Average consistency time synchronization method based on multi-hop virtual link and event triggering

By adopting the average consistent time synchronization method of multi-hop virtual links and event-triggered average consistency time synchronization in wireless sensor networks, the problem of communication delay affecting time synchronization is solved, and high-precision and fast network-wide clock synchronization is achieved.

WO2025107831A1PCT designated stage expired Publication Date: 2025-05-30CHONGQING UNIV OF POSTS & TELECOMM

Patent Information

Application Number
PCT/CN2024/117878
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-11-24
Filing Date
2024-09-10
Publication Date
2025-05-30

AI Technical Summary

Technical Problem

In wireless sensor networks, communication delay affects the accuracy of time synchronization, and traditional consistent time synchronization algorithms cannot effectively handle the adverse effects of time delay, resulting in large communication overhead and slow synchronization speed.

Method used

The average consistent time synchronization method based on multi-hop virtual links and event triggers is adopted, and the iterative least squares method is used to estimate the relative frequency deviation. Combined with the multi-hop virtual link clock parameter information sharing strategy, event trigger conditions are designed to reduce unnecessary transmissions, thereby improving the time synchronization speed and accuracy.

Benefits of technology

Effectively suppress the impact of delay on time synchronization, improve synchronization accuracy and speed, reduce communication overhead, and achieve fast global consistency of the clocks of nodes across the network.

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Abstract

The present invention relates to the technical field of wireless sensor networks, and to an average consistency time synchronization method based on a multi-hop virtual link and event triggering. According to the method, in the case that a communication delay is present in a wireless network, a least squares estimator is used to restrain the effect of the delay in the relative frequency offset estimation process; clock information of nodes is fully called by means of the multi-hop virtual link for update, thereby effectively increasing the clock synchronization speed; an event triggering policy is used to reduce a transmission frequency between the nodes, thereby effectively reducing communication overhead; and a consistency algorithm is used to update logic clock parameters of the nodes, thereby realizing global consistency of clocks of the nodes in a wireless sensor network. According to the present invention, the effect of the communication delay in the wireless sensor network is taken into consideration, an iterative least squares estimator is used to obtain a high-precision relative frequency offset value to improve the synchronization precision, and by using an interaction mechanism of the multi-hop virtual link and event triggering, the communication overhead is effectively reduced while increasing the convergence speed of a clock synchronization error.
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Description

Average consistency time synchronization method based on multi-hop virtual link and event triggering Technical Field

[0001] The invention belongs to the technical field of wireless sensor networks and relates to an average consistency time synchronization method based on multi-hop virtual links and event triggering. Background Art

[0002] Time synchronization provides a global reference clock for wireless sensor networks, a prerequisite for the effective operation of applications and services such as data fusion, time division multiple access, and target location. Due to factors such as crystal oscillator operation and environmental changes, clocks drift over time, leading to differences in the clocks of nodes in wireless sensor networks. Therefore, the research and development of time synchronization technologies that maintain clock synchronization errors within a certain range is of great significance. Consensus time synchronization algorithms are distributed algorithms that have been widely studied because they do not rely on a fixed network topology and offer high robustness and stability. Each node exchanges clock information with all neighboring nodes to obtain relative states. This state is then used to compensate clock parameters, forcing all nodes' clocks to converge to a common value.

[0003] However, in practical wireless sensor networks, communication delays inevitably occur during information exchange, compromising synchronization accuracy. Early consensus time synchronization algorithms that failed to account for delays were unable to achieve global time synchronization in practical applications. Therefore, it is crucial to explore effective methods to address the adverse effects of delays. Leveraging the distributed nature of consensus algorithms, a relative frequency offset estimator designed by leveraging relative clock values ​​between nodes combined with statistical signal processing methods can effectively mitigate the adverse effects of delays. Consequently, consensus time synchronization algorithms based on least squares estimators, sequential least squares estimators, and Bayesian estimators have been proposed. These algorithms effectively converge clock synchronization errors and maintain high synchronization accuracy in the presence of delays. However, these algorithms all employ a time-triggered mechanism, where nodes periodically update and broadcast clock parameters. This mechanism cannot meet the dynamic requirements of the necessary frequency of updates during the early and later stages of clock synchronization, resulting in significant communication overhead and unnecessary energy waste. Therefore, it is necessary to develop methods that can effectively reduce communication overhead. At the same time, in traditional consistency algorithms, nodes can only receive the clock values ​​of neighboring nodes, and clock synchronization of the entire network is achieved only by updating the clock parameters of single-hop neighboring nodes, resulting in slow convergence of time synchronization errors and a long global synchronization cycle.

