A precise clock synchronization parameter tracking method based on augmented Kalman neural network

Abstract

The present invention relates to a precise clock synchronization parameter tracking method based on an augmented Kalman neural network, and belongs to the field of time synchronization. This method is oriented to multi-hop network scenarios with environmental temperature changes and asymmetric link transmission delays. It considers the impact of the cumulative asymmetric link transmission delay in the multi-hop network on the clock synchronization accuracy, obtains a multi-hop network clock observation equation containing the cumulative asymmetric link delay, and establishes a recursive state equation of clock frequency offset and temperature change based on a quadratic polynomial model of temperature and clock frequency offset; the evolution process of the cumulative asymmetric delay and the unknown temperature coefficient is modeled as a first-order linear difference equation, and augmented to a clock parameter tracking state space model, and the augmented Kalman neural network algorithm is used to realize the joint tracking of the clock phase deviation and clock frequency deviation of the slave node. This method adopts the idea of ​​joint driving of data and model to jointly track the clock phase deviation and frequency deviation, thereby improving the accuracy and robustness of clock parameter tracking.

Description

Technical Field

[0001] The invention belongs to the field of time synchronization and relates to a precise clock synchronization parameter tracking method based on an augmented Kalman neural network. Background Art

[0002] Time synchronization provides a unified time reference for many time-critical network applications, such as data fusion, resource scheduling, energy management, and collaborative measurement. It is a fundamental requirement for ensuring the normal operation of the network. Traditional time synchronization protocols include the Global Positioning System (GPS), the Network Time Protocol (NTP), and the Precision Time Protocol (PTP). The Precision Time Protocol has become one of the most commonly used protocols in distributed networks due to its limited restrictions, high cost-effectiveness, and ability to ensure efficient distributed interaction.

[0003] The key to precise clock synchronization is eliminating clock phase offset from a reference clock. This is corrected by collecting hardware timestamps. However, due to the accumulation of clock frequency offset, even after calibration, clocks may still experience unbounded clock phase offset, leading to frequent clock resynchronization. Therefore, to extend the synchronization interval, it is necessary to simultaneously track both clock phase offset and clock frequency offset. Existing research on the joint tracking of clock phase offset and clock frequency offset for precise clock synchronization in multi-hop networks mostly assumes symmetric uplink and downlink delays and thus employs traditional Kalman filters to jointly track clock phase offset and frequency offset. However, these studies have the following shortcomings: 1) In actual multi-hop networks, due to routing asymmetry, line speed asymmetry, and variable processing delays of intermediate devices, the uplink and downlink delays between the master clock and the clock to be synchronized are asymmetric. 2) Due to the volatile temperature of the network deployment environment, temperature changes will affect the inherent characteristics of the clock crystal oscillator, causing the clock crystal oscillator output frequency to change, thereby generating unbounded clock phase offset. 3) In actual multi-hop networks, the observation noise covariance is difficult to determine empirically or the given observation noise covariance is inaccurate. Traditional Kalman filtering is very sensitive to the observation noise covariance. Unknown observation noise covariance will lead to a decrease in the tracking performance of the Kalman filter for clock parameters.

[0004] Based on the above shortcomings, the present invention urgently needs to solve the problem of joint reliable tracking of precise clock phase offset and frequency offset with unknown observation noise covariance under the influence of accumulated delay asymmetry and temperature variation in multi-hop networks. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a precise clock synchronization parameter tracking method based on an augmented Kalman neural network. In a multi-hop network composed of a source node, a target node and a plurality of intermediate nodes, the influence of the cumulative asymmetric link transmission delay in the multi-hop network on the clock synchronization accuracy is considered, and a multi-hop network clock observation equation containing the cumulative asymmetric link delay is derived. A recursive state equation of the clock frequency offset and temperature change is established based on a quadratic polynomial model of temperature and clock frequency offset; the evolution process of the cumulative asymmetric delay and the unknown temperature coefficient is modeled as a first-order linear difference equation, and augmented to a clock parameter tracking state space model, and the augmented Kalman neural network algorithm is used to realize the joint tracking of the clock phase offset and clock frequency offset of the slave node. The present invention takes into account the influence of the cumulative asymmetric link delay and temperature change in the multi-hop network, and augments the cumulative asymmetric link delay and the unknown temperature coefficient to the state space vector through a quadratic augmented Kalman filter, thereby compensating for the influence of the asymmetric delay and temperature change on the tracking clock phase offset and frequency offset. In addition, the present invention further introduces a deep learning method to learn the Kalman gain through a neural network, thereby overcoming the problem of unknown observation noise covariance in multi-hop networks and significantly improving the accuracy and robustness of clock parameter tracking.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for accurately tracking clock synchronization parameters based on an augmented Kalman neural network, the method specifically comprising the following steps:

