WO2021056761A1 - 一种面向平均一致性时钟同步的频率偏移估计方法 - Google Patents

一种面向平均一致性时钟同步的频率偏移估计方法 Download PDF

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WO2021056761A1
WO2021056761A1 PCT/CN2019/118864 CN2019118864W WO2021056761A1 WO 2021056761 A1 WO2021056761 A1 WO 2021056761A1 CN 2019118864 W CN2019118864 W CN 2019118864W WO 2021056761 A1 WO2021056761 A1 WO 2021056761A1
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boundary
frequency offset
vertices
node
clock
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王恒
陈柳清
龚鹏飞
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重庆邮电大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J3/00—Time-division multiplex systems
    • H04J3/02—Details
    • H04J3/06—Synchronising arrangements
    • H04J3/0635—Clock or time synchronisation in a network
    • H04J3/0638—Clock or time synchronisation among nodes; Internode synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W56/00—Synchronisation arrangements
    • H04W56/004—Synchronisation arrangements compensating for timing error of reception due to propagation delay
    • H04W56/005—Synchronisation arrangements compensating for timing error of reception due to propagation delay compensating for timing error by adjustment in the receiver
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W56/00—Synchronisation arrangements
    • H04W56/001—Synchronization between nodes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0024—Carrier regulation at the receiver end
    • H04L2027/0026—Correction of carrier offset
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0044—Control loops for carrier regulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • the invention belongs to the technical field of wireless sensor network communication, and relates to a frequency offset estimation method in average consistency clock synchronization based on maximum likelihood estimation.
  • Clock synchronization is a basic supporting technology for wireless sensor networks. Many applications and services such as routing, sleep scheduling, and data fusion work on the basis of keeping the clocks of nodes in the network synchronized. In recent years, a large amount of research has focused on solving the clock synchronization problem in wireless sensor networks, among which the more typical protocols are RBS, TPSN, FTSP, and PBS. These clock synchronization protocols are generally divided into two categories: reference node-based clock synchronization protocols and distributed clock synchronization protocols. Compared with the reference clock synchronization protocol, distributed synchronization does not require any reference nodes, and has significant advantages in robustness and scalability. Among them, the consistency-based clock synchronization not only has the advantages of distributed synchronization algorithms, but also can achieve high-precision synchronization of the entire network.
  • the communication process of wireless sensor network is inevitably accompanied by the appearance of delay.
  • the components of communication delay can be divided into fixed delay and random delay. Random delay can be modeled as Gaussian distribution, exponential distribution, gamma distribution, etc.
  • the early consensus synchronization protocol assumes that the information between nodes can arrive instantaneously, ignoring the effect of time delay.
  • accurate synchronization effects may not be achieved, or even out of synchronization.
  • the estimation accuracy of the relative frequency offset directly affects the performance of consistent clock synchronization. Therefore, consistent synchronization mechanisms such as RoATS, LSTS, and NMTS improve the relative frequency offset estimation method to cope with the influence of delay on the synchronization effect.
  • these synchronization methods consider bounded communication delays, they are not optimized for the distribution characteristics of delays.
  • the current clock synchronization mechanism in wireless sensor networks mainly has the following problems: First, the existing consistent clock synchronization mechanism under delay only considers the bounded delay, and does not consider the fixed and random parts of the delay separately, resulting in relative frequency. The offset estimation is not accurate enough, which limits the synchronization performance; secondly, the consistent clock synchronization is not optimized for a specific random delay distribution type, and the exponential random delay conforms to the point-to-point assumed reference link cumulative link delay, truncating the exponential delay The consistent synchronization of the following is of practical significance.
  • the purpose of the present invention is to provide an average consistency-oriented clock synchronization frequency offset estimation method. Aiming at the problem that the consistent clock synchronization mechanism cannot effectively converge when the communication delay exists, the fixed delay and the truncation index are randomly selected. Time delay, taking into account the distributed characteristics of the wireless sensor network, and combining the consistency method to update the logical clock parameters of the node, so that the network can achieve accurate clock synchronization.