[0004] Therefore, there is an urgent need for a consistent time synchronization method that can reduce communication overhead and improve convergence speed in wireless sensor networks with time delay.

[0005] Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide an average consistency time synchronization method based on multi-hop virtual links and event triggering, taking into account the adverse effects of communication delay on time synchronization performance and the interaction mechanism of distributed nodes, an iterative least squares estimator is used to estimate the relative frequency deviation, and a broadcast mechanism based on event triggering conditions is proposed to reduce unnecessary transmission, thereby saving communication resources, and combining the multi-hop virtual link clock parameter information sharing strategy to achieve full utilization of the clock information of nodes in the entire network, effectively ensuring that the method improves the time synchronization speed while achieving synchronization error convergence.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A time synchronization method based on multi-hop virtual links and event triggering for average consistency. This method addresses the presence of communication delays in wireless networks and uses a least squares estimator to suppress the impact of delays in the relative frequency offset estimation process. Multi-hop virtual links are used to fully mobilize the clock information of each node for updating, effectively improving the speed of clock synchronization. Event triggering strategies are used to reduce the transmission frequency between nodes, effectively reducing communication overhead. A consistency algorithm is used to update the logical clock parameters of nodes, achieving global clock consistency among nodes in wireless sensor networks.

[0009] The method specifically comprises the following steps:

[0010] S1: Set the network update period and initialize the logical frequency offset compensation value, logical phase offset compensation value and relative frequency offset estimation value of each node in the network;

[0011] S2: Under the premise of meeting the update cycle conditions, evaluate whether the current update value meets the trigger conditions. If so, broadcast the clock information to the neighboring nodes and record the broadcast parameters. If the sending node is a single-neighbor node, the node directly broadcasts its local clock information and logical clock information to the neighboring node; if it is a node with multiple neighbors, it combines the received neighbor node clock information with its own local clock and logical clock information and broadcasts it to the next neighbor node;

[0012] S3: After receiving the data packet sent by the neighboring node, the node calls the clock parameters in it and uses the iterative least squares method to estimate the relative frequency deviation value, and uses the average consistency algorithm to update the logical frequency deviation compensation value and the logical phase deviation compensation value. Steps S2 to S3 are repeated periodically until the logical clocks of all nodes in the network are globally consistent.

[0013] Furthermore, step S1 specifically includes: setting the network update period T, for any node i in the network, setting the number of updates to m=1, initializing the relative frequency offset estimation value, logical frequency offset compensation value and logical phase offset compensation value of node i respectively. set up is the absolute time of the mth update of node i, at which the local clock reading of node i is

[0014] Furthermore, step S2 specifically includes: in order to evaluate whether the updated clock information needs to be broadcast to neighboring nodes, when m=1 or m>2 and the local clock value of node i meets the update period condition When the current updated logic frequency offset compensation value Logic phase offset compensation value The logical frequency offset compensation value of the most recent broadcast Logic phase offset compensation value Substitute into the trigger equation for judgment:

[0015] Among them, η s and η o is the trade-off parameter in the trigger equation;

[0016] If the conditions of the above trigger equation are met, node i will and Updated to and The updated logical clock parameters are recorded. The network topology of the sending node is then determined. If the sending node has a single neighbor, it directly broadcasts its local clock information and logical clock information to neighbor node j. If it has multiple neighbors, it combines the received neighbor node clock information with its own local clock and logical clock information and broadcasts it to the next neighbor node j.