[0008] S1: Synchronization messages are sent in a point-to-point manner using a precise clock protocol in a multi-hop network. Considering the accumulated asymmetric delay, the target node establishes a clock observation equation based on the received synchronization message. Considering the impact of temperature on the clock crystal oscillator, a recursive model of the node clock frequency offset and temperature is established. Based on the two-state clock model, the clock state equation is established.

[0009] S2: Combine the clock observation equation and the clock state equation to establish a clock state space model, model the unknown temperature coefficient and the accumulated asymmetric delay as a first-order linear difference equation, and expand the unknown temperature coefficient and the accumulated asymmetric delay to the state space vector;

[0010] S3: The clock parameters are tracked using the augmented Kalman neural network method. The observed values ​​and true values ​​of the clock state parameters are used as training sets, and the clock parameters are trained using a recurrent neural network to obtain a prediction model. The prediction gain of the prediction model output is obtained by inputting the posterior estimate value of the previous moment and the observation value of the current moment into the prediction model. This prediction gain is used to weigh the trust of the observed value and the predicted value.

[0011] Furthermore, in S1, the observation equation and state equation for precise clock synchronization in a multi-hop network under the influence of cumulative asymmetric delay and ambient temperature are established. The specific steps are as follows:

[0012] S11: Intermediate node i calculates the clock offset from the master clock based on the received timestamp Expressed as:

[0013]

[0014] in, Indicates the time when the master clock sends the Sync message. Indicates the downstream transparent clock TC i Time when the Sync message is received; Expressed as:

[0015]

[0016] in, represents the link delay between transparent clock i and node i-1, Indicates the residence time of the synchronization message at node i-1, Represents the total delay from the previous node i to the master clock, the initial value is zero; the residence time of node i-1 can be calculated as:

[0017]

[0018] where ε (i-1,i-1) is a random variable, usually assumed to be Gaussian white noise, representing the timestamp contribution associated with different clock readings;

[0019] S12: In the kth round of synchronization, assume that the clock offset between node i and node i-1 is And further assuming that the clock phase offset remains constant over a sufficiently short time interval, we have:

[0020]

[0021] in, and They represent the uplink and downlink fixed delays between nodes i and i-1, respectively, and their relationship is: in represents the fixed delay asymmetry measure between node i and node i-1 in the kth synchronization cycle;

[0022] S13: Assume that the average link delay is but It can be expressed as:

[0023]

[0024] S14: The formula for measuring the clock offset between the master clock and the transparent clock i is:

[0025]

[0026] in, represents the measurement of clock offset, and They correspond to the cumulative residence time and the cumulative unknown asymmetric delay of the synchronization information between the master clock and the transparent clock i, respectively; represents the entire observation noise and is expressed as:

[0027]

[0028] in represents the measurement error of the i-th node in the k-th round of synchronization; in a multi-hop network, It is difficult to obtain through experience. is a Gaussian noise signal with zero mean and unknown covariance;

[0029] S15: Measured value of the clock frequency deviation between the master clock and transparent clock i The value can be measured by clock phase deviation gives:

[0030]

[0031] S16: Establish a parabolic model with unknown coefficients related to clock frequency offset and temperature change, and treat interference as noise input. If the sampling interval is small enough, the recursive equation for clock frequency offset can be modeled as:

[0032]

[0033] in, is the unknown relationship between the current clock frequency offset and temperature change of intermediate node i;

[0034] S17: For curves with unknown parabolic coefficients, The change is related to the central axis of the parabola, which is the reference temperature Celsius, approximately:

[0035]

[0036] in, represents the unknown temperature coefficient of node i at the kth round of synchronization, which is an unknown value fluctuating within a small range;

[0037] Then the recursive form of the clock phase offset can be obtained as:

[0038]

[0039] S18: When designing the state equation, use a two-state clock model to determine the clock phase offset to describe the clock's behavior at successive synchronization moments; the clock recursive state equation is as follows:

[0040]

[0041] Furthermore, in S2, a clock state space model is established, the unknown temperature coefficient and the accumulated asymmetric delay are modeled as a first-order linear difference equation, and the unknown temperature coefficient and the accumulated asymmetric delay are expanded to a state space vector. The specific steps are:

[0042] S21: Combining the clock state equation and clock observation equation of intermediate node i, the clock state space equation is:

[0043]

[0044] in B=[1 0] T ,

[0045] S22: The accumulated asymmetric delay between the master clock and the transparent clock i is expressed as:

[0046]

[0047] The asymmetric delay between two adjacent transparent clocks is modeled as a first-order difference equation:

[0048]

[0049] represents Gaussian noise with zero mean;

[0050] S23: The recursive form of accumulating asymmetric delays is:

[0051]

[0052] Due to the accumulation of multiple zero-mean Gaussian noises, the covariance is difficult to obtain accurately;

[0053] S24: Similarly, the unknown temperature coefficient is modeled as a first-order difference equation:

[0054]

[0055] S25: Augment the accumulated asymmetric delay and the unknown temperature coefficient to the state space vector, and obtain the augmented clock state space model as follows:

[0056]

[0057] in,

[0058] Furthermore, in S3, the clock parameter tracking is performed using an augmented Kalman neural network method, and the specific steps are as follows:

[0059] S31: Calculate the prior state estimate of transparent node i based on the augmented state space model The calculation formula is:

[0060]

[0061] in is the posterior estimate of node i at the previous moment;

[0062] S32: Use the measurement value of node i at time k and the prior estimate residual is calculated as:

[0063]

[0064] S33: Augmented Kalman Neural Network-based method uses neural networks to learn Kalman gains Through learning Perform execution status update, expressed as:

[0065]

[0066] S34: Kalman gain The calculation method is to optimize the mean square error loss function of the parameter Θ through end-to-end training; the dataset consists of N sequences of length m, expressed as in is the observation vector sequence of trajectory j, is the true value sequence of trajectory j; extending the recursion to m time steps, we get a sequence-to-sequence supervised training scheme; for each trajectory j, the empirical minimum mean square error loss function is measured as:

[0067]

[0068] Among them, Θ (.) is the output of the recurrent neural network, Θ is its trainable parameter, and α is the regularization coefficient;

[0069] S35: To optimize the parameter Θ, an adaptive momentum stochastic optimization method is adopted, which combines the second-order momentum with stochastic gradient descent. For each batch of trajectories indexed by r, L < N training indices are randomly selected, and the batch loss ξ r (Θ) is as follows:

[0070]

[0071] The beneficial effects of the present invention are as follows:

[0072] (1) The present invention fully considers the influence of the cumulative uplink and downlink transmission delay asymmetry on the clock phase offset and the influence of temperature change on the clock frequency offset in the actual multi-hop network, and uses the augmented Kalman neural network algorithm to jointly track the clock phase offset and frequency offset in the multi-hop network, significantly reducing the influence of temperature change and cumulative asymmetric delay on the clock parameter tracking accuracy in the multi-hop network.

[0073] (2) The present invention uses the neural network to learn the Kalman gain, and weighs the trust degree of the estimated value and the measured value through the learned gain, overcoming the problem of the decline in the joint tracking accuracy of the clock phase offset and frequency offset caused by the unknown observation noise covariance, and significantly improving the accuracy and robustness of the clock parameter tracking.

