WO2022267496A1 - 基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法 - Google Patents

基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法 Download PDF

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WO2022267496A1
WO2022267496A1 PCT/CN2022/076843 CN2022076843W WO2022267496A1 WO 2022267496 A1 WO2022267496 A1 WO 2022267496A1 CN 2022076843 W CN2022076843 W CN 2022076843W WO 2022267496 A1 WO2022267496 A1 WO 2022267496A1
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clock
time
node
synchronization
observation
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王恒
彭政岑
鲁锐
郭曦
王平
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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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/29—Graphical models, e.g. Bayesian networks
    • G06F18/295—Markov models or related models, e.g. semi-Markov models; Markov random fields; Networks embedding Markov models
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/0248—Filters characterised by a particular frequency response or filtering method
    • H03H17/0255—Filters based on statistics
    • H03H17/0257—KALMAN filters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W56/00—Synchronisation arrangements
    • H04W56/001—Synchronization between nodes
    • H04W56/0015—Synchronization between nodes one node acting as a reference for the others
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks
    • 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 networks, and relates to a time stamp-free synchronization clock parameter tracking method based on extended Kalman filtering.
  • wireless sensor networks Due to its advantages of low power consumption, easy deployment and low price, wireless sensor networks are widely used, such as object tracking, data fusion and deterministic scheduling. These applications require the nodes in the network to run on a common time base, so time synchronization technology is an important supporting technology for wireless sensor networks.
  • Timestamp-free synchronization is a low-power synchronization mechanism that can achieve synchronization between nodes without interactive timestamps. Because time information is not transmitted during the synchronization process, and the synchronization function is easy to embed into the network data stream, this type of synchronization mechanism has received extensive attention. Most of the current timestamp-free synchronization methods are designed based on the assumption that the clock skew parameters remain unchanged. However, due to factors such as the external environment and the life of the crystal oscillator itself, the clock skew of wireless sensor nodes will show nonlinear time-varying. Although there are schemes that can track the clock skew parameters of time-stamp-free synchronization, they fail to estimate the instantaneous clock skew parameters, which restricts the application of time-stamp-free synchronization in practical wireless sensor networks.
  • the object of the present invention is to provide a time-stamp-free synchronization clock parameter tracking method based on extended Kalman filtering, using a first-order Gaussian Markov model and a clock model to model time-varying clock offsets and skews , using an extended Kalman filter-based tracking method for joint tracking of time-stamp-free synchronized clock instantaneous offset and clock skew.
  • the entire tracking process follows the network data flow, without the need for a dedicated synchronization frame to transmit timestamp information.
  • the node to be synchronized can achieve long-term synchronization with the reference clock node according to the recorded timestamp and known response time, saving communication bandwidth and energy, and improving synchronization accuracy.
  • the present invention provides the following technical solutions:
  • a time-stamp-free synchronization clock parameter tracking method based on extended Kalman filtering comprising the following steps:
  • time-varying parameter model is a first-order Gaussian Markov model and a clock model
  • S2 Establish an observation equation, use the extended Kalman filter-based tracking method to jointly track clock skew and clock instantaneous offset, and realize the synchronization between the node to be synchronized and the reference clock node.
  • the observation equation is composed of time-stamp-free synchronization and Observational Model Formation of Clock Instantaneous Offsets.
  • step S1 regards the dynamically changing clock skew as a random variable, and uses a first-order Gaussian Markov model to describe its characteristics, and the specific formula is as follows:
  • ⁇ [n] represents the clock skew of the node to be synchronized relative to the reference clock node at the nth sampling moment
  • m represents a coefficient smaller than and close to 1, which is assumed to be known
  • u[n] represents the mean value is 0, and the variance is Gaussian driving noise
  • the clock model is used to describe the instantaneous clock offset, and the specific formula is as follows:
  • ⁇ [n] represents the clock offset of the node to be synchronized relative to the reference clock node at the nth sampling moment
  • step S2 the steps for establishing the observation equation described in step S2 are as follows:
  • ⁇ i (1+ ⁇ i )[(T 4,i -T 1.i )-2 ⁇ -( ⁇ i + ⁇ i )]
  • ⁇ i is the response time of the reference clock node
  • T 1,i and T 4,i respectively represent the time for the node to be synchronized to send and receive data packets
  • ⁇ is the fixed delay of message transmission between two nodes
  • ⁇ i and ⁇ i is the random time delay of the uplink and downlink during message transmission, which is modeled as an independent Gaussian distribution with mean value 0 and variance ⁇ 2 and ⁇ 2 respectively;
  • S′[n] is the observed value at the nth sampling moment
  • ⁇ [n] represents the clock skew at the nth sampling moment
  • w′[n] represents the observation noise at the nth sampling moment
  • ⁇ ′[n ] ⁇ i +1 - ⁇ i ;
  • the observed value in the observation equation has a nonlinear relationship with the state value of the clock skew between nodes, so the extended Kalman filter method is used instead of the general Kalman filter method to track the clock parameters, and the tracking based on the extended Kalman filter is used Before the method, the observation equation is linearized, and the specific steps are as follows:
  • the node to be synchronized records the time stamp of time-stamp-free interaction, and calculates the observed value according to the time stamp, combined with the predicted value of the clock skew and skew state model, adopts the tracking method based on the extended Kalman filter to track the instantaneous clock skew and clock skew Oblique joint tracking, the extended Kalman filter method formula is:
  • A is the update coefficient matrix
  • n-1] represents the minimum predicted mean square error matrix at the nth sampling moment
  • K[n] represents the Kalman gain matrix at the nth sampling moment
  • H[n] represents the Jacobian matrix at the nth sampling moment
  • R[n] represents the observation value matrix of the nth sampling moment
  • n] represents the minimum mean square error matrix after correction at the nth sampling moment.
