A particle filter based time-stamp free synchronization clock parameter tracking method

Abstract

The application relates to a particle filtering-based time-stamp-free synchronization clock parameter tracking method and belongs to the technical field of wireless sensor networks.The method comprises the following steps: S1, establishing a state equation according to a first-order Gauss Markov model and a clock model, and then establishing an observation equation according to an observation model of clock instantaneous offset in combination with time-stamp-free synchronization; and S2, utilizing an adaptive Gauss mixed extended Kalman particle filtering algorithm to jointly track clock frequency deviation and clock phase deviation, so that clock synchronization between a to-be-synchronized node and a clock reference node under arbitrary random time delay is realized.The application considers the diversity of random time delay models, utilizes an improved particle filtering algorithm to jointly track clock synchronization parameters, is robust to arbitrary random time delay, is more in line with actual application scenarios, and does not need to transmit any time stamp in the whole clock synchronization parameter tracking process, so that the energy consumption of nodes is significantly reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless sensor networks, and relates to a timestamp-free synchronization clock parameter tracking method based on particle filtering. BACKGROUND

[0002] Wireless sensor networks are widely applied in the fields of transmission scheduling, data fusion, tracking and positioning, and the like, and all nodes need to maintain a unified time reference, so that the time synchronization technology becomes one of the key technologies in wireless sensor networks. Each node in the wireless sensor network maintains a local clock provided by a crystal oscillator. Due to the changes of temperature, air pressure and the like in the environment, the crystal oscillator will have a certain frequency offset when running, so that the local clocks of each node are different, which needs the time synchronization algorithm to track the changing clock parameters and maintain time synchronization. In actual wireless sensor networks, the distribution of random time delay is often arbitrary and cannot be accurately described by a certain time delay distribution model, so it is particularly important to track the synchronization parameters under arbitrary time delay.

[0003] Timestamp-free synchronization is a mechanism that does not need to interact with timestamps and can realize time synchronization only according to existing data streams in the network. The mechanism does not depend on special synchronization messages and can save a large amount of energy consumption, so it has attracted widespread attention. However, the existing timestamp-free synchronization parameter tracking method assumes that the random time delay obeys a Gaussian distribution, and cannot track the synchronization parameters under arbitrary time delay, which restricts the application of the timestamp-free synchronization parameter tracking method in actual wireless sensor networks. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a timestamp-free synchronization clock parameter tracking method based on particle filtering, which considers the characteristic that the random time delay in actual wireless sensor networks is arbitrarily distributed, and realizes long-term tracking of clock frequency offset and phase offset by using an adaptive Gaussian mixture extended Kalman particle filter. The entire parameter tracking process does not need to transmit timestamps, and can realize long-term tracking of clock frequency offset and phase offset only according to the locally recorded time node information, significantly reduces the node overhead and saves a large amount of energy.

[0005] To achieve the above purpose, the present application provides the following technical scheme:

[0006] A timestamp-free synchronization clock parameter tracking method based on particle filtering comprises the following steps:

[0007] S1: establishing a state equation according to a first-order Gaussian Markov model and a clock model, and then establishing an observation equation according to an observation model of clock instantaneous offset combined with timestamp-free synchronization;

[0008] S2: Using adaptive Gaussian mixture extended Kalman particle filter algorithm, jointly tracking clock frequency offset and clock phase offset, realizing clock synchronization between the to-be-synchronized node and the clock reference node under any random time delay.

[0009] Further, in step S1, the state equation specifically comprises: using a clock model to describe the instantaneous offset of the clock, and a specific formula is as follows:

[0010] θ[k] = θ[k-1] + φ[k]ξ[k]

[0011] Wherein, θ[k] represents the clock phase offset of the to-be-synchronized node relative to the clock reference node at the kth sampling time, φ[k] represents the clock frequency offset of the to-be-synchronized node relative to the clock reference node at the kth sampling time, and ξ[k] represents the sampling interval of the kth sample, which is assumed to be a fixed value, i.e. ξ[k] = ξ0;

[0012] The first-order Gaussian Markov model is used to describe the dynamic clock frequency offset characteristics, and a specific formula is as follows:

[0013] φ[k] = mφ[k-1] + u[k]

[0014] Wherein, m is assumed to be a known coefficient less than and close to 1, and u[k] represents Gaussian driving noise with a mean of 0 and a variance of ;

[0015] The clock frequency offset and phase offset formulas of the to-be-synchronized node S and the clock reference node M are written in matrix form, and the state equation is as follows:

[0016] X[k] = AX[k-1] + U[k]

[0017] Wherein,

[0018] Further, in step S1, the observation equation specifically comprises the following steps:

[0019] S11: The to-be-synchronized node S and the clock reference node M perform timestamp-free interaction, and in the i th synchronization round, the response time Δ i of the clock reference node M is expressed as:

[0020]

[0021] Wherein, and are the sending and receiving times of the data packet of the to-be-synchronized node S, d (SM) represents the fixed time delay of message transmission between the two nodes, and The random delays of uplink and downlink, respectively, are modeled as arbitrary delay distribution models with independent distributions;

[0022] S12: Repeat step S11, subtract the i-th round general formula from the i+1-th round general formula, while assuming The timestamp-free observation model can be obtained as:

[0023]

[0024] wherein, and i is an odd number,

[0025] S13: After sampling, the timestamp-free synchronization discrete observation model of the node S to be synchronized can be obtained as:

[0026]

[0027] wherein, V′ (SM) [k] is the observation value at the k-th sampling time, represents the clock frequency offset between the node S to be synchronized and the clock reference node M at the k-th sampling time, and Δ′[k] = Δ i+1 -Δ i , and δ′[k] represents the observation noise of the frequency offset at the k-th sampling time;

[0028] S14: The observation model of the clock instantaneous offset can be expressed as wherein, is the observation value of the clock instantaneous offset, and v[k] represents the observation noise of the phase offset at the k-th sampling time;

[0029] The timestamp-free discrete observation model and the observation model of the clock instantaneous offset are jointly written in matrix form, and the observation equation can be obtained as:

[0030] Z[k] = h(X[k]) + W[k]

[0031] wherein, W[k] obeys an arbitrary random delay distribution.

[0032] Further, in step S2, the adaptive Gaussian mixture extended Kalman particle filtering algorithm specifically includes the following steps:

[0033] S21: Fit the random delay model with an arbitrary distribution with a Gaussian mixture model, specifically as follows:

[0034] The driving noise is expressed as:

[0035]

[0036] where p(u[k]) represents the probability density function of the driving noise at time k, β b represents the proportion of each Gaussian component, B represents the number of Gaussian components of u[k], and represents that each Gaussian component of u[k] obeys a Gaussian distribution with mean and variance ;

[0037] Similarly, the observation noise can be represented as:

[0038]

[0039]

[0040] where J and G represent the number of Gaussian components of v[k] and δ'[k], respectively; γ j and τ g represent the proportion of each component in the Gaussian mixture model, respectively; represents that each Gaussian component of v[k] obeys a Gaussian distribution with mean and variance ; represents that each Gaussian component of δ'[k] obeys a Gaussian distribution with mean and variance ;

[0041] S22: Predict the mean and mean square deviation of the sample using the extended Kalman filter, and the specific formula is as follows:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] where f(·) is the mapping relationship between X[k] (i) and X[k-1] (i) , represents the update coefficient matrix, C s and C o represent the Jacobian matrices of the driving noise and the observation noise, respectively, represents the Jacobian matrix at the k-th sampling time, and K k represent the mean square deviation and the Kalman gain, respectively, denotes the mean square error of prediction;

[0048] S23: update the i-th particle using the mean and mean square error predicted in step S22, and the specific formula is as follows:

[0049]

[0050] wherein, L denotes the number of Gaussian components in l , and λ (i) denotes the weight of each Gaussian component, and q(X[k (i) |X[0:k-1] (i) , Z[1:k]) represents the posterior distribution of X[k];

[0051] S24: calculate the number of particles for the next round of sampling using the mean square error updated in step S22, and the specific formula is as follows:

[0052]

[0053] wherein, N denotes the number of particles for sampling, M denotes the confidence, and r α / 2 denotes the confidence interval when the confidence is α; in order to avoid too large or too small variance, the upper limit N top and the lower limit N bottom of the number of particles for sampling are set, and when N bottom ≤N≤N top , the number of particles for the next round of sampling is updated, otherwise, the number of particles for sampling is unchanged;

[0054] S25: calculate the mean of the sample point as its output, and the specific formula is as follows:

[0055]

[0056] wherein, denotes the probability distribution to which X[0:k] conforms.