[0017] Further, step S3 specifically includes: any neighbor node j of node i in the network, at absolute time After receiving the data packet from node i, the local clock of the receiving time is immediately recorded as The local clock of node i that records the time when the data packet is sent is The received data packet sequence is recorded as l. At this time, node j estimates the relative frequency offset value using the least squares method based on the obtained clock information, and brings the estimated value into the consistency algorithm to update the logical frequency offset compensation value and the logical phase offset compensation value, and then calculates the logical clock value. Specifically, the following steps are included:

[0018] S31: (1) Based on the relationship between communication delay and the relative clock of nodes, the communication delay is considered as an error function:

[0019] in, is the local clock reading of node j, is the local clock reading of node i, s ij Represents the relative frequency offset between nodes, o ij Represents the relative phase deviation between nodes;

[0020] (2) Apply the least squares principle to process the error function and obtain the cost function including relative frequency deviation and relative phase deviation:

[0021] Where n represents the number of data packets received by node j from node i; the cost function includes the clock information of the receiving node and the sending node, and the relative frequency offset estimate and relative phase offset estimate are the values ​​obtained by minimizing the cost function;

[0022] (3) In order to reduce storage resources and computational costs, the relative frequency offset estimate and the relative phase offset estimate are expressed in an iterative form:

[0023] in, and Represent the gain matrix and covariance matrix of the nth round respectively, Indicates the estimated value of the clock parameter in the nth round, setting the initial value ∑(1)=(Φ T (1) Φ(1)) -1 ,

[0024] S32: Substitute the relative clock value calculated in step S31 and other logical clock parameters in the data packet into the consistency algorithm to update the logical clock value.

[0025] Furthermore, step S32 specifically includes: substituting the calculated relative clock value and other logical clock parameters in the data packet into the consistency algorithm to update the logical clock value:

[0026] Among them, node j is the neighbor node of node i, node k is the multi-hop virtual link neighbor node of node j that node i passes through, ρ s , ρ s ′,ρ o ,ρ o ′∈(0,1) is the adjustment parameter, and Respectively represent the updated logic frequency offset compensation value and logic phase offset compensation value, and is the most recently updated logical frequency offset compensation value and logical phase offset compensation value of node i, s ij represents the relative frequency offset estimate between node i and node j, s ik represents the relative frequency offset estimate of node i and node k, and Both are the logical frequency deviation values ​​of the most recent broadcast. and Indicates the logical clock value of the most recent broadcast, N i represents all one-hop neighbor nodes of node i, N i ′ represents all multi-hop virtual neighbor nodes of node i.

[0027] The beneficial effects of the present invention are:

[0028] 1) Compared with the existing event-triggered average consistency clock synchronization method, the present invention takes into account the existence of communication delay in wireless sensor networks, uses the iterative least squares method to estimate the relative frequency offset to resist the adverse effects of delay, and obtains a high-precision relative frequency offset estimate, thereby improving the time synchronization accuracy.

[0029] 2) Based on the event-triggered node interaction mechanism, the present invention designs a time-varying trigger function to dynamically evaluate whether the current updated value needs to be transmitted. Different thresholds are set according to the changing characteristics of the logical frequency deviation and the logical phase deviation. The updated logical frequency deviation value and the logical phase deviation value are calculated with the logical clock value of the most recent transmission, and the relationship between the difference and the threshold is evaluated to determine whether it is necessary to transmit. While maintaining a high synchronization accuracy, the communication overhead in the synchronization process is reduced.

[0030] 3) Based on the distributed node interaction mechanism, the present invention proposes a strategy of transmitting the clock parameters of non-neighbor nodes through multi-hop virtual links. Without building physical links, the clock parameters of neighbor nodes and non-neighbor nodes are jointly updated, effectively improving the convergence speed of the clock synchronization error of the entire network. This is conducive to the application of the average consistency time synchronization method based on multi-hop virtual links and event triggering in actual wireless networks.

