Clock error prediction method based on Kalman filtering combined with long and short term memory network

Abstract

The invention discloses a clock error prediction method based on Kalman filtering in combination with a long and short term memory network, and belongs to the technical field of bidirectional comparison clock error prediction. The method comprises the following steps: constructing an LSTM network; constructing a KF algorithm model; obtaining training data, and carrying out normalization processing; performing joint training on the LSTM network and the KF algorithm model by using the normalized training data; acquiring clock error data in an actual scene, and performing normalization processing; and inputting the processed clock error data into the trained LSTM network, taking the output of the LSTM network as parameters Qt and Rt in the KF algorithm model, and obtaining a clock error prediction result through operation of the KF algorithm model. According to the invention, the Kalman filtering algorithm is optimized by using the long and short term memory network, the problem that the Kalman filtering algorithm depends on priori knowledge is solved, and more accurate clock error prediction is realized by combining the long-term memory ability of the long and short term memory network and the real-time updating characteristic of the Kalman filtering algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of two-way comparison clock error prediction in a time synchronization system, and specifically relates to a clock error prediction method based on a Kalman filter (KF) combined with a long short-term memory (LSTM) network. Background Art

[0002] In the field of modern science and technology, time synchronization plays a vital role, and clock error prediction is one of the key technologies for time synchronization to achieve accurate operation. Existing technologies have conducted a lot of research in the field of clock error prediction, and developed a variety of prediction models, such as linear regression model, polynomial model, grey model, least squares support vector machine and KF algorithm model. Among them, the KF algorithm is widely used due to its recursive form, small data storage volume and applicability to multidimensional and non-stationary random processes.

[0003] The traditional KF algorithm uses the state space model of signal and noise, and uses the estimated value of the previous moment and the observed value of the current moment to update the estimate of the state variable, and calculates the estimated value of the current moment, which is of great significance for real-time data processing. However, the information of KF, such as the state matrix, state noise and observation noise, all comes from prior knowledge and is affected by people's prior knowledge, so the calculation ability of KF is greatly limited.

[0004] It can be seen that although the KF algorithm has been widely used in practice, its prediction performance is often limited by the accuracy and completeness of prior knowledge. In recent years, the LSTM network has attracted much attention due to its excellent time series prediction ability, providing a new idea for solving the limitations of the KF algorithm. LSTM is a special recurrent neural network (RNN) that aims to solve the long-term dependency problem in RNN, that is, it cannot effectively learn features in longer time series. LSTM achieves this goal by introducing memory cells and three logic gates (input gate, forget gate and output gate) that control information transmission. It is suitable for processing and predicting events with relatively long intervals and delays in time series.

[0005] For the LSTM network, the signal control at time t is jointly determined by the output at time t-1 and the input at time t, including the memory unit, forget gate, input gate and output gate. The forget control determines whether the data stored in the memory unit is valid. When the forget gate is valid, the data in the memory unit is cleared; the input gate controls whether the input data at that moment is valid; the input data and the memory unit data passing through the forget gate are operated, and the output gate determines whether the data is output. When the output gate is valid, the data at that moment is output.

[0006] However, there is no application in the prior art that combines the LSTM network with the KF algorithm model for clock error prediction. Summary of the invention

[0007] In view of this, the present invention proposes a clock error prediction method based on Kalman filtering combined with long short-term memory network, which effectively solves the problem that the KF algorithm relies on prior knowledge, improves the accuracy and stability of clock error prediction, and thus enhances the performance of the time synchronization system.

[0008] The technical solution adopted by the present invention is:

[0009] A clock error prediction method based on Kalman filtering combined with long short-term memory network includes the following steps:

[0010] Step 1, build an LSTM network, including input layer, hidden layer and output layer;

[0011] Step 2, construct a KF algorithm model, wherein the first equation of the KF algorithm model is used to derive the state prediction at time t+1 from the state estimation at time t, and the second equation of the KF algorithm model is used to adjust the prediction value at time t+1 to obtain the state estimation at time t+1;

[0012] Step 3: Obtain the measured clock error data, extract a portion of the measured clock error data as training data, and merge the training data into a 1-row n-column data matrix x t , n is the length of training data, and normalization is performed;

[0013] Step 4: Use the normalized training data to jointly train the LSTM network and KF algorithm model;

[0014] Step 5: Get the clock error data in the actual scene and merge them into a 1-row and m-column data matrix x' t , m is the length of clock error data, and normalization is performed;

[0015] Step 6: Input the data processed in step 5 into the trained LSTM network, and use the output of the LSTM network as the parameter Q in the KF algorithm model. t and R t , after the operation of the KF algorithm model, the clock error prediction result is obtained.

[0016] Furthermore, in step 1, the input layer includes 1 node, the hidden layer includes 4 nodes, and the output layer includes 2 nodes. The change relationship of each node in the LSTM network is as follows:

[0017] f t =s(W fh ×h t-1 +W fxx t +b f ) (1)

[0018] i t =s(W ih h t-1 +W ix x t +b i ) (2)

[0019] o t =s(W oh h t-1 +W ox x t +b o ) (3)

[0020]

[0021] Among them, x represents the input data of the current node, σ represents the sigmoid activation function, tanh is an activation function, W is the weight matrix of each gate, the subscript of W represents two corresponding parameters, and b is the bias term of each gate. represents element-wise multiplication, f represents the forget gate parameter, i represents the input gate parameter, and o represents the output gate parameter. represents the current memory unit state, c represents the current memory unit output, h represents the output value of the current node, and the subscripts t and t-1 represent two adjacent moments.

[0022] Furthermore, the first equation of the KF algorithm model is:

[0023]

[0024] Among them, F t Indicates the operating rules of the system itself. represents the state estimate at time t, Represents the state prediction at time t+1;

[0025] The second equation of the KF algorithm model is:

[0026]

[0027] in, represents the state estimate at time t+1, Y t+1 represents the data observation value at time t+1, H t+1 represents the observation matrix, G t+1 is the Kalman gain, and the calculation formula is:

[0028]

[0029] Among them, Rt+1 represents the variance of the observation noise, P t+1 / t It represents the prediction error of the data at time t+1 predicted by the data at time t, and its calculation method is:

[0030] P t+1 / t =F t P t / t F t T +Q t (10)

[0031] Among them, Q t represents the variance of the state noise, P t / t It represents the estimation error of the estimated value at time t estimated by the data at time t;

[0032] The estimation error of the estimated value at time t+1 estimated by the data at time t+1 is:

[0033]

[0034] Furthermore, the specific method of step 4 is:

[0035] Step 401: train the data x t Input the LSTM network and use the output of the LSTM network as the parameter Q of the KF algorithm model t and R t ;

[0036] Step 402: Q t and R t The two parameters are input into the KF algorithm model and calculated according to equations (7) to (11) to obtain the Kalman estimate That is the calculation result of formula (7);

[0037] Step 403, calculate the error term error of the LSTM network according to formula (12):

[0038]

[0039] Step 404, feeding back the error term error to the LSTM network to update the weight matrix;

[0040] Step 405, perform multiple rounds of iterations to complete the joint training of the LSTM network and the KF algorithm model.

[0041] Furthermore, in step 6, the operation of the KF algorithm model refers to the calculation according to equations (7) to (11), and the obtained clock error prediction result is the calculation result of equation (7).

[0042] The present invention has the following beneficial effects:

[0043] 1. By combining the long-term memory capability of the LSTM network and the real-time update characteristics of the KF algorithm, the present invention can achieve more accurate clock error prediction and improve the accuracy and stability of clock error prediction.

[0044] 2. The present invention helps to improve the performance of the time synchronization system and provides new methods and ideas for research in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Flow chart of the clock error prediction method in an embodiment of the present invention.

[0046] Figure 2 Schematic diagram of iterative training error of the clock error prediction method in an embodiment of the present invention.

[0047] Figure 3 Schematic diagram comparing the prediction results of clock error data using different methods in the embodiments of the present invention.

[0048] Figure 4 Schematic diagram of Q and R prediction results output by the clock error prediction method in an embodiment of the present invention.

[0049] Figure 5 Schematic diagram of the comparison between the predicted value and the measured value of the KF algorithm model.

[0050] Figure 6 This is a schematic diagram comparing the predicted values ​​and measured values ​​of the LSTM algorithm model.