  • the joint tracking method of clock skew and clock instantaneous offset based on the extended Kalman filter method for sensor nodes without timestamp interaction specifically includes the following steps:
  • D3 Time stamp-free interaction between the node to be synchronized and the reference clock node, and record the time when it sends and receives data packets;
  • the node to be synchronized calculates the observation value R[n] and observation matrix H[n] according to the timestamp information and the known response time, and predicts time n from the value of clock skew and offset at time n-1 according to the state equation The always parameter state vector of Finally, the minimum forecast mean square error is calculated;
  • D10 Increase the number of synchronization rounds by 1 and enter process D3;
  • D11 The tracking process of clock instantaneous skew and dynamic clock skew ends.
  • the nodes to be synchronized track the clock parameters by recording the time stamps of sending and receiving data packets.
  • the synchronization function can be embedded in the existing network traffic, avoiding The waste of communication bandwidth also reduces energy consumption.
  • the present invention considers that the clock offset and skew cannot be tracked at the same time in the time stamp-free synchronization scenario, and the node crystal oscillator cannot run at a stable frequency, resulting in dynamic changes in the clock offset and skew.
  • the Mann filter tracking method realizes the joint tracking of the instantaneous offset and clock skew of the time-stamp-free synchronization clock, improves the synchronization accuracy between nodes, and reduces the frequency of re-synchronization.
  • FIG. 1 is a schematic diagram of time-stamp-free synchronization between a node to be synchronized and a reference clock node in the present invention
  • Fig. 2 is the flow chart of the time stamp-free synchronous clock parameter tracking method based on extended Kalman filtering according to the present invention
  • FIG. 3 is an effect diagram of the instantaneous offset tracking of the time-stamp-free synchronous clock based on the extended Kalman filter according to the present invention
  • FIG. 4 is an effect diagram of the skew tracking of the time-stamp-free synchronous clock based on the extended Kalman filter according to the present invention
  • FIG. 5 is a performance comparison diagram of the instant offset tracking method for time-stamp-free synchronous clocks based on extended Kalman filtering according to the present invention
  • FIG. 6 is a performance comparison diagram of the time-stamp-free synchronization clock skew tracking method based on the extended Kalman filter according to the present invention.
  • Figures 1 to 6 are schematic diagrams of time-stamp-free synchronization provided by Figure 1 in the present invention, wherein node R is a reference clock node that provides reference time, and node A is a node to be synchronized, interacting with node R through time-stamp-free interaction Synchronization, the specific steps are as follows:
  • the node A to be synchronized sends a data packet without timestamp information to the reference clock node R, and records the time as
  • the recording time is T 2,i
  • the implementation model of T 2,i can be expressed as:
  • T 2,i T 1,i + ⁇ i + ⁇ + ⁇ i + ⁇ i (T 1,i -T 1,1 + ⁇ + ⁇ i ) (1)
  • ⁇ i and ⁇ i represent the clock offset and skew between node A and node R respectively
  • ⁇ is the fixed delay in the data packet transmission process
  • ⁇ i is the random delay in the data packet transmission process
  • the reference clock node R waits for a fixed response time ⁇ i after receiving the data packet, and returns the data packet at T 3,i time , which also does not contain a timestamp.
  • Node A receives the data packet at T 4,i time, and T 3 , the implementation model of i can be expressed as:
  • T 3,i T 4,i + ⁇ i - ⁇ - ⁇ i + ⁇ i (T 4,i -T 1,1 - ⁇ - ⁇ i ) (2)
  • S′[n] is the observed value at the nth sampling moment
  • ⁇ [n] represents the clock skew at the nth sampling moment
  • W[n] represents the observation noise of the mean value at the nth sampling moment
  • ⁇ ′[n ] ⁇ i +1 ⁇ ⁇ i .
  • the observed value of clock instantaneous offset is composed of its real value plus noise, and the offset in the state equation is the real value, then the observation model of clock instantaneous offset can be written as: in is the observed value of the offset, ⁇ [n] represents the Gaussian observation noise, the mean is 0, and the variance is Combining the discrete observation model without time stamp synchronization and the clock instantaneous offset observation model, the observation equation is obtained as:
  • the extended Kalman filter method is used instead of the general Kalman filter method to track the clock parameters.
  • the observation equation needs to be linearized, and the specific steps are as follows:
  • the present invention regards clock skew as a random variable, and uses a first-order Gaussian Markov model to model the variable.
  • the specific model is as follows:
  • ⁇ [n] represents the clock skew of the node A to be synchronized relative to the reference clock node R at the nth sampling moment; m represents a coefficient smaller than and close to 1, which is considered known; u[n] represents the mean value of 0, Variance is Gaussian driving noise.
  • the clock model is used to describe the instantaneous clock offset.
