Implicit clock synchronization method based on augmented Kalman filtering
By using the augmented Kalman filter algorithm to establish a recursive state equation of clock frequency offset and temperature in wireless networks, the problems of high node energy consumption and frequency drift are solved, low-energy, high-precision clock synchronization is achieved, and long-term stable operation of the network is supported.
Patent Information
- Application Number
- CN202511032174.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-25
- Publication Date
- 2025-10-03
AI Technical Summary
Existing wireless network clock synchronization schemes have high node energy consumption and poor frequency drift compensation when the ambient temperature changes. This results in excessive communication energy consumption and accumulated clock synchronization errors, affecting the long-term deployment and synchronization accuracy of the network.
An implicit clock synchronization method based on augmented Kalman filtering is adopted. By establishing a recursive state equation of clock frequency offset and temperature, a clock parameter observation equation is constructed, and the augmented Kalman filtering algorithm is used to jointly track the clock phase offset and frequency offset, thereby reducing the energy consumption of synchronization message interaction and improving synchronization accuracy and robustness.
In wireless networks with fluctuating ambient temperatures, the energy consumption of synchronization message interactions is significantly reduced, the accuracy and reliability of clock synchronization are improved, and the long-term deployment of resource-constrained networks is ensured.
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Figure CN120751476A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of time synchronization and relates to an implicit clock synchronization method based on augmented Kalman filtering. Background Art
[0002] Time synchronization is a fundamental technology that supports key functions such as wireless network data fusion, event coordination triggering, and distributed positioning. Its synchronization accuracy and energy efficiency directly affect network performance. Current mainstream synchronization schemes for wireless networks can be divided into three categories based on the communication mechanism: two-way interactive protocols achieve microsecond-level synchronization accuracy through hierarchical, multiple-time two-way message exchanges; broadcast protocols broadcast synchronization messages based on reference nodes, and synchronization is achieved between receiving nodes by comparing message timestamps; hybrid schemes introduce limited two-way interactions or filtering estimation mechanisms on the basis of retaining the reference node broadcast synchronization messages to improve the system's clock synchronization accuracy and stability. Although the above schemes perform well in specific scenarios, they require nodes to actively send or forward synchronization messages, and do not consider the impact of ambient temperature changes. They also have the following shortcomings:
[0003] 1) In actual wireless networks, node energy consumption is limited. Frequent node participation in message interaction will result in excessive communication energy consumption, thereby shortening the network lifecycle and severely restricting the long-term deployment of resource-constrained networks.
[0004] 2) The nonlinear drift of the crystal oscillator frequency with changes in ambient temperature is not effectively compensated, and there is a lack of a correction mechanism for temperature and frequency offset, which causes the clock frequency offset to continue to accumulate and convert into a phase estimation error.
[0005] Therefore, there is an urgent need for a clock synchronization method that takes into account the energy consumption constraints of wireless network nodes, so that it can jointly track clock phase offset and frequency offset in wireless network communication scenarios where the ambient temperature changes in real time, thereby ensuring the reliability of wireless network clock synchronization and the long-term deployment of resource-constrained networks. Summary of the Invention
[0006] In view of this, the purpose of the present invention is to provide an implicit clock synchronization method based on augmented Kalman filtering, which is aimed at wireless network communication scenarios with changing ambient temperature. Based on the second-order model of temperature and clock crystal oscillation frequency, a recursive state equation between clock frequency offset and temperature is established, and a clock parameter observation equation between implicit nodes and reference nodes is constructed; the evolution process of the unknown temperature coefficient is modeled as a first-order linear differential equation and then augmented into the clock state variable, and the augmented Kalman filtering algorithm is used to realize the joint tracking of the implicit node clock frequency offset and clock phase offset, so as to achieve significant reduction of transmission energy consumption caused by synchronization message interaction through receiver-only synchronization assisted by temperature, while improving the accuracy and robustness of clock synchronization.
[0007] In order to achieve the above object, the present invention provides the following technical solutions:
[0008] An implicit clock synchronization method based on augmented Kalman filtering, the method comprising:
[0009] For wireless network communication scenarios with real-time ambient temperature changes, a clock parameter observation equation is established between the implicit node and the reference node. Considering the impact of temperature changes on the oscillation frequency of the clock crystal, a recursive clock state equation is established to account for the implicit node clock frequency offset and temperature changes.
