Clock Synchronization in Wireless Sensor Networks: Analysis and Design of Error Precision Based on Lossy Networked Control Perspective
TL;DR: The model of synchronization error variance analysis and design issues is established and an optimal clock information exchange rate between synchronization node and reference node which offers the optimal tradeoff between energy consumption and synchronization precision at synchronization node is found.
Abstract: Motivated by the importance of the clock synchronization in wireless sensor networks (WSNs), due to the packet loss, the synchronization error variance is a random variable and may exceed the designed boundary of the synchronization variance. Based on the clock synchronization state space model, this paper establishes the model of synchronization error variance analysis and design issues. In the analysis issue, assuming sensor nodes exchange clock information in the network with packet loss, we find a minimum clock information packet arrival rate in order to guarantee the synchronization precision at synchronization node. In the design issue, assuming sensor node freely schedules whether to send the clock information, we look for an optimal clock information exchange rate between synchronization node and reference node which offers the optimal tradeoff between energy consumption and synchronization precision at synchronization node. Finally, simulations further verify the validity of clock synchronization analysis and design from the perspective of synchronization error variance.
Citations
More filters
TL;DR: A statistical tool based on the maximum probability theory for selecting the reference clock offset for time synchronization protocols is proposed and a subset selection algorithm is proposed to support the proposed statistical tool.
Abstract: Synchronizing time between the sensors of wireless sensor network has vital importance. It helps in maintaining a consistent and reliable frame of time across the network. Two clocks are stated to be synchronized when their frequency source runs with equal rate and their offsets are set identical. Basically, due to the manufacturing difference there is slight variation in their clock oscillator which affects the degree of frequency source and accuracy. Therefore this leads to the problem of synchronizing time between the sensor clocks. To attain time synchronization in a network typical contention-based message passing techniques are used. In this paper two-way message passing scheme is utilized. It proposes a statistical tool based on the maximum probability theory for selecting the reference clock offset for time synchronization protocols. It also proposes a subset selection algorithm to support the proposed statistical tool. The results obtained consist of the selection of most probable estimate for clock offset. The proposed algorithm utilizes the two-way message passing scheme for the exchange of timing messages within the network. The proposed algorithm is compared with the existing algorithms for estimation of clock offset. It was observed that the proposed works gives better results in terms of efficiency i.e. 99.8% efficient.
14 citations
01 Sep 2018
TL;DR: The results prove that the proposed methods can successfully reduce the negative effects of clock inaccuracies and achieve localization accuracy of 3cm in average is achieved when a proper oscillator is used.
Abstract: This paper discusses the synchronization issues of the unilateral TDoA method applied in ultra-wideband (UWB) localization systems. Focus of the paper is on implementation aspects of the synchronization. At first, the structure of unilateral TDoA method is explained and a method for synchronization is proposed. In the next step, typical implementation challenges of synchronization such as rounding effect, outliers, filtering, packet loss detection and thermal dependencies are discussed and for each problem a solution is provided. A set of experiments have been performed on different clock sources to study their effect on the accuracy of synchronization. The results of the experiments confirm that the voltage and temperature compensated oscillator has the highest accuracy, lowest frequency jitter but longest steady state time among the other variants applied. At the end, the performance of the synchronization solution in real experiments are demonstrated. The results prove that the proposed methods can successfully reduce the negative effects of clock inaccuracies. According to the results, localization accuracy of 3cm in average is achieved when a proper oscillator is used.
11 citations
Cites methods from "Clock Synchronization in Wireless S..."
...We have used the model suggested in [21]....
[...]
TL;DR: A new measurement model of observability under the equivalent transformation of minimum mean square error ( MMSE ) is constructed based on basic measurement unit ( BMU ) , which can realize the scaled expansion of MMSE measurement.
Abstract: In the cyber-physical environment, the clock synchronization algorithm is required to have better expansion for network scale. In this paper, a new measurement model of observability under the equivalent transformation of minimum mean square error ( MMSE ) is constructed based on basic measurement unit ( BMU ) , which can realize the scaled expansion of MMSE measurement. Based on the state updating equation of absolute clock and the decoupled measurement model of MMSE-like equivalence, which is proposed to calculate the positive definite invariant set by using the theoretical-practical Luenberger observer as the synthetical observer, the local noncooperative optimal control problem is built, and the clock synchronization system driven by the ideal state of local clock can reach the exponential convergence for synchronization performance. Different from the problem of general linear system regulators, the state estimation error and state control error are analyzed in the established affine system based on the set-theory-in-control to achieve the quantification of state deviation caused by noise interference. Based on the BMU for isomorphic state map, the synchronization performance of clock states between multiple sets of representative nodes is evaluated, and the scale of evaluated system can be still expanded. After the synchronization is completed, the state of perturbation system remains in the maximum range of measurement accuracy, and the state of nominal system can be stabilized at the ideal state for local clock and realizes the exponential convergence of the clock synchronization system.
4 citations
Cites background or methods from "Clock Synchronization in Wireless S..."
