Data and model hybrid driven implicit node clock parameter tracking method

Abstract

The invention relates to a data and model hybrid driven implicit node clock parameter tracking method, and belongs to the technical field of time synchronization. The method comprises the following steps: establishing a clock observation equation between a hidden node and a clock source node for a wireless network communication scene with unknown ambient temperature real-time change and observation noise covariance priori knowledge, and establishing a clock state equation related to hidden node clock frequency deviation and temperature change; establishing a clock state space model of hidden nodes by combining the clock observation equation and the clock state equation, and augmenting a clock state vector; and a data and model hybrid driving method is adopted to track clock parameters. According to the method, the message interaction frequency and the communication overhead are reduced, clock frequency error accumulation caused by environment temperature difference can be inhibited, the clock parameter tracking precision and the long-term stability are improved, the robustness of a system to noise disturbance is enhanced, and the problem of performance degradation and even divergence caused by improper covariance setting is avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of time synchronization and relates to a data and model hybrid driven implicit node clock parameter tracking method. Background Art

[0002] In wireless networks, time synchronization technology is fundamental to supporting key functions such as multi-node collaboration, data fusion, and event sequencing. It is widely used in scenarios requiring high time accuracy and consistency, such as wireless sensor networks, the Industrial Internet of Things, and unmanned system collaboration. Current mainstream wireless network synchronization solutions can be categorized as two-way interactive protocols, broadcast protocols, and hybrid synchronization schemes. Two-way interactive protocols use bidirectional message exchanges between pairs of nodes within a constructed hierarchical network to estimate propagation delay and correct clock offsets. Broadcast protocols rely on reference nodes to periodically broadcast synchronization information, which other nodes passively receive and correct their local clocks. Hybrid schemes incorporate auxiliary interaction mechanisms and estimation algorithms into the broadcast framework to improve synchronization accuracy. To enhance system robustness and dynamic adaptability, these protocols often incorporate estimation algorithms such as recursive least squares and Kalman filtering to filter and smooth clock states, achieving more robust tracking performance.

[0003] Although the above methods have improved synchronization accuracy to a certain extent, they still have the following shortcomings in resource-constrained and complex wireless networks: 1) To ensure the real-time and stability of clock parameter estimation, most solutions rely on frequent synchronization message exchanges, which results in high communication energy consumption and is not suitable for energy-constrained wireless network scenarios. 2) Existing models generally do not consider the nonlinear impact of ambient temperature changes on crystal oscillator frequency. In actual deployments, nodes are significantly affected by ambient temperature differences, and frequency drift is not accurately modeled, which will lead to the continuous accumulation of clock parameter tracking errors. 3) Traditional Kalman filters are highly sensitive to observation noise covariance when performing synchronization parameter tracking. However, in real wireless networks, the statistical characteristics of observation noise are often partially unknown or dynamically changing. Improper covariance setting will significantly reduce estimation accuracy and even cause filter divergence.

[0004] Therefore, a low-energy wireless network clock parameter tracking method is urgently needed, which can jointly track clock phase offset and frequency offset under the real-time changes of ambient temperature and unknown prior knowledge of observation noise covariance, so as to ensure the reliability and robustness of wireless network time synchronization. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a data- and model-driven hybrid implicit node clock parameter tracking method. This method, designed for wireless network scenarios with limited node energy consumption, considers the impact of ambient temperature changes on the oscillation frequency of the clock crystal, establishes a time-varying clock state equation between clock frequency offset and temperature, and simultaneously constructs clock observation equations for the clock source node and the implicit node. The method augments the unknown temperature coefficient to the clock parameter state vector and utilizes a data- and model-driven hybrid method to accurately track the implicit node clock parameters. This method predicts the Kalman gain through a recurrent neural network. Under the condition that the prior knowledge of the observation noise covariance is unknown, a data- and model-driven hybrid method is used to achieve joint dynamic tracking of the implicit node clock phase offset and frequency offset. This method can significantly improve the accuracy of clock parameter tracking and reduce the communication overhead during synchronization.

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

[0007] A data and model hybrid driven implicit node clock parameter tracking method, the method comprising:

[0008] For wireless network communication scenarios where the ambient temperature changes in real time and the observation noise covariance is unknown a priori, a clock observation equation is established between the implicit node and the clock source node. Considering the impact of temperature changes on the clock crystal oscillator, a clock state equation is established that relates the implicit node clock frequency offset to temperature changes.

[0009] Combining the clock observation equation and the clock state equation, a clock state space model of the implicit node is established, and the clock state vector is augmented;

[0010] During the period when the active node and the clock source node in the wireless network exchange synchronization messages, the hidden node monitors the interaction process and obtains the timestamp information;

[0011] The clock observation vector is obtained according to the clock observation equations and timestamp information of the implicit node and the clock source node. The ambient temperature at a certain sampling moment in the synchronization period is obtained and the clock state vector at that moment is predicted according to the clock state equation. The clock parameters are tracked using a data and model hybrid driving method.

[0012] Furthermore, in a wireless network communication scenario where the ambient temperature changes in real time and the observation noise covariance is unknown, only the receiver synchronizes the information exchange. During the interaction, the active node A is at local time The synchronization data packet is sent to the clock source node M at the same time. When the clock source node M receives the data packet, it records the local time as and in When the active node A receives the ACK from the clock source node M, it records the local time as When the implicit node F monitors the data packet from the active node A and the ACK from the clock source node M, it records the local time as and

[0013] The clock models between active node A and clock source node M and between active node A and implicit node F are expressed as:

[0014]

[0015] Where, and They represent the clock phase offset and frequency offset between the active node A and the clock source node M, respectively. and denote the clock 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 clock source node M, respectively. and denote the fixed and random parts of the overall end-to-end delay between active node A and hidden node F, respectively. The time when active node A sends the synchronization data packet in the first synchronization cycle.

[0016] According to the above formula, the clock model relationship between the clock source node M and the implicit node F is:

[0017]

[0018] Where, is the asymmetric delay difference, is the random delay difference;

[0019] Then the clock observation equation is:

[0020] O i =H i X i +μ i +v i

[0021] Where, is the clock observation vector at the i-th synchronization, is the observation matrix, is the state vector at the i-th synchronization.

[0022] Similarly, based on the unknown coefficient second-order parabola model related to the crystal oscillator frequency and temperature change, the relationship between clock frequency offset and temperature change is:

[0023]

[0024] Where S0 represents the standard clock frequency deviation under i represents the absolute clock frequency deviation caused by temperature change, β represents the unknown temperature coefficient; w S,i Represents random external environmental interference and quantitative errors in the temperature measurement process; the unknown temperature coefficient change is modeled as a first-order linear difference equation:

[0025] β i =β i-1 +w β,i

[0026] Where w β,i represents Gaussian white noise with a mean of 0 and unknown covariance. Combining the above formula, the recursive relationship between temperature change and clock frequency offset is:

[0027]

[0028] Where, represents the cumulative Gaussian noise with a mean of 0 and unknown covariance; combined with the two-state clock model, the clock state equation is:

[0029]

[0030] Where τ represents the sampling interval, w θ,i represents Gaussian noise with mean 0 and unknown covariance.

[0031] Furthermore, the clock state space model of the implicit node is established by combining the clock observation equation and the clock state equation, which is expressed as:

[0032]

[0033] Where, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, the state noise matrix

[0034] Augment the unknown temperature coefficient and asymmetric delay to the state vector X i middle:

[0035]

[0036] According to the state vector Reconstruct the clock state space model:

[0037]

[0038] Where, I is the identity matrix.

[0039] Furthermore, a data and model hybrid-driven method is adopted to track clock parameters, including:

[0040] Using historical clock state observations and true values to form a training set, learning the evolution law of clock parameters through a recurrent neural network, and establishing a Kalman gain prediction model;

[0041] Inputting the posterior state estimate value at the previous moment and the current observation value into the model, dynamically predicting the optimal Kalman gain, and updating the posterior state estimate value through the predicted Kalman gain;

[0042] Judging whether the synchronization round reaches a preset value. If it has reached, end the tracking; otherwise, enter the next synchronization round to continue the clock parameter tracking process.

[0043] Among them, the recurrent neural network is first trained and then used to predict the optimal Kalman gain. The training data set of this network contains N trajectories, and each trajectory contains m time steps, denoted as Among them represents the observation sequence of the j-th trajectory, represents the corresponding true state sequence; the training objective of this recurrent neural network is to minimize the mean square error loss function with the recurrent neural network parameter Θ as the optimization variable:

[0044]

[0045] In the formula, Ψ Θ (·) represents the output of this neural network; α is the regularization coefficient.

[0046] Among them, the recurrent neural network parameter Θ is optimized through an adaptive momentum-based stochastic optimization algorithm. At each training iteration r, a small batch of data of L < N trajectories is randomly sampled and the batch loss ξ r (Θ) is calculated:

[0047] Furthermore, the posterior state estimate value is updated through the Kalman gain predicted by the recurrent neural network:

[0048]

[0049] In the formula, is the prior state estimate value, K i (Θ) is the Kalman gain predicted by the recurrent neural network, and O i represents the state observation value at the current moment.

[0050] The beneficial effects of this invention are as follows: <(1) The present invention adopts an implicit synchronization mechanism. By constructing a clock observation model and tracking algorithm at the implicit node end, the receiver alone can complete the clock parameter estimation without actively initiating synchronization requests or participating in complex two-way interactions. This significantly reduces the frequency of message interactions and communication overhead, making it suitable for deployment in energy-constrained wireless networks.

[0052] (2) The present invention takes into account the nonlinear effect of ambient temperature changes on the crystal oscillator frequency, integrates the unknown temperature coefficient as an augmented state variable into the Kalman filter framework, compensates for the frequency offset caused by temperature changes, and effectively suppresses the accumulation of clock frequency errors caused by ambient temperature differences, thereby improving the clock parameter tracking accuracy and long-term stability.

[0053] (3) The present invention adopts a data and model hybrid driving method, and uses a neural network to learn the mapping relationship between the system state residual and the optimal Kalman gain, thereby getting rid of the dependence on the precise statistical characteristics of noise. It can achieve stable and effective clock parameter tracking even when the covariance of the observed noise is partially unknown or dynamically changing, thereby enhancing the system's robustness to noise disturbances in non-ideal environments and avoiding performance degradation or even divergence problems caused by improper covariance settings.

[0054] 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

[0055] 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:

[0056] Figure 1 Schematic diagram of the process of synchronous information exchange for the wireless network receiver only;

[0057] Figure 2 This is a flow chart of a data and model hybrid driven implicit node clock parameter tracking method provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0058] 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.

[0059] 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.

[0060] 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.

[0061] An embodiment of the present invention provides a data- and model-driven implicit node clock parameter tracking method, which jointly tracks clock phase offset and frequency offset when the ambient temperature changes in real time and the prior knowledge of the observation noise covariance is unknown, thereby ensuring the reliability and robustness of wireless network time synchronization.

[0062] The method specifically comprises the following steps:

[0063] 1. For wireless network communication scenarios where the prior knowledge of the observation noise covariance is unknown, a clock observation equation is established between the implicit node and the clock source node. Considering the impact of temperature on the clock crystal oscillator, a clock state equation is established that relates the implicit node clock frequency offset to temperature changes.

[0064] like Figure 1 Figure 1 shows the process of synchronization information exchange in a wireless network communication scenario, where only the wireless network receiver exchanges synchronization information. Node A represents the active node, node M represents the clock source node, and node F represents the hidden node. The specific synchronization interaction process is as follows:

[0065] The local time of active node A is The synchronization data packet is sent to the clock source node M at the same time. When the clock source node M receives the data packet, it records the local time as and in When the active node A receives the ACK from the clock source node M, it records the local time as When the implicit node F monitors the data packet from the active node A and the ACK from the clock source node M, it records the local time as and At this point, the synchronization information exchange ends.

[0066] Based on the above timestamp information, the clock models between active node A and clock source node M, and between active node A and implicit node F are expressed as:

[0067]

[0068] in, and They represent the clock phase offset and frequency offset between the active node A and the clock source node M, respectively. and denote the clock 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 clock source node M, respectively. and denote the fixed part and random part of the total end-to-end delay between active node A and hidden node F, respectively. and is modeled as a Gaussian random variable with unknown variance. The time when active node A sends the synchronization data packet in the first synchronization cycle.

[0069] Subtracting Equation (1) from Equation (2) yields the clock model relationship between the clock source node M and the implicit node F:

[0070]

[0071] in, is the asymmetric delay difference, is the random delay difference. The clock observation equation in the asymmetric link transmission delay scenario is obtained from formula (3):

[0072] O i =H i X i +μ i +v i (4)

[0073] in, is the clock observation vector at the i-th synchronization, is the observation matrix, is the state vector at the i-th synchronization.

[0074] Based on the second-order parabolic model with unknown coefficients related to the crystal oscillator frequency and temperature changes, the relationship between clock frequency offset and temperature change is:

[0075]

[0076] Where S0 represents the standard clock frequency deviation at the reference temperature T0 = 25°C, Δs i represents the absolute clock frequency deviation caused by temperature change, β represents the unknown temperature coefficient; w S,i Representing random external environmental interference and quantitative errors in the temperature measurement process, it is modeled as a Gaussian random variable with a mean of 0 and unknown covariance. The unknown temperature coefficient change is modeled as a first-order linear difference equation, expressed as:

[0077] β i =β i-1 +w β,i (6)

[0078] Among them, w β,i represents Gaussian white noise with mean 0 and unknown covariance.

