Clock Synchronization Algorithm Research Articles

An improved clock synchronization model for typical IoT applications

In today’s scenario, the Internet of Things (IoT) has transformed people’s lives by enabling data exchange among pervasive devices in various applications. However, clock synchronization is essential to ensure seamless transmission and synchronization among IoT entities involved in processing and communication. This paper proposes a clock synchronization algorithm based on linear-quadratic regression (LQR) to address synchronization-errors in IoT applications. The algorithm uses a linear model of skew and offsets to estimate clock parameters, and performance is evaluated in terms of R-square error (RSE) and Root Mean Square Error (RMSE). Our proposed algorithm outperformed traditional algorithms with an R-Square Error of 0.71% and RMSE of 0.379%. This paper also evaluated the stability of the proposed model using the correlation coefficient, which indicated a high correlation among the variables at 86%. The results below demonstrate the proposed algorithm’s effectiveness and goodness of fit in addressing clock synchronization errors for IoT applications.

Clock synchronization with partial timestamp information for wireless sensor networks

Most existing clock synchronization algorithms in wireless sensor networks require full timestamp information to estimate clock skew and offset so as to maintain the same time scale between nodes. However, in many scenarios, with the purpose of decreasing energy consumption, reducing communication overhead, or improving security, timestamps are not exchanged in synchronization process, resulting in insufficient access to all time information by nodes to be synchronized. Hence, how to jointly estimate clock skew and offset with limited observation is a significant challenge. In order to solve this issue, this paper proposes a partial timestamp synchronization (PTS) scheme, which can implement complete synchronization function only according to the local timestamps and the timestamp relationships obtained by the basic synchronization protocol. Then, based on PTS, a joint Maximum Likelihood Estimator is developed to estimate clock skew and offset when stochastic delays follow Gaussian distribution. In addition, a Best Linear Unbiased Estimator for PTS with exponential random delays is presented, which can also estimate clock skew and offset simultaneously. Finally, simulations are conducted to illustrate the effectiveness of the proposed algorithms.

Formal Modelling and Verification of the Clock Synchronization Algorithm of FlexRay


 
 
 
 The hundreds of electronic control devices used in an automotive system can effectively communicate with one another, thanks to an in-vehicle network (IVN) like FlexRay. Even though every node in the network will be running on its local clock, a global notion of time is essential. The clock synchronisation algorithm accomplishes this global time between the nodes in FlexRay. In this era of self-driving cars, the vehicle’s safety is paramount. For the vehicle to operate safely and smoothly, timely communication of information is critical, and the clock synchronisation algorithm plays a vital role in this. It is essential to formally test the clock synchronisation algorithm’s correctness. This paper attempts to model and verify the clock synchronisation algorithm of FlexRay using formal methods, which in turn enhance the reliability of safety-critical automotive systems. The clock synchronisation is modelled as a network of six timed automata in the UPPAAL model checker. Three system models were developed, a model for an ideal clock, another for a drifting clock, and a third model considering propagation delay. The precision of the clocks is verified to be within the prescribed limits. Simulation studies are also conducted on the model to ensure that the clock’s drift is always within the precision.
 
 
 

Resilient Synchronization of Pulse-coupled Oscillators with Time Continuity

Clock synchronization of wireless sensor networks (WSNs) using pulse-coupled oscillators has been extensively studied. In this paper, we propose a resilient clock synchronization algorithm that can mitigate the influence of adversarial nodes that emit pulses at arbitrary time instants. Under the assumption that a bound on the number of nodes in the network is known, we provide distributed protocols that guarantee continuity of clocks by varying the phase speeds. We illustrate the usefulness of the proposed algorithms by comparing them with a conventional method in a numerical example.

Formal modeling of the gPTP clock synchronization algorithm in automotive ethernet

Formal modeling of the gPTP clock synchronization algorithm in automotive ethernet

Design, Simulation and Validation of Fault Tolerant Averaging Algorithm for Clock Synchronization With Custom Time Triggered Deterministic Protocol

Time triggered communication provides fault tolerance and determinism in a distributed dependable real time systems. These systems crucially depend on fault tolerant clock synchronization. The article presents simulation of fault tolerant averaging algorithm for clock synchronization and it's modification for improved convergence. We present the simulation results of synchronization algorithm to verify fault tolerance and convergence to a single time base. By modification, we show how a two node system can also be synchronized eliminating the criteria of minimum three nodes. This article also reports a custom time triggered protocol named as deterministic fault tolerant communication protocol particularly suitable for mission critical applications or safety-critical control applications such as in automotive “by-wire” and aerospace systems. The article also presents a different approach for membership service which is based on majority voting and can be used in systems based on time triggered architecture.