...Based on the framework in [16] and [17], the present paper constructs the measurement model of observability of BMU under the transformation of minimum mean square error (MMSE), which meets the necessary conditions of the state’s estimation of system....
[...]
...Reference [16] proposed the stochastic optimal control of the networked control perspective based on the relative clock state space model....
[...]
...Control Strategy in Clock Synchronization” in [16])....
[...]
...The main contributions of this paper are: 1) Based on the previous research [16], [17], this paper constructs an observable measurement model under the BMU for absolute clock in the large-scale network from the viewpoint of networked control theory; 2) Aiming at the calculation problem of positive definite invariant sets, the observability measurement model of MMSE-like equivalence is proposed to calculate the positive definite invariant set by using the Luenberger observer as the synthetical observer....
[...]
...It is assumed that the clock parameters have hardly changed in one round of exchange since the time spent in a round of exchange of the message is very short [16]....
[...]
TL;DR: Maximum probability theory is applied to estimate the best value of clock offset between two sensor clocks and it is observed that for a small network, proposed work gives better and efficient results with Time-Sync Protocol for Sensor Network.
Abstract:
In recent research, time synchronization has a great importance in the various
application of wireless sensor network. Localization, tracking, message passing using contention-based
schemes and communication are some of the fields where synchronization between sensor clocks is
highly required. Therefore, several algorithms were designed to achieve a rational and reliable frame of
time within the wireless sensor network. Patents related to time synchronization in WSN were also analyzed.
This paper discusses the powerful statistical tool using maximum probability theory for synchronizing
the time within the sensor's clock. In this paper, maximum probability theory is applied to
estimate the best value of clock offset between two sensor clocks. The proposed algorithm is analyzed
by exchanging timing messages between nodes using two-way message exchange schemes.
The proposed algorithm is also implemented along with a Time-Sync Protocol for Sensor Network.
It reduces error deviation from 2.32 to 0.064 ms as compared with Time-Sync Protocol for Sensor
Network without proposed works.
It was observed that for a small network, proposed work gives better and efficient results
with Time-Sync Protocol for Sensor Network.
3 citations
TL;DR: The experimental results show that the multi-heterogeneous curve fitting algorithm is effective and the mildew indices of indoor and outdoor have cyclical differences.
Abstract: Complex computing based on multi-heterogeneous parameters can utilize the Lebesgue measure to measure their linear and non-linear relations in infinite dimensional Hilbert space, which can characterize those different dimensional characteristics in a set of autonomous learning base. The temporal-spatial micro-scale mildew indices can be fitted by using four heterogeneous parameters, including temperature, humidity, wind force, and water vapor pressure. This paper proposes a fitting process of heterogeneous parameter curves, which is based on a common reference coordinate base. The multi-scale functional fitting tree is constructed by R*-tree and the Lebesgue similarity measure algorithm. When the similarity of two tree nodes representative of similar environmental sub-space exceeds a given threshold, these nodes can be combined into a parent node, which represents the environmental characteristic of combined bigger-space and its mildew curve is the fitted result of all the son-node mildew curves. The curve similarity measurement based on the Lebesgue multi-dimensional matrix and the functional curve generating process of multi-heterogeneous data curves are proposed in the micro-space mildew index fitting example. The boundary finding of fitting curves can be realized by envelop curve algorithm. Based on two years environmental measurement parameters of ancient dwellings, the mildew index comparison of indoor and outdoor can be obtained. The experimental results show that the multi-heterogeneous curve fitting algorithm is effective and the mildew indices of indoor and outdoor have cyclical differences.
3 citations
Cites background or methods from "Clock Synchronization in Wireless S..."
...RELATED WORK The precision and error analysis of WSN measurement data can detect the running state of the probing network and the quality of measurement data [8], [9]....
[...]
...[8] established the model of synchronized error and variance analysis based on the clock synchronized state space model to guarantee the synchronized precision....
[...]
References
More filters
09 Dec 2002
TL;DR: Reference Broadcast Synchronization (RBS) as discussed by the authors is a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts, and receivers use their arrival time as a point of reference for comparing their clocks.
Abstract: Recent advances in miniaturization and low-cost, low-power design have led to active research in large-scale networks of small, wireless, low-power sensors and actuators. Time synchronization is critical in sensor networks for diverse purposes including sensor data fusion, coordinated actuation, and power-efficient duty cycling. Though the clock accuracy and precision requirements are often stricter than in traditional distributed systems, strict energy constraints limit the resources available to meet these goals.We present Reference-Broadcast Synchronization, a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts. A reference broadcast does not contain an explicit timestamp; instead, receivers use its arrival time as a point of reference for comparing their clocks. In this paper, we use measurements from two wireless implementations to show that removing the sender's nondeterminism from the critical path in this way produces high-precision clock agreement (1.85 ± 1.28μsec, using off-the-shelf 802.11 wireless Ethernet), while using minimal energy. We also describe a novel algorithm that uses this same broadcast property to federate clocks across broadcast domains with a slow decay in precision (3.68 ± 2.57μsec after 4 hops). RBS can be used without external references, forming a precise relative timescale, or can maintain microsecond-level synchronization to an external timescale such as UTC. We show a significant improvement over the Network Time Protocol (NTP) under similar conditions.
