysis. At time t, the node local time t can be expressed as: t = a t b. (2) The master node initiates the synchronization process by broadcasting the first timamp ts 1 measured by the master node's timescale. After a certain time delay d 1, representing the complete send-to-receive delay, the node receives the timamp at tr 1, measured in the receiving node's time scale. tr 1 is expressed as: tr 1 = a ts 1 d 1 b (3) For the node to be able to imate its clock's two parameters a and b, two transmissions are required. So, the master node broadcasts a second timamp ts 2 which, after a delay d 2, is received by the node at tr 2 : tr 2 = a ts 2 d 2 b (4) Generally, further transmissions from the master node can be expressed as: tr i = a ts i d i b (5) where ts i, tr i, and d i are the timamp, reception time, and the delay of the ith transmission respectively

3 3.1. Clock drift imation Once the second timamp has been received, a first imation can be performed, in the hypothesis that the sensors haven't moved much, and that d 1 d 2. In this case, a can be imated using Eq.s(3, 4) as: a = tr 2 tr 1. (6) ts 2 ts 1 Typically, however, d 1 d 2, and a drift imation error a error is calculated, which can be expressed by substituting the reception times from Eq.s(3, 4) into Eq.(6) and setting i =a d i, obtaining a error = a a = 2 1. (7) ts 2 ts 1 It can be seen that a error 1/ ts 2 ts 1, so that the longer the time between two timamps, the more accurate the drift imation. To enhance the drift imation, each node calculates a using the lat ith and the first transmissions: a = tr i tr 1 ts i ts 1. (8) Since a error 1/ ts i ts 1, and ts i increases after each transmission, then a error decreases accordingly Clock offset imation Rearranging Eq.(2), we have: b= t a t. (9) Then, the offset imation b at tr 2 can be evaluated as b = tr 2 a ts 2. (10) The offset imation error b error is: b error = b b = 2 a a ts 2 (11) and in general: b error = i a error ts i (12) Note that we have b error a error and b error i d i. So, even if a error decreases after each imation, d i remains, in general, completely unknown Time imation Starting from Eq.(2), the master node time t can be expressed as t = t b (13) a Then, the imated time t can be obtained as t = t b. (14) a Substituting b and re-arranging Eq.(14), a node can evaluate the imated time as t = t tr 2 ts a 2. (15) Note that by using τ(t), tr 2, a, ts 2, the node can imate the time without explicitly calculating b. Starting from Eq.(14), time imation error t error is: t error = t t = a error t ts a 2 a d a 2 (16) and in general: t error = a error t ts a i a d a i. (17) Eq.(17) expresses the time synchronization error. It can be observed from the first term of Eq.(17) that t ts i, equals 0 when the node receives the ith timamp, then it linearly increases as t increases, with rate a error /a. Furthermore, though, the second term in Eq.(17), we have t error d i. It has been mentioned that this term is the major notdeterministic source of synchronization error, due to the sendto-receive delay. To improve synchronization accuracy, this error must be reduced, as explained in the next subsection Reducing the effect of the time delay Once the third time-stamp has been transmitted, and in order to reduce the effect of the time delay d i(t), the idea is that each node locally calculates another instance of tr 3 denoted as tr calc, which can be obtained using the current value of a and ts 2,tr 2,ts 3. In fact, ts 3 ts 2 is the time interval between the last two transmissions, while a ts 3 ts 2 is the same interval evaluated on the node timescale. Adding tr 2 we obtain an imation of the third transmission time, delayed by d 2 instead of d 3, that we denote as tr 3,2 calc. Then: tr 3,2 calc = ts 3 ts 2 a tr 2. (18) Substituting tr 2 and rearranging Eq.(18), we have tr 3,2 calc =a [ts 3 a a d 2] b a a ts 2 (19) Afterwards, the node takes the minimum between tr 3 and tr 3,2calc, which is denoted as tr 3 corrected : tr 3 corrected = min {tr 3, tr 3,2 calc }. (20) This means that the node is selecting the reception time with the minimum delay d min among d 2 and d 3 d min = min{d 3,d 2 } (21) thus reducing the effect of the delay (error source), and improving synchronization accuracy according to Eq.(17). The previous process is graphically illustrated in Fig.2, while comparing the node's clock with the actual time. Figure 2. Different delays associated to each transmission