[0010] During the period of synchronization message interaction between the active node and the reference node, the hidden node monitors the interaction process and obtains the timestamp information;
[0011] Obtain a clock observation vector based on the observation equations of the implicit node and the reference node clock parameters and the timestamp information; obtain the ambient temperature at the sampling moment within the synchronization period and predict the clock state vector at that moment based on the clock state equation;
[0012] The clock state vector is augmented, and the augmented Kalman filter state space equation is constructed based on the augmented clock state vector and the clock parameter observation equation. The augmented Kalman filter algorithm is used to jointly dynamically track the clock phase offset and clock frequency offset.
[0013] Furthermore, in a wireless network communication scenario where the ambient temperature changes in real time, assume that in the i-th synchronization cycle, the active node A sends a synchronization data packet to the reference node M at the beginning, which is monitored by the implicit node F. The sending time of the active node A is The receiving time of reference node M is The receiving time of the implicit node F is After the reference node M successfully receives the data packet sent by the active node A, at time Send a timestamp to active node A. and The implicit node F monitors the communication from the reference node M to the active node A and records the packet arrival time as
[0014] The clock model relationships between the active node A and the reference node M and between the active node A and the implicit node F are modeled as follows:
[0015]
[0016] Where, and denote the clock phase offset and frequency offset between the active node A and the reference node M, respectively. and denote the phase offset and frequency offset between active node A and hidden node F, respectively. and denote the fixed and random parts of the overall end-to-end delay between the active node A and the reference node M, respectively. and They are represented as the fixed part and random part of the overall end-to-end delay between the active node A and the hidden node F, respectively; The time when the active node A sends the synchronization data packet in the first synchronization cycle;
[0017] According to the clock models between active node A and reference node M, and between active node A and implicit node F, the clock model relationship between reference node M and implicit node F is:
[0018]
[0019] Where, is the asymmetric delay difference, is the random delay difference, and are the phase offset and frequency offset between the implicit node F and the reference node M, respectively;
[0020] According to the above formula, the clock parameter observation equation between the implicit node and the reference node is:
[0021] O i =H i X i +μ i +v i
[0022] Where, is the observed value of the clock phase offset at the i-th synchronization, is the observation matrix, is the clock state vector at the i-th synchronization.
[0023] Furthermore, at sampling time i, the recursive relationship between ambient temperature change and clock frequency offset is modeled as:
[0024]
[0025] Where, β i is the unknown temperature coefficient, w S,i is zero-mean Gaussian noise;
[0026] Model the unknown temperature coefficient variation as a first-order linear difference equation:
[0027] β i =β i-1 +w β,i
[0028] Where w β,i means the mean is 0 and the covariance is Gaussian white noise;
[0029] Combining the above formula, we can get the recursive relationship between temperature and clock frequency offset considering the change of unknown temperature coefficient:
[0030]
[0031] Where, means the mean is 0 and the covariance is The accumulated Gaussian noise of
[0032] Then the clock state equation of the implicit node's clock phase frequency offset and temperature change is:
[0033] X i =PX i-1 +C i β i +DW i
[0034] Where, is the clock state vector, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, is the state noise matrix, τ is the sampling interval, w θ,i and The mean is 0 and the variance is and Gaussian driven noise.
[0035] Furthermore, during the synchronization period, the asymmetric delay difference between nodes and the unknown temperature coefficient during the synchronization message exchange process are augmented into the clock state vector, and the quadratic augmented Kalman filter state space equation is constructed in combination with the clock parameter observation equation. The specific process is as follows:
[0036] The asymmetric delay difference μ i Modeled as a first-order linear difference equation:
[0037] μ i =μ i-1 +w μ,i
[0038] Where w μ,i means the mean is 0 and the covariance is Gaussian white noise;
[0039] μ i Augmented to the clock state vector X i The clock state vector after the intermediate step is:
[0040]
[0041] in accordance with Construct the augmented Kalman filter state space equation:
[0042]
[0043] Where, w μ,i means the mean is 0 and the covariance is Gaussian white noise, I is the identity matrix.