2,537 citations
TL;DR: This work addresses the problem of performing Kalman filtering with intermittent observations by showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs.
Abstract: Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.
2,343 citations
03 Nov 2004
TL;DR: The FTSP achieves its robustness by utilizing periodic flooding of synchronization messages, and implicit dynamic topology update and comprehensive error compensation including clock skew estimation, which is markedly better than that of the existing RBS and TPSN algorithms.
Abstract: Wireless sensor network applications, similarly to other distributed systems, often require a scalable time synchronization service enabling data consistency and coordination. This paper describes the Flooding Time Synchronization Protocol (FTSP), especially tailored for applications requiring stringent precision on resource limited wireless platforms. The proposed time synchronization protocol uses low communication bandwidth and it is robust against node and link failures. The FTSP achieves its robustness by utilizing periodic flooding of synchronization messages, and implicit dynamic topology update. The unique high precision performance is reached by utilizing MAC-layer time-stamping and comprehensive error compensation including clock skew estimation. The sources of delays and uncertainties in message transmission are analyzed in detail and techniques are presented to mitigate their effects. The FTSP was implemented on the Berkeley Mica2 platform and evaluated in a 60-node, multi-hop setup. The average per-hop synchronization error was in the one microsecond range, which is markedly better than that of the existing RBS and TPSN algorithms.
2,267 citations
"Clock Synchronization in Wireless S..." refers methods in this paper
...For the issue of clock synchronization, early studies focus on the design of protocols, such as the Time Synchronization Protocol for Sensor Networks (TPSN) [3], the ReferenceBroadcast Synchronization (RBS) [4], the Flooding Time Synchronization Protocol (FTSP) [5], and the Pairwise Broadcast Synchronization (PBS) [6]....
[...]
05 Nov 2003
TL;DR: It is argued that TPSN roughly gives a 2x better performance as compared to Reference Broadcast Synchronization (RBS) and verify this by implementing RBS on motes and use simulations to verify its accuracy over large-scale networks.
Abstract: Wireless ad-hoc sensor networks have emerged as an interesting and important research area in the last few years. The applications envisioned for such networks require collaborative execution of a distributed task amongst a large set of sensor nodes. This is realized by exchanging messages that are time-stamped using the local clocks on the nodes. Therefore, time synchronization becomes an indispensable piece of infrastructure in such systems. For years, protocols such as NTP have kept the clocks of networked systems in perfect synchrony. However, this new class of networks has a large density of nodes and very limited energy resource at every node; this leads to scalability requirements while limiting the resources that can be used to achieve them. A new approach to time synchronization is needed for sensor networks.In this paper, we present Timing-sync Protocol for Sensor Networks (TPSN) that aims at providing network-wide time synchronization in a sensor network. The algorithm works in two steps. In the first step, a hierarchical structure is established in the network and then a pair wise synchronization is performed along the edges of this structure to establish a global timescale throughout the network. Eventually all nodes in the network synchronize their clocks to a reference node. We implement our algorithm on Berkeley motes and show that it can synchronize a pair of neighboring motes to an average accuracy of less than 20ms. We argue that TPSN roughly gives a 2x better performance as compared to Reference Broadcast Synchronization (RBS) and verify this by implementing RBS on motes. We also show the performance of TPSN over small multihop networks of motes and use simulations to verify its accuracy over large-scale networks. We show that the synchronization accuracy does not degrade significantly with the increase in number of nodes being deployed, making TPSN completely scalable.
2,215 citations
"Clock Synchronization in Wireless S..." refers methods in this paper
...Referencing TPSN [3] synchronization protocol, we also adopt the classical mechanism [1, 3, 20] of two-way message exchange between two adjacent nodes, which is depicted in Figure 1....
[...]
...For the issue of clock synchronization, early studies focus on the design of protocols, such as the Time Synchronization Protocol for Sensor Networks (TPSN) [3], the ReferenceBroadcast Synchronization (RBS) [4], the Flooding Time Synchronization Protocol (FTSP) [5], and the Pairwise Broadcast Synchronization (PBS) [6]....
[...]
05 Mar 2007
TL;DR: In this paper, the authors consider control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network and characterize the impact of the network reliability on the performance of the feedback loop.
Abstract: This paper considers control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network. In contrast to traditional control and estimation problems, here the observation and control packets may be lost or delayed. The unreliability of the underlying communication network is modeled stochastically by assigning probabilities to the successful transmission of packets. This requires a novel theory which generalizes classical control/estimation paradigms. The paper offers the foundations of such a novel theory. The central contribution is to characterize the impact of the network reliability on the performance of the feedback loop. Specifically, it is shown that for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g., TCP-like protocols), there exists a critical threshold of network reliability (i.e., critical probabilities for the successful delivery of packets), below which the optimal controller fails to stabilize the system. Further, for these protocols, the separation principle holds and the optimal LQG controller is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g., UDP-like protocols), the LQG optimal controller is in general nonlinear. Consequently, the separation principle does not hold in this circumstance
1,390 citations