[0057] Further, in step S2, the specific steps for realizing clock synchronization between the to-be-synchronized node and the clock reference node under an arbitrary random delay are as follows:

[0058] D1: start the clock frequency offset and clock phase offset joint tracking process;

[0059] D2: initialize the adaptive Gaussian mixture extended Kalman particle filter;

[0060] D3: the to-be-synchronized node and the clock reference node perform timestamp-free interaction, and the to-be-synchronized node records the transmission and reception times of the data packet;

[0061] D4: in the importance sampling stage, the extended Kalman filter algorithm is used to predict the mean and mean square deviation, the particles are updated according to the predicted mean and mean square deviation, and then the particle weights are normalized;

[0062] D5: in the resampling stage, the polynomial resampling algorithm is used, and the particle set is copied and eliminated according to the size of the normalized weight;

[0063] D6: according to the predicted mean square deviation, the number of sampling particles in the next round is calculated and updated;

[0064] D7: whether the synchronization round reaches the set value is judged, if not, step D8 is entered, otherwise step D9 is entered;

[0065] D8: the synchronization round is added by 1, and step D3 is entered;

[0066] D9: the joint tracking process of the clock frequency offset and the clock phase offset is ended.

[0067] The beneficial effects of the application are:

[0068] 1) In the process of tracking the clock parameters, the application does not need to exchange time stamps, and the synchronization node can realize clock synchronization only according to the locally recorded packet transmission and reception time, which combines the time stamp-free synchronization with the time synchronization method under any time delay, saves the energy consumption required for time synchronization in the wireless sensor network, and is more in line with the complex and variable scene of random time delay in actual application.

[0069] 2) The application considers the characteristics that the random time delay in the actual wireless sensor network presents an arbitrary distribution, adopts the tracking algorithm based on the adaptive Gaussian mixture extended Kalman particle filter, realizes the joint long-term tracking of the clock frequency offset and the clock phase offset under the arbitrary random time delay distribution, has robustness to the random time delay with arbitrary distribution in actual application, improves the synchronization accuracy between nodes, and reduces the frequency of resynchronization.

[0070] Other advantages, objects and features of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or can be learned from practice of the application. The objects and other advantages of the application can be realized and attained by the methods and instrumentalities set forth in the description. BRIEF DESCRIPTION OF DRAWINGS

[0071] In order to make the objects, technical solutions and advantages of the application clearer, the preferred detailed description of the application will be made below in combination with the drawings, in which:

[0072] Figure 1 It is a schematic diagram of time stamp-free interaction between the synchronization node and the clock reference node in the application;

[0073] Figure 2 Flow chart of the method for tracking the parameters of the free-timestamped synchronization clock under any time delay according to the present application;

[0074] Figure 3 Effect diagram of the method for tracking the frequency deviation of the free-timestamped synchronization clock based on particle filtering under exponential random time delay distribution according to the present application;

[0075] Figure 4 Effect diagram of the method for tracking the phase deviation of the free-timestamped synchronization clock based on particle filtering under exponential random time delay distribution according to the present application;

[0076] Figure 5 Effect diagram of the method for tracking the frequency deviation of the free-timestamped synchronization clock based on particle filtering under gamma random time delay distribution according to the present application;

[0077] Figure 6 Effect diagram of the method for tracking the phase deviation of the free-timestamped synchronization clock based on particle filtering under gamma random time delay distribution according to the present application. DETAILED DESCRIPTION

[0078] Other advantages and effects of the present application can be easily understood by those skilled in the art from the above description. The present application can also be implemented or applied in other different specific embodiments, and the details in the present description can be modified or changed in various ways based on different views and applications without departing from the spirit of the present application. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0079] Please refer to Figures 1-6 , Figure 1 The schematic diagram of the free-timestamp interaction between the node to be synchronized and the clock reference node provided by the present application is shown in Figure 1 The clock reference node M and the node to be synchronized S perform free-timestamp interaction, and the specific process is as follows:

[0080] For the ith synchronization period, the node S sends a data frame without any timestamp to the node M, and records the local time as The implementation model can be expressed as:

[0081]

[0082] wherein, and respectively represent the initial clock phase deviation and frequency deviation between the node S and the node M, d (SM) and respectively represent the fixed time delay and the random time delay in the transmission process.

[0083] After receiving the data frame from node S, node M waits for a response time Δ i and sends back a confirmation frame to node S, and node S records the time of receiving the confirmation frame The implementation model can be expressed as:

[0084]

[0085] Assume d (SM) and d (MS) are known and equal, let Then, the general formula can be obtained by subtracting formula (1) from formula (2):

[0086]

[0087] Subtract the general formula of the i+1 round from the general formula of the i round, assuming The timestamp-free observation model is obtained as:

[0088]

[0089] wherein, and i is an odd number,

[0090] After sampling, the timestamp-free synchronization discrete observation model of the to-be-synchronized node S is:

[0091]

[0092] wherein, V′ (SM) [k] is the observation value at the kth sampling time, represents the clock frequency offset between the to-be-synchronized node S and the clock reference node M at the kth sampling time, Δ′[k]=Δ i+1 -Δ i , and δ′[k] represents the observation noise of the frequency offset at the kth sampling time;

[0093] The observation model of the clock instantaneous offset can be expressed as wherein is the observation value of the clock instantaneous offset, and v[k] represents the observation noise of the phase offset at the kth sampling time;

[0094] The timestamp-free discrete observation model and the observation model of the clock instantaneous offset are jointly written in matrix form, and the observation equation is obtained as:

[0095] Z[k]=h(X[k])+W[k] (6)

[0096] wherein, and W[k] obeys an arbitrary random delay distribution.

[0097] The instantaneous offset of the clock is described by using a clock model, and the specific formula is as follows:

[0098] θ[k]=θ[k-1]+φ[k]ξ[k] (7)

[0099] Wherein, θ[k] represents the clock phase offset of the to-be-synchronized node relative to the reference clock node at the kth sampling moment, φ[k] represents the clock frequency offset of the to-be-synchronized node relative to the reference clock node at the kth sampling moment, and ξ[k] represents the sampling interval of the kth sample, which is assumed to be a fixed value, that is, ξ[k]=ξ0;

[0100] In order to accurately reflect the change of the clock frequency offset, the present application regards the clock frequency offset as a random variable, adopts a first-order Gauss Markov model to model the variable, and the specific model is as follows:

[0101] φ[k]=mφ[k-1]+u[k] (8)

[0102] Wherein, m is assumed to be a known coefficient less than and close to 1, and u[k] represents a Gauss driving noise with a mean value of 0 and a variance of

[0103] The clock frequency offset and the clock phase offset formula of the to-be-synchronized node S and the clock reference node M are written in matrix form, and the state equation is as follows:

[0104] X[k]=AX[k-1]+U[k] (9)

[0105] Wherein And

[0106] Based on the observation equation (6) and the state equation (9), the present application adopts a tracking method based on adaptive Gauss mixture extended Kalman particle filtering to jointly track the clock frequency offset and the clock phase offset two parameters, and the specific process includes:

[0107] The random delay model of arbitrary distribution is fitted by using a mixed Gauss model, and the specific formula is as follows:

[0108] The driving noise is represented as:

[0109]

[0110] Wherein, p(u[k]) represents the driving noise probability density function at the kth moment, β b represents the proportion of each Gauss component, B represents the number of Gauss components of u[k], and Each Gauss component of u[k] is subject to a mean value of and a variance of ​Gaussian distribution;

[0111] Similarly, the observation noise can be expressed as:

[0112]

[0113]

[0114] where J and G represent the number of Gaussian components of v[k] and δ'[k], respectively; γ j and τ g represent the proportion of each component in the Gaussian mixture model, respectively. It is shown that each Gaussian component of v[k] obeys a Gaussian distribution with mean and variance It is shown that each Gaussian component of δ'[k] obeys a Gaussian distribution with mean and variance

[0115] The mean and variance of the sample are predicted by the extended Kalman filter algorithm, and the specific formula is as follows:

[0116]

[0117] where f(·) is the mapping relationship between X[k] (i) and X[k-1] (i) , and represents the update coefficient matrix, C s and C o represent the Jacobian matrices of the driving noise and the observation noise, respectively, represents the Jacobian matrix at the k-th sampling time, and K k represent the mean square error and the Kalman gain, respectively, represents the predicted mean square error;

[0118] The mean and variance predicted by the extended Kalman filter are used to update the i-th particle, and the specific formula is as follows:

[0119]

[0120] where

[0121] Further, the number of sampling particles in the next round is calculated by using the mean square error updated by the extended Kalman filter, and the specific formula is as follows:

[0122]

[0123] ​​Where N represents the number of particles sampled, M represents the confidence level, and r α / 2 This represents the confidence interval when the confidence level is α. To avoid excessively large or small variances, an upper limit N is set for the number of sampled particles. top and lower limit N bottom When N bottom ≤N≤N top If the number of particles is updated in the next round of sampling, then the number of particles sampled remains unchanged.

