Unpowered ship drifting trajectory prediction method

Abstract

The invention discloses an unpowered ship drifting trajectory prediction method, and relates to the technical field of ship trajectory prediction, and the method comprises the following steps: 1, obtaining historical trajectory data of an unpowered ship, and carrying out the preprocessing of data filtering and abnormal data elimination on the historical trajectory; step 2, carrying out normalization processing on the ship historical trajectory data after interpolation; step 3, dividing a ship historical trajectory data set obtained after interpolation normalization; step 4, using CEEMDAN to decompose the data of the training set; step 5, noise screening is carried out on the decomposed data according to a kurtosis screening method; step 6, putting the screened and denoised data and the original data into a BiLSTM model, then outputting the data through a full connection layer, and adjusting model parameters through a minimization MSE (Minimum Square Error); and step 7, inputting the test set into the trained CEEMDAN-BiLSTM model, predicting trajectory data in the test set by using a sliding window mode, and verifying the accuracy of a prediction result through MAE and RMSE.

Description

Technical Field

[0001] The invention relates to the technical field of ship trajectory prediction, and in particular to a method for predicting the drifting trajectory of an unpowered ship. Background Art

[0002] At present, there are few studies on the prediction of unpowered ship trajectories. The current prediction of marine ship drift trajectories is mainly carried out by establishing wind pressure models or theoretical models, using local ocean currents and wind field data as forcing fields. Therefore, most of the current unpowered ship drift trajectory prediction models only consider the effects of flow and wind on the target object.

[0003] Wind pressure drift is the movement of the part of the target above the water surface relative to the local ocean current caused by wind and waves. The research on wind pressure model methods obtains drift observation data by conducting a large number of drift tests of offshore targets, and uses empirical statistical methods to fit and determine model parameters. For example, the Lagrange tracking method predicts based on the drift velocity, which is caused by fluid flow. The Lagrange tracking method establishes a fluid mechanics equation based on the drift velocity to describe the velocity field of the fluid. According to the fluid velocity field and the position of the particles, the particle trajectory is calculated by the motion equation (usually the acceleration and velocity equation of the object moving in the fluid). The establishment of the motion equation is different in different situations. The establishment of the theoretical model usually adopts a semi-analytical method, that is, it is simplified under reasonable assumptions through force analysis. Since these two methods need to fit parameters according to data to establish formulas, for large-scale or high-resolution simulations, a lot of resources and time are required to determine the parameters of the model, and the model often relies on a series of simplified physical assumptions and the limitations of the environment where the data area is located, and may not be well adapted to the rapid or complex changes in environmental conditions.

[0004] With the popularity of deep learning, more and more people are applying deep learning to all aspects of life. Li Xiaobin and others proposed to predict the trajectory of unpowered ships based on LSTM (Long Short-Term Memory Network). By obtaining the historical trajectory data of unpowered ships and training based on the historical trajectory data, a trajectory prediction model is obtained. Then, based on the trajectory prediction model and the time series of the navigation trajectory in the historical data, the motion trajectory of the unpowered ship in the future period can be predicted, thus realizing the prediction of the motion trajectory of the unpowered ship. LSTM is a special type of recurrent neural network (RNN) that aims to solve the gradient vanishing and gradient exploding problems encountered by traditional RNN when processing long time series data. LSTM is controlled by three gates to control the cell state. The three gates work together to ensure that LSTM can handle long-term dependency problems. LSTM can save and transmit important information when processing long time series, but LSTM can only use the forward information of the sequence data to make predictions. Using only one-way information may not be enough to understand the entire sequence. For some tasks, especially those that need to consider contextual information, one-way LSTM may lose the information at the back of the sequence. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the drift trajectory of an unpowered ship, so as to solve the problem that the existing prediction model in the prior art is difficult to adapt to environmental conditions and make changes, thereby resulting in inaccurate data extraction and low prediction accuracy.

