Multi-space trajectory prediction method based on maximum mean-variance difference

Abstract

The invention discloses a multi-space transfer learning trajectory prediction method based on maximum mean-variance difference, and the method comprises the steps: mapping data of a source domain and a target domain into a time space, a frequency space and an air space through a trend-period long-short term memory neural network and a dynamic self-attention convolutional neural network; original data features are comprehensively expressed, and meanwhile respective feature attributes are reserved. Secondly, a maximum mean-variance difference algorithm is proposed to align feature distribution of a source domain and a target domain in multiple spaces; and finally, constraining the feature distribution of the source domain and the target domain through a cyclic consistent adversarial network to ensure the reversibility of inter-domain feature migration and the retention of key information. The invention provides an efficient and accurate trajectory prediction method, and the method has good generalization and robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of trajectory prediction, and in particular, to a multi - spatial transfer learning trajectory prediction method based on maximizing the mean - variance difference. Background Art

[0002] In the field of trajectory prediction, accurate trajectory prediction is crucial for many application scenarios, such as autonomous driving, unmanned aerial vehicle navigation, logistics transportation, etc. Traditional trajectory prediction methods are usually based on physical models or statistical models. These methods can achieve good results under specific conditions, but often perform poorly in complex and changing environments. In recent years, with the development of deep learning technology, deep - learning - based trajectory prediction methods have gradually become a research hotspot. These methods can achieve high - precision trajectory prediction in various scenarios by learning complex patterns in large - scale data. However, there are still some challenges in practical applications, especially the lack of labeled data, which limits the generalization ability and prediction accuracy of the model. Moreover, the actual traffic environment is often more complex and changeable, requiring higher prediction accuracy and speed of the model. As a typical transfer learning method, domain adaptation can effectively solve the problem of lack of labeled data in the target domain by migrating the model established in the source domain to the target domain. Through transfer learning, the complexity of the model can be reduced, and the prediction accuracy and speed can be improved. However, traditional domain adaptation methods based on a single space and a single statistical feature cannot comprehensively and fully express and align the feature distributions of the source domain and the target domain, affecting the migration effect of the model. Therefore, the research on accurate trajectory prediction methods based on multiple spaces has important research significance.

[0003] Trajectory prediction methods can be divided into two categories: traditional physical methods and data - driven methods. Common traditional physical trajectory prediction models include single - trajectory method, Kalman filtering method, and Monte Carlo method, etc. Their limitation is that they can only perform short - term prediction of no more than 1 s. And they do not consider mutual factors such as interaction, resulting in low prediction accuracy. Different from traditional physical models, data - driven trajectory prediction models only rely on vehicle traffic data, do not require any prior conditions and complex expert knowledge, and only need to select a suitable algorithm to learn the non - linear relationship between easily measurable auxiliary variables and difficult - to - measure target outputs. Deep - learning - based trajectory prediction methods can consider physical, road, and interaction - related factors and have higher adaptability to complex scenarios. In recent years, deep - learning - based trajectory prediction models have emerged in an endless stream, improving the prediction accuracy. Although these models can achieve better performance, with the continuous improvement of the models, the model complexity and computational amount have both increased significantly, bringing challenges to the computing power of real - time decision - making for intelligent vehicles. For complex traffic scenarios, transfer learning can quickly and accurately predict the future trajectory of vehicles, greatly improving the prediction calculation efficiency.

[0004] Due to the great difficulty and high complexity of trajectory prediction in the scenario of urban complex traffic road networks. And there are complex influencing factors such as the interaction relationship between vehicles in the real scenario. Therefore, trajectory prediction is a non-static and non-linear complex process, and has high requirements for computing power. To solve the problem of lack of labels and improve the prediction accuracy and speed, transfer learning is used for trajectory prediction, and a transfer learning trajectory prediction method considering multiple spaces is proposed. Experiments show that this method has achieved very good results in terms of prediction accuracy and speed. Summary of the Invention

[0005] To solve the limitations and defects existing in the prior art, the present invention provides a multiple-space transfer learning trajectory prediction method based on maximizing the mean-variance difference, including:

[0006] Obtain the original data of the source domain and the target domain, where the original data includes the dominant variables and their auxiliary variable datasets in trajectory prediction;

[0007] Use a trend-period long short-term memory unit to decompose the original data into a trend signal and a periodic signal, and extract the time-domain features and frequency-domain features of the original data. The expression is as follows:

[0008] [h t ,h p = TPLSTM(x) (1)

[0009] where x is the original data, h t is the time-domain feature of the original data, and h p is the frequency-domain feature of the original data;

[0010] The trend-period long short-term memory unit is provided with a periodic gate above the input gate, forget gate and output gate, and the periodic gate is used to extract the time-domain features and frequency-domain features of the decoupled process data;

[0011] While extracting the time-domain features and frequency-domain features of the original data, use a dynamic self-attention convolutional neural network to extract the spatial-domain features of the original data. The expression is as follows:

[0012] h s = DSACNN(x) (2)

[0013] where h s is the spatial-domain feature of the original data;

[0014] Use the maximizing mean-variance difference algorithm to align the multiple-space feature distributions of the source domain and the target domain. The expression is as follows:

[0015] MMVD[h S ,h T = MMD[hS , h T + VD[h S , h T (3)

[0016] Among them, h S is the input variable of the source domain, and h T is the input variable of the target domain. MMD[h S , h T is the maximum mean difference algorithm, and VD[h S , h T is the introduced variance difference term;

[0017] Using a cycle-consistent adversarial network to constrain the feature distributions of the source domain and the target domain, the expression is as follows:

[0018]

[0019] Among them, the arrow → represents a mapping relationship. G S→T represents the mapping from the source domain to the target domain, and G T→S represents the mapping from the target domain to the source domain, and G T→S (G S→T (h S )) means mapping the source domain features to the target domain and then back to the source domain. G S→T (G T→S (h T )) means mapping the target domain features to the source domain and then back to the target domain, represents the risk expectation of the source domain, represents the risk expectation of the target domain. The source domain follows the p(h S ) distribution, and the target domain follows the p(h T ) distribution;

[0020] Using the gradient descent algorithm to train the model to minimize the overall loss, the expression of the overall loss function is as follows:

[0021]

[0022] Among them, j ∈ {t, p, s} represents the feature spaces in the time domain, frequency domain, and spatial domain. L Cycle is the cycle-consistent loss, and L MMVD is the loss function for maximizing the mean-variance difference.

[0023] Optionally, the steps of using the trend-period long short-term memory unit to decompose the original data into a trend signal and a periodic signal, and extracting the time-domain features and frequency-domain features of the original data include:

[0024] Decompose the original data into the trend signal and the periodic signal using the variational mode decomposition algorithm;

[0025] Learn the time-domain features and the frequency-domain features through the trend-period long short-term memory unit, where the trend signal is learned through the long short-term memory unit and the periodic signal is learned through the Fourier layer. The expressions are as follows:

[0026] h t = LSTM(h t-1 , x t ) (6)

[0027] c t = FourierLayer(c t-1 , x t ) (7)

[0028] where h t represents the hidden state at time step t, x t represents the input data at time step t, and c t represents the cell state at time step t.

[0029] Optionally, the step of using the dynamic self-attention convolutional neural network to extract the spatial-domain features of the original data includes:

[0030] Capture the dynamic spatial relationship between input variables through the dynamic self-attention mechanism;

[0031] Use the convolutional neural network to extract spatial features. The expressions are as follows:

[0032] f i = Conv(x i ; W) (8)

[0033] α i = softmax(Attention(f i )) (9)

[0034]

[0035] where f i represents the feature of the i-th input variable, W represents the weight matrix, α i represents the attention weight, z i represents the final spatial feature, and α ij represents the attention weight, indicating the degree of attention to each position j in the feature map f j at position i.

[0036] Optionally, the step of aligning the multiple spatial feature distributions of the source domain and the target domain using the maximum mean-variance difference algorithm includes:

[0037] Align the feature distributions of the source domain and the target domain in the time domain, frequency domain, and spatial domain using the maximum mean-variance difference algorithm;

[0038] Calculate the maximum mean-variance difference loss function, which is used to measure the degree of alignment of the feature distributions. The expression is as follows:

[0039]

[0040] where n s represents the number of samples in the source domain, and n t represents the number of samples in the target domain, φ(·) represents the mapping function, represents the spatio-temporal-frequency features of the source domain, represents the spatio-temporal-frequency features of the target domain.