4 As the network operates, multiple timamps are available, and the node can store several pairs of timamp and reception times, using them to obtain multiple instances of tr i, j calc, taking the minimum among them and achieving better synchronization accuracy. In general: tr i, j calc = ts i ts j a tr j (22) and: tr icorrected = min {tr i, tr i, i 1 calc, tr i, i 2 calc, } (23) which corresponds to: d min = min{d i, d i 1, d i 2, }. (24) Then, the time imation following Eq.(15) becomes: t = t tr i corrected ts a i (25) and consequently, t error according to Eq.(17) becomes: t error = t t = a error t ts a i a d a min (26) This delay reduction method has the limitation on the number of stored pairs tr,ts due to the memory constraints of the sensor node. The effect of taking the minimum delay is now discussed. If the delay d i t has a probability density function (pdf) f i { } which we imagine as first-order stationary (the pdf remains equal regardless of time shift), then the cumulative density function (cdf) of the minimum of two delays d min t can be expressed as: p{d min } = p{d i } p{d i 1 } (27) p{d i,d i 1 } where is a given delay, and p{d i } is the cdf of d i t evaluated at which is represented from now on as F i { }. Given that d i t, d i 1 t are independent identically distributed (iid) processes, then the joint probability p{d i, d i 1 } becomes p{d i } p{d i 1 }, and given that: f i { } = d d F i { } (28) then, the distribution of the minimum can be obtained as: f min { } = f i { } 1 F i 1 { } (29) f i 1 { } 1 F i { } The delay distribution of the minimum has a mean value smaller than that of the original delay distribution, so, the time synchronization error after using tr i corrected has a smaller mean than that of the original delay. Then by using multiple instances of tr i, j calc, the mean value becomes even smaller. Several probability distributions can be used to model queuing time delays [12]. Using the experimental results obtained by the authors of TPSN [6], the delay d(t) is modeled as a Gamma distribution [10], with approximated Rate parameter = and Shape parameter k=3, such that: f d =u 3 2 e (30) 2 This distribution is shown in Fig.3.a. It can be observed that the delay distribution has a mean value at 30μs. Applying Eq.(29), the minimum pdf of two Gamma distributions is obtained and shown in Fig.3.b. It can be seen that the distribution has a mean value at approximately 20μs, smaller than the original delay. In addition, the pdf has a smaller variance, i.e. it is more concentrated on lower values, giving a narrower range for the error. Fig.s(3.c, 3.d) show the pdf of the minimum delay among 3 and 4 random variables with Gamma distributions, having mean values at 16.8 and 14.6 μs respectively. The minimum distributions of 5 and 6 Gamma distributed random variables (not shown) have mean values at 13.2 and 12.1 μs respectively. However it is not possible to get a simple closed-form expression for the mean. Figure 3. a) Gamma distributed delay. b) to d) pdf of min. delay among 2 to 4 random variables with Gamma pdf. 4. Summarizing ADSP 1. The master node broadcasts the first timamp ts The master node waits for a certain time interval. 3. The master node broadcasts the second timamp ts Each node calculates a according to Eq.(6): a = tr 2 tr 1 ts 2 ts 1 5. Each node can imate the master node time according to Eq.(15): t = t tr 2 a ts 2 6. The master node broadcasts a new timamp ts i. 7. Each node calculates a according to Eq.(8): a = tr i tr 1 ts i ts 1 8. Each node stores the desired number of ts, tr pairs. 9. Each node uses the stored information to calculate a number of instances of tr i, j calc, and takes the minimum of them to obtain tr i corrected according to Eq.s (22, 23): tr i, j calc = ts i ts j a tr j tr icorrected = min {tr i, tr i, i 1 calc,tr i, i 2 calc, } 10. When required, each node imates the master node time according to Eq.(25): t = t tr i corrected ts i 11. Steps 6 to 10 are repeated throughout the life-time of the node. a