[0079] Combining equations (5) and (6), we can obtain the recursive relationship between temperature change and clock frequency offset:

[0080]

[0081] in, represents cumulative Gaussian noise with zero mean and unknown covariance.

[0082] Further combining the two-state clock model, the clock state equation is:

[0083]

[0084] Where τ represents the sampling interval, w θ,i represents Gaussian noise with mean 0 and unknown covariance.

[0085] 2. A clock state space model of implicit nodes is established by combining the clock observation equation and the clock state equation. The unknown temperature coefficient is expanded to the state vector, and the clock parameters are tracked using a data-model hybrid drive method. The historical clock state observations and true values ​​constitute a training set, and the evolution law of clock parameters is learned through a recurrent neural network to establish a Kalman gain prediction model. The posterior state estimate of the previous moment and the current observation value are input into the model to dynamically predict the optimal gain, thereby adaptively balancing the confidence weights of the prediction and observation.

[0086] The specific process is as follows:

[0087] Combining Equation (4) and Equation (8), the implicit node clock state space model is obtained as:

[0088]

[0089] in, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, the state noise matrix

[0090] Similar to equation (6), the asymmetric delay variation is modeled as a first-order linear difference equation, expressed as:

[0091] μ i =μ i-1 +w μ,i (10)

[0092] Among them, w μ,i represents Gaussian white noise with mean 0 and unknown covariance.

[0093] Augment the unknown temperature coefficient and asymmetric delay to the state vector X i In the example, the augmented state vector is:

[0094]

[0095] The state space model is constructed based on the state vector of formula (11), and the expression is:

[0096]

[0097] in, I is the identity matrix.

[0098] According to the state space model shown in formula (12), the prior state estimate is calculated using the following formula:

[0099]

[0100] in, represents the prior state estimate value, represents the posterior state estimate value at the previous moment.

[0101] The Kalman gain K i (Θ) is predicted through end-to-end (E2E) training, with the neural network parameter Θ as the optimization variable, and is achieved by minimizing the mean square error loss function; the training dataset contains N trajectories, each trajectory contains m time steps, denoted as where represents the observation sequence of the j-th trajectory, represents the corresponding true state sequence; the recursive estimation process is carried out over m time steps. For each trajectory j, the minimum mean square error loss function is defined as follows:

[0102]

[0103] where, Ψ Θ (·) represents the output of the neural network, and α is the regularization coefficient for suppressing overfitting and enhancing generalization ability.

[0104] The parameters Θ are optimized using the stochastic optimization algorithm based on adaptive momentum. At each training iteration r, a small batch of data of L < N trajectories is randomly sampled and the batch loss ξ r (Θ) is calculated by the following formula:

[0105]

[0106] The state update is performed by the Kalman gain predicted by the neural network, which is expressed as:

[0107]

[0108] where, represents the posterior state estimate value, O i represents the state observation value at the current moment.

[0109] Figure 2 The implicit node clock parameter tracking method described in this embodiment is shown. This method provides joint tracking of clock phase offset and frequency offset applicable to low-power wireless networks affected by real-time changes in environmental temperature and unknown prior knowledge of observation noise covariance. Specifically, it includes the following steps:

[0110] P1: The data and model hybrid-driven implicit node clock parameter tracking process starts;

[0111] P2: Initialize the data and model hybrid-driven method;

[0112] P3: The active node and the clock source node perform synchronous message interaction, and the implicit node listens to the interaction process;

[0113] P4: Obtain the clock phase offset observation value based on the clock model and timestamp information of the implicit node and the clock source node;

[0114] P5: Predict the state value at time i based on the clock state model;

[0115] P6: Predicting Kalman Gain via Recurrent Neural Networks;

[0116] P7: Use the gains of the neural network prediction to weight the predicted values ​​and the observed values ​​to update the posterior estimate;

[0117] P8-P9: 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 P3 to continue the clock parameter tracking process;

[0118] P10: The implicit node clock parameter tracking process driven by data and model hybrid is completed.

[0119] 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 data and model hybrid driven implicit node clock parameter tracking method, characterized in that: The method includes: For wireless network communication scenarios where the ambient temperature changes in real time and the observation noise covariance is unknown a priori, a clock observation equation is established between the implicit node and the clock source node. Considering the impact of temperature changes on the clock crystal oscillator, a clock state equation is established that relates the implicit node clock frequency offset to temperature changes. Combining the clock observation equation and the clock state equation, a clock state space model of the implicit node is established, and the clock state vector is augmented; During the period when the active node and the clock source node in the wireless network exchange synchronization messages, the hidden node monitors the interaction process and obtains the timestamp information; The clock observation vector is obtained according to the clock observation equations and timestamp information of the implicit node and the clock source node. The ambient temperature at the sampling moment in the synchronization period is obtained and the clock state vector at that moment is predicted according to the clock state equation. The clock parameters are tracked using a data and model hybrid driving method.