  • the specific model is as follows:
  • ⁇ [n] represents the clock offset of the node A to be synchronized relative to the reference clock node R at the nth sampling moment
  • the present invention uses the tracking method based on extended Kalman filter to jointly track two parameters of clock skew and offset, and the specific formula is as follows:
  • the posterior Cramero bound (posterior Cramer– Rao Bound, PCRB):
  • FIG. 2 is a flow chart of a method for tracking parameters of time-varying clocks synchronously without time stamps provided by an embodiment of the present invention.
  • This embodiment provides a joint tracking method of clock skew and clock instantaneous offset based on the extended Kalman filter method for sensor nodes performing timestamp-free interaction, as shown in FIG. 2 , specifically including the following steps:
  • D3 Time stamp-free interaction between the node to be synchronized and the reference clock node, and record the time when it sends and receives data packets;
  • the node to be synchronized calculates the observation value R[n] and observation matrix H[n] according to the timestamp information and the known response time, and predicts time n from the value of clock skew and offset at time n-1 according to the state equation The always parameter state vector of Finally, the minimum forecast mean square error is calculated;
  • D10 Increase the number of synchronization rounds by 1 and enter process D3;
  • D11 The tracking process of clock instantaneous skew and dynamic clock skew ends.
  • FIGS. 5 to 6 show the effect and performance comparison of the time stamp-free synchronous clock parameter tracking based on the extended Kalman filter provided by the present invention. From Figures 3 to 4, it can be seen that the tracking method based on extended Kalman filter can effectively track the real value of time-varying clock skew and offset in the time stamp-free synchronization scenario, which proves the effectiveness of the clock parameter tracking method provided by the present invention. reliability. It can be seen from FIGS. 5 to 6 that the performance of the method for tracking instantaneous clock offset and clock skew provided by the present invention can reach PCRB.

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Abstract

本发明涉及一种基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，属于无线传感器网络技术领域。以一阶高斯马尔可夫模型和时钟模型作为状态方程，描述时钟偏斜和时钟瞬时偏移的演化过程。再建立由免时间戳同步和时钟瞬时偏移的观测模型构成的观测方程，利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和时钟瞬时偏移，实现待同步节点与参考时钟节点之间的同步。该方法跟随网络数据流就能够完成两个时变参数的同时跟踪，无需专用同步帧交互同步信息，减少了能量消耗，提高了同步精度。

Description

基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法 技术领域
本发明属于无线传感器网络技术领域，涉及一种基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法。
背景技术
无线传感器网络由于其具有功耗低、易部署和价格低廉等优点被广泛应用，例如，目标跟踪、数据融合和确定性调度等。这些应用要求网络中的节点运行在共同的时间基准上，因此时间同步技术是无线传感器网络的重要支撑技术。