[0044] The unknown temperature coefficient β i Augmented to clock state vector In the equation, we get the clock state vector:
[0045]
[0046] according to Construct the quadratic augmented Kalman filter state space equation:
[0047]
[0048] Where,
[0049] Furthermore, based on the quadratic augmented Kalman filter state space equation, an augmented Kalman filter algorithm is used to perform joint dynamic tracking of clock phase offset and clock frequency offset, including:
[0050] In the current synchronization cycle, obtain the clock phase offset observation value O i and the a priori prediction of the clock state By O i and Calculate the filter residual r i , calculate the prior prediction mean square error matrix M based on the quadratic augmented Kalman filter state space equation i|i-1 ;
[0051] According to the prior prediction mean square error matrix M i|i-1 Calculate the augmented Kalman gain K i ;
[0052] Based on the predicted value Augmented Kalman gain K i and residual r i Compute the posterior state estimate And calculate the posterior estimated mean square error matrix M i|i ;
[0053] Determine whether the synchronization round has reached the preset value. If it has, the tracking is ended; otherwise, enter the next synchronization round to continue the parameter tracking process.
[0054] Among them, the prior prediction value of the clock state Calculated by the following formula:
[0055]
[0056] Filter residual r i Calculated by the following formula:
[0057]
[0058] Prior prediction mean square error matrix M i|i-1 Calculated by the following formula:
[0059]
[0060] Where M i-1|i-1 is the posterior estimated mean square error matrix at time i-1, E(W i W i T ) represents the state noise covariance matrix;
[0061] Augmented Kalman gain K i Calculated by the following formula:
[0062]
[0063] Where,
[0064] Posterior state estimate Calculated by the following formula:
[0065]
[0066] Where r i Represents the difference between the observed value and the predicted value;
[0067] The posterior estimated mean square error matrix M i|i Calculated by the following formula:
[0068]
[0069] The beneficial effects of the present invention are:
[0070] 1) This invention fully considers the problem of limited node energy consumption in actual wireless networks, adopts a receiver-only synchronization scheme, and uses a listening strategy to implicitly obtain synchronization information. Based on the clock model relationship between the active node and the reference node, and between the active node and the hidden node, a clock model relationship between the reference node and the hidden node is constructed, and then the clock parameter observation equation between the hidden node and the reference node is constructed. At the same time, considering the recursive relationship between the temperature and clock frequency offset of the unknown temperature coefficient change, the clock state equation of the clock phase frequency offset and temperature change of the hidden node is constructed. Based on the phase offset observation equation and state equation, combined with the augmented Kalman filter algorithm, the long-term stability of the clock synchronization accuracy is guaranteed, and the transmission energy consumption caused by the synchronization message interaction is significantly reduced.
[0071] 2) Based on a second-order model of temperature and crystal oscillation frequency, this paper establishes a recursive clock state equation for clock frequency offset and temperature variation. By augmenting the temperature coefficient into the clock state vector, a quadratic augmented Kalman filter state-space equation is constructed, making the crystal oscillation frequency robust to ambient temperature variations. Finally, an augmented Kalman filter algorithm is employed to dynamically track both clock phase offset and clock frequency offset, further enhancing the reliability and robustness of clock synchronization.
[0072] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS
[0073] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:
[0074] Figure 1 Schematic diagram of clock information interaction between active nodes, reference nodes and implicit nodes;
[0075] Figure 2 This is a flow chart of an implicit clock synchronization method based on augmented Kalman filtering provided by one embodiment of the present invention. DETAILED DESCRIPTION
[0076] 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.
[0077] 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.
[0078] 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.
[0079] An embodiment of the present invention provides an implicit clock synchronization method based on augmented Kalman filtering. This method takes into account the problem of limited energy consumption of wireless network nodes. In a wireless network communication scenario where the ambient temperature changes in real time, it can jointly track clock phase offset and frequency offset, thereby ensuring the reliability of wireless network clock synchronization and the long-term deployment of resource-constrained networks.
[0080] The method is described as follows:
[0081] 1. For wireless network communication scenarios with real-time ambient temperature changes, a clock observation equation is established between the implicit node and the reference node. Considering the impact of ambient temperature changes on the oscillation frequency of the clock crystal, a recursive clock state equation is established for the implicit node clock frequency offset and temperature changes.