Time-delay interferometry without clock synchronization

Time-delay interferometry (TDI) is a data processing technique for LISA designed to suppress the otherwise overwhelming laser noise by several orders of magnitude. It is widely believed that TDI can only be applied once all phase or frequency measurements from each spacecraft have been synchronized to a common time frame. We demonstrate analytically, using as an example the commonly-used Michelson combination X, that TDI can be computed using the raw, unsynchronized data, thereby avoiding the need for an initial synchronization processing step and significantly simplifying the initial noise reduction pipeline. Furthermore, the raw data is free of any potential artifacts introduced by clock synchronization and reference frame transformation algorithms, which allows to operate directly on the MHz beatnotes. As a consequence, in-band clock noise is directly suppressed as part of TDI, in contrast to the approach previously proposed in the literature (in which large trends in the beatnotes are removed before the main laser-noise reduction step, and clock noise is suppressed in an extra processing step). We validate our algorithm with full-scale numerical simulations that use LISA Instrument and PyTDI and show that we reach the same performance levels as the previously proposed methods, ultimately limited by the clock sideband stability.

Clock Synchronization Algorithm for Structural Modal Measurement

The modal of a structure is the natural vibration characteristic of the structure, which is very important for damage identification of the system. To accurately measure the structural modal, it is necessary to perform clock synchronization operations on the vibration sensors at each measuring point of the structure. This paper uses an improved TSPN algorithm for clock synchronization. It is assumed that the delay of the data in the transmission process obeys normal distribution. The fitting degree of a normal distribution is tested by fitting the delay distribution curve. Then, an interval estimation method is used to estimate the delay. The synchronization of multiple sensors and onsite structural modal testing verifies the correctness of the process after synchronization. The method in this paper is suitable for MCU‐based vibration sensors to perform clock synchronization for structural modal measurements.

Clock Synchronization Algorithm of Distributed System Based on Adaptive Technology

Clock Synchronization Algorithm of Distributed System Based on Adaptive Technology

Pair Nodes Clock Synchronization Algorithm Based on Kalman Filter for Underwater Wireless Sensor Networks.

Time synchronization is the basis of many applications. Aiming at the limitations of the existing clock synchronization algorithms in underwater wireless sensor networks, we propose a pairwise synchronization algorithm called K-Sync, which is based on the Kalman filter. The algorithm does not need the assistance of the position sensor or the speed sensor, and the high time synchronization accuracy can be realized only by utilizing the time-stamps information in the process of message exchange. The K-Sync uses the general constraints of the motion characteristics of the sensor nodes to establish the recursive equations of the clock skew, clock offset, relative mobility velocity, and relative distance. At the same time, the time-stamps are viewed as the observation variables and the system observation equation is obtained. The K-Sync estimates the normalized clock skew and offset of the node via the Kalman filter to achieve high-precision clock synchronization between the two nodes. The simulation shows that the K-Sync has obvious advantages in the key indicators such as the estimated accuracy of clock skew and clock offset, convergence speed, etc. In addition, the K-Sync is more robust to a variety of underwater motion scenes.

A Clock Synchronization Algorithm for the Satellite System Based on MF-TDMA

In order to ensure microsecond slot scheduling, all terminals must maintain high precision of time synchronization in MF-TDMA(Multi-Frequency Time Division Multiple Access) satellite communication system. Due to the different frequency of crystal oscillator at the terminal, the absolute value of the clock deviation is constantly increasing, so a clock synchronization algorithm is required to keep the time synchronization of the satellite system. The traditional satellite clock synchronization algorithm minimizes the clock error through periodic synchronization, but it only considers the phase offset, not the crystal frequency offset, the synchronization accuracy is low and waste of bandwidth resources. Based on the traditional satellite clock synchronization, this paper proposes a gradient descent algorithm for the satellite system based on MF-TDMA(GDAS), adding clock frequency offset prediction and compensation mechanism to improve clock synchronization accuracy and bandwidth resource utilization rate. The simulation results of the proposed algorithm has optimized the precision performance of clock synchronization.