2. The method according to claim 1, characterized in that In a wireless network communication scenario where the ambient temperature changes in real time and the observation noise covariance is unknown, only the receiver synchronizes the information exchange. During the interaction, the active node A is at the local time The synchronization data packet is sent to the clock source node M at the same time. When the clock source node M receives the data packet, it records the local time as and in When the active node A receives the ACK from the clock source node M, it records the local time as When the implicit node F monitors the data packet from the active node A and the ACK from the clock source node M, it records the local time as and The clock models between active node A and clock source node M and between active node A and implicit node F are expressed as: Where, and They represent the clock phase offset and frequency offset between the active node A and the clock source node M, respectively. and denote the clock 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 clock source node M, respectively. and denote the fixed and random parts of the overall end-to-end delay between active node A and hidden node F, respectively; The time when active node A sends synchronization data packets in the first synchronization cycle; According to the above formula, the clock model relationship between the clock source node M and the implicit node F is: Where, is the asymmetric delay difference, is the random delay difference; Then the clock observation equation 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 state vector at the i-th synchronization.

3. The method according to claim 2, characterized in that Based on the second-order parabolic model with unknown coefficients related to the crystal oscillator frequency and temperature changes, the relationship between clock frequency offset and temperature change is: Where S0 represents the standard clock frequency deviation under i represents the absolute clock frequency deviation caused by temperature change, β represents the unknown temperature coefficient; w S,i Represents random external environmental interference and quantitative errors in the temperature measurement process; the unknown temperature coefficient change is modeled as a first-order linear difference equation: β i ＝β i-1 +w β,i Where w β,i represents Gaussian white noise with a mean of 0 and unknown covariance. Combining the above formula, the recursive relationship between temperature change and clock frequency offset is: Where, represents the cumulative Gaussian noise with a mean of 0 and unknown covariance; combined with the two-state clock model, the clock state equation is: Where τ represents the sampling interval, w θ,i represents Gaussian noise with mean 0 and unknown covariance.

4. The method according to claim 3, characterized in that Combining the clock observation equation and the clock state equation, the clock state space model of the implicit node is established, which is expressed as: Where, is the state transition matrix, is the coefficient matrix related to the temperature coefficient, is the unit coefficient matrix, the state noise matrix Augment the unknown temperature coefficient and asymmetric delay to the state vector X i middle: According to the state vector Reconstruct the clock state space model: Where, I is the identity matrix.

5. The method according to claim 4, characterized in that Obtain the clock phase offset observation value based on the clock observation equation and timestamp information, obtain the ambient temperature at a certain sampling time within the synchronization period, and predict the clock state vector at that time based on the clock state equation; A hybrid data and model-driven approach is used to track clock parameters, including: The historical clock state observations and true values ​​constitute a training set, and the evolution law of clock parameters is learned through a recurrent neural network to establish a Kalman gain prediction model; Input the previous moment's posterior state estimate and the current observation value into the model, dynamically predict the optimal Kalman gain, and update the posterior state estimate with the predicted Kalman gain; Determine whether the synchronization round has reached the preset value. If so, end the tracking; otherwise, enter the next synchronization round to continue the clock parameter tracking process.

6. The method according to claim 5, characterized in that The recurrent neural network is trained to predict the optimal Kalman gain. The training dataset contains N trajectories, each with m time steps, denoted as in represents the observation sequence of the j-th trajectory, Represents the corresponding true state sequence; the training goal of the recurrent neural network is to minimize the mean square error loss function with the recurrent neural network parameter Θ as the optimization variable: Where, Θ (·) represents the output of the neural network; α is the regularization coefficient.

7. The method according to claim 6, characterized in that The parameters Θ of the recurrent neural network are optimized by the stochastic optimization algorithm based on adaptive momentum. At each training iteration r, a small batch of data of L < N trajectories is randomly sampled and the batch loss ξ r (Θ) is calculated:

8. The method according to claim 7, characterized in that Update the posterior state estimate using the Kalman gain predicted by the recurrent neural network: Where, is the prior state estimate, K i (Θ) is the Kalman gain predicted by the recurrent neural network, O i Represents the state observation value at the current moment.

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