  • the present invention provides the following technical solutions:
  • An average consistency-oriented clock synchronization frequency offset estimation method includes: adopting a maximum likelihood estimation method to estimate the relative frequency offset between nodes, and a clock synchronization method based on average consistency to achieve clock synchronization between nodes, so that The logical clocks of nodes in the network reach a common global clock, including the following specific steps:
  • ⁇ ij and Respectively represent the relative frequency offset and relative phase offset of node i with respect to node j Represents the random communication delay that satisfies the mean value ⁇ and the upper bound is D truncated exponential distribution; Indicates that there is a fixed delay in the transmission of data packets;
  • the nodes in the network periodically broadcast clock synchronization messages, and the local clock of the broadcast node is an integer multiple of the broadcast period T, so the solution under the maximum likelihood estimation of the relative frequency deviation ⁇ ij is converted to
  • the linear optimization problem is:
  • the relative frequency offset estimation problem under the maximum likelihood estimation method is simplified to a linear objective function with linear constraints.
  • the feasible region of the objective function is two clusters of constraint lines formed by the truncated boundary of the time delay. Below and In the upper public area, the optimal value is located on the vertex of the feasible region boundary; by comparing the intersection of the constraint lines, the iterative method is used to store only the vertex information on the boundary to reduce storage overhead.
  • the specific steps include:
  • the present invention Compared with the existing consistent clock synchronization mechanism under the bounded delay, the present invention fully considers the distribution characteristics of the communication delay between nodes in the wireless sensor network, and not only considers the fixed delay, but also considers the random exponential distribution. Time delay, and the maximum likelihood estimation method is applied to the frequency offset estimation process, so that the estimated relative frequency offset is more accurate, thereby effectively improving the consistent clock synchronization performance.
  • the present invention Compared with the common clock synchronization protocol under exponential delay, the present invention considers the bounded characteristics of the delay, and according to the boundary constraint of the delay, in the estimation process of the frequency offset, for the truncated exponential random delay, Make full use of the characteristics of distributed nodes that periodically broadcast clock synchronization messages, transform the solution of maximum likelihood estimation into a simpler linear objective function optimization problem, and design an iterative comparison method, the node does not need to store all the received clock information , The estimated value of the frequency offset can be obtained, which reduces the storage overhead of the node.
  • the clock interaction mode of the present invention is based on one-way broadcast, and does not need to specify any reference nodes. It is completely distributed. Each node in the network runs the same clock synchronization algorithm. There is no need to design for individual nodes separately, which has a good Robustness and scalability.
  • Figure 1 is a diagram of the communication topology of a fully distributed network
  • Figure 2 is a schematic diagram of a synchronous clock information exchange mechanism between nodes
  • Fig. 3 is a schematic diagram of linear programming of the frequency offset estimation method according to the present invention.
  • Fig. 4 is a flowchart of the frequency offset estimation method according to the present invention.
  • Figure 1 is a diagram of the communication topology of the distributed network used in the present invention.
  • nodes are randomly distributed in the network, and each node not only broadcasts its own local clock message, but also receives Information of other nodes within its communication range.
  • (i, j) ⁇ E means that node j can successfully receive information from node i.
  • the synchronization clock information exchange mechanism between nodes is shown in Figure 2. Taking two nodes as an example, node i broadcasts local clock information in period T The node's neighbor node j receives the clock message, and records the current local clock of the neighbor node itself Due to the fixed delay in the transmission of data packets And random delay Therefore, neighboring nodes establish a relative clock relationship based on the known local clock information and time delay.
  • ⁇ ij and Respectively represent the relative frequency offset and relative phase offset of node i with respect to node j Represents the communication delay that satisfies the truncation exponential distribution.
  • neighbor node j After neighbor node j receives the synchronization message, according to the relative clock relationship,
  • the maximum likelihood estimation is to find the parameters to maximize the formula (3) under the condition of satisfying the constraints, which is to make maximum.