[0041] Optionally, the step of constraining the feature distributions of the source domain and the target domain using the cycle-consistent adversarial network includes:

[0042] Constrain the feature distributions of the source domain and the target domain using the adversarial loss and the cycle-consistent loss.

[0043] The present invention has the following beneficial effects:

[0044] The present invention provides a multiple spatial transfer learning trajectory prediction method based on the maximum mean-variance difference. First, the data of the source domain and the target domain are mapped to the spatio-temporal-frequency feature space by using the trend-period long short-term memory and the dynamic self-attention convolutional neural network, which not only comprehensively expresses the data characteristics of the source domain and the target domain, but also retains their respective feature attributes. Then, the maximum mean-variance difference algorithm is used to align the multi-spatial feature distributions of the source domain and the target domain. Finally, the cycle adversarial loss is used to constrain the feature distributions of the source domain and the target domain, and a reciprocal feature relationship between the source domain and the target domain is established. The multiple spatial transfer learning trajectory prediction method based on the maximum mean-variance difference provided by the present invention achieves high prediction accuracy and generalization accuracy, has strong robustness in the face of complex traffic scenarios, as well as good transfer effect and universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the multiple spatial transfer learning trajectory prediction model based on the maximum mean-variance difference provided in the first embodiment of the present invention.

[0046] Figure 2Schematic diagram of the structure of the trend cycle long short-term memory unit provided in the first embodiment of the present invention.

[0047] Figure 3 Schematic diagram of the structure of the trend cycle long short-term memory neural network provided in the first embodiment of the present invention.

[0048] Figure 4 Schematic diagram of the structure of the cycle-consistent loss and adversarial loss provided in the first embodiment of the present invention.

[0049] Figures 5a-5b Schematic diagram of the comparative experiment results provided in the first embodiment of the present invention.

[0050] Figures 6a-6b Schematic diagram of the ablation experiment results provided in the first embodiment of the present invention. Detailed implementation manners

[0051] To enable those skilled in the art to better understand the technical solutions of the present invention, the multi-space transfer learning trajectory prediction model based on maximizing the mean-variance difference provided by the present invention will be described in detail below with reference to the accompanying drawings.

[0052] Embodiment 1

[0053] Aiming at the problems that the traditional trajectory prediction method has a single application scenario and cannot adapt to complex traffic environments, and the high model complexity of common deep learning trajectory prediction methods leads to a significant increase in the amount of calculation, and thus the generalization and robustness will be greatly affected. Therefore, this embodiment proposes a multi-space method based on maximizing the mean-variance difference to construct a trajectory prediction model for complex traffic scenarios.

[0054] Domain adaptation, as an effective method of transfer learning, aims to map the data from the source domain and the target domain into the same feature space and align the feature distributions of the source domain and the target domain in this space. Traditional domain adaptation methods use the same neural network to map data from different domains into the same feature space. In this feature space, effective alignment methods are designed to reduce the differences between domain feature distributions, thereby achieving cross-domain adaptation. However, the same neural network model can only map the original data into a specific space, which means that the features learned by the model only contain partial information of the original data. If this part of the information varies greatly across domains, it will affect the transfer performance of the model. Different from traditional domain adaptation methods that can only map the original data into a specific space using the same neural network, the Multiple-Space Transfer Learning Trajectory Prediction Method Based on Maximizing Mean-Variance Difference (MMVD-MSTL) maps the data into three different high-dimensional feature spaces of time, frequency, and space through the Trend-Period Long Short-Term Memory Neural Network (TPLSTM) and the Dynamic Self-Attention Convolutional Neural Network (DSACNN). First, the input data of the source domain and the target domain are input into the TPLSTM and DSACNN modules to map the original data into the triple space. Second, the Maximizing Mean-Variance Difference algorithm (MMVD) is used to align the feature distributions of the source domain and the target domain in the three spaces of time, frequency, and space. Finally, a cyclic adversarial loss is used to constrain the feature distributions of the source domain and the target domain to establish a reciprocal feature relationship between the source domain and the target domain. To illustrate the effectiveness and superiority of the multiple-space transfer learning trajectory prediction model based on maximizing mean-variance difference proposed in this example, MMVD-MSTL is applied to an actual vehicle traffic dataset for experimental verification. The experimental results show that compared with other state-of-the-art methods, the MMVD-MSTL proposed in this embodiment achieves the highest prediction accuracy and has strong robustness in the face of changing complex environments.