免时间戳同步是一类无需交互时间戳，就能够实现节点间同步的低功耗同步机制。由于在同步过程中不传递时间信息，且易于将同步功能嵌入到网络数据流中，该类同步机制受到了广泛关注。当前大部分免时间戳同步方法基于时钟偏斜参数保持不变这一假设进行设计，但由于受外界环境和晶振自身寿命等因素的影响，无线传感器节点的时钟偏斜会呈现非线性时变，虽然有方案能够跟踪免时间戳同步的时钟偏斜参数，但未能实现对时钟瞬时偏移参数的估计，制约了免时间戳同步在实际无线传感器网络中的应用。
发明内容
有鉴于此，本发明的目的在于提供一种基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，采用一阶高斯马尔可夫模型和时钟模型来建模时变的时钟偏移和偏斜，利用基于扩展卡尔曼滤波的跟踪方法，实现对免时间戳同步时钟瞬时偏移和时钟偏斜的联合跟踪。整个跟踪过程跟随网络数据流，无需专用的同步帧传递时间戳信息，待同步节点根据记录的时间戳及已知的响应时间就能实现与参考时钟节点的长期同步，节约通信带宽和能量，提高同步精度。
为达到上述目的，本发明提供如下技术方案：
一种基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，包括以下步骤：
S1：以时变的参数模型作为状态方程，描述时钟偏斜和时钟瞬时偏移的演化过程，所述时变的参数模型为一阶高斯马尔可夫模型和时钟模型；
S2：建立观测方程，利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和时钟瞬时偏移，实现待同步节点与参考时钟节点之间的同步，所述观测方程由免时间戳同步和时钟瞬时偏移的观测模型构成。
进一步，步骤S1中所述的状态方程，将动态变化的时钟偏斜视为一个随机变量，采用一阶高斯马尔可夫模型来描述其特性，具体公式如下：
ρ[n]＝mρ[n-1]+u[n]
其中ρ[n]表示第n个采样时刻待同步节点相对于参考时钟节点的时钟偏斜；m表示小于且接近于1的系数，假设为已知；u[n]表示均值为0，方差为
Figure PCTCN2022076843-appb-000001
的高斯驱动噪声；
利用时钟模型来描述时钟瞬时偏移，具体公式如下：
θ[n]＝θ[n-1]+ρ[n]τ[n]
其中θ[n]表示第n个采样时刻待同步节点相对于参考时钟节点的时钟偏移；τ[n]表示第n个样本的采样间隔，假设为一个固定值，即τ[n]＝τ 0；
将时钟瞬时偏移和时钟偏斜的公式联立构成矩阵形式，得到状态方程如下：
x[n]＝Ax[n-1]+u[n]
其中
Figure PCTCN2022076843-appb-000002
和
Figure PCTCN2022076843-appb-000003
进一步，步骤S2中所述观测方程的建立步骤如下：
S21：在第i个同步轮次中，待同步节点与参考时钟节点之间进行免时间戳交互，则有同步通式为：
Δ i＝(1+ρ i)[(T 4,i-T 1.i)-2δ-(ν i+ω i)]
其中Δ i是参考时钟节点的响应时间，T 1,i和T 4,i分别表示待同步节点发送和接收数据包的时间，δ是两个节点间消息传输的固定时延，ν i和ω i为消息传输过程中上下行链路的随机时延，被建模为独立的均值为0，方差分别为ε 2，σ 2的高斯分布；
S22：重复步骤S21，用第i+1轮次通式减去第i轮次通式，并假设连续两个轮次内时钟偏斜不变，即ρ i+1＝ρ i，其中i为奇数，得到免时间戳同步的观测模型为：
Figure PCTCN2022076843-appb-000004
其中
Figure PCTCN2022076843-appb-000005
且i为奇数，S i＝T 4,i-T 1,i，w i＝ν i+ω i；
S23：经过采样，待同步节点免时间戳同步的离散观测模型为：
Figure PCTCN2022076843-appb-000006
其中S′[n]是第n个采样时刻的观测值，ρ[n]表示第n个采样时刻的时钟偏斜，w′[n]表示第n个采样时刻的观测噪声，Δ′[n]＝Δ i+1-Δ i；
S24：时钟瞬时偏移的观测值是由其真实值加噪声组成，而状态方程中的时钟瞬时偏移是真实值，则时钟瞬时偏移的观测模型写为：
Figure PCTCN2022076843-appb-000007
其中
Figure PCTCN2022076843-appb-000008
是时钟瞬时偏移的观测值，υ[n]表示高斯观测噪声，均值为0，方差为
Figure PCTCN2022076843-appb-000009
将免时间戳同步的离散观测模型和时钟瞬时偏移观测模型结合，得到观测方程如下：
R[n]＝h(x[n])+W[n]
其中
Figure PCTCN2022076843-appb-000010
S25：观测方程中观测值与节点间时钟偏斜的状态值呈现非线性关系，因此采用扩展卡尔曼滤波方法而不是一般的卡尔曼滤波方法来跟踪时钟参数，在使用基于扩展卡尔曼滤波的跟踪方法之前将观测方程线性化，具体步骤如下：
S251：
Figure PCTCN2022076843-appb-000011
进行一阶泰勒级数展开：
Figure PCTCN2022076843-appb-000012
S252：h(x[n])分别对θ[n]，ρ[n]求导，求解雅可比矩阵为：
Figure PCTCN2022076843-appb-000013
S253：重写观测方程为：
Figure PCTCN2022076843-appb-000014
进一步，不是S2中所述利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和时钟瞬时偏移，具体包括：
待同步节点记录免时间戳交互的时间戳，并且根据时间戳计算观测值，结合时钟偏斜和 偏移状态模型的预测值，采用基于扩展卡尔曼滤波的跟踪方法对时钟瞬时偏移和时钟偏斜进行联合跟踪，所述扩展卡尔曼滤波方法公式为：
预测：
Figure PCTCN2022076843-appb-000015
最小预测均方误差：M[n|n-1]＝AM[n-1|n-1]A Τ+C s
卡尔曼增益：
Figure PCTCN2022076843-appb-000016
修正：
Figure PCTCN2022076843-appb-000017
最小均方误差：M[n|n]＝(I-K[n]H[n])M[n|n-1]
其中
Figure PCTCN2022076843-appb-000018
表示第n个采样时刻的时钟瞬时偏移和时钟偏斜的预测值矩阵，A是更新系数矩阵，M[n|n-1]表示第n个采样时刻的最小预测均方误差矩阵，
Figure PCTCN2022076843-appb-000019
表示驱动噪声的协方差矩阵，K[n]表示第n个采样时刻的卡尔曼增益矩阵，H[n]表示第n个采样时刻的雅可比矩阵，
Figure PCTCN2022076843-appb-000020
是观测噪声的协方差矩阵，