  • the maximum likelihood method estimates the relative frequency offset ⁇ ij between nodes as:
  • the node periodically broadcasts clock synchronization messages, so the local clock of the broadcast node is an integer multiple of the broadcast period T, that is Therefore, the solution under the maximum likelihood estimation of the relative frequency offset ⁇ ij can be transformed into an optimization problem:
  • the relative frequency offset estimation problem under the maximum likelihood method is a linear objective function maximum value problem with linear constraints
  • the feasible region of the objective function is two clusters of constraint lines Below and The public area above. It can be seen from the above that as the number of synchronization information packets increases, the number of constraint lines also increases, and neighbor nodes need to store more and more information.
  • not every constraint line is useful for constructing feasible regions. Therefore, it is necessary to construct an effective algorithm to simplify estimation and solving and reduce storage overhead. Because this is a linear objective function with linear constraints, the optimal value must be located at the vertex of the boundary of the feasible region. Therefore, by comparing the intersections of the constraint lines, the iterative method is used to store only the vertex information on the boundary, which reduces storage overhead.
  • the specific steps include:
  • Step1 First discuss the upper boundary B1 of the feasible region and its vertices.
  • L constraint lines The upper boundary of the feasible region of the siege has P vertices.
  • node j receives the L+1th synchronization packet from i
  • the new constraint line constructs a new boundary B1, and the boundary vertex is If Time, Is not established, the new constraint line and the first boundary B1 And the first The lines of the vertices intersect, and the coordinates of the intersection point Satisfy:
  • the number of vertices on the new boundary B1 is Of which Replaced the front of the old boundary B1 Vertices.
  • Step 2 Discuss the lower boundary B2 and its vertices of the feasible region. Similar to Step1, when node j receives the L+1th synchronization packet from i, a new constraint line is generated The new constraint line is compared with the Q vertices of the old lower boundary B2, and the new lower boundary vertices are obtained.
  • Step 3 The boundary of the feasible region is formed by the common area between the boundaries B1 and B2. Therefore, combining the relative position relationship of B1 and B2, compare the vertices on B1 and B2 to obtain the usable boundary vertices.
  • the estimated relative frequency offset will be used in the subsequent logic clock compensation.
  • Fig. 4 is a flowchart of the frequency offset estimation method for average consistent clock synchronization according to the present invention.
  • This embodiment provides a method for estimating relative frequency offset based on maximum likelihood estimation for average consistency synchronization, as shown in the figure, specifically including the following steps:
  • V1 The synchronization process begins.
  • V2 ⁇ V4 Initialize the message broadcast cycle, the node judges whether the broadcast condition is met, if so, it broadcasts the clock synchronization message, otherwise it waits until the condition is met.
  • V5 ⁇ V6 The neighboring node receives and records its own local clock, and analyzes the relative clock relationship between the nodes.
  • Neighbor nodes perform maximum likelihood estimation of relative frequency deviation according to the new clock relationship, update the likelihood function, that is, update the objective function and constraint conditions, and compare with the existing boundary position information to update the feasible region .
  • V11 Compare the vertex values of the feasible region to obtain the relative frequency deviation under the maximum likelihood estimation.
  • V12 Use average consistency synchronization method for clock parameter compensation.
  • V13 ⁇ V14 Determine whether the synchronization end condition is met. If the synchronization has been reached, it ends. Otherwise, continue to monitor the clock information, update the estimation and compensation, etc., until the synchronization end condition is met.

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Abstract

本发明涉及一种面向平均一致性时钟同步的频率偏移估计方法，属于无线传感器网络技术领域。该方法结合分布式单向广播特性，将最大似然估计的求解转换为线性最优化问题，并采用迭代法获得相对频率偏移估计值。通过将估计值用于节点间逻辑时钟参数补偿中，能够达到网络节点逻辑时钟保持一致的效果。本发明充分考虑了通信时延的分布特点，能够实现精确的相对频率偏移估计，从而有效提高平均一致性时钟同步的同步精度，并且采用迭代法进行最大似然估计求解，简化了估计算法、降低了存储开销。

Description

一种面向平均一致性时钟同步的频率偏移估计方法 技术领域
本发明属于无线传感器网络通信技术领域，涉及基于最大似然估计的一种平均一致性时钟同步中的频率偏移估计方法。
背景技术
时钟同步是无线传感器网络的一项基本支撑技术，许多应用和服务比如路由、休眠调度、数据融合等都工作在网络中节点的时钟保持同步的基础上。近年来，大量的研究聚焦于解决无线传感网中的时钟同步问题，其中比较典型的有RBS、TPSN、FTSP、PBS协议等。这些时钟同步协议普遍分为两类：基于参考节点的时钟同步协议和分布式时钟同步协议。与参考时钟同步协议相比，分布式同步无需任何参考节点，在鲁棒性、可扩展性等方面具有显著优势。其中，基于一致性的时钟同步不仅具有分布式同步算法的优势，而且能达到全网高精度同步。
无线传感网的通信过程中不可避免地伴随着时延的出现，通信时延的组成成分可以被分为固定时延和随机时延，其中随机时延在不同的场景下可以被建模为高斯分布、指数分布、伽马分布等。然而，早期的一致性同步协议假设节点间的信息能瞬时到达，忽略了时延的影响，当考虑通信时延时，可能达不到精确的同步效果，甚至不同步。而相对频率偏移的估计精度直接影响一致性时钟同步的性能。因此，RoATS、LSTS、NMTS等一致性同步机制改进了相对频偏估计方法来应对时延对同步效果的影响。这些同步方法虽然考虑了有界通信时延，但是没有针对时延的分布特点进行优化。
目前无线传感器网络中的时钟同步机制主要存在如下问题：首先，现有的时延下的一致性时钟同步机制只考虑有界时延，没有分别考虑时延的固定部分和随机部分，导致相对频率偏移估计不够准确，限制了同步性能；其次，一致性时钟同步没有针对特定的随机时延分布类型进行优化，而指数随机时延符合点对点假定参考链接时的累计链路延迟，截断指数时延下的一致性同步具有现实意义。
因此，亟需一种能够使网络达到精确的时钟同步的频率偏移估计方法。
发明内容
有鉴于此，本发明的目的在于提供一种面向平均一致性的时钟同步频率偏移估计方法，针对通信时延存在时一致性时钟同步机制无法有效收敛的问题，围绕固定时延和截断指数随机时延，并考虑无线传感网的分布式特征，结合一致性方法来更新节点的逻辑时钟参数，使 得网络达到精确的时钟同步效果。
为达到上述目的，本发明提供如下技术方案：
一种面向平均一致性的时钟同步频率偏移估计方法，包括：采用最大似然估计方法估计节点间的相对频率偏移，并基于平均一致性的时钟同步方法来实现节点间的时钟同步，使得网络中节点的逻辑时钟达到一个共同的全局时钟，包括如下具体步骤：
S1：假设网络中的每个节点i都周期性地广播本地时钟消息
Figure PCTCN2019118864-appb-000001
其邻居节点j接收时钟消息，并且记录下邻居节点自身的当前本地时钟
Figure PCTCN2019118864-appb-000002
由于数据包传输过程中存在固定时延
Figure PCTCN2019118864-appb-000003
和随机时延
Figure PCTCN2019118864-appb-000004
的影响，于是邻居节点根据已知的本地时钟信息和时延情况建立相对时钟关系：
Figure PCTCN2019118864-appb-000005
其中，ω ij和
Figure PCTCN2019118864-appb-000006
分别表示节点i相对于节点j的相对频率偏移和相对相位偏移，
Figure PCTCN2019118864-appb-000007
表示满足均值为λ、上界为D截断指数分布的随机通信时延；
Figure PCTCN2019118864-appb-000008
表示数据包传输过程中存在固定时延；
S2：邻居节点j每个周期收到同步消息后，都根据相对时钟关系，进行相对频偏估计；在节点j收到L个来自节点i的同步消息时，采用最大似然法估计节点间的相对频率偏移ω ij为：
Figure PCTCN2019118864-appb-000009
Figure PCTCN2019118864-appb-000010
其中，
Figure PCTCN2019118864-appb-000011
进一步，所述步骤S2中，网络中的节点周期性地广播时钟同步消息，广播节点的本地时钟为广播周期T的整数倍，于是相对频率频偏ω ij的最大似然估计下的求解转换为线性最优化问题为：
Figure PCTCN2019118864-appb-000012
Figure PCTCN2019118864-appb-000013
进一步，最大似然估计法下的相对频率偏移的估计问题求解简化为一个带线性约束条件的线性目标函数，目标函数的可行域为根据时延的截断边界所形成的两簇约束线
Figure PCTCN2019118864-appb-000014
下方及
Figure PCTCN2019118864-appb-000015
上方的公共区域，最优值位于可行域边界的顶点上；通过比较约束线的交点，采用迭代法只存储边界上的顶点信息，减低存储开销，具体步骤包括：
S21:计算可行域的上边界B1及其顶点；假设L条约束线
Figure PCTCN2019118864-appb-000016
围城的可行域上边界有P个顶点，当节点j收到来自i的第L+1个同步数据包，产生新的约束线
Figure PCTCN2019118864-appb-000017
新的约束线与旧边界B1上的P个顶点进行比较，得出新的上边界顶点；
S22：计算可行域的下边界B2及其顶点，与S21类似，当节点j收到来自i的第L+1个同步数据包，产生新的约束线
Figure PCTCN2019118864-appb-000018
新的约束线与旧的下边界B2的Q个顶点进行比较，得出新的下边界顶点；
S23：上下边界顶点进行比较，得到可用的边界顶点，以及与之对应的新的B1、B2，再将边界顶点的值带入目标函数z，使的目标函数z最大的情况下的点对应的ω ij即为迭代最大似然估计下的相对频偏值。
进一步，所述步骤S21中，得出新的上边界顶点具体包括：首先，检验当θ ij＝θ ij_ min时，
Figure PCTCN2019118864-appb-000019
是否成立，其中θ ij_min表示θ ij的先验最小值；如果不成立，则新的约束线被忽略；如果成立，则继续检验p＝2,…P，
Figure PCTCN2019118864-appb-000020
时，
Figure PCTCN2019118864-appb-000021
是否成立，其中
Figure PCTCN2019118864-appb-000022
和
Figure PCTCN2019118864-appb-000023
分别表示上边界B1的第p个顶点的横纵坐标值；如果全部成立，则新的约束线构建新的边界B1，并且边界顶点为
Figure PCTCN2019118864-appb-000024
Figure PCTCN2019118864-appb-000025
如果当
Figure PCTCN2019118864-appb-000026
时，
Figure PCTCN2019118864-appb-000027
不成立，则新的约束线与旧边界B1的第
Figure PCTCN2019118864-appb-000028
和第
Figure PCTCN2019118864-appb-000029
个顶点的连线相交，交点的坐标
Figure PCTCN2019118864-appb-000030
满足：
Figure PCTCN2019118864-appb-000031
新的边界B1顶点数为
Figure PCTCN2019118864-appb-000032
个，其中
Figure PCTCN2019118864-appb-000033
替代旧边界B1的前
Figure PCTCN2019118864-appb-000034
个顶点。
本发明的有益效果在于：
1)本发明与现有的有界时延下的一致性时钟同步机制相比，充分考虑无线传感器网络中节点间通信时延的分布特性，不仅考虑了固定时延，而且考虑了指数分布随机时延，并且将最大似然估计法应用于频率偏移的估计过程中，使得估计出的相对频率偏移更加准确，从而有效提高一致性时钟同步性能。
2)本发明与普通的指数时延下的时钟同步协议相比，考虑了时延的有界特性，针对截断指数随机时延，根据时延的边界约束，在频率偏移的估计过程中，充分利用分布式节点周期性广播时钟同步消息的特点，将最大似然估计的求解转化为更为简单的线性目标函数最优化问题，并且设计了迭代比较方法，节点无需存储接收到的全部时钟信息，便可得到频率偏移的估计值，降低了节点的存储开销。
3)本发明的时钟交互模式是基于单向广播，不需要指定任何参考节点，是完全分布式，网络中的每个节点都运行相同的时钟同步算法，无需针对个别节点进行单独设计，具有良好的鲁棒性和可扩展性。
本发明的其他优点、目标和特征在某种程度上将在随后的说明书中进行阐述，并且在某种程度上，基于对下文的考察研究对本领域技术人员而言将是显而易见的，或者可以从本发明的实践中得到教导。本发明的目标和其他优点可以通过下面的说明书来实现和获得。