[0006] To achieve the above object, the present invention provides a method for predicting the drift trajectory of an unpowered ship, comprising the following steps: Step 1, obtain the historical trajectory data of the unpowered ship, and perform data filtering and abnormal data elimination preprocessing on the historical trajectory; the historical trajectory data includes longitude and latitude, flow velocity, flow direction, wind speed, and wind direction; among them, the sampling interval of longitude and latitude, flow velocity, and flow direction data is small, and the outliers in the longitude and latitude information are deleted, and the mean of the two points before and after is used for interpolation; the sampling frequency of wind speed and wind direction is large, and in order to align with the sampling frequency of longitude and latitude, flow velocity, and flow direction data, cubic spline interpolation is used; Step 2, normalizing the interpolated historical trajectory data of the ship; Step 3: Divide the ship historical trajectory data set obtained after interpolation normalization into a training set and a test set according to a ratio of 8:2, and use a sliding window to segment the preprocessed ship historical trajectory data for the divided training set and test set. Use a sliding window to divide the historical navigation time into multiple time periods, and then use the divided time periods and the corresponding navigation trajectories as a set of data to obtain multiple sets of such data. The purpose of segmenting the ship historical trajectory data is to determine the training data that can be used to train the trajectory prediction model through the obtained historical trajectory segmentation data, and to determine the prediction target in the subsequent prediction process; Step 4: Use CEEMDAN to decompose the training set data, and decompose the flow velocity and flow direction data of each sliding window respectively. The process of decomposing the flow velocity and flow direction data is the same; Step 5: Filter noise from the decomposed data using the kurtosis screening method; Step 6: Put the filtered and denoised data and the original longitude, latitude, wind speed, and wind direction data into the BiLSTM model and output them through a fully connected layer, and adjust the model parameters by minimizing MSE; Step 7: Input the test set into the trained CEEMDAN-BiLSTM model, use the sliding window method to predict the trajectory data in the test set, and verify the accuracy of the prediction results through MAE (mean absolute error) and RMSE (root mean square error).

[0007] Preferably, the calculation expression for filling in the mean of the two points before and after in step 1 is as follows: ; In the formula, Indicates missing data, , Respectively represent the valid data before and after.

[0008] Preferably, the process of using the cubic spline interpolation method to fill in step 1 is as follows: Suppose there are n+1 data points , for each pair of adjacent data points and A cubic polynomial segment is used to interpolate between the two intervals. , define a cubic polynomial , the expression is as follows: ; In the formula, 、 、 、 is the coefficient to be determined, where The following constraints are met: Constraint 1: Function continuity, at each data point At , the polynomial values ​​of adjacent intervals must be the same; Constraint 2: First-order derivative continuity, at each data point At , the first-order derivatives of the polynomials in adjacent intervals must be the same; Constraint three: Second-order derivative continuity, at each data point At , the second-order derivatives of the polynomials in adjacent intervals must also be the same; Constraint 4: At the boundary nodes, the second-order derivative is zero.

[0009] Preferably, in step 2, the interpolated historical trajectory data of the ship is normalized. The expression is as follows:

[0010] In the formula, The average of each type of data in the training set, including latitude and longitude, flow velocity, flow direction, wind speed, and wind direction, is calculated to obtain 6 values; The minimum value of each type of data in the training set, namely longitude and latitude, flow velocity, flow direction, wind speed, and wind direction, is calculated to obtain 6 values; x is the sum of the training set and the test set (training set data + test set data), and the longitude value in x is subtracted from the average longitude value, and then divided by the maximum longitude value minus the minimum longitude value to obtain The same applies to the longitude, latitude, flow velocity, flow direction, wind speed and wind direction.

[0011] Preferably, the process of decomposing the flow rate using CEEMDAN is as follows: S41, first generate a white noise sequence, and superimpose the white noise sequence with the flow rate sequence x to obtain different noise-added signals , the calculation expression is as follows: ; In the formula, represents the velocity sequence x plus the The value obtained after white noise, is the added white noise; S42, perform the first decomposition, The noisy signal is decomposed by EMD, and we get IMF components; S43, yes The IMF components are added and averaged to obtain , the calculation expression is as follows: ; In the formula, Represents the first decomposition IMF components; S44. Subtract the extracted mean from the velocity series x , and the remaining As a new signal for the next decomposition, the calculation expression is as follows: ; S45, yes Add a white noise sequence and superimpose it to obtain different noise signals; then start the second decomposition and calculate the average value to obtain ,from Extract ,get , and then As a new signal for the next decomposition, repeat the above steps until the decomposition stops. Assuming that After the decomposition is completed, as follows: ; In the formula, is the residual of the final decomposition.

[0012] Preferably, the BiLSTM includes two LSTMs, one to process the sequence forward and one to process the sequence backward. After processing, the outputs of the two LSTMs are concatenated. Specifically, the BiLSTM processes the LSTM forward to obtain the hidden state of each time step. Hidden state at each time step obtained by reverse processing with LSTM Splice to get Finally, the BiLSTM obtained Put it into a fully connected layer to get the final output. The full connection is calculated by the following formula: ; in, is the output value, W is the weight matrix, and b is the bias; Among them, LSTM uses three gates to control the cell state. The three gates are called forget gate, input gate and output gate, as follows: 1) Forget gate. The purpose of the forget gate is to decide which information should be forgotten or retained from the memory unit at each time step; it is calculated by the following formula: ; in, is the logistic activation function, and are the weight matrix and bias term of the forget gate respectively, is the concatenation of the hidden state of the previous time step and the input of the current time step, is the output of the forget gate, Determines how much information about the memory cell state at the previous moment should be "forgotten" or "discarded"; 2) The input gate consists of two parts: a sigmoid layer that determines which values ​​will be updated, and a tanh layer that creates a new vector of candidate values ​​that will be added to the state. The formula for the input gate is as follows: ; in, is the output of the input gate, is the candidate memory cell state, , and , are the relevant weights and biases, Refers to the sigmoid layer; 3) The output gate is responsible for determining which part of the memory cell state will be output to the hidden state, and is calculated by the following formula: ; in, Combining the information of the forget gate and the input gate, is the output of the sigmoid function of the output gate, is the updated memory cell state, is the final hidden state output, It is the weight matrix of the output gate, which is used to adjust the influence of the input data and the hidden state of the previous moment on the current output. is the bias term of the output gate, used to adjust the calculated offset.

[0013] Preferably, the calculation expressions of MAE and RMSE are as follows: ; ; Where n is the total number of trajectory data points in the prediction set, It is the first The true value of the trajectory data point, The prediction focus is on The predicted value of each trajectory data point.

[0014] Therefore, the present invention adopts the above-mentioned method for predicting the drift trajectory of an unpowered ship, which has the following beneficial effects: (1) The historical data of unpowered ship drifting are decomposed by the CEEMDAN method, and then the noise is filtered out of the decomposed data according to the kurtosis screening method, so that more real and accurate information can be extracted from the data, which is suitable for subsequent modeling and prediction; (2) The BiLSTM network structure can capture the context information before and after the current time step at the same time, thereby improving the performance of the model and improving the effect of trajectory prediction.

[0015] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is an overall flow chart of a method for predicting the drift trajectory of an unpowered ship according to the present invention; Figure 2 It is a decomposition structure diagram of CEEMDAN according to an embodiment of the present invention; Figure 3 This is a diagram of the internal structure of the LSTM of an embodiment of the present invention; Figure 4 This is a BiLSTM structure diagram of an embodiment of the present invention; Figure 5 This is a sliding window diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] See also Figure 1-Figure 5 , a method for predicting the drift trajectory of an unpowered ship, comprising the following steps: Step 1, obtain the historical trajectory data of the unpowered ship, and perform data filtering and abnormal data elimination preprocessing on the historical trajectory; the historical trajectory data includes longitude and latitude, flow velocity, flow direction, wind speed, and wind direction; among them, the sampling interval of longitude and latitude, flow velocity, and flow direction data is small, and the outliers in the longitude and latitude information are deleted, and the mean of the two points before and after is used for interpolation; the sampling frequency of wind speed and wind direction is large, and in order to align with the sampling frequency of longitude and latitude, flow velocity, and flow direction data, cubic spline interpolation is used; Among them, the calculation expression for filling using the mean of the two points before and after is as follows: ; In the formula, Indicates missing data, , Respectively represent the valid data before and after.