[0124] Finally, the mean of the sample points is calculated as its output, and the specific formula is as follows:

[0125]

[0126] in, Let X[0:k] represent the probability distribution that X[0:k] follows.

[0127] Figure 2 This is a flowchart illustrating a timestamp-free synchronization clock parameter tracking method based on particle filtering, provided in an embodiment of the present invention. This embodiment provides a method for jointly tracking the frequency offset and phase offset of timestamp-free synchronization clocks under arbitrary delays in wireless sensor networks, such as... Figure 2 As shown, the specific steps include:

[0128] D1: The combined tracking process of clock frequency offset and clock phase offset begins;

[0129] D2: Adaptive Gaussian mixture extended Kalman particle filter initialization;

[0130] D3: The node to be synchronized interacts with the clock reference node without timestamps, and the node to be synchronized records the time of sending and receiving data packets.

[0131] D4: In the importance sampling phase, the extended Kalman filter algorithm is used to predict the mean and mean square error. The particles are updated based on the predicted mean and mean square error, and then the particle weights are normalized.

[0132] D5: In the resampling phase, the multinomial resampling algorithm is used to copy and eliminate particles based on the normalized weights.

[0133] D6: Calculate and update the number of sampled particles for the next round based on the predicted mean square error;

[0134] D7: Determine whether the synchronization cycle has reached the set value. If not, proceed to process D8; otherwise, proceed to process D9.

[0135] D8: Increment the synchronization round by 1, proceed to process D3;

[0136] D9: the clock frequency offset and clock phase offset joint tracking process ends.

[0137] Figure 3 And Figure 4 The clock frequency offset tracking effect diagram and the clock phase offset tracking effect diagram based on particle filtering under the exponential random delay distribution provided by the application are respectively shown. Figure 5 And Figure 6 The clock frequency offset tracking effect diagram and the clock phase offset tracking effect diagram based on particle filtering under the gamma random delay distribution provided by the application are respectively shown. Figures 3-6 It can be known that the time-stamp-free synchronization parameter tracking method based on adaptive Gaussian mixture extended Kalman particle filtering can effectively track the real values of the clock frequency offset and the clock phase offset under different random delay distribution models, and the tracking precision is higher than that of the Gaussian mixture particle filtering algorithm of the same kind, which proves the reliability of the clock parameter tracking method provided by the application.

[0138] Finally, it should be explained that the above examples are only used to illustrate the technical solutions of the application and not to limit it, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the application can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should be covered in the scope of the claims of the application.

Claims

1. A particle filter based time-stamp free synchronization clock parameter tracking method, characterized in that, The method comprises the following steps: S1: establishing a state equation according to a first-order Gaussian Markov model and a clock model, and then establishing an observation equation according to an observation model of clock instantaneous offset combined with a time-stamp-free synchronization; S2: using an adaptive Gaussian mixture extended Kalman particle filter algorithm to jointly track clock frequency offset and clock phase offset, and realizing clock synchronization between a to-be-synchronized node and a clock reference node under arbitrary random time delay; The adaptive Gaussian mixture extended Kalman particle filter algorithm specifically comprises the following steps: S21: fitting an arbitrary-distribution random time delay model by using a Gaussian mixture model, and the specific process is as follows: The driving noise is expressed as: wherein, represents k the driving noise probability density function at time represents the proportion of each Gaussian component, represents the number of Gaussian components of ; represents each of the Gaussian components of obeys a Gaussian distribution with mean and variance ; represents a Gaussian driving noise with mean 0 and variance Similarly, the observation noise is expressed as: wherein, and respectively represent and the number of Gaussian components, represents the observation noise of the phase offset at the k th sampling time, represents the observation noise of the frequency offset at the k th sampling time; and respectively represent the proportion of each component in the mixture Gaussian model; represents each Gaussian component is subject to a Gaussian distribution with a mean of and a variance of ; represents each Gaussian component is subject to a Gaussian distribution with a mean of and a variance of ; S22: predicting the mean and mean square deviation of the sample by using an extended Kalman filter, and the specific formula is as follows: in, yes and The mapping relationship between them , and They represent the first k Each sampling time node to be synchronized S Relative to clock reference node Clock phase offset and clock frequency offset, i Indicates the round; This indicates updating the coefficient matrix. and Let these be the Jacobian matrices of the driving noise and the observation noise, respectively. , , It is a fixed value; Indicates the first k Jacobian matrix at each sampling time and These represent the mean square error and the Kalman gain, respectively. This represents the mean squared error of the prediction; , It is the observed value of the instantaneous clock offset. It is the first k Observations at each sampling time; , , Indicates the first i Clock reference node in each synchronization round M Response time; subscript pre Indicates prediction; S23: update the first particle with the mean and mean square deviation predicted in step S22, according to the following formula: i S23: update the first particle with the mean and mean square deviation predicted in step S22, according to the following formula: wherein, , , L denotes the number of Gaussian components in , denotes the weight of each Gaussian component, denotes the posterior distribution of , denotes the 1 ~ k particles sampled; S24: calculating the number of sampling particles in the next round by using the updated mean square deviation in step S22, and the specific formula is as follows: in, Indicates the number of particles sampled. Indicates the confidence level. Indicates a confidence level of The confidence interval at that time; to avoid excessively large or small variance, an upper limit is set for the number of sampled particles. and lower limit ,when If the number of particles is updated in the next round of sampling, then the number of particles sampled remains unchanged. S25: calculating the mean of the sample point as the output thereof, and the specific formula is as follows: wherein , denotes a probability distribution of compliance.