附图说明
为了使本发明的目的、技术方案和优点更加清楚，下面将结合附图对本发明作优选的详细描述，其中：
图1为完全分布式网络的通信拓扑结构图；
图2为节点间的同步时钟信息交互机制示意图；
图3为本发明所述的频率偏移估计方法的线性规划示意图；
图4为本发明所述的频率偏移估计方法流程图。
具体实施方式
以下通过特定的具体实例说明本发明的实施方式，本领域技术人员可由本说明书所揭露的内容轻易地了解本发明的其他优点与功效。本发明还可以通过另外不同的具体实施方式加以实施或应用，本说明书中的各项细节也可以基于不同观点与应用，在没有背离本发明的精神下进行各种修饰或改变。需要说明的是，以下实施例中所提供的图示仅以示意方式说明本发明的基本构想，在不冲突的情况下，以下实施例及实施例中的特征可以相互组合。
请参阅图1～图4，图1为本发明采用的分布式网络的通信拓扑结构图，如图1所示，节点随机分布在网络中，每个节点既广播自己的本地时钟消息，又接收其通信范围内其他节点的信息。无线传感网的通信交互拓扑可以建模为一个强连通图G＝(N,E)，其中N＝{1,2,…,n}表示网络中节点的集合，E表示可靠的通信链路的集合，比如(i,j)∈E表示节点j能成功收到来自节点i的信息。节点i的邻居节点被表示为N i＝{j∈N:(i,j)∈E}。
节点间的同步时钟信息交互机制如图2所示，以两个节点为例，节点i以周期T广播本地时钟信息
Figure PCTCN2019118864-appb-000035
节点其邻居节点j接收时钟消息，并且记录下邻居节点自身的当前本地时钟
Figure PCTCN2019118864-appb-000036
由于数据包传输过程中存在固定时延
Figure PCTCN2019118864-appb-000037
和随机时延
Figure PCTCN2019118864-appb-000038
的影响，于是邻居节点根据已知的本地时钟信息和时延情况建立相对时钟关系，
Figure PCTCN2019118864-appb-000039
其中ω ij和
Figure PCTCN2019118864-appb-000040
分别表示节点i相对于节点j的相对频率偏移和相对相位偏移，
Figure PCTCN2019118864-appb-000041
表示满足截断指数分布的通信时延。
邻居节点j收到同步消息后，根据相对时钟关系得，
Figure PCTCN2019118864-appb-000042
在节点j收到L个来自节点i的同步消息时，由于随机时延是相互独立的截断指数分布变量，随机时延
Figure PCTCN2019118864-appb-000043
的联合概率密度函数为：
Figure PCTCN2019118864-appb-000044
将(1)带入(2)可得关于已知本地时钟和待估计的参数的似然函数为：
Figure PCTCN2019118864-appb-000045
其中
Figure PCTCN2019118864-appb-000046
最大似然估计就是在满足约束条件的情况下找到参数使得式(3)最大，也就是使得
Figure PCTCN2019118864-appb-000047
最大。最大似然法估计下节点间的相对频偏ω ij为：
Figure PCTCN2019118864-appb-000048
节点周期性广播时钟同步消息，于是广播节点的本地时钟为广播周期T的整数倍，即
Figure PCTCN2019118864-appb-000049
于是相对频偏ω ij的最大似然估计下的求解可以转换为最优化问题：
Figure PCTCN2019118864-appb-000050
最大似然法下的相对频率偏移的估计问题为一个带线性约束条件的线性目标函数最大值 问题，目标函数的可行域为两簇约束线
Figure PCTCN2019118864-appb-000051
下方及
Figure PCTCN2019118864-appb-000052
上方的公共区域。由上可知，随着同步信息包的数量增多，约束线的条数也增加，邻居节点需要存储的信息越来越多。然而，如图3所示，并不是每条约束线都对构建可行域有用，因此需要构建一个有效的算法来简化估计求解、降低存储开销。又由于这是一个带线性约束条件的线性目标函数，最优值必然位于可行域边界的顶点上。于是通过比较约束线的交点，采用迭代法只存储边界上的顶点信息，减低存储开销。具体步骤包括：
Step1：首先讨论可行域的上边界B1及其顶点。假设L条约束线
Figure PCTCN2019118864-appb-000053
围城的可行域上边界有P个顶点，当节点j收到来自i的第L+1个同步包，产生新的约束线
Figure PCTCN2019118864-appb-000054