[0019] The process of filling using cubic spline interpolation is as follows: Suppose there are n+1 data points , for each pair of adjacent data points and A cubic polynomial segment is used to interpolate between the two intervals. , define a cubic polynomial , the expression is as follows: ; In the formula, 、 、 、 is the coefficient to be determined, where The following constraints are met: Constraint 1: Function continuity, at each data point At , the polynomial values ​​of adjacent intervals must be the same; Constraint 2: First-order derivative continuity, at each data point At , the first-order derivatives of the polynomials in adjacent intervals must be the same; Constraint three: Second-order derivative continuity, at each data point At , the second-order derivatives of the polynomials in adjacent intervals must also be the same; Constraint 4: At the boundary nodes, the second-order derivative is zero.

[0020] The above conditions generate a system of 4n equations (four coefficients per interval) involving all 、 、 、 Solving this system of equations yields these coefficients, thus determining all the cubic polynomial segments.

[0021] Step 2: The expression for normalizing the interpolated historical ship trajectory data is as follows:

[0022] In the formula, The average of each type of data in the training set, including latitude and longitude, flow velocity, flow direction, wind speed, and wind direction, is calculated to obtain 6 values; The minimum value of each type of data in the training set, namely longitude and latitude, flow velocity, flow direction, wind speed, and wind direction, is calculated to obtain 6 values; x is the sum of the training set and the test set (training set data + test set data), and the longitude value in x is subtracted from the average longitude value, and then divided by the maximum longitude value minus the minimum longitude value to obtain The same applies to the longitude, latitude, flow velocity, flow direction, wind speed and wind direction.

[0023] Step 3: Divide the ship historical trajectory data set obtained after interpolation normalization into a training set and a test set according to a ratio of 8:2, and use a sliding window to segment the preprocessed ship historical trajectory data for the divided training set and test set. Use a sliding window to divide the historical navigation time into multiple time periods, and then use the divided time periods and the corresponding navigation trajectories as a set of data to obtain multiple sets of such data. The purpose of segmenting the ship historical trajectory data is to determine the training data that can be used to train the trajectory prediction model through the obtained historical trajectory segmentation data, and to determine the prediction target in the subsequent prediction process; Step 4: Use CEEMDAN to decompose the training set data, and decompose the flow velocity and flow direction data of each sliding window respectively. The process of decomposing the flow velocity and flow direction data is the same. The process of decomposing the flow velocity using CEEMDAN is as follows: S41, first generate a white noise sequence, and superimpose the white noise sequence with the flow rate sequence x to obtain different noise-added signals , the calculation expression is as follows: ; In the formula, represents the velocity sequence x plus the The value obtained after white noise, is the added white noise; S42, perform the first decomposition, The noisy signal is decomposed by EMD, and we get IMF components; S43, yes The IMF components are added and averaged to obtain , the calculation expression is as follows: ; In the formula, Represents the first decomposition IMF components; S44. Subtract the extracted mean from the velocity series x , and the remaining As a new signal for the next decomposition, the calculation expression is as follows: ; S45, yes Add a white noise sequence and superimpose it to obtain different noise signals; then start the second decomposition and calculate the average value to obtain ,from Extract ,get , and then As a new signal for the next decomposition, repeat the above steps until the decomposition stops. Assuming that After the decomposition is completed, as follows: ; In the formula, is the residual of the final decomposition.

[0024] Step 5. Filter the noise from the decomposed data according to the kurtosis screening method; kurtosis is an indicator to measure the distribution of signal extreme values. Generally speaking, if the kurtosis value of an IMF is large, then the IMF may contain more spikes or heavy-tailed distributions, which are usually related to noise. Therefore, we can calculate the kurtosis of each IMF and filter it accordingly. Specifically, set a kurtosis threshold, and then filter out IMFs with kurtosis lower than the threshold. In this way, we can remove those IMFs that may contain noise, thereby achieving noise reduction. Finally, perform signal reconstruction, superimpose the filtered IMFs, and obtain the denoised flow velocity sequence.

[0025] Suppose we have an original signal , five IMF components were obtained through CEEMDAN decomposition , , , , , and a residual value After analysis, we found , is the noise component, and , , is the useful signal component. Therefore, we choose , , Refactoring.