A novel precise and accurate clock synchronization algorithm

Execution of a task in a synchronized manner in a distributed setting, one needs the common idea of time. To accomplish this task, clock synchronization is conceptualized. Clock drifting is an intrinsic property of a clock, which necessitates the synchronization and resynchronization. A network consists of nodes, which may behave appropriately or behave badly. The mischievous node may pose difficulty in clock synchronization. We require a method to overcome the effect of mischievous nodes. Synchronization can be achieved in two ways namely accuracy and precision. In this paper, we present an accurate weighted average clock synchronization algorithm to execute a coordinated activity in a fault-tolerant manner. We use trusted clock value from GPS/GLONASS/IRNSS as a reference clock to achieve better accuracy. We also use behavior of the node to compute normalized weight in a localized manner, which lies between unit intervals. This weight assignment enables us to contain the effect of misbehavior up to some extent. This algorithm offers better accuracy and precision while tolerating mischievous nodes. The upper bound of tolerance boundary is one-third of the network size.

Clock synchronization error compensation algorithm based on BP neural network model

Error compensation is an important guarantee method to ensure the accuracy of clock synchronization in underwater sensor networks. Existing research methods mainly use linear fitting and least square method to compensate for clock synchronization parameters. Underwater wireless sensor network nodes are mobile, which leads the network nodes to be always in a time-varying state. In the process of synchronous forwarding, the position where the node sends and receives data packets will change, resulting in a relative moving distance, leading the dynamic delay to an increase in. In this way, as the number of forwarding nodes increases, the error of the clock gradually increases, causing the synchronization accuracy of the underwater sensor wireless network to gradually decrease. The existing underwater wireless sensor network clock synchronization algorithm does not fully consider the dynamic time delay caused by the movement of the node with the ocean current. It only uses the time stamp mechanism to solve the clock synchronization parameters, and then uses the traditional linear fitting to refine the synchronization parameters. The accurate solution of dynamic time delay is a key factor of synchronization accuracy. The use of traditional optimization algorithms to refine the synchronization parameters can easily fall into a local optimum, which makes the synchronization accuracy not high. Therefore, the existing traditional research on clock synchronization algorithms cannot well solve the problem of clock synchronization accuracy caused by node mobility. However this type of method does not consider the clock synchronization accuracy of node movement affected by ocean currents. To solve this problem, this paper proposes a clock synchronization error compensation algorithm based on BP neural network model. First, the deep-sea Lagrangian ocean current model is used to describe the movement of underwater nodes and simulate the movement speed of underwater nodes, and then a clock synchronization parameter model is established, and finally a BP neural network clock synchronization error compensation model is build, which conforms to the underwater environment, and the excitation function is defined, and regular term factor and compensatory factor are introduced to avoid model over-fitting. The BP neural network model clock synchronization error compensation algorithm is established for error back propagation. Simulation experiments show that compared with the comparison algorithm TSHL, MM-sync, and MU-sync, the accuracy of clock synchronization, namely the error between clock synchronization time and standard time, increased by 37.42%, 17.29% and 21.86%, and the mean square error is significantly reduced.

One Study on IEEE1588 clock synchronization algorithm based on Kalman filter

Clock synchronization is a major indicator of the distributed network test and control system. The precise time synchronization is also one of the core technologies of the network communication of test and control system. The paper illustrates the fundamental principle for clock synchronization under IEEE1588 protocol and concludes that its synchronized accuracy is influenced by the accuracy of time stamp and transmission delay jitter through analysis. An autoregressive clock drift model has been put forward in the paper in an effort to improve the time synchronization accuracy. It makes use of the Kalman filter to estimate the deviation and drift of the master and slave clock so as to offset it. The results of simulation indicate that the method can effectively ease the impact on time synchronization for time stamp and improve its accuracy of the test and control system.

Clock Synchronization Algorithms Over PTP-Unaware Networks: Reproducible Comparison Using an FPGA Testbed

This work explores clock synchronization algorithms used to process timestamps from the IEEE 1588 precision time protocol (PTP). It focuses on the PTP-unaware network scenario, where the network nodes do not actively contribute to PTP’s operation. This scenario typically imposes a harsh environment for accurate clock distribution, primarily due to the packet delay variation experienced by PTP packets. In this context, it is essential to process the noisy PTP measurements using algorithms and strategies that consider the underlying clock and packet delay models. This work surveys some attractive algorithms and introduces an open-source analysis library that combines several of them for better performance. It also provides an unprecedented comparison of the algorithms based on datasets acquired from a sophisticated testbed composed of field-programmable gate arrays (FPGAs). The investigation provides insights regarding the synchronization performance under various scenarios of background traffic and oscillator stability.