[0051] Figure 7 This is a schematic diagram comparing the predicted values ​​and measured values ​​of the LSTM+KF algorithm model. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0053] A clock error prediction method based on Kalman filtering combined with long short-term memory network, such as Figure 1 As shown, the following steps are included:

[0054] Step 1: Build an LSTM network, including an input layer, a hidden layer, and an output layer. Specifically, the input layer includes 1 node, the hidden layer includes 4 nodes, and the output layer includes 2 nodes. The change relationship of each node in the LSTM network is as follows:

[0055] f t =s(W fh ×h t-1 +W fx x t +b f ) (1)

[0056] it =s(W ih h t-1 +W ix x t +b i ) (2)

[0057] o t =s(W oh h t-1 +W ox x t +b o ) (3)

[0058]

[0059] Among them, x represents the input data of the current node, σ represents the sigmoid activation function, tanh is also an activation function, W is the weight matrix of each gate, and b is the bias term of each gate. represents element-wise multiplication, f represents the forget gate parameter, i represents the input gate parameter, and o represents the output gate parameter. represents the current memory unit state, c represents the current memory unit output, and h represents the output value of the current node.

[0060] The training method of LSTM is the same as that of RNN, which is back propagation. First, based on equations (1) to (6), the output value of each neuron is forward calculated, and then the error term of each neuron is calculated and back propagated. The error calculation formula is:

[0061]

[0062] According to the calculated error value, back propagation is performed to obtain the gradient of each weight, and the weight matrix is ​​updated. The training of the LSTM network is finally completed after iteration.

[0063] Step 2: Construct the KF algorithm model, specifically:

[0064] The first equation of the KF algorithm model is to derive the state prediction at time t+1 from the state estimation at time t:

[0065]

[0066] Among them, F t Indicates the operating rules of the system itself. represents the state estimate at time t, Represents the state prediction at time t+1. By adjusting the predicted value at time t+1, we get the state estimate at time t+1, which is the second equation of the KF algorithm model:

[0067]

[0068] in, represents the state estimate at time t+1, Y t+1 represents the data observation value at time t+1, H t+1 represents the observation matrix, G t+1 Kalman gain, calculated as:

[0069]

[0070] Among them, R t+1 represents the variance of the observation noise, P t+1 / t It represents the prediction error of the data at time t+1 predicted by the data at time t, and its calculation method is:

[0071] P t+1 / t =F t P t / t F t T +Q t (10)

[0072] Among them, Q t represents the variance of the state noise, P t / t represents the estimated error of the estimated value at time t estimated by the data at time t, then the estimated error of the estimated value at time t+1 estimated by the data at time t+1 is:

[0073]

[0074] Step 3: Obtain the clock error data in the actual scene, extract a part of the measured data as training data, and merge it into a 1-row n-column data matrix x t (n is the length of training data), and normalize it;

[0075] Step 4: Use the training data to jointly train the LSTM network and KF algorithm model. The specific method is as follows:

[0076] Step 401: train the data x t Input the LSTM network and use the output of the LSTM network as the parameter Q of the KF algorithm t and R t ;

[0077] Step 402: Q t and R t The two parameters are input into the KF algorithm and calculated according to equations (7) to (11) to obtain the Kalman estimate

[0078] Step 403, calculate the error term error of the LSTM network according to formula (12):

[0079]

[0080] Step 404, feeding back the error term error to the LSTM network to update the weight matrix;

[0081] Step 405, perform 50 rounds of iterations to complete the training of the LSTM+KF algorithm;

[0082] Step 5: Obtain the clock error data in the actual scene. Except for the training data intercepted in step 3, all of them are used as test data and merged into a data matrix x' with 1 row and m columns t (m is the length of the test data), and normalize it;

[0083] Step 6: Test data x' t Input the trained LSTM network and calculate the parameter Q in the output KF algorithm model t and R t , and then through the KF algorithm model operation of formula (7) to formula (11), the Kalman estimation value is obtained That is, the clock error prediction result obtained by the LSTM+KF algorithm.

[0084] Since the KF algorithm relies heavily on prior knowledge, namely the state matrix F, state noise V t With the observation noise W t Therefore, this method uses the LSTM network to optimize the KF algorithm so that it does not require the input of prior knowledge, can be used directly, and has stronger linear fitting and data prediction capabilities.