[0082] Among them, the clock information interaction between active nodes, reference nodes and implicit nodes in wireless network communication scenarios is as follows: Figure 1As shown, node A represents the active node, which sends synchronization data packets to the reference node at a fixed period. Node M represents the reference node, which sends synchronization response packets to the active node. Node F represents the hidden node, which monitors the communication between the active node and the reference node in each period.
[0083] The data interaction process between nodes is as follows: for the i-th synchronization cycle, the active node A sends a synchronization data packet to the reference node M at the beginning, which is monitored by the implicit node F. The sending time of node A is determined by Indicates that the receiving time of node M is given by The receiving time of node F is represented by Indicates that after the reference node M successfully receives the data packet sent by the active node A, at time Send a timestamp to node A. and The data response packet is sent, and the implicit node F monitors the communication from node M to node A and records the packet arrival time as At this point, the data interaction process ends.
[0084] According to the affine clock model, the clock model relationships between the active node A and the reference node M and between the active node A and the implicit node F can be modeled as follows:
[0085]
[0086] in, and denote the clock phase offset and frequency offset between the active node A and the reference node M, respectively. and denote the phase offset and frequency offset between active node A and hidden node F, respectively. and denote the fixed and random parts of the overall end-to-end delay between the active node A and the reference node M, respectively. and are represented as the fixed part and random part of the overall end-to-end delay between the active node A and the hidden node F, respectively. The time when the active node A sends the synchronization data packet in the first synchronization cycle. and are modeled as independent and identically distributed Gaussian random variables.
[0087] According to the clock models between active node A and reference node M and between active node A and implicit node F, the clock model relationship between reference node M and implicit node F is modeled as:
[0088]
[0089] in, is the asymmetric delay difference, is the random delay difference, and are the phase offset and frequency offset between the implicit node F and the reference node M, respectively.
[0090] According to formula (3), the clock parameter observation equation between the implicit node and the reference node in the asymmetric link transmission delay scenario can be obtained as follows:
[0091] O i =H i X i +μ i +v i (4)
[0092] Among them, the observation vector at the i-th synchronization is the observation matrix, the state vector at the i-th synchronization
[0093] Considering the impact of ambient temperature changes on the oscillation frequency of the clock crystal oscillator, a quadratic polynomial model with unknown coefficients of ambient temperature changes and crystal oscillator oscillation frequency is established as follows:
[0094] f i =f0(1+β(T i -T0) 2 ) (5)
[0095] Where f0 represents the standard oscillator frequency at the reference temperature T0 = 25°C, T i represents the discrete temperature measurement value at the i-th sampling moment. β is the unknown temperature coefficient.
[0096] Calculate the absolute drift of the crystal oscillator's oscillation frequency:
[0097]
[0098] Combining equations (5) and (6), when the sampling period is small enough, the recursive relationship between ambient temperature change and clock frequency offset is modeled as:
[0099]
[0100] Among them, β i is the unknown temperature coefficient, w S,i is zero-mean Gaussian noise.
[0101] Model the unknown temperature coefficient change as a first-order linear difference equation as shown below:
[0102] β i =β i-1 +wβ,i (8)
[0103] Among them, w β,i means the mean is 0 and the covariance is Gaussian white noise.
[0104] Combining equations (7) and (8), the recursive relationship between temperature and clock frequency offset considering the unknown temperature coefficient variation can be expressed as:
[0105]
[0106] in, means the mean is 0 and the covariance is The accumulated Gaussian noise.
[0107] Combined with the two-state clock model, the clock phase frequency offset state equation is established as:
[0108] X i =PX i-1 +C i β i +DW i (10)
[0109] in, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, the state noise matrix τ represents the sampling interval, w θ,i and Indicates that the two means are 0 and the variances are and Gaussian driven noise.
[0110] 2. Combining the clock observation equation and the clock state equation, a clock state space model between the implicit node and the reference node is established. The unknown temperature coefficient is augmented into the state vector, and the augmented Kalman filter algorithm is used to jointly dynamically track the clock phase offset and clock frequency offset.
[0111] Similar to equation (8), the asymmetric delay variation is modeled as a first-order linear difference equation, as shown below:
[0112] μ i =μ i-1 +w μ,i (11)
[0113] Among them, w μ,i means the mean is 0 and the covariance is Gaussian white noise.