[0055] Figure 1 FIG. is a schematic diagram of the multiple-space transfer learning trajectory prediction model based on maximizing mean-variance difference provided in Embodiment 1 of the present invention. First, the trend signal and the periodic signal decomposed from the original data are input into the TPLSTM to learn decoupled trend features and periodic features. The trend features are learned in the time domain, and the periodic features are learned in the frequency domain. Second, the DSACNN is used to capture the dynamic spatial features in the spatial domain. The TPLSTM and the DSACNN are used to map the source domain and the target domain data into the spatio-temporal frequency feature space. Then, the maximum mean square error is used to align the multi-space feature distributions of the source domain and the target domain. Finally, in order to establish a reciprocal feature relationship between the source domain and the target domain, a cyclic adversarial loss is used to constrain the feature distributions of the source domain and the target domain.

[0056] First, select the required dataset. In this embodiment, the model is applied to the actual urban vehicle traffic data to verify the effectiveness of the proposed method. The dataset is divided into two parts. One part is the vehicle traffic data in the past 5 years, which is dataset 1, and the other part is the vehicle traffic data in the recent 5 years, which is dataset 2, for verifying the migration performance.

[0057] Due to the low-dimensionality of the original data, directly aligning the data distributions of the source domain and the target domain is challenging. Usually, the original data in the source domain and the target domain are mapped to a high-dimensional feature space, where the feature distributions of the source domain and the target domain are aligned. To map the original data to the spatio-temporal frequency feature space, TPLSTM and DSACNN are adopted, as shown in formulas (1)-(2). Figure 2 It is a schematic diagram of the structure of the trend periodic long short-term memory unit provided in Embodiment 1 of the present invention. Figure 3 It is a schematic diagram of the structure of the trend periodic long short-term memory neural network provided in Embodiment 1 of the present invention. The TPLSTM unit adds a periodic gate on the basis of the input gate, forget gate, and output gate, aiming to extract time-domain and frequency-domain features to decouple the process data. The TPLSTM extracts the time-domain and frequency-domain features of the decoupled process data, and the DSACNN uses dynamic time warping (DTW) to replace the traditional cosine similarity to calculate the dynamic similarity between two vectors, thereby extracting the spatial-domain features of the process data.

[0058] [h t ,h p = TPLSTM(x) (1)

[0059] h s = DSACNN(x) (2)

[0060] Among them, x is the original data, h t is the time-domain feature, h p is the frequency-domain feature, h s is the spatial-domain feature.

[0061] After that, in order to align the feature distributions of the source domain and the target domain in each feature space respectively, this embodiment proposes a new algorithm based on the traditional maximum mean discrepancy algorithm (MMD), called the maximum mean-variance discrepancy algorithm (MMVD), and gives the final MMVD loss function as shown in formula (11).

[0062]

[0063] Among them, n s represents the number of samples in the source domain, n tLet \(n\) denote the number of samples in the target domain, \(\varphi(\cdot)\) denote the mapping function, and \(j\in\{t,p,s\}\) which represents three feature spaces in the time domain, frequency domain, and space domain. denotes the spatio - temporal - frequency features of the source domain, denotes the spatio - temporal - frequency features of the target domain.

[0064] The MMD algorithm essentially calculates the difference in means between the mapped source domain and target domain. However, a single mean statistic cannot fully represent the distribution. Even if the mean values of the feature distributions in two domains are similar, their feature distributions may still be significantly different. By introducing a variance statistic, MMVD can better represent the feature distribution of a domain.