首先，检验当θ ij＝θ ij_min时，
Figure PCTCN2019118864-appb-000055
是否成立。如果不成立，则这条约束线可以被忽略。因为可行域位于所有约束线
Figure PCTCN2019118864-appb-000056
的下方，而且新的约束线的斜率的绝对值越来越小。如果成立，则继续检验p＝2,…P，
Figure PCTCN2019118864-appb-000057
时，
Figure PCTCN2019118864-appb-000058
是否成立。如果全部成立，则新的约束线构建了新的边界B1，并且边界顶点为
Figure PCTCN2019118864-appb-000059
如果当
Figure PCTCN2019118864-appb-000060
时，
Figure PCTCN2019118864-appb-000061
不成立，则新的约束线与旧边界B1的第
Figure PCTCN2019118864-appb-000062
和第
Figure PCTCN2019118864-appb-000063
个顶点的连线相交，交点的坐标
Figure PCTCN2019118864-appb-000064
满足：
Figure PCTCN2019118864-appb-000065
新的边界B1顶点数为
Figure PCTCN2019118864-appb-000066
个，其中
Figure PCTCN2019118864-appb-000067
替代了旧边界B1的前
Figure PCTCN2019118864-appb-000068
个顶点。
Step 2：讨论可行域的下边界B2及其顶点，与Step1类似，当节点j收到来自i的第L+1个同步包，产生新的约束线
Figure PCTCN2019118864-appb-000069
新的约束线与旧的下边界B2的Q个顶点进行比较，得出新的下边界顶点。
Step 3：可行域的边界由边界B1和B2间的公共区域构成，因此结合B1和B2的相对位置关系来，将B1和B2上的顶点进行比较，得到可用的边界顶点。
在分析新的约束线对可行域造成的所有影响并得到新的可行域的边界顶点后，将新边界的顶点坐标值带入目标函数z＝θ ij+(L+1)Tω ij/2中，使得z最大的顶点对应的ω ij为迭代最大似然估计下的相对频偏值。估计出的相对频偏将用于后续的逻辑时钟补偿中。
实施例
图4为本发明所述的面向平均一致性时钟同步的频率偏移估计方法流程图。本实施例提供了使用于平均一致性同步的基于最大似然估计的相对频偏估计方法，如图所示，具体包括以下步骤：
V1：同步过程开始。
V2～V4：初始化消息广播周期，节点判断是否满足广播条件，若是则广播时钟同步消息，否则等待直到满足条件。
V5～V6：邻居节点接收并记录自己的本地时钟，分析节点间的相对时钟关系。
V7～V10：邻居节点根据新的时钟关系，进行相对频偏的最大似然估计，更新似然函数，也就是更新目标函数和约束条件，并与已有的边界位置信息进行比较，更新可行域。
V11：比较可行域顶点值，得到最大似然估计下的相对频偏。
V12：使用平均一致性同步方法进行时钟参数补偿。
V13～V14：判断是否满足同步结束条件，若已达到同步则结束，否则继续监听时钟信息，更新估计和补偿等操作，直到满足同步结束条件。
最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。

Claims (4)

  1. 一种面向平均一致性时钟同步的频率偏移估计方法，其特征在于，该方法具体包括以下步骤：
    S1：假设网络中的每个节点i都周期性地广播本地时钟消息
    Figure PCTCN2019118864-appb-100001
    其邻居节点j接收时钟消息，并且记录下邻居节点自身的当前本地时钟
    Figure PCTCN2019118864-appb-100002
    于是邻居节点根据已知的本地时钟信息和时延情况建立相对时钟关系：
    Figure PCTCN2019118864-appb-100003
    其中，ω ij和
    Figure PCTCN2019118864-appb-100004
    分别表示节点i相对于节点j的相对频率偏移和相对相位偏移，
    Figure PCTCN2019118864-appb-100005
    表示满足均值为λ、上界为D截断指数分布的随机通信时延；
    Figure PCTCN2019118864-appb-100006
    表示数据包传输过程中存在固定时延；
    S2：邻居节点j每个周期收到同步消息后，都根据相对时钟关系，进行相对频偏估计；在节点j收到L个来自节点i的同步消息时，采用最大似然法估计节点间的相对频率偏移ω ij为：