5 5. Simulation The algorithm has been verified through a computer MATLAB simulation. The simulator assumes a master node distributing the reference time by frequently broadcasting timamps that actually contain its clock's time at transmission instant. After the first timamp, the master node is set to wait 10 seconds until it transmits the second timamp (this affects the drift imation error as shown in Eq.(7)). The code simulates the algorithm for 6 minutes (360 seconds). The master node is set to transmit a timamp every 3 seconds. The time delay is modeled as a Gamma distributed random variable with Rate parameter = and Shape parameter k =3, representing the complete send-to-receive delay. This model of delay assumes that packet timamping is performed at the MAC layer. Each node is set to store 4 pairs of tr,ts values (the lat one and the previous three), then takes the minimum according to Eq.s(22, 23). A node with a = 100 part per million (ppm), and b = 0.2 seconds has been simulated. Fig.4.a shows the drift imation error at the node. It can be observed that the error is decreasing (on average) after each imation. Fig.4.b shows the time synchronization error (absolute) of the node when the time is imated according to Eq.(25). In Fig.4.b, the average synchronization error is 14.45μs using 4 stored (tr,ts) pairs. Fig.5 shows an enlarged portion of Fig.4.b. It can be observed that during the time intervals between two consecutive master node transmissions, the nodes can still imate the time, but the error increases or decreases with a certain slope a error / a according to Eq.(17) due to the drift imation error. Figure 4. a)drift imation error. b)synchronization error. average of 15.20μs, maximum of 42.8μs, and standard deviation of 7.89μs. Figure 6. Histogram of synchronization error values. 6. Special Scenarios 6.1. Multi-hop synchronization The previous discussion has assumed a single-hop network, where every node is able to receive timamps directly from the master node. If the network is spread over a large area, due to a certain topology or application, and a portion of the network is completely out of the range of the master node, a synchronized node can operate as a reference for the other nodes. In this scenario, the nodes should include timamps within every transmitted packet, in order to be able to synchronize other nodes. Then, if a node timeouts while still unsynchronized, it must start to synchronize to one of the nodes it can hear, possibly the first one it receives a timamp from. A node requires two timamps to synchronize, so if it receives only one then timeouts, it must broadcast a synchronization requ, and a recipient must transmit two timamps, acting as a master, according to the previous discussion. In addition to the timamp, a node includes a hop number representing how many hops it is away from the master node. When the hop number is equal to 1, the node can hear the master node, when it is equal to 2 a node receives packets from a node with hop number 1, and so on. In this way, a node can determine its hop number by incrementing the small one among the received packets. If a node receives packets from multiple hops, it synchronizes to the small. Synchronization error in the second hop will be twice as in the first hop on average, because of the two synchronization processes. In general, the average synchronization error equals e h =h e 1 for a node in hop-number h Register overflow Figure 5. Enlarged portion of synchronization error. Fig.6 shows a histogram of the time synchronization error values. Synchronization accuracy has a minimum of 2.7μs, The limitations on memory size of a sensor node introduces constraints on the memory usage, such that a certain variable can only occupy a limited number of bits. This limitation is faced in ADSP when a node tries to calculate a according to Eq. (8). In fact, the quantities (tr i-tr 1), (ts i-ts 1) are always growing as tr i, ts i increase, causing the registers to overflow after a certain interval

6 A possible solution is setting ts 1 to ts (i-1) when the register overflows, starting a new drift imation, but at the cost of increasing the drift imation error, which will improve gradually afterwards as discussed previously. However, resetting the drift imation starts a new time window, such that the most recent observations are used to adapt to the instability in the clock drift Removal or addition of nodes WSN operation may involve a sudden disappearance of one or more of the nodes, due to power depletion, movement, or druction. In case the master node disappears, the nodes can elect a new leader [11] and then resynchronize. If a node relocates within hops, or a new node is added to the network after the synchronization started, it follows the scheme discussed in the multi-hop case, by synchronizing to the low hop-number node. 7. Future work So far, ADSP performance has been observed through computer simulations only, based on the presented mathematical model. The implementation of ADSP on real platforms, in particular Mica2 and Telos, and the extension of the protocol to multi-hop scenarios, are the research activities of our main inter in the immediate future. 