[0031] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0033] FIG1 is a diagram of a wireless network topology structure used in the present invention;

[0034] FIG2 is a flow chart of the average consistency time synchronization method based on multi-hop virtual links and event triggering according to the present invention. DETAILED DESCRIPTION

[0035] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0036] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0037] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0038] Please refer to Figures 1 and 2. Figure 1 shows the distributed network topology structure in the wireless network considered by the present invention. As shown in Figure 1, the nodes in the wireless sensor network are randomly distributed. Each node has an equal status in the network. When the trigger condition is met, the node broadcasts its own clock information to other nodes based on the physical link and multi-hop virtual link, and also receives the clock information broadcast by its neighboring nodes. The communication topology of the wireless sensor network is regarded as an undirected graph. Where N = {1, 2, L, N} represents the node set, Represents the edge set of reliable communication links between nodes. If (i, j)∈E, it means that node i can successfully receive the data packet transmitted by node j, and node i can also successfully transmit the data packet to node j. The neighborhood set of node i, that is, the set of all neighbor nodes, is represented by N i = {j|(i,j)∈E}, considering the multi-hop communication topology as an undirected graph The set of multi-hop virtual link neighbor nodes of node i is represented as N i ′={k|(i,k)∈E′}.

[0039] Set the network update period T, set the update times to m=1 for any node i in the network, initialize the relative frequency offset estimation value, logical frequency offset compensation value and logical phase offset compensation value of node i to be set up is the absolute time of the mth update of node i, at which the local clock reading of node i is

[0040] In order to evaluate whether the updated clock information needs to be broadcast to neighboring nodes, when m=1 or m>2 and the local clock value of node i meets the update period condition When the current updated logic frequency offset compensation value Logic phase offset compensation value The logical frequency offset compensation value of the most recent broadcast Logic phase offset compensation value Substitute into the trigger equation for judgment:

[0041] Among them, η s and η o is the trade-off parameter in the trigger equation;

[0042] If the conditions of the above trigger equation are met, node i will and Updated to and The updated logical clock parameters are recorded. The network topology of the sending node is then determined. If the sending node has a single neighbor, it directly broadcasts its local clock information and logical clock information to neighbor node j. If it has multiple neighbors, it combines the received neighbor node clock information with its own local clock and logical clock information and broadcasts it to the next neighbor node j.

[0043] Any neighbor node j of node i in the network, at absolute time After receiving the data packet from node i, the local clock of the receiving time is immediately recorded as The local clock of node i that records the time when the data packet is sent is The received data packet sequence is recorded as l. At this time, node j uses the least squares method to estimate the relative frequency deviation value based on the obtained clock information, and brings the estimated value into the consistency algorithm to update the logical frequency deviation compensation value and the logical phase deviation compensation value, and then calculates the logical clock value.

[0044] (1) According to the relationship between communication delay and the relative clock of nodes, the communication delay is considered as an error function:

[0045] in, is the local clock reading of node j, is the local clock reading of node i, s ij Represents the relative frequency offset between nodes, o ij Represents the relative phase deviation between nodes;

[0046] (2) Apply the least squares principle to process the error function and obtain the cost function including relative frequency deviation and relative phase deviation:

[0047] The cost function includes the clock information of the receiving node and the sending node. The relative frequency offset estimation and relative phase offset estimation are the values ​​obtained by minimizing the cost function.