Figure PCTCN2022076843-appb-000021
表示第n个采样时刻修正后的时钟瞬时偏移和时钟偏斜的修正值矩阵，R[n]表示第n个采样时刻的观测值矩阵，
Figure PCTCN2022076843-appb-000022
表示第n个采样时刻时钟瞬时偏移和时钟偏斜状态变量到理想观测的变换矩阵，M[n|n]表示第n个采样时刻修正后的最小均方误差矩阵。
进一步，免时间戳交互的传感器节点基于扩展卡尔曼滤波方法的时钟偏斜和时钟瞬时偏移联合跟踪方法具体包括以下步骤：
D1：时钟参数跟踪过程开始；
D2：扩展卡尔曼滤波器初始化；
D3：待同步节点和参考时钟节点之间进行免时间戳交互，并记录自己收发数据包的时间；
D4：判断同步轮次是否为奇数，若为奇数，进入流程D5，反之进入流程D6；
D5：同步轮次增加1，进入流程D3；
D6：待同步节点根据时间戳信息和已知的响应时间计算观测值R[n]和观测矩阵H[n]，并且根据状态方程由n-1时刻时钟偏斜和偏移的值预测n时刻的始终参数状态矢量
Figure PCTCN2022076843-appb-000023
最后计算最小预测均方误差；
D7：根据观测矩阵H[n]计算卡尔曼增益；
D8：根据卡尔曼增益和观测值R[n]计算n时刻的时钟瞬时偏移和时钟偏斜的修正值和最小均方误差；
D9：判断同步轮次是否达到预测值，若没有达到，进入流程D10，反之，进入流程D11；
D10：同步轮次增加1，进入流程D3；
D11：时钟瞬时偏移和动态时钟偏斜的跟踪过程结束。
本发明的有益效果在于：
1)本发明的时钟参数跟踪过程中无需专用的同步帧交互时间戳信息，待同步节点通过记录收发数据包的时间戳来跟踪时钟参数，同步功能可以嵌入到现有的网络流量中，避免了通信带宽的浪费，也减少了能量消耗。
2)本发明考虑免时间戳同步场景下时钟偏移和偏斜不能同时跟踪，并且节点晶体振荡器的不能以稳定的频率运行，导致时钟偏移和偏斜动态变化的情况，采用基于扩展卡尔曼滤波的跟踪方法，实现对免时间戳同步时钟瞬时偏移和时钟偏斜的联合跟踪，提高了节点间的同步精度，降低了再同步的频率。
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为本发明待同步节点和参考时钟节点的免时间戳同步示意图；
图2为本发明所述的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法流程图；
图3为本发明所述的基于扩展卡尔曼滤波的免时间戳同步时钟瞬时偏移跟踪效果图；
图4为本发明所述的基于扩展卡尔曼滤波的免时间戳同步时钟偏斜跟踪效果图；
图5为本发明所述的基于扩展卡尔曼滤波的免时间戳同步时钟瞬时偏移跟踪方法性能对比图；
图6为本发明所述的基于扩展卡尔曼滤波的免时间戳同步时钟偏斜跟踪方法性能对比图。
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。
其中，附图仅用于示例性说明，表示的仅是示意图，而非实物图，不能理解为对本发明的限制；为了更好地说明本发明的实施例，附图某些部件会有省略、放大或缩小，并不代表实际产品的尺寸；对本领域技术人员来说，附图中某些公知结构及其说明可能省略是可以理解的。
本发明实施例的附图中相同或相似的标号对应相同或相似的部件；在本发明的描述中，需要理解的是，若有术语“上”、“下”、“左”、“右”、“前”、“后”等指示的方位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，因此附图中描述位置关系的用语仅用于示例性说明，不能理解为对本发明的限制，对于本领域的普通技术人员而言，可以根据具体情况理解上述术语的具体含义。
请参阅图1～图6，为图1为本发明所提供的免时间戳同步示意图，其中节点R是参考时钟节点，提供参考时间，节点A是待同步节点，通过免时间戳交互与节点R同步，具体步骤如下：
在第i个同步轮次中，待同步节点A发送不含时间戳信息的数据包给参考时钟节点R，并记录时间为
Figure PCTCN2022076843-appb-000024
参考时钟节点R接收到数据包时记录时间为T 2,i，T 2,i的实施模型可表示为：
T 2,i＝T 1,i+θ i+δ+ω i+ρ i(T 1,i-T 1,1+δ+ν i)   (1)
其中θ i和ρ i分别表示节点A与节点R之间的时钟偏移和偏斜，δ是数据包传输过程的固定时延，ν i是数据包传输过程中的随机时延，被建模为独立的均值为0，方差为ε 2的高斯分布。
参考时钟节点R接收到数据包后等待一段固定的响应时间Δ i，在T 3,i时刻返回数据包，同样也不包含时间戳，节点A在T 4,i时刻接收到数据包，T 3,i的实施模型可表示为：
T 3,i＝T 4,i+θ i-δ-ω i+ρ i(T 4,i-T 1,1-δ-ω i)   (2)
其中δ和ω i分别是数据包传输过程中的固定时延和随机时延，随机时延被建模为独立的均值为0，方差为σ 2的高斯分布。(2)式减(1)式得到通式为：
Δ i＝(1+ρ i)[(T 4,i-T 1.i)-2δ-(ν i+ω i)]   (3)
用第i+1轮次通式减去第i轮次通式，假设连续两个轮次内时钟偏斜不变，即ρ i+1＝ρ i，其中i为奇数。得到免时间戳同步的观测模型为：
Figure PCTCN2022076843-appb-000025
其中
Figure PCTCN2022076843-appb-000026
且i为奇数，S i＝T 4,i-T 1,i，w i＝ν i+ω i。
经过采样，待同步节点A免时间戳同步的离散观测方程为：
Figure PCTCN2022076843-appb-000027
其中S′[n]是第n个采样时刻的观测值，ρ[n]表示第n个采样时刻的时钟偏斜，W[n]表示均值第n个采样时刻的观测噪声，Δ′[n]＝Δ i+1-Δ i。
时钟瞬时偏移的观测值是由其真实值加噪声组成，而状态方程中的偏移是真实值，则时钟瞬时偏移的观测模型可以写为：
Figure PCTCN2022076843-appb-000028
其中
Figure PCTCN2022076843-appb-000029
是偏移的观测值，υ[n]表示高斯观测噪声，均值为0，方差为
Figure PCTCN2022076843-appb-000030
将免时间戳同步的离散观测模型和时钟瞬时偏移观测模型结合，得到观测方程为：
R[n]＝h(x[n])+W[n]   (6)
其中
Figure PCTCN2022076843-appb-000031
观测方程中观测值与节点间时钟偏斜的状态值呈现非线性关系，因此采用扩展卡尔曼滤波方法而不是一般的卡尔曼滤波方法来跟踪时钟参数，在使用基于扩展卡尔曼滤波的跟踪方法之前需将观测方程线性化，具体步骤如下：
(1)
Figure PCTCN2022076843-appb-000032