[0114] μi Augmented to the state vector X i The state vector after the intermediate stage is:
[0115]
[0116] The augmented Kalman filter state space equation is constructed based on the state vector of formula (12), as shown below:
[0117]
[0118] in, w μ,i means the mean is 0 and the covariance is Gaussian white noise, I is the identity matrix.
[0119] Similarly, the unknown temperature coefficient β i Augmented to state vector The state vector after the intermediate stage is:
[0120]
[0121] According to the state vector of formula (14), the quadratic augmented Kalman filter state space equation is constructed as shown below:
[0122]
[0123] in,
[0124] According to the state space equation constructed by formula (15), the quadratic augmented Kalman filter algorithm is used to perform joint dynamic tracking of the clock phase offset and the clock frequency offset. The calculation formula of the quadratic augmented Kalman filter algorithm includes:
[0125] Prior state prediction:
[0126] Minimum a priori prediction mean square error matrix:
[0127] Residuals:
[0128] Kalman gain:
[0129] Posterior state estimate:
[0130] Minimum a posteriori estimation mean square error matrix:
[0131] in, express The prior prediction of express The posterior estimate of M i|i-1 represents the prior prediction mean square error matrix, M i|i represents the posterior estimated mean square error matrix, K i represents the Kalman gain, r i represents the difference between the actual measured value and its predicted value,
[0132] Figure 2 The implicit clock synchronization method based on augmented Kalman filtering provided in this embodiment is shown, which can achieve clock synchronization in a scenario where the temperature of a wireless network environment changes in real time. The method specifically includes the following steps:
[0133] M1: The clock synchronization process starts when the ambient temperature changes in real time.
[0134] M2: Augmented Kalman filter initialization;
[0135] M3: The active node exchanges synchronization messages with the reference node, and the implicit node monitors the interaction process;
[0136] M4: Obtain clock phase offset observation value based on implicit node and reference node clock models and timestamp information;
[0137] M5: Obtain the temperature at time i through the temperature sensor and predict the clock state value at time i based on the clock state model;
[0138] M6: Calculate the prior prediction mean square error and calculate the filter residual based on the observed value and the predicted value;
[0139] M7: Calculate the augmented Kalman gain based on the clock state model shown in formula (15) and the prior prediction mean square error;
[0140] M8: Use the predicted value and the observed value to weight and update the posterior estimate;
[0141] M9: Calculate the mean square error of the posterior estimate;
[0142] M10-M11: Determine whether the synchronization round has reached the preset value. If it has, the process ends; otherwise, the synchronization round is increased by 1 and the process enters M3 to continue the parameter tracking process.
[0143] M12: The clock synchronization process in the scenario where the ambient temperature changes in real time is completed.
[0144] 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. An implicit clock synchronization method based on augmented Kalman filtering, characterized in that: The method includes: For wireless network communication scenarios with real-time ambient temperature changes, a clock parameter observation equation is established between the implicit node and the reference node. Considering the impact of temperature changes on the oscillation frequency of the clock crystal, a recursive clock state equation is established to account for the implicit node clock frequency offset and temperature changes. During the period of synchronization message interaction between the active node and the reference node, the hidden node monitors the interaction process and obtains the timestamp information; Obtain a clock observation vector based on the observation equations of the implicit node and the reference node clock parameters and the timestamp information; obtain the ambient temperature at the sampling moment within the synchronization period and predict the clock state vector at that moment based on the clock state equation; The clock state vector is augmented, and the augmented Kalman filter state space equation is constructed based on the augmented clock state vector and the clock parameter observation equation. The augmented Kalman filter algorithm is used to jointly dynamically track the clock phase offset and clock frequency offset.