[0074] Other advantages, objectives and features of the present invention will be described in part in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0076] Figure 1 is a schematic diagram of clock synchronization information interaction in the multi-hop network of the present invention;

[0077] Figure 2 is the flow chart of the precise clock synchronization parameter tracking method based on the augmented Kalman neural network in the present invention;

[0078] Figure 3 is a performance comparison diagram of the precise clock phase offset tracking method based on the augmented Kalman neural network in the present invention; <着

[0079] Figure 4 is a performance comparison diagram of the precise clock frequency offset tracking method based on the augmented Kalman neural network in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0080] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0081] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0082] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0083] See also Figures 1 to 4 , Figure 1 This is a schematic diagram of time message interaction in the multi-hop network precise clock synchronization provided by the present invention, such as Figure 1 As shown in the figure, the master clock and the slave clock exchange dedicated synchronization messages for precise clock synchronization through multiple intermediate transparent clock nodes. The specific process is as follows:

[0084] 1) In the kth round of synchronization message, the master clock is The Sync message is sent at all times and forwarded by the intermediate transparent clock to the slave clock, which records the time when the message is received. 2) After the Sync message is sent, the master clock sends the Forwarded to the slave clock by the middle n-1 cascaded transparent clocks; 3) Transparent clock TC i-1 After receiving the Sync message, record the time of receipt The message is then forwarded by other active ports to the downstream transparent clock TC i , TC i Record the time of reception And record its forwarding time as At the same time, the transparent clock TC i-1 Calculate the dwell time of the Sync message as Indicates transparent clock TC i-1 The processing delay from receiving the Sync message to forwarding it is accumulated and recorded in the correctionField field of the Follow_Up message; 4) Transparent clock TC i The synchronization message is obtained by point-to-point delay measurement in TC i-1 With TC i Specifically, TC i Send a Pdelay_Req message to the upstream clock and record its sending time as After the upstream clock receives the message, it records the receiving time as and in Time, to TC i Reply to Pdelay_Res message. TC i After receiving the message, record the receiving time as Subsequently, the upstream clock sends the Pdelay_Res_Follow_Up message to Send to TC i At this time, the transparent clock TC i Collected Four timestamps, and under the assumption of symmetric link delay, calculate TC i-1 With TC i The average link transmission delay between the two packets is recorded in the correctionField field of the Follow_Up message.

[0085] Intermediate node i calculates the clock offset from the master clock based on the received timestamp It can be expressed as:

[0086]

[0087] in represents the total path delay from the master clock to the intermediate transparent clock node i. It can be expressed as:

[0088]

[0089] in, represents the link delay between transparent clock i and node i-1, Indicates the residence time of the synchronization message at node i-1, Represents the total delay from the previous node i to the master clock, the initial value is zero. The residence time of node i-1 can be calculated as:

[0090]

[0091] where ε (i-1,i-1) is a random variable, usually assumed to be Gaussian white noise, representing the timestamp contribution associated with different clock readings.

[0092] In the kth round of synchronization, node i collects the Timestamp, which can calculate the clock offset between node i and node i-1 for

[0093]

[0094] in, and They represent the uplink and downlink fixed delays between nodes i and i-1, respectively, and their relationship is: in represents the fixed delay asymmetry measure between nodes i and i-1 in the kth synchronization cycle.

[0095] Assume that the average link delay is set to Subtracting the two formulas in (4), and further assuming that the clock phase offset remains constant within a sufficiently short time interval, the average link delay can be calculated as

[0096]

[0097] Combining formulas (1), (2), (3), and (5), the clock phase offset formula between the master clock and transparent clock i can be obtained as

[0098]

[0099] in, represents the measurement of clock offset, and They correspond to the cumulative residence time and cumulative asymmetric link delay of the synchronization information between the master clock and transparent clock i, respectively. represents the entire observation noise and can be expressed as:

[0100]

[0101] in represents the measurement error of the i-th node in the k-th round of synchronization. It is difficult to obtain empirically, so it is assumed is an unknown noise signal with zero mean and covariance.