[0085] The basic idea of ​​the LSTM+KF algorithm is to use LSTM network training to predict prior knowledge that cannot be directly obtained in KF. Generally speaking, it is assumed that the input noise is Gaussian white noise with a mean of 0 and a variance of Q t and R t In addition, the state matrix F and the transfer matrix H can be considered as unit matrices in clock error prediction applications, that is, F = H = I. The modified LSTM + KF algorithm process is as follows Figure 1 shown.

[0086] like Figure 1 As shown in (a), the KF parameter Q is obtained by LSTM network training t and R t , and then substitute it into the KF algorithm to estimate the clock error data. Then calculate the error term error according to formula (14), feed the error back to the LSTM network to update the weight matrix, and iterate repeatedly to complete the establishment of the LSTM+KF algorithm model.

[0087] like Figure 1 As shown in (b), for the trained LSTM+KF algorithm model, the clock error data is input into the LSTM network to calculate the KF prior parameter Q t and R t , then use the KF algorithm to estimate and predict the clock error and output the prediction result

[0088] Next, we select the clock difference data obtained by measuring the time synchronization system based on two-way comparison. The measurement method is to shut down the time synchronization algorithm program and only measure the time difference between the clock signal transmitted from the near end to the far end and the local clock signal at the far end. The measurement result is used to perform clock difference prediction simulation.

[0089] The number of LSTM network nodes is set. According to the actual application of the LSTM+KF algorithm model in clock error prediction, the input node is set to 1, which is used to input the measured value of the clock error; the intermediate nodes are set to 4; and the output nodes are set to 2, which are used to output the prior knowledge in the KF algorithm, that is, the state noise variance Q t and the observation noise variance R t .

[0090] First, the LSTM+KF model training was completed, and the clock error data was input into the preset algorithm model. 50 rounds of iterative training were performed to achieve model convergence. The error curve of the iterative process is shown in the figure below: Figure 2 As shown in the figure, the LSTM+KF model has been updated 50 times and converged after about 15 times. Therefore, the number of iterations can be appropriately reduced in subsequent algorithm model optimization to improve learning efficiency.

[0091] The same set of clock error data was estimated and predicted using a separate KF algorithm (using the empirical values ​​in practice as prior parameters), a separate trained LSTM algorithm, and the above trained LSTM+KF algorithm. The results are as follows: Figure 3 The clock error data is based on about 3 hours of measurement data with a measurement interval of 1 second. Since the clock error data has a deviation of about 90ms, in order to facilitate demonstration and calculation, the large deviation is subtracted and only the clock error change trend is retained in the result.

[0092] like Figure 3 As shown in the figure, we can see that the KF algorithm can achieve good prediction results, but there is still room for optimization and improvement. This is mainly due to the influence of prior knowledge. If we want to improve the prediction ability of the KF algorithm, we need to further improve the prior parameters.

[0093] By using a separate LSTM algorithm for training and performing estimated predictions based on clock error data, it can be found that the prediction results deviate when the slope of the clock error data changes significantly. This is mainly because the training data set is small and does not cover all clock error change scenarios. The LSTM network can be trained and iterated by collecting longer clock error data to improve its prediction accuracy and prediction ability.

[0094] The use of LSTM+KF algorithm avoids the above problems. It not only solves the problem that the KF algorithm requires prior knowledge, but also solves the problem that the LSTM algorithm has poor model generalization ability due to the small training data set.

[0095] After training, the state noise variance Q output by the LSTM+KF model is t and the observation noise variance R t Curve like Figure 4 As shown in the figure, the comparison between the predicted values ​​of the clock error and the actual measured values ​​of the clock error by the three different algorithm models is shown in Figure 5 , Figure 6 and Figure 7 shown.

[0096] In order to more intuitively compare the results obtained by the three different algorithms, the predicted values ​​were compared with the clock error measurement values. Since the LSTM algorithm model did not achieve good prediction ability in the prediction of the clock error test set, the variance of the clock error result predicted by it was not calculated, and the variance of the actual measured value of the clock error was 1.26ns, the KF algorithm model predicted the clock error value variance to be 1.248ns, and the LSTM+KF algorithm model predicted the clock error value variance to be 1.239ns. Therefore, it can be said that the LSTM+KF algorithm model proposed in the present invention has a large application prospect in the field of clock error prediction, and provides a new solution for the correction of the clock error model of the time synchronization system.