[0048] (3) In order to reduce storage resources and computational costs, the relative frequency offset estimate and the relative phase offset estimate are expressed in an iterative form:

[0049] in, and Represent the gain matrix and covariance matrix of the nth round respectively, Indicates the estimated value of the clock parameter in the nth round, setting the initial value ∑(1)=(Φ T (1) Φ(1)) -1 ,

[0050] Substitute the calculated relative clock value and other logical clock parameters in the data packet into the consistency algorithm to update the logical clock value:

[0051] Among them, node j is the neighbor node of node i, node k is the multi-hop virtual link neighbor node of node j that node i passes through, ρ s ,ρ s ′,ρ o ,ρ o ′∈(0,1) is the adjustment parameter, and Respectively represent the updated logic frequency offset compensation value and logic phase offset compensation value, and is the most recently updated logical frequency offset compensation value and logical phase offset compensation value of node i, s ij represents the relative frequency offset estimate between node i and node j, s ikrepresents the relative frequency offset estimate of node i and node k, and Both are the logical frequency deviation values ​​of the most recent broadcast. and Indicates the logical clock value of the most recent broadcast, N i represents all one-hop neighbor nodes of node i, N i ′ represents all multi-hop virtual neighbor nodes of node i.

[0052] FIG2 is a flow chart of the average consistency time synchronization method based on multi-hop virtual links and event triggering of the present invention. This embodiment provides an average consistency time synchronization method based on multi-hop virtual links and event triggering in the presence of communication delay, as shown in FIG2, which specifically includes the following steps:

[0053] V1: The consistency clock synchronization process begins.

[0054] V2~V3: Initialize the logical frequency offset compensation value, logical phase offset compensation value, and relative frequency offset estimation value of each node in the network, set the network update cycle, and gradually update the logical frequency offset compensation value and logical phase offset compensation value according to this cycle.

[0055] V4: Substitute the updated logical frequency offset compensation value and logical phase offset compensation value into the trigger equation to evaluate whether this node meets the conditions for broadcasting clock information.

[0056] V5: If the trigger condition is met, it determines whether this node is a single-neighbor node and broadcasts different amounts of clock information according to the node type.

[0057] V6-V7: If this node has a single neighbor, it directly broadcasts its local clock information and logical clock information to the neighbor. If it has multiple neighbor nodes, it combines the received neighbor clock information with its own local clock and logical clock information and broadcasts it to the next neighbor. This node records the broadcast parameters.

[0058] V8-V10: After receiving a data packet, a node uses the iterative least squares method to estimate the relative frequency offset using the clock parameters in the packet. It then uses the average consistency algorithm to update the logical frequency offset compensation and logical phase offset compensation. The above steps are repeated periodically until the logical clocks of all nodes in the network are globally consistent.

[0059] V11~V12: Determine whether the logical clocks of all nodes in the wireless sensor network meet the global consistency termination conditions, that is, whether the logical frequency offset error, logical phase offset error, and logical clock error are maintained within a small range. If all three conditions are met at the same time, it is considered that the global conditions are met and the clock synchronization process ends. Otherwise, the synchronization process such as updating the relative frequency offset estimation and logical clock parameter compensation continues until the global synchronization termination conditions are met.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for averaging consistent time synchronization based on multi-hop virtual links and event triggering, characterized in that: In view of the existence of communication delay in wireless networks, the least squares estimator is used to suppress the influence of delay in the relative frequency offset estimation process. The clock information of each node is fully mobilized through multi-hop virtual links for update. The event triggering strategy is used to reduce the transmission frequency between nodes. The consistency algorithm is used to update the logical clock parameters of the nodes to achieve global consistency of the clocks of nodes in wireless sensor networks. The method specifically comprises the following steps: S1: Set the network update cycle and initialize the logical frequency offset compensation value, logical phase offset compensation value and relative frequency offset estimation value of each node in the network; S2: Under the premise of meeting the update cycle conditions, evaluate whether the current update value meets the trigger conditions. If it meets the conditions, broadcast the clock information to the neighboring nodes and record the broadcast parameters. If the sending node is a single-neighbor node, the node directly broadcasts its local clock information and logical clock information to the neighboring nodes; if it is a non-single-neighbor node, the node broadcasts the received neighbor node clock information and its own local clock and logical clock information together to the next neighbor node; S3: After receiving the data packet sent by the neighboring node, the node calls the clock parameters therein to estimate the relative frequency deviation value using the iterative least squares method, and uses the average consistency algorithm to update the logical frequency deviation compensation value and the logical phase deviation compensation value. Steps S2 to S3 are repeated periodically until the logical clocks of all nodes in the network are globally consistent.