[0102] The measured value of the clock frequency deviation between the master clock and the transparent clock i The value can be measured by clock phase offset The calculation shows that:

[0103]

[0104] Furthermore, a recursive form of clock frequency offset in a multi-hop model is established. The specific steps are as follows:

[0105] A parabolic model with unknown coefficients related to clock frequency offset and temperature change is established, and interference is considered as noise input. If the sampling interval is small enough, the recursive equation for clock frequency offset can be modeled as:

[0106]

[0107] in, is the unknown relationship between the current clock frequency offset of intermediate node i and the temperature change.

[0108] For a curve with unknown parabolic coefficients, The change of the central axis of the parabola (i.e. the reference temperature Celsius), can be approximated as:

[0109]

[0110] in, It represents the unknown temperature coefficient of node i at the kth round of synchronization, which is an unknown value that fluctuates within a small range.

[0111] Combining equations (9) and (10), the recursive form of the clock phase offset can be obtained as:

[0112]

[0113] When designing the state equation, a two-state clock model is used to determine the clock phase offset to describe the behavior of the clock at continuous synchronization moments. Combined with Equation (11), the clock recursive state equation is as follows:

[0114]

[0115] Furthermore, a clock state space model is established, and the unknown temperature coefficient and accumulated asymmetric delay are modeled as first-order linear difference equations. At the same time, the unknown temperature coefficient and accumulated asymmetric delay are expanded to the state space vector. The specific steps are as follows:

[0116] Combining equations (6), (8) and (12), the clock state space equation of intermediate node i is:

[0117]

[0118] in B=[1 0] T ,

[0119] Subsequently, the accumulated asymmetric link delay and the unknown temperature coefficient are augmented. First, the accumulated asymmetric delay between the master clock and the transparent clock i is expressed as:

[0120]

[0121] The asymmetric delay between two adjacent transparent clocks can be modeled as a first-order difference equation:

[0122]

[0123] represents zero-mean Gaussian noise.

[0124] Combining equations (14) and (15), the recursive form of the accumulated asymmetric delay can be obtained:

[0125]

[0126] Due to the accumulation of multiple zero-mean Gaussian noises, the covariance is difficult to obtain accurately.

[0127] Similarly, the unknown temperature coefficient can be modeled as a first-order difference equation:

[0128]

[0129] The accumulated asymmetric delay and unknown temperature coefficient are augmented to the state space vector, and the augmented clock state space model is obtained as follows:

[0130]

[0131] in,

[0132] Furthermore, an accurate clock synchronization parameter tracking method based on augmented Kalman neural network is adopted, and the specific steps are as follows:

[0133] Calculate the prior state estimate of node i according to the augmented state space model The calculation formula is:

[0134]

[0135] where is the posterior estimate value of node i at the previous moment.

[0136] Using the measurement value of node i at time k and the prior estimate value The residual can be calculated as:

[0137]

[0138] The method based on the augmented Kalman neural network uses the Kalman gain learned by the neural network to perform state updates, expressed as:

[0139]

[0140] The Kalman gain is calculated by optimizing the mean square error loss function of the parameter Θ through end-to-end training. The dataset consists of N sequences of length m, expressed as where is the observed vector sequence of trajectory j, is the true value sequence of trajectory j. The recursion is extended to m time steps, resulting in a sequence-to-sequence supervised training scheme. For each trajectory j, the empirical minimum mean square error loss function metric is:

[0141] [[ID=4t]]

[0142] where, where, Ψ Θ (.) is the output of the recurrent neural network, Θ is its trainable parameter, and α is the regularization coefficient.