[0097] In summary, the present invention optimizes the Kalman filter algorithm using the long short-term memory network, establishes a Kalman filter algorithm model based on the long short-term memory network, and uses the model to predict the clock error of the time synchronization system based on two-way comparison. The present invention solves the problem that the Kalman filter algorithm relies on prior knowledge, and combines the long-term memory capacity of the long short-term memory network and the real-time update characteristics of the Kalman filter algorithm to achieve more accurate clock error prediction. The present invention helps to improve the performance of the time synchronization system and also provides new methods and ideas for research in related fields.

[0098] It should be noted that the technical solution of the present invention is not limited to the above-mentioned specific embodiments, and all technical variations made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims

1. A clock error prediction method based on Kalman filtering combined with long short-term memory network, characterized in that: The following steps are involved: Step 1, build an LSTM network, including input layer, hidden layer and output layer; Step 2, construct a KF algorithm model, wherein the first equation of the KF algorithm model is used to derive the state prediction at time t+1 from the state estimation at time t, and the second equation of the KF algorithm model is used to adjust the prediction value at time t+1 to obtain the state estimation at time t+1; Step 3: Obtain the measured clock error data, extract a portion of the measured clock error data as training data, and merge the training data into a 1-row n-column data matrix x t , n is the length of training data, and normalization is performed; Step 4: Use the normalized training data to jointly train the LSTM network and KF algorithm model; Step 5: Get the clock error data in the actual scene and merge them into a 1-row and m-column data matrix x' t , m is the length of clock error data, and normalization is performed; Step 6: Input the data processed in step 5 into the trained LSTM network, and use the output of the LSTM network as the parameter Q in the KF algorithm model. t and R t , after the operation of the KF algorithm model, the clock error prediction result is obtained.

2. According to claim 1, a clock error prediction method based on Kalman filtering combined with long short-term memory network is characterized in that: In step 1, the input layer includes 1 node, the hidden layer includes 4 nodes, and the output layer includes 2 nodes. The change relationship of each node in the LSTM network is as follows: f t =s(W fh ×h t-1 +W fx x t +b f ) (1) i t =s(W ih h t-1 +W ix x t +b i ) (2) o t =s(W oh h t-1 +W ox x t +b o ) (3) Among them, x represents the input data of the current node, σ represents the sigmoid activation function, tanh is an activation function, W is the weight matrix of each gate, the subscript of W represents two corresponding parameters, and b is the bias term of each gate. represents element-wise multiplication, f represents the forget gate parameter, i represents the input gate parameter, and o represents the output gate parameter. represents the current memory unit state, c represents the current memory unit output, h represents the output value of the current node, and the subscripts t and t-1 represent two adjacent moments.

3. According to claim 2, a clock error prediction method based on Kalman filtering combined with long short-term memory network is characterized in that: The first equation of the KF algorithm model is: Among them, F t Indicates the operating rules of the system itself. represents the state estimate at time t, Represents the state prediction at time t+1; The second equation of the KF algorithm model is: in, represents the state estimate at time t+1, Y t+1 represents the data observation value at time t+1, H t+1 represents the observation matrix, G t+1 is the Kalman gain, and the calculation formula is: Among them, R t+1 represents the variance of the observation noise, P t+1 / t It represents the prediction error of the data at time t+1 predicted by the data at time t, and its calculation method is: Among them, Q t represents the variance of state noise, P t / t It represents the estimation error of the estimated value at time t estimated by the data at time t; The estimation error of the estimated value at time t+1 estimated by the data at time t+1 is:

4. According to claim 3, a clock error prediction method based on Kalman filtering combined with long short-term memory network is characterized in that: The specific method of step 4 is: Step 401: train the data x t Input the LSTM network and use the output of the LSTM network as the parameter Q of the KF algorithm model t and R t ; Step 402: Q t and R t The two parameters are input into the KF algorithm model and calculated according to equations (7) to (11) to obtain the Kalman estimate That is the calculation result of formula (7); Step 403, calculate the error term error of the LSTM network according to formula (12): Step 404, feeding back the error term error to the LSTM network to update the weight matrix; Step 405, perform multiple rounds of iterations to complete the joint training of the LSTM network and the KF algorithm model.

5. According to claim 3, a clock error prediction method based on Kalman filtering combined with long short-term memory network is characterized in that: In step 6, the operation of the KF algorithm model refers to the calculation according to equations (7) to (11), and the obtained clock error prediction result is the calculation result of equation (7).

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