[0026] ; After denoising the velocity data, the same decomposition and denoising operation is performed on the flow direction data; Step 6: Put the filtered and denoised data and the original longitude, latitude, wind speed, and wind direction data into the BiLSTM model and output them through a fully connected layer, and adjust the model parameters by minimizing the MSE; where BiLSTM includes two LSTMs, one to process the sequence forward and the other to process the sequence backward. After processing, the outputs of the two LSTMs are concatenated, specifically: BiLSTM processes the LSTM forward to obtain the hidden state of each time step Hidden state at each time step obtained by reverse processing with LSTM Splice to get Finally, the BiLSTM obtained Put it into a fully connected layer to get the final output. The full connection is calculated by the following formula: ; in, is the output value, W is the weight matrix, and b is the bias; Among them, LSTM uses three gates to control the cell state. The three gates are called forget gate, input gate and output gate, as follows: 1) Forget gate. The purpose of the forget gate is to decide which information should be forgotten or retained from the memory unit at each time step; it is calculated by the following formula: ; in, is the logistic activation function, and are the weight matrix and bias term of the forget gate respectively, is the concatenation of the hidden state of the previous time step and the input of the current time step, is the output of the forget gate, Determines how much information about the memory cell state at the previous moment should be "forgotten" or "discarded"; 2) The input gate consists of two parts: a sigmoid layer that determines which values ​​will be updated, and a tanh layer that creates a new vector of candidate values ​​that will be added to the state. The formula for the input gate is as follows: ; in, is the output of the input gate, is the candidate memory cell state, , and , are the relevant weights and biases, Refers to the sigmoid layer; 3) The output gate is responsible for determining which part of the memory cell state will be output to the hidden state, and is calculated by the following formula: ; in, Combining the information of the forget gate and the input gate, is the output of the sigmoid function of the output gate, is the updated memory cell state, is the final hidden state output, It is the weight matrix of the output gate, which is used to adjust the influence of the input data and the hidden state of the previous moment on the current output. is the bias term of the output gate, used to adjust the calculated offset.

[0027] Step 7: Input the test set into the trained CEEMDAN-BiLSTM model, use the sliding window method to predict the trajectory data in the test set, and verify the accuracy of the prediction results through MAE (mean absolute error) and RMSE (root mean square error).

[0028] The calculation expressions of MAE and RMSE are as follows: ; ; Where n is the total number of trajectory data points in the prediction set, is the true value of the i-th trajectory data point in the prediction set, is the predicted value of the i-th trajectory data point in the prediction set.

[0029] Therefore, the present invention adopts the above-mentioned method for predicting the drifting trajectory of an unpowered ship, performs signal decomposition on the data based on adaptive noise control, and screens the decomposed data according to the kurtosis to eliminate noise, so that the noise in the original time series data is effectively removed, and the main characteristics of the signal are retained, thereby reflecting the true trend and law of the data, helping to extract more real and accurate information therefrom, which is suitable for subsequent modeling and prediction, capturing complex nonlinear relationships and time changes, and improving the prediction effect; and through BiLSTM, the context information before and after the current time step can be captured at the same time, thereby improving the performance of the model, capturing the time dependency in the sequence, and improving the trajectory prediction effect.

[0030] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the drift trajectory of an unpowered ship, characterized in that: The following steps are involved: Step 1, obtain the historical trajectory data of the unpowered ship, and perform data filtering and abnormal data elimination preprocessing on the historical trajectory; the historical trajectory data includes longitude and latitude, flow velocity, flow direction, wind speed, and wind direction; among them, the sampling interval of longitude and latitude, flow velocity, and flow direction data is small, and the outliers in the longitude and latitude information are deleted, and the mean of the two points before and after is used for interpolation; the sampling frequency of wind speed and wind direction is large, and cubic spline interpolation is used; Step 2, normalizing the interpolated historical trajectory data of the ship; Step 3: The ship historical trajectory data set obtained after interpolation normalization is divided into a training set and a test set according to a ratio of 8:2, and the preprocessed ship historical trajectory data is segmented using a sliding window for the divided training set and test set; Step 4: Use CEEMDAN to decompose the training set data, and decompose the flow velocity and flow direction data of each sliding window respectively. The process of decomposing the flow velocity and flow direction data is the same; Step 5: Filter noise from the decomposed data using the kurtosis screening method; Step 6: Put the filtered and denoised data and the original longitude, latitude, wind speed, and wind direction data into the BiLSTM model and output them through a fully connected layer, and adjust the model parameters by minimizing MSE; Step 7: Input the test set into the trained CEEMDAN-BiLSTM model, use the sliding window method to predict the trajectory data in the test set, and verify the accuracy of the prediction results through MAE and RMSE.