进行一阶泰勒级数展开：
Figure PCTCN2022076843-appb-000033
(2)h(x[n])分别对θ[n]，ρ[n]求导，求解雅可比矩阵为：
Figure PCTCN2022076843-appb-000034
(3)重写观测方程如下：
Figure PCTCN2022076843-appb-000035
由于晶体振荡器的非线性和相位噪声的影响，另外，还有外界环境(温度、湿度、压强等)，时钟偏斜会随时间随机变化。为准确反映时钟偏斜的变化，本发明将时钟偏斜视为一个随机变量，采用一阶高斯马尔可夫模型来建模该变量，具体的模型如下：
ρ[n]＝mρ[n-1]+u[n]   (10)
其中ρ[n]表示第n个采样时刻待同步节点A相对于参考时钟节点R的时钟偏斜；m表示小于且接近于1的系数，视为已知；u[n]表示均值为0，方差为
Figure PCTCN2022076843-appb-000036
的高斯驱动噪声。
采用时钟模型来描述时钟瞬时偏移，具体模型如下：
θ[n]＝θ[n-1]+ρ[n]τ[n]   (11)
其中θ[n]表示第n个采样时刻待同步节点A相对于参考时钟节点R的时钟偏移；τ[n]表示第n个样本的采样间隔，假设为一个固定值，即τ[n]＝τ 0。
将时钟偏斜和偏移的模型联立构成矩阵形式，得到状态方程如下：
x[n]＝Ax[n-1]+u[n]   (12)
其中
Figure PCTCN2022076843-appb-000037
和
Figure PCTCN2022076843-appb-000038
基于状态方程(12)和观测方程(9)，本发明利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和偏移两个参数，具体公式如下：
预测：
Figure PCTCN2022076843-appb-000039
最小预测均方误差：M[n|n-1]＝AM[n-1|n-1]A Τ+C s          (14)
卡尔曼增益：
Figure PCTCN2022076843-appb-000040
修正：
Figure PCTCN2022076843-appb-000041
最小均方误差：M[n|n]＝(I-K[n]H[n])M[n|n-1]        (17)
为了验证本发明提供的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法的有效性，根据状态方程和观测方程算出时钟偏斜和时钟瞬时偏移的后验克拉美罗界限(posterior Cramer–Rao Bound，PCRB)：
Figure PCTCN2022076843-appb-000042
Figure PCTCN2022076843-appb-000043
其中，
Figure PCTCN2022076843-appb-000044
实施例：
图2为本发明实施例提供的免时间戳同步时变时钟参数跟踪方法流程图。本实施例提供了进行免时间戳交互的传感器节点基于扩展卡尔曼滤波方法的时钟偏斜和时钟瞬时偏移联合跟踪方法，如图2所示，具体包括以下步骤：
D1：时钟参数跟踪过程开始；
D2：扩展卡尔曼滤波器初始化；
D3：待同步节点和参考时钟节点之间进行免时间戳交互，并记录自己收发数据包的时间；
D4：判断同步轮次是否为奇数，若为奇数，进入流程D5，反之进入流程D6；
D5：同步轮次增加1，进入流程D3；
D6：待同步节点根据时间戳信息和已知的响应时间计算观测值R[n]和观测矩阵H[n]，并且根据状态方程由n-1时刻时钟偏斜和偏移的值预测n时刻的始终参数状态矢量
Figure PCTCN2022076843-appb-000045
最后计算最小预测均方误差；
D7：根据观测矩阵H[n]计算卡尔曼增益；
D8：根据卡尔曼增益和观测值R[n]计算n时刻的时钟瞬时偏移和时钟偏斜的修正值和最小均方误差；
D9：判断同步轮次是否达到预测值，若没有达到，进入流程D10，反之，进入流程D11；
D10：同步轮次增加1，进入流程D3；
D11：时钟瞬时偏移和动态时钟偏斜的跟踪过程结束。
图3～图6给出了本发明提供的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪效果和性能对比图。由图3～图4可知，基于扩展卡尔曼滤波的跟踪方法能有效地跟踪免时间戳同步场景下时变的时钟偏斜和偏移的真实值，证明了本发明提供的时钟参数跟踪方法的可靠性。 由图5～图6可知，本发明提供的时钟瞬时偏移和时钟偏斜的跟踪方法性能可以达到PCRB。
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 (5)

  1. 一种基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，其特征在于：包括以下步骤：
    S1：以时变的参数模型作为状态方程，描述时钟偏斜和时钟瞬时偏移的演化过程，所述时变的参数模型为一阶高斯马尔可夫模型和时钟模型；
    S2：建立观测方程，利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和时钟瞬时偏移，实现待同步节点与参考时钟节点之间的同步，所述观测方程由免时间戳同步和时钟瞬时偏移的观测模型构成。
  2. 根据权利要求1所述的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，其特征在于：步骤S1中所述的状态方程，将动态变化的时钟偏斜视为一个随机变量，采用一阶高斯马尔可夫模型来描述其特性，具体公式如下：
    ρ[n]＝mρ[n-1]+u[n]
    其中ρ[n]表示第n个采样时刻待同步节点相对于参考时钟节点的时钟偏斜；m表示小于且接近于1的系数，假设为已知；u[n]表示均值为0，方差为
    Figure PCTCN2022076843-appb-100001
    的高斯驱动噪声；
    利用时钟模型来描述时钟瞬时偏移，具体公式如下：
    θ[n]＝θ[n-1]+ρ[n]τ[n]
    其中θ[n]表示第n个采样时刻待同步节点相对于参考时钟节点的时钟偏移；τ[n]表示第n个样本的采样间隔，假设为一个固定值，即τ[n]＝τ 0；
    将时钟瞬时偏移和时钟偏斜的公式联立构成矩阵形式，得到状态方程如下：
    x[n]＝Ax[n-1]+u[n]
    其中
    Figure PCTCN2022076843-appb-100002
    和
    Figure PCTCN2022076843-appb-100003
  3. 根据权利要求1所述的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，其特征在于：步骤S2中所述观测方程的建立步骤如下：
    S21：在第i个同步轮次中，待同步节点与参考时钟节点之间进行免时间戳交互，则有同步通式为：
    Δ i＝(1+ρ i)[(T 4,i-T 1.i)-2δ-(ν i+ω i)]
    其中Δ i是参考时钟节点的响应时间，T 1,i和T 4,i分别表示待同步节点发送和接收数据包的时间，δ是两个节点间消息传输的固定时延，ν i和ω i为消息传输过程中上下行链路的随机 时延，被建模为独立的均值为0，方差分别为ε 2，σ 2的高斯分布；
    S22：重复步骤S21，用第i+1轮次通式减去第i轮次通式，并假设连续两个轮次内时钟偏斜不变，即ρ i+1＝ρ i，其中i为奇数，得到免时间戳同步的观测模型为：
    Figure PCTCN2022076843-appb-100004
    其中
    Figure PCTCN2022076843-appb-100005
    且i为奇数，S i＝T 4,i-T 1,i，w i＝ν i+ω i；
    S23：经过采样，待同步节点免时间戳同步的离散观测模型为：
    Figure PCTCN2022076843-appb-100006
    其中S′[n]是第n个采样时刻的观测值，ρ[n]表示第n个采样时刻的时钟偏斜，w′[n]表示第n个采样时刻的观测噪声，Δ′[n]＝Δ i+1-Δ i；
    S24：时钟瞬时偏移的观测模型写为：
    Figure PCTCN2022076843-appb-100007
    其中
    Figure PCTCN2022076843-appb-100008
    是时钟瞬时偏移的观测值，υ[n]表示高斯观测噪声，均值为0，方差为
    Figure PCTCN2022076843-appb-100009
    将免时间戳同步的离散观测模型和时钟瞬时偏移观测模型结合，得到观测方程如下：
    R[n]＝h(x[n])+W[n]
    其中
    Figure PCTCN2022076843-appb-100010
    S25：采用扩展卡尔曼滤波方法来跟踪时钟参数，在使用基于扩展卡尔曼滤波的跟踪方法之前将观测方程线性化，具体步骤如下：
    S251：
    Figure PCTCN2022076843-appb-100011
    进行一阶泰勒级数展开：
    Figure PCTCN2022076843-appb-100012
    S252：h(x[n])分别对θ[n]，ρ[n]求导，求解雅可比矩阵为：
    Figure PCTCN2022076843-appb-100013
    S253：重写观测方程为：
    Figure PCTCN2022076843-appb-100014
  4. 根据权利要求3所述的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法，其特征在于：不是S2中所述利用基于扩展卡尔曼滤波的跟踪方法来联合跟踪时钟偏斜和时钟瞬时偏移，具体包括：
    待同步节点记录免时间戳交互的时间戳，并且根据时间戳计算观测值，结合时钟偏斜和偏移状态模型的预测值，采用基于扩展卡尔曼滤波的跟踪方法对时钟瞬时偏移和时钟偏斜进行联合跟踪，所述扩展卡尔曼滤波方法公式为：
    预测：
    Figure PCTCN2022076843-appb-100015
    最小预测均方误差：M[n|n-1]＝AM[n-1|n-1]A Τ+C s
    卡尔曼增益：
    Figure PCTCN2022076843-appb-100016
    修正：
    Figure PCTCN2022076843-appb-100017
    最小均方误差：M[n|n]＝(I-K[n]H[n])M[n|n-1]
    其中
    Figure PCTCN2022076843-appb-100018
    表示第n个采样时刻的时钟瞬时偏移和时钟偏斜的预测值矩阵，A是更新系数矩阵，M[n|n-1]表示第n个采样时刻的最小预测均方误差矩阵，
    Figure PCTCN2022076843-appb-100019
    表示驱动噪声的协方差矩阵，K[n]表示第n个采样时刻的卡尔曼增益矩阵，H[n]表示第n个采样时刻的雅可比矩阵，
    Figure PCTCN2022076843-appb-100020
    是观测噪声的协方差矩阵，
    Figure PCTCN2022076843-appb-100021
    表示第n个采样时刻修正后的时钟瞬时偏移和时钟偏斜的修正值矩阵，R[n]表示第n个采样时刻的观测值矩阵，
    Figure PCTCN2022076843-appb-100022
    表示第n个采样时刻时钟瞬时偏移和时钟偏斜状态变量到理想观测的变换矩阵，M[n|n]表示第n个采样时刻修正后的最小均方误差矩阵。
  5. 根据权利要求1-4任一所述的基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法， 其特征在于：本方法具体包括以下步骤：
    D1：时钟参数跟踪过程开始；
    D2：扩展卡尔曼滤波器初始化；
    D3：待同步节点和参考时钟节点之间进行免时间戳交互，并记录自己收发数据包的时间；
    D4：判断同步轮次是否为奇数，若为奇数，进入流程D5，反之进入流程D6；
    D5：同步轮次增加1，进入流程D3；
    D6：待同步节点根据时间戳信息和已知的响应时间计算观测值R[n]和观测矩阵H[n]，并且根据状态方程由n-1时刻时钟偏斜和偏移的值预测n时刻的始终参数状态矢量
    Figure PCTCN2022076843-appb-100023
    最后计算最小预测均方误差；
    D7：根据观测矩阵H[n]计算卡尔曼增益；
    D8：根据卡尔曼增益和观测值R[n]计算n时刻的时钟瞬时偏移和时钟偏斜的修正值和最小均方误差；
    D9：判断同步轮次是否达到预测值，若没有达到，进入流程D10，反之，进入流程D11；
    D10：同步轮次增加1，进入流程D3；
    D11：时钟瞬时偏移和动态时钟偏斜的跟踪过程结束。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116125512A (zh) * 2023-04-13 2023-05-16 中国科学院精密测量科学与技术创新研究院 顾及时钟频率时变特性的ppp自适应钟差模型估算方法

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113438045B (zh) * 2021-06-25 2022-03-29 重庆邮电大学 基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法
CN113452466B (zh) * 2021-06-28 2022-06-10 重庆邮电大学 基于加权观测融合和免时间戳交互的时钟频偏跟踪方法
CN114845377B (zh) * 2022-05-05 2024-02-23 中南大学 一种基于uwb的高精度无线时钟同步方法与系统

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20160209236A1 (en) * 2013-11-20 2016-07-21 Continental Teves Ag & Co. Ohg Method, fusion filter, and system for fusing sensor signals with different temporal signal output delays into a fusion data set
CN113438045A (zh) * 2021-06-25 2021-09-24 重庆邮电大学 基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102819830B (zh) * 2012-08-15 2015-04-22 北京交通大学 一种新的基于卡尔曼滤波的点扩散函数估计方法
EP3053288A1 (en) * 2013-10-02 2016-08-10 Khalifa University of Science, Technology and Research Method and devices for time and frequency synchronization
US9579025B1 (en) * 2015-08-14 2017-02-28 The United States Of America, As Represented By The Secretary Of The Navy Timestamp-free synchronization for wireless body area networks
CN108668356A (zh) * 2018-04-19 2018-10-16 厦门大学 一种水下传感器时间同步方法
US20220210607A1 (en) * 2019-04-19 2022-06-30 Be Spoon Ultra-wideband location systems and methods
CN110572232B (zh) * 2019-09-12 2020-11-06 重庆邮电大学 一种基于动态响应的免时间戳同步频率偏移跟踪方法
CN110460553B (zh) * 2019-09-12 2021-08-31 重庆邮电大学 一种免时间戳交互的隐含节点时钟频率偏移估计方法
CN111220946A (zh) * 2020-01-20 2020-06-02 南京烽火星空通信发展有限公司 基于改进扩展卡尔曼滤波的多移动目标定位误差消除方法
CN111556559B (zh) * 2020-05-09 2021-11-26 重庆邮电大学 基于免时间戳交互与单向消息传播的混合时钟同步方法

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20160209236A1 (en) * 2013-11-20 2016-07-21 Continental Teves Ag & Co. Ohg Method, fusion filter, and system for fusing sensor signals with different temporal signal output delays into a fusion data set
CN113438045A (zh) * 2021-06-25 2021-09-24 重庆邮电大学 基于扩展卡尔曼滤波的免时间戳同步时钟参数跟踪方法

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
WANG HENG; LU RUI; PENG ZHENGCEN; LI MIN: "Timestamp-Free Clock Parameters Tracking Using Extended Kalman Filtering in Wireless Sensor Networks", IEEE TRANSACTIONS ON COMMUNICATIONS, vol. 69, no. 10, 6 July 2021 (2021-07-06), PISCATAWAY, NJ. USA, pages 6926 - 6938, XP011883370, ISSN: 0090-6778, DOI: 10.1109/TCOMM.2021.3095155 *
WANG HENG; YU FEI; LI MIN; ZHONG YANG: "Clock Skew Estimation for Timestamp-Free Synchronization in Industrial Wireless Sensor Networks", IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, vol. 17, no. 1, 20 February 2020 (2020-02-20), US , pages 90 - 99, XP011818858, ISSN: 1551-3203, DOI: 10.1109/TII.2020.2975289 *
YU FEI: "Study on Parameter Estimation Methods for Clock Synchronization with Timestamp Free Exchanges in Wireless Sensor Networks", CHINA MASTER'S THESES FULL-TEXT DATABASE, 20 June 2020 (2020-06-20), pages 1 - 67, XP093016017, DOI: 10.27675/d.cnki.gcydx.2020.000234 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116125512A (zh) * 2023-04-13 2023-05-16 中国科学院精密测量科学与技术创新研究院 顾及时钟频率时变特性的ppp自适应钟差模型估算方法

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