8. Conclusions Sensor nodes, realized according to the recent technology advances, they can revolutionize sensing in different ways. In a sensor network, data is continuously routed and exchanged between nodes. This requires cooperation between nodes to perform complex tasks. Here comes the importance of time synchronization, as it is required to optimize the operations of these networks. Although several time synchronization methods have been developed for traditional networks, they are not well-suited for sensor networks. Time synchronization protocols such as RBS and TPSN have been proposed, but although they can achieve accurate synchronization, their energy ratings are rather high. We presented the ADSP method, which solves some of the problems introduced by previous approaches. The main characteristics of the proposed method are: 1. Broadcast-based transmissions: Offering an efficient utilization of the wireless channel and energy. 2. Always-on synchronization: Providing network-wide time-scale, immediately after an event occurs, as each node can locally imate the actual time. 3. Accuracy versus resources trade-off: Synchronization accuracy can be set to different levels, according to the dedicated resources. 4. Scalability and mobility: If nodes are moved around or added to the network, they can be synchronized by listening to the surrounding nodes. 5. Background operation: Nodes can include the timamp and hop-number in the transmitted packet, performing transparent synchronization without additional traffic. However, some of the drawbacks that may hold the performance of ADSP, are mainly the increased complexity when aiming for better accuracies, as more memory, processing and consequently energy are required. Another drawback may arise from the additional complexity and latency in multi-hop cases, due to the several timeouts, and to the dependency of a node on its master for timamps. This issue can be a major concern in low-traffic networks. 9. References [1] F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, "A Survey on Sensor Networks," IEEE Communications Magazine, pp. 102, [2] Archana Bharathidasan, Vijay Anand Sai Ponduru, Sensor Networks: An Overview. [3] Fikret Sivrikaya, Bulent Yener, Time Synchronization in Sensor Networks: A Survey, IEEE Network magazine's special issue on Ad Hoc Networking: Data Communications & Topology Control, vol. 18, issue 4, pages 45-50, July/August [4] J. Elson, K. Romer, Wireless Sensor Networks: A New Regime for Time Synchronization, Proceedings of the First Workshop on Hot Topics In Networks (HotNets-I), Princeton, New Jersey. October [5] Jeremy Elson, Lewis Girod and Deborah Estrin, Fine-Grained Network Time Synchronization using Reference Broadcasts, In the proceedings of the fifth symposium on Operating System Design and Implementation (OSDI 2002), December [6] S. Ganeriwal, R. Kumar, M.B. Srivastava, Timing Synch Protocol for Sensor Networks, In Proceedings of 1st International Conference on Embedded Network Sensor Systems 2003, ACM Press, pp [7] M. Maroti, B. Kusy, G. Simon, A. Ledeczi. The Flooding Time Synchronization Protocol, Proceedings of the Second ACM Conference on Embedded Networked Sensor Systems (Sensys), November [8] D. L. Mills, Internet time synchronization: The Network Time Protocol In Z. Yang and T.A. Marsland, editors, Global States and Time in Distributed Systems. IEEE Computer Society Press, [9] Elliott D. Kaplan. Understanding GPS: Principles and Applications, Artech House, [10] N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous univariate distributions, Vol. 2, John Wiley, New York, [11] N. Malpani, J. L. Welch, N. Vaidya, Leader election algorithm for mobile ad-hoc networks, In Proceedings of 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communication, pp , August [12] K. Noh, Q. M. Chaudhari, E. Serpedin, and B. W. Suter, Novel Clock Phase Offset and Skew Estimation Using Two-Way Timing Message Exchanges for Wireless Sensor Networks, IEEE transactions on communications, vol. 55, no. 4, pages , April