2. A method for predicting the drift trajectory of an unpowered ship according to claim 1, characterized in that: The calculation expression for filling in the mean of the two points before and after in step 1 is as follows: ； In the formula, Indicates missing data, , Respectively represent the valid data before and after.

3. A method for predicting the drift trajectory of an unpowered ship according to claim 2, characterized in that: The process of using cubic spline interpolation to fill in step 1 is as follows: Suppose there are n+1 data points , for each pair of adjacent data points and A cubic polynomial segment is used to interpolate between the two intervals. , define a cubic polynomial , the expression is as follows: ； In the formula, 、 、 、 is the coefficient to be determined, where The following constraints are met: Constraint 1: Function continuity, at each data point At , the polynomial values ​​of adjacent intervals must be the same; Constraint 2: First-order derivative continuity, at each data point At , the first-order derivatives of the polynomials in adjacent intervals must be the same; Constraint three: Second-order derivative continuity, at each data point At , the second-order derivatives of the polynomials in adjacent intervals must also be the same; Constraint 4: At the boundary nodes, the second-order derivative is zero.

4. A method for predicting the drift trajectory of an unpowered ship according to claim 3, characterized in that: In step 2, the interpolated historical trajectory data of the ship is normalized The expression is as follows: ； In the formula, The average of each type of data in the training set, including latitude and longitude, flow velocity, flow direction, wind speed, and wind direction, is calculated to obtain 6 values; It is to find the minimum value of each type of latitude and longitude, flow velocity, flow direction, wind speed, and wind direction data in the training set, and calculate 6 values; x is the sum of the training set and the test set.

5. A method for predicting the drift trajectory of an unpowered ship according to claim 4, characterized in that: The process of decomposing flow velocity using CEEMDAN is as follows: S41, first generate a white noise sequence, and superimpose the white noise sequence with the flow rate sequence x to obtain different noise-added signals , the calculation expression is as follows: ； In the formula, Represents flow rate series Plus the The value obtained after white noise, is the added white noise; S42, perform the first decomposition, The noisy signal is decomposed by EMD, and we get IMF components; S43, yes The IMF components are added and averaged to obtain , the calculation expression is as follows: ； In the formula, Represents the first decomposition IMF components; S44. Subtract the extracted mean from the velocity series x , and the remaining As a new signal for the next decomposition, the calculation expression is as follows: ； S45, yes Add a white noise sequence and superimpose it to obtain different noise signals; then start the second decomposition and calculate the average value to obtain ,from Extract ,get , and then As a new signal for the next decomposition, repeat the above steps until the decomposition stops. Assuming that After the decomposition is completed, as follows: ； In the formula, is the residual of the final decomposition.

6. A method for predicting the drift trajectory of an unpowered ship according to claim 5, characterized in that: BiLSTM consists of two LSTMs, one to process the sequence forward and the other to process the sequence backward. After processing, the outputs of the two LSTMs are concatenated. Specifically, BiLSTM processes the LSTM forward to obtain the hidden state of each time step. Hidden state at each time step obtained by reverse processing with LSTM Splice to get Finally, the BiLSTM obtained Put it into a fully connected layer to get the final output. The full connection is calculated by the following formula: ； in, is the output value, W is the weight matrix, and b is the bias.

7. A method for predicting the drift trajectory of an unpowered ship according to claim 6, characterized in that: The calculation expressions of MAE and RMSE are as follows: ； ； Where n is the total number of trajectory data points in the prediction set, It is the first The true value of the trajectory data point, The prediction focus is on The predicted value of each trajectory data point.

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