[0065] In addition to evaluating the similarity of the features of two domains based on their inherent statistical characteristics, their mutual conversion can also be evaluated through external features. For this purpose, this embodiment introduces a cyclic adversarial loss to ensure the reversibility of domain features. Figure 4 FIG. 12 is a schematic structural diagram of the cyclic consistency loss and adversarial loss provided in the first embodiment of the present invention. Specifically, the cyclic adversarial loss constrains the mutual conversion of source - domain and target - domain features by splicing the source - domain and target - domain features together. The cyclic adversarial loss consists of two generators and two discriminators. One generator \(G\) S→T (\(h\) S ;\(\theta\) gS→T ) is used to map from the source domain to the target domain, and another generator \(G\) T→S (\(h\) T ;\(\theta_g\) T→S ) is used to map from the target domain to the source domain. Correspondingly, each generator has a discriminator, called the source - domain discriminator and the target - domain discriminator The generators \(G\) S→T (\(\cdot\)), \(G\) T→S (\(\cdot\)) and the discriminators \(D\) S (\(\cdot\)), \(D\) T (\(\cdot\)) are three - layer multi - layer perceptrons.

[0066] In addition, the cyclic adversarial loss introduces a cyclic consistency loss to further constrain the features generated by the generator. The specific description is shown in formulas (12) and (13).

[0067] \(h\) S \(\to G\) S→T (\(h\) S ) \(\to G\) T→S (\(G\) S→T (\(h\) S )) \(\approx h\) S (12)

[0068] \(h\) T \(\to G\) T→S(h T ) → G S→T (G T→S (h T )) ≈ h T (13)

[0069] The arrow → represents a mapping relationship, where h S → G S→T (h S ) represents the mapping from the source domain to the target domain, and h T → G T→S (h T ) represents the mapping from the target domain to the source domain. Here, G S→T (h S ) → G T→S (G S→T (h S ))G T→S (h T ) → G S→T (G T→S (h T )) represents the source domain features mapped to the target domain and then back to the source domain, and G T→S (G S→T (h S )) represents the target domain features mapped to the source domain and then back to the target domain. The cycle adversarial loss aims to ensure that the source domain features obtained through the cycle mapping function G T→S (G S→T (h S )) are consistent with the original features in the source domain, denoted as G T→S (G S→T (h S )) ≈ h S . Similarly, it is also sought that the target domain features obtained through the cycle mapping function G S→T (G T→S (h T )) are consistent with the original features in the target domain, denoted as G S→T (G T→S (h T )) ≈ h T . Based on this, the cycle adversarial loss introduces cycle consistency loss to constrain the two generators in the network, as shown in formula (4).

[0070]

[0071] In summary, the overall loss function of MMVD - MSTL can be expressed as formula (5).

[0072]

[0073] Among them, \(j\in\{t,p,s\}\) represents three feature spaces in the time domain, frequency domain, and space domain. By optimizing and solving formula (5), similar and transferable feature representations can be obtained.

[0074] Finally, through the above specific implementation, a multi-space transfer learning trajectory prediction model MMVD-MSTL based on maximizing the mean-variance difference is constructed. Experiments show that compared with other algorithms, the proposed MMVD-MSTL has good generalization and universality.

[0075] In order to establish a trajectory prediction model with strong generalization, high robustness, transferability, and adaptability to complex dynamic traffic environments, this embodiment proposes a multi-space transfer learning trajectory prediction model based on maximizing the mean-variance difference. Different from traditional domain adaptation methods based on single space and single statistical features, which cannot comprehensively and fully express and align the feature distributions of the source domain and the target domain, this embodiment uses a trend-cycle long short-term memory neural network and a dynamic self-attention convolutional neural network to extract decoupled trend features, periodic features, and spatial features.