2. The timestamp-free synchronization clock parameter tracking method of claim 1, wherein, In step S1, the establishment of the state equation specifically comprises the following steps: in, Indicates the first k At each sampling time, the clock phase offset of the node to be synchronized relative to the clock reference node is... Indicates the first k The clock frequency offset of the node to be synchronized relative to the clock reference node at each sampling time. Indicates the first k The sampling interval for each sample is assumed to be a fixed value, i.e. ; The clock model is used to describe the instantaneous offset of the clock, and the specific formula is as follows: wherein, Assume a known coefficient less than and close to 1, denotes a Gaussian driving noise with mean 0 and variance . The clock frequency and phase offset formulas of the nodes to be synchronized and the clock reference node are written in matrix form as follows: wherein , , .

3. The timestamp-free synchronization clock parameter tracking method of claim 2, wherein, The first-order Gaussian Markov model is used to describe the dynamic clock frequency offset characteristics, and the specific formula is as follows: S11: Node to be synchronized With clock reference node To perform timestamp-free interaction, the first i In each synchronization round, the clock reference node M Response time The expression is: wherein, and are the nodes to be synchronized the time at which a data packet is sent and received, denotes the fixed delay of the message transmission between the two nodes, and are the random delays of the uplink and downlink, respectively, modeled as independent distributed arbitrary delay distribution models; S12: repeat step S11 with the (i+1)th i +1th round formula minus the i-th i round formula, while assuming , the free-timestamped observation model is obtained as: wherein and is odd, , ; S13: Obtain the node to be synchronized after sampling The timestamp-free synchronization discrete observation model of the node to be synchronized is: wherein, is the observation value at the k th sampling instant, denotes the clock frequency offset between the k th sampling instant between the synchronization node and the clock reference node, , denotes the observation noise of the frequency offset at the k th sampling instant.​ S14: The observation model of clock transient offset is expressed as wherein, is the observation value of clock transient offset, represents the observation noise of phase offset at the k th sampling time. In step S1, the establishment of the observation equation specifically comprises the following steps: wherein , , , subject to any random delay distribution.

4. The timestamp-free synchronization clock parameter tracking method of claim 1, wherein, The discrete observation model of the time-stamp-free model is combined with the observation model of the clock instantaneous offset to obtain the observation equation in the form of a matrix: In step S2, the specific steps of realizing clock synchronization between the to-be-synchronized node and the clock reference node under arbitrary random time delay are as follows: D1: starting the joint tracking process of the clock frequency offset and the clock phase offset; D2: initializing the adaptive Gaussian mixture extended Kalman particle filter; D3: the to-be-synchronized node and the clock reference node perform time-stamp-free interaction, and the to-be-synchronized node records the transmission and reception times of the data packets; D4: in the importance sampling stage, the mean and mean square deviation are predicted by using the extended Kalman filter algorithm, the particles are updated according to the predicted mean and mean square deviation, and then the particle weights are normalized; D5: in the resampling stage, the particle set is copied and eliminated according to the size of the normalized weights by using the polynomial resampling algorithm; D6: calculating and updating the number of sampling particles in the next round according to the predicted mean square deviation; D7: judging whether the synchronization round reaches a set value, if not, entering step D8, otherwise entering step D9; D8: increasing the synchronization round by 1, and entering step D3; D9: ending the joint tracking process of the clock frequency offset and the clock phase offset.

Images