A novel precise and accurate clock synchronization algorithm

Execution of a task in a synchronized manner in a distributed setting, one needs the common idea of time. To accomplish this task, clock synchronization is conceptualized. Clock drifting is an intrinsic property of a clock, which necessitates the synchronization and resynchronization. A network consists of nodes, which may behave appropriately or behave badly. The mischievous node may pose difficulty in clock synchronization. We require a method to overcome the effect of mischievous nodes. Synchronization can be achieved in two ways namely accuracy and precision. In this paper, we present an accurate weighted average clock synchronization algorithm to execute a coordinated activity in a fault-tolerant manner. We use trusted clock value from GPS/GLONASS/IRNSS as a reference clock to achieve better accuracy. We also use behavior of the node to compute normalized weight in a localized manner, which lies between unit intervals. This weight assignment enables us to contain the effect of misbehavior up to some extent. This algorithm offers better accuracy and precision while tolerating mischievous nodes. The upper bound of tolerance boundary is one-third of the network size.

The Issues on Time Synchronization Technology in Time Triggered Ethernet

Based on the idea of time-triggered, global unified high precision time synchronization is the foundation of network deterministic communication. In the process of time synchronization, clock synchronization algorithm, transmission delay, clock drift and so on will affect the accuracy of clock synchronization. It is a great technical challenge to realize high precision and reliable clock synchronization. This paper collates and analyses the relevant literature, first introduces the time-triggered Ethernet, then analyses the time synchronization protocol that can be used for high-precision clock synchronization, reviews the development status of time synchronization technology and makes an overall analysis. Finally summarizes the clock synchronization difficulty and prospects the development trend of the time synchronization technology.

Scalable clock synchronization analysis: A symmetric noncooperative output feedback tubes-MPC approach

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.

Characterization, Statistical Analysis and Method Selection in the Two-Clocks Synchronization Problem for Pairwise Interconnected Sensors.

Time synchronization among sensor devices connected through non-deterministic media is a fundamental requirement for sensor fusion and other distributed tasks that need a common time reference. In many of the time synchronization methods existing in literature, the estimation of the relation between pairs of clocks is a core concept; moreover, in applications that do not have general connectivity among its devices but a simple pairwise topology, such as embedded systems, mobile robots or home automation, two-clock synchronization is actually the basic form of the time estimation problem. In these kinds of applications, especially for critical ones, not only the quality of the estimation of the relation between two clocks is important, but also the bounds the methods provide for the estimated values, and their computational effort (since many are small systems). In this paper, we characterize, with a thorough parameterization, the possible scenarios where two-clock synchronization is to be solved, and then conduct a rigorous statistical study of both scenarios and methods. The study is based on exhaustive simulations run in a super-computer. Our aim is to provide a sound basis to select the best clock synchronization algorithm depending on the application requirements and characteristics, and also to deduce which ones of these characteristics are most relevant, in general, when solving the problem. For our comparisons we have considered several representative methods for clock synchronization according to a novel taxonomy that we also propose in the paper, and in particular, a few geometrical ones that have special desirable characteristics for the two-clock problem. We illustrate the method selection procedure with practical use-cases of sensory systems where two-clock synchronization is essential.

Adaptive Fractional-Order Operator Clock Synchronization Algorithm Based on Grey Prediction

As a result of the influence of clock drift and uncertainty delay in synchronous message transmission, the clock synchronization model based on statistical distribution cannot accurately describe clock deviation. This model also requires a large number of timestamp samples that cause a storage occupation issue for wireless sensor nodes with limited resources. The modeling method based on grey prediction has advantages of low sample demand and simple modeling process. However, the accuracy of the existing clock synchronization models needs to be improved. Based on the grey prediction theory, this paper proposes an adaptive fractional-order operator clock synchronization algorithm considering uncertainty delay. First, based on the clock model and clock offset model, the frequency offset between nodes is optimized by taking the mean on the clock frequencies. Second, a grey prediction algorithm based on a fractional-order operator is proposed by estimating the uncertainty delay in message transmission to obtain the clock offset. Finally, the order of the fractional-order accumulation is adjusted adaptively in the grey prediction model according to the collected timestamp sample values so that the estimation of the uncertainty delay is more accurate, thereby improving the accuracy of the clock offset. Compared with the first-order accumulative grey prediction clock synchronization algorithms and timing-sync protocol for sensor networks, the proposed scheme improved the synchronization accuracy by 29.18% and 44.01%, respectively, and reduced the variance of the clock offset by 48.66% and 64.89%. Thus, the proposed algorithm is characterized by improved stability.