2. The average consistency time synchronization method according to claim 1, characterized in that: Step S1 specifically includes: setting the network update period T, for any node i in the network, setting the update number to m=1, initializing the relative frequency offset estimation value, logical frequency offset compensation value and logical phase offset compensation value of node i to be respectively set up is the absolute time of the mth update of node i, at which the local clock reading of node i is 3. The average consistency time synchronization method according to claim 2, characterized in that: Step S2 specifically includes: in order to evaluate whether the updated clock information needs to be broadcast to neighboring nodes, when m=1 or m>2 and the local clock value of node i meets the update period condition When the current updated logic frequency offset compensation value is Logic phase offset compensation value The logical frequency deviation compensation value of the most recent broadcast Logic phase offset compensation value Substitute into the trigger equation for judgment: Among them, η s and η o is the trade-off parameter in the trigger equation; If the conditions of the above trigger equation are met, node i will and Updated to and And record more The new logical clock parameters are then used to determine the network topology of the sending node. If the sending node is a single-neighbor node, the node directly broadcasts its local clock information and logical clock information to neighbor node j. If it is not a single-neighbor node, the node broadcasts the received neighbor node clock information together with its own local clock and logical clock information to the next neighbor node j.

4. The average consistency time synchronization method according to claim 3, characterized in that: Step S3 specifically includes: any neighbor node j of node i in the network, at absolute time After receiving the data packet from node i, the local clock at the receiving time is immediately recorded as The local clock recording the time when node i sends the data packet is The received data packet sequence is recorded as l. At this time, node j estimates the relative frequency deviation value using the least square method based on the obtained clock information, and brings the estimated value into the consistency algorithm to update the logical frequency deviation compensation value and the logical phase deviation compensation value, and then calculates the logical clock value, which specifically includes the following steps: S31: (1) According to the relationship between the communication delay and the relative clock of the nodes, the communication delay is considered as an error function: in, is the local clock reading of node j, is the local clock reading of node i, s ij represents the relative frequency deviation between nodes, o ij Represents the relative phase deviation between nodes; (2) Apply the least squares principle to process the error function and obtain the cost function including relative frequency deviation and relative phase deviation: Where n represents the number of packets received by node j from node i; the cost function includes the clock information of the receiving node and the sending node, and the relative frequency deviation estimation and relative phase deviation estimation are the values ​​obtained by minimizing the cost function; (3) The relative frequency deviation estimate and the relative phase deviation estimate are expressed in an iterative form: in, and Respectively represent the gain matrix and covariance matrix of the nth round, Indicates the estimated value of the clock parameter in the nth round, setting the initial value ∑(1)=(Φ T (1) Φ(1)) -1 , S32: Substitute the relative clock value calculated in step S31 and other logical clock parameters in the data packet into the consistency algorithm to update the logical clock value.

5. The average consistency time synchronization method according to claim 4, characterized in that: Step S32 specifically includes: substituting the calculated relative clock value and other logical clock parameters in the data packet into the consistency algorithm to update the logical clock value: Among them, node j is the neighbor node of node i, node k is the multi-hop virtual link neighbor node of node j that node i passes through, ρ s , ρ′ s , ρ o , ρ′ o ∈(0,1) is the adjustment parameter, and Respectively represent the updated logic frequency offset compensation value and logic phase offset compensation value, and is the most recently updated logical frequency offset compensation value and logical phase offset compensation value of node i, s ij represents the relative frequency offset estimate between node i and node j, s ik represents the relative frequency offset estimate of node i and node k, and They are all the logical frequency deviation values ​​of the most recent broadcast. and Indicates the logical clock value of the most recent broadcast, N i represents all one-hop neighbor nodes of node i, N′ i Represents all multi-hop virtual neighbor nodes of node i.

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