[0076] Figures 5a-5b It is a schematic diagram of the comparative experiment results provided in Embodiment 1 of the present invention. Figure 5a To transfer from dataset 1 to dataset 2, Figure 5b On the contrary. To verify the transfer effect of MMVD-MSTL, MMVD-MSTL is compared with traditional deep learning methods and classical transfer learning methods, and the evaluation metrics are selected as RMSE, MAE, and R2. These methods are respectively Residual Neural Network (ResNet), Transfer Component Analysis (TCA), Cross-Domain Extreme Learning Machine based on Unified Features (CDELM), Domain Adaptive Extreme Learning Machine (DAELM), Domain Adaptive Mixture Model based on Gaussian Process (DAMGP), and Deep Probabilistic Transfer Regression Model (DPTR). Table 1 shows the comparison results. 1→2 means using the vehicle traffic dataset in the past five years as the source domain data for modeling, and then migrating it to the data in the recent 5 years for verification, and vice versa.

[0077] Table 1 Comparison Results

[0078]

[0079] As can be seen from Table 1, the method proposed in this embodiment not only has the highest transfer accuracy but also the most stable transfer performance. When transferring from 1 to 2, the R2 of MMVD-MSTL increases by 5% and 3% respectively, and when transferring from 2 to 1, the R2 of MMVD-MSTL increases by 6% and 1% respectively.

[0080] In addition, this embodiment also conducts ablation experiments to illustrate the importance of each component of the proposed method.Figures 6a-6b Schematic diagram of ablation experiment results provided by Embodiment 1 of the present invention.

[0081] Figure 6a For migrating from dataset 1 to dataset 2 Figure 6b Conversely. The experiment decomposes MMVD-MSTL into three main modules, and verifies the contribution of each module in MMVD-MSTL to the overall method by excluding each module one by one. The three modules are: a domain adaptation method (DA-1) based on a single space and MMD (mapped to a specific space through the DSACNN method), a multi-space domain adaptation method (DA-2) based on MMD, and a multi-space domain adaptation method (DA3) based on MMVD. The experimental results are shown in Table 2.

[0082] Table 2 Ablation Experiment Results

[0083]

[0084] As can be seen from Table 2, when the dataset is transferred from 1 to 2 and from 2 to 1, the R2 of DA-2 is significantly higher than that of DA-1, indicating that multi-space alignment is more effective than traditional single-space alignment. In addition, compared with DA-2, the R2 of DA-3 increases significantly, indicating that the improved MMVD algorithm is superior to the traditional MMD algorithm. In addition, compared with DA-3, the R2 of MMVD-MSTL increases by 8%, 3%, 2% and 5% respectively. These results show that the cyclic consistent alignment loss plays a certain role.

[0085] Through the above comparative experiments and ablation experiments, the effectiveness and robustness of the model proposed in this embodiment are effectively proved. At the same time, it is also proved that the method has good transferability.

[0086] Aiming at the problems of high model complexity, high computational cost and poor transferability faced by current trajectory prediction, this embodiment proposes a transfer learning trajectory prediction method called MMVD-MSTL. First, TPLSTM and DSACNN map the source domain and target domain data into the spatio-temporal frequency feature space. Then, the maximum mean variance is used to align the multi-space feature distributions of the source domain and the target domain. Finally, in order to establish a reciprocal feature relationship between the source domain and the target domain, the cyclic adversarial loss constrains the feature distributions of the source domain and the target domain. Experimental results show that compared with other state-of-the-art methods, MMVD-MSTL achieves the highest prediction accuracy and generalization accuracy.

[0087] It is understandable that the above embodiments are merely exemplary embodiments adopted to illustrate the principles of the present invention. However, the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also regarded as the protection scope of the present invention.