[0143] To optimize the parameter Θ, an adaptive momentum stochastic optimization method is adopted, which combines the second-order momentum with stochastic gradient descent and has the advantages of simple implementation, high computational efficiency, and small memory overhead. For each batch of trajectories indexed by r, L < N training indices are randomly selected, and the batch loss ξ r (Θ) is

[0144]

[0145] Figure 2 is the flow chart of the precise clock synchronization parameter tracking method based on the augmented Kalman neural network in this embodiment. This embodiment provides a joint tracking method for clock phase offset and frequency offset applicable to unknown observation noise covariance under the influence of temperature change and link delay asymmetry in multi-hop networks, as Figure 2 shown, specifically including the following steps:

[0146] P1: The precise clock synchronization parameter tracking process based on the augmented Kalman neural network begins;

[0147] P2: Initialization based on the augmented Kalman neural network method;

[0148] P3: The slave clock interacts with the master clock for precise clock synchronization through an intermediate transparent clock, and the slave clock records the relevant timestamps;

[0149] P4: Obtain the observed values ​​of clock phase offset and frequency offset based on the recorded timestamp;

[0150] P5: Obtain the temperature at time K through the temperature sensor and establish the clock state equation;

[0151] P6: Use the clock state model to predict the prior state estimate of the clock phase offset and frequency offset at time K;

[0152] P7: Calculate the filter residual based on the observed value and the predicted value;

[0153] P8: Input the observation value at the current moment and the posterior estimate value at the previous moment, and use the neural network to calculate the Kalman gain;

[0154] P9: Use the gains calculated by the neural network to weight the predicted values ​​and observed values ​​and update the posterior estimate;

[0155] P10~P12: Determine whether the synchronization round has reached the preset value. If it has, the clock phase offset tracking process ends; otherwise, the synchronization round is increased by 1, and the process enters P3 to continue the clock parameter tracking process.