    Figure PCTCN2019118864-appb-100007
    Figure PCTCN2019118864-appb-100008
    其中，
    Figure PCTCN2019118864-appb-100009
  2. 根据权利要求1所述的一种面向平均一致性时钟同步的频率偏移估计方法，其特征在于，所述步骤S2中，网络中的节点周期性地广播时钟同步消息，广播节点的本地时钟为广播周期T的整数倍，于是相对频率频偏ω ij的最大似然估计下的求解转换为线性最优化问题为：
    Figure PCTCN2019118864-appb-100010
    Figure PCTCN2019118864-appb-100011
  3. 根据权利要求2所述的一种面向平均一致性时钟同步的频率偏移估计方法，其特征在于，最大似然估计法下的相对频率偏移的估计问题求解简化为一个带线性约束条件的线性目 标函数，目标函数的可行域为根据时延的截断边界所形成的两簇约束线
    Figure PCTCN2019118864-appb-100012
    下方及
    Figure PCTCN2019118864-appb-100013
    上方的公共区域，最优值位于可行域边界的顶点上；通过比较约束线的交点，采用迭代法只存储边界上的顶点信息，减低存储开销，具体步骤包括：
    S21:计算可行域的上边界B1及其顶点；假设L条约束线
    Figure PCTCN2019118864-appb-100014
    围城的可行域上边界有P个顶点，当节点j收到来自i的第L+1个同步数据包，产生新的约束线
    Figure PCTCN2019118864-appb-100015
    新的约束线与旧边界B1上的P个顶点进行比较，得出新的上边界顶点；
    S22：计算可行域的下边界B2及其顶点，与S21类似，当节点j收到来自i的第L+1个同步数据包，产生新的约束线
    Figure PCTCN2019118864-appb-100016
    新的约束线与旧的下边界B2的Q个顶点进行比较，得出新的下边界顶点；
    S23：上下边界顶点进行比较，得到可用的边界顶点，以及与之对应的新的B1、B2，再将边界顶点的值带入目标函数z，使得目标函数z最大的情况下的点对应的ω ij即为迭代最大似然估计下的相对频偏值。
  4. 根据权利要求3所述的一种面向平均一致性时钟同步的频率偏移估计方法，其特征在于，所述步骤S21中，得出新的上边界顶点具体包括：首先，检验当θ ij＝θ ij_min时，
    Figure PCTCN2019118864-appb-100017
    是否成立，其中θ ij_min表示θ ij的先验最小值；如果不成立，则新的约束线被忽略；如果成立，则继续检验p＝2,…P，
    Figure PCTCN2019118864-appb-100018
    时，
    Figure PCTCN2019118864-appb-100019
    是否成立，其中
    Figure PCTCN2019118864-appb-100020
    和
    Figure PCTCN2019118864-appb-100021
    分别表示上边界B1的第p个顶点的横纵坐标值；如果全部成立，则新的约束线构建新的边界B1，并且边界顶点为
    Figure PCTCN2019118864-appb-100022
    Figure PCTCN2019118864-appb-100023
    如果当
    Figure PCTCN2019118864-appb-100024
    时，
    Figure PCTCN2019118864-appb-100025
    不成立，则新的约束线与旧边界B1的第
    Figure PCTCN2019118864-appb-100026
    和第
    Figure PCTCN2019118864-appb-100027
    个顶点的连线相交，交点的坐标
    Figure PCTCN2019118864-appb-100028
    满足：
    Figure PCTCN2019118864-appb-100029
    新的边界B1顶点数为
    Figure PCTCN2019118864-appb-100030
    个，其中
    Figure PCTCN2019118864-appb-100031
    替代旧边界B1的前
    Figure PCTCN2019118864-appb-100032
    个顶点。
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