Claims

1. A multi-space transfer learning trajectory prediction method based on maximizing mean-variance difference, characterized in that: include: Acquire original data of a source domain and a target domain, wherein the original data includes a dominant variable and an auxiliary variable data set in trajectory prediction; The original data is decomposed into trend signals and periodic signals using trend cycle long short-term memory units, and the time domain features and frequency domain features of the original data are extracted. The expressions are as follows: [h t ,h p ]=TPLSTM(x) (1) Among them, x is the original data, h t is the time domain feature of the original data, h p is the frequency domain feature of the original data; The trend cycle long short-term memory unit is provided with a cycle gate on the input gate, the forget gate and the output gate, and the cycle gate is used to extract the time domain characteristics and the frequency domain characteristics of the decoupling process data; While extracting the time domain features and frequency domain features of the original data, a dynamic self-attention convolutional neural network is used to extract the spatial domain features of the original data. The expression is as follows: h s =DSACNN(x) (2) Among them, h s is the spatial domain feature of the original data; The multiple spatial feature distributions of the source domain and the target domain are aligned using the maximum mean-variance difference algorithm, as expressed as follows: MMVD[h S ,h T ]=MMD[h S ,h T ]+VD[h S ,h T ] (3) Among them, h S is the input variable of the source domain, h T is the input variable of the target domain, MMD[h S ,h T ] is the maximum mean difference algorithm, VD[h S ,h T ] is the introduced variance difference term; A cycle-consistent adversarial network is used to constrain the feature distribution of the source domain and the target domain. The expression is as follows: Among them, the arrow → represents the mapping relationship, G S→T represents the mapping from the source domain to the target domain, G T→S represents the mapping from the target domain to the source domain, G T→S (G S→T (h S )) means mapping the source domain features to the target domain and then mapping them back to the source domain. S→T (G T→S (h T )) means mapping the target domain features to the source domain and then mapping them back to the target domain. represents the risk expectation of the source domain, represents the risk expectation of the target domain, and the source domain obeys p(h S ) distribution, the target domain obeys p(h T )distributed; Use the gradient descent algorithm to train the model and minimize the overall loss. The expression of the overall loss function is as follows: Among them, j∈{t,p,s} represents the feature space of time domain, frequency domain and space domain, L Cycle is the cycle consistency loss, L MMVD is the loss function that maximizes the mean-variance difference.

2. The multi-space transfer learning trajectory prediction method based on maximizing mean-variance difference according to claim 1 is characterized in that: The steps of using the trend cycle long short-term memory unit to decompose the original data into a trend signal and a periodic signal, and extracting the time domain features and frequency domain features of the original data include: Decomposing the original data into the trend signal and the periodic signal using a variational mode decomposition algorithm; The time domain features and the frequency domain features are learned through the trend period long short-term memory unit, wherein the trend signal is learned through the long short-term memory unit, and the periodic signal is learned through the Fourier layer, and the expression is as follows: h t =LSTM(h t-1 ,x t ) (6) c t =FourierLayer(c t-1 ,x t ) (7) Among them, h t represents the hidden state at time step t, x t represents the input data at time step t, c t represents the cell state at time step t.

3. The multi-space transfer learning trajectory prediction method based on maximizing mean-variance difference according to claim 1 is characterized in that: The step of extracting the spatial domain features of the original data using a dynamic self-attention convolutional neural network comprises: Capturing dynamic spatial relationships between input variables through a dynamic self-attention mechanism; Use convolutional neural network to extract spatial features, the expression is as follows: f i =Conv(x i ;W) (8) a i =softmax(Attention(f i )) (9) Among them, f i represents the characteristics of the i-th input variable, W represents the weight matrix, α i represents the attention weight, z i represents the final spatial feature, α ij Represents the attention weight, which represents the attention to the feature map f at position i j The attention level of each position j in .

4. The multi-space transfer learning trajectory prediction method based on maximizing mean-variance difference according to claim 1 is characterized in that: The step of aligning the multiple spatial feature distributions of the source domain and the target domain using the maximum mean-variance difference algorithm comprises: Using the maximum mean-variance difference algorithm to align the feature distributions of the source domain and the target domain in the time domain, frequency domain, and spatial domain; The maximum mean-variance difference loss function is calculated. The maximum mean-variance difference function loss is used to measure the degree of alignment of feature distributions. The expression is as follows: Among them, n s represents the number of samples in the source domain, n t represents the number of samples in the target domain, φ(·) represents the mapping function, represents the spatiotemporal frequency characteristics of the source domain, Represents the spatiotemporal-frequency characteristics of the target domain.

5. The multi-space transfer learning trajectory prediction method based on maximizing mean-variance difference according to claim 1 is characterized in that: The step of constraining the feature distribution of the source domain and the target domain using a cycle-consistent adversarial network comprises: Adversarial loss and cycle-consistent loss are used to constrain the feature distributions of the source domain and the target domain.

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