[0156] Figure 3 and Figure 4 A performance comparison chart of the precise clock synchronization parameter tracking method based on the augmented Kalman neural network provided in this embodiment is given. Figure 3 and Figure 4 It can be seen that the augmented Kalman neural network method can effectively eliminate the impact of accumulated asymmetric link delay and compensate for rapid temperature changes in the environment on the precise tracking of clock phase offset and frequency offset, and more accurately and reliably track the true values ​​of clock phase offset and frequency offset, which proves the practicality of the precise clock synchronization parameter tracking method based on the augmented Kalman neural network provided by the present invention.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for accurately tracking clock synchronization parameters based on an augmented Kalman neural network, characterized by: The method specifically comprises the following steps: S1: Synchronization messages are sent in a point-to-point manner using a precise clock protocol in a multi-hop network. Considering the accumulated asymmetric delay, the target node establishes a clock observation equation based on the received synchronization message. Considering the impact of temperature on the clock crystal oscillator, a recursive model of the node clock frequency offset and temperature is established. Based on the two-state clock model, the clock state equation is established. S2: Combine the clock observation equation and the clock state equation to establish a clock state space model, model the unknown temperature coefficient and the accumulated asymmetric delay as a first-order linear difference equation, and expand the unknown temperature coefficient and the accumulated asymmetric delay to the state space vector; S3: Track clock parameters using an augmented Kalman neural network. Using the observed and true values ​​of the clock state parameters as a training set, a recurrent neural network is used to train the clock parameters to obtain a prediction model. The prediction model is fed with the posterior estimate of the previous moment and the observation at the current moment to obtain the prediction gain of the prediction model output. This prediction gain is used to balance the confidence of the observed and predicted values. In S1, the observation equation and state equation for precise clock synchronization in a multi-hop network under the influence of cumulative asymmetric delay and ambient temperature are established. The specific steps are: S11: Intermediate node i calculates the clock offset from the master clock based on the received timestamp Expressed as: in, Indicates the time when the master clock sends the Sync message. Indicates the downstream transparent clock TC i The time when the Sync message is received, and represents the total path delay from the master clock to the intermediate transparent clock node i; Expressed as: in, represents the link delay between transparent clock i and node i-1, Indicates the residence time of the synchronization message at node i-1, Represents the total delay from the previous node i to the master clock, the initial value is zero; the residence time of node i-1 is calculated as: where ε (i-1,i-1) is a random variable, assumed to be Gaussian white noise, representing the timestamp contribution associated with different clock readings; S12: In the kth round of synchronization, let the clock offset between node i and node i-1 be Assuming that the clock phase offset remains constant within a sufficiently short time interval, we have: in, and They represent the uplink and downlink fixed delays between nodes i and i-1, respectively, and their relationship is: in represents the fixed delay asymmetry measure between node i and node i-1 in the kth synchronization cycle; S13: Assume that the average link delay is but Expressed as: Indicates TC i The time when the Pdelay_Req message is sent to the upstream clock; Indicates the receiving time recorded after the upstream clock receives the message; Indicates to TC i Time to reply to Pdelay_Res message; Indicates TC i The receiving time recorded after receiving the message; S14: The formula for measuring the clock offset between the master clock and the transparent clock i is: in, represents the measurement of clock offset, and They correspond to the cumulative residence time and the cumulative unknown asymmetric delay of the synchronization information between the master clock and the transparent clock i, respectively; represents the entire observation noise and is expressed as: in represents the measurement error of the i-th node in the k-th round of synchronization; in a multi-hop network, let is a Gaussian noise signal with zero mean and unknown covariance; S15: Measured value of the clock frequency deviation between the master clock and transparent clock i Measured by clock phase deviation gives: S16: Establish a parabolic model with unknown coefficients related to clock frequency offset and temperature change, and treat interference as noise input. If the sampling interval is small enough, the recursive equation for clock frequency offset can be modeled as: in, is the unknown relationship between the current clock frequency offset and temperature change of intermediate node i; S17: For curves with unknown parabolic coefficients, The change is related to the central axis of the parabola, which is the reference temperature Celsius, approximately: in, represents the unknown temperature coefficient of node i at the kth round of synchronization, which is an unknown value fluctuating within a small range; The recursive form of the clock phase offset is: S18: When designing the state equation, use a two-state clock model to determine the clock phase offset to describe the clock's behavior at continuously synchronized times; the clock recursive state equation is as follows: Where τ represents the sampling interval; In S2, a clock state space model is established, the unknown temperature coefficient and the accumulated asymmetric delay are modeled as a first-order linear difference equation, and the unknown temperature coefficient and the accumulated asymmetric delay are expanded to a state space vector. The specific steps are: S21: Combining the clock state equation and clock observation equation of intermediate node i, the clock state space equation is: in B=[1 0] T , S22: The cumulative asymmetric delay between the master clock and the transparent clock i is expressed as: The asymmetric delay between two adjacent transparent clocks is modeled as a first-order difference equation: represents Gaussian noise with zero mean; S23: The recursive form of accumulating asymmetric delays is: Due to the accumulation of multiple zero-mean Gaussian noises, the covariance is difficult to obtain accurately; S24: Similarly, the unknown temperature coefficient is modeled as a first-order difference equation: S25: Augment the accumulated asymmetric delay and the unknown temperature coefficient to the state space vector, and obtain the augmented clock state space model as follows: in, In S3, the clock parameter tracking is performed using the augmented Kalman neural network method, and the specific steps are as follows: S31: Calculate the prior state estimate of transparent node i based on the augmented state space model The calculation formula is: in is the posterior estimate of node i at the previous time; S32: Use the measurement value of node i at time k and the prior estimate residual is calculated as: S33: Augmented Kalman Neural Network-based method uses neural networks to learn Kalman gains Through learning Perform execution status update, expressed as: S34: Kalman gain The calculation method is to optimize the mean square error loss function of the parameter Θ through end-to-end training; the dataset consists of N sequences of length m, expressed as in is the observation vector sequence of trajectory j, is the true value sequence of trajectory j; extending the recursion to m time steps, we get a sequence-to-sequence supervised training scheme; for each trajectory j, the empirical minimum mean square error loss function is measured as: Among them, Θ (.) is the output of the recurrent neural network, Θ is its trainable parameter, and α is the regularization coefficient; S35: To optimize the parameter Θ, an adaptive momentum stochastic optimization method is adopted, which combines the second-order momentum with stochastic gradient descent. For each batch of trajectories indexed by r, L < N training indices are randomly selected, and the batch loss ξ r (Θ) is as follows:

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