2. The method according to claim 1, characterized in that In a wireless network communication scenario where the ambient temperature changes in real time, assume that in the i-th synchronization cycle, the active node A sends a synchronization data packet to the reference node M at the beginning, which is monitored by the implicit node F. The sending time of the active node A is The receiving time of reference node M is The receiving time of the implicit node F is After the reference node M successfully receives the data packet sent by the active node A, at time Send a timestamp to active node A. and The implicit node F monitors the communication from the reference node M to the active node A and records the packet arrival time as The clock model relationships between the active node A and the reference node M and between the active node A and the implicit node F are modeled as follows: Where, and denote the clock phase offset and frequency offset between the active node A and the reference node M, respectively. and denote the phase offset and frequency offset between active node A and hidden node F, respectively. and denote the fixed and random parts of the overall end-to-end delay between active node A and reference node M, respectively. and They are represented as the fixed part and random part of the overall end-to-end delay between the active node A and the hidden node F, respectively; The time when the active node A sends the synchronization data packet in the first synchronization cycle; According to the clock models between active node A and reference node M, and between active node A and implicit node F, the clock model relationship between reference node M and implicit node F is: Where, is the asymmetric delay difference, is the random delay difference, and are the phase offset and frequency offset between the implicit node F and the reference node M, respectively; According to the above formula, the clock parameter observation equation between the implicit node and the reference node is: The i =H i X i +m i +v i Where, is the clock observation vector at the i-th synchronization, is the observation matrix, is the clock state vector at the i-th synchronization.
3. The method according to claim 2, characterized in that At sampling time i, the recursive relationship between ambient temperature change and clock frequency offset is modeled as: Where, β i is the unknown temperature coefficient, w S,i is zero-mean Gaussian noise; Model the unknown temperature coefficient variation as a first-order linear difference equation: β i ＝β i-1 +w β,i Where w β,i means the mean is 0 and the covariance is Gaussian white noise; Combining the above formula, we can get the recursive relationship between temperature and clock frequency offset considering the change of unknown temperature coefficient: Where, means the mean is 0 and the covariance is The accumulated Gaussian noise of Then the clock state equation of the implicit node's clock phase frequency offset and temperature change is: X i =PX i-1 +C i β i +DW i Where, is the clock state vector, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, is the state noise matrix, τ is the sampling interval, w θ,i and The mean is 0 and the variance is and Gaussian driven noise.
4. The method according to claim 3, characterized in that During the synchronization period, the asymmetric delay difference between nodes and the unknown temperature coefficient during the synchronization message interaction are augmented into the clock state vector, and the quadratic augmented Kalman filter state space equation is constructed in combination with the clock parameter observation equation.
5. The method according to claim 4, characterized in that The asymmetric delay difference μ i Modeled as a first-order linear difference equation: m i =μ i-1 +w μ,i Where w μ,i means the mean is 0 and the covariance is Gaussian white noise; μ i Augmented to the clock state vector X i The clock state vector after the intermediate step is: in accordance with Construct the augmented Kalman filter state space equation: Where, w μ,i means the mean is 0 and the covariance is Gaussian white noise, I is the identity matrix.
6. The method according to claim 5, characterized in that The unknown temperature coefficient β i Augmented to clock state vector In the equation, we get the clock state vector: according to Construct the quadratic augmented Kalman filter state space equation: Where, 7. The method according to claim 6, characterized in that Based on the quadratic augmented Kalman filter state space equation, the augmented Kalman filter algorithm is used to perform joint dynamic tracking of clock phase offset and clock frequency offset, including: In the current synchronization cycle, obtain the clock phase offset observation value O i and the a priori prediction of the clock state By O i and Calculate the filter residual r i , calculate the prior prediction mean square error matrix M based on the quadratic augmented Kalman filter state space equation i|i-1 ; According to the prior prediction mean square error matrix M i|i-1 Calculate the augmented Kalman gain K i ; Based on the predicted value Augmented Kalman gain K i and residual r i Compute the posterior state estimate And calculate the posterior estimated mean square error matrix M i|i ; Determine whether the synchronization round has reached the preset value. If it has, the tracking is ended; otherwise, enter the next synchronization round to continue the parameter tracking process.
8. The method according to claim 7, characterized in that A priori prediction of the clock state Calculated by the following formula: Filter residual r i Calculated by the following formula: Prior prediction mean square error matrix M i|i-1 Calculated by the following formula: Where M i-1|i-1 is the posterior estimated mean square error matrix at time i-1, E(W i W i T ) represents the state noise covariance matrix; Augmented Kalman gain K i Calculated by the following formula: Where, Posterior state estimate Calculated by the following formula: Where r i Represents the difference between the observed value and the predicted value; The posterior estimated mean square error matrix M i|i Calculated as: