A wavelet transform based state space aircraft trajectory prediction method and system

Abstract

The application discloses a state space aircraft trajectory prediction method based on wavelet transform, comprising the following steps: obtaining a historical observation sequence of an original trajectory of a target aircraft; extracting frequency domain features of the historical observation sequence through discrete wavelet transform; constructing and training a state space prediction model, wherein the state space prediction model is composed of a Transformer encoder, a Mamba state space module and a Transformer decoder; inputting the frequency domain features of the historical observation sequence into the trained state space trajectory prediction model to generate frequency domain features of a future predicted trajectory; restoring the trajectory sequence of the aircraft through inverse wavelet transform on the frequency domain features of the future predicted trajectory to determine a prediction result; and the application improves the prediction speed in each dimension and the accuracy of the prediction result of the trajectory prediction based on the wavelet transform and the Transformer model embedded with the Mamba.

Description

Technical Field

[0001] This specification relates to the field of trajectory prediction, and in particular to a method and system for predicting the trajectory of a state-space vehicle based on wavelet transform. Background Technology

[0002] Spatial trajectory prediction refers to the analysis of a target aircraft's three-dimensional trajectory over a past period to predict its flight trajectory over a future period. In certain special flight scenarios, trajectory prediction can effectively perform critical tasks such as threat assessment, target tracking, and maneuver decision-making. Accurate prediction of target aircraft motion plays an important role in some application scenarios.

[0003] Early methods for aircraft trajectory prediction relied on aerodynamic models and state estimation algorithms. Aerodynamic models modeled the aircraft's motion by considering factors such as performance, state, environment, and intent, thus predicting its trajectory. State estimation algorithms estimated the aircraft's state at the next moment by constructing state transitions. However, these methods involved a large number of modeling parameters and limited prediction length, making them difficult to apply to real-world environments. With the rise of artificial intelligence, deep neural networks began to be applied to target trajectory prediction. In its early stages, this direction used various sequence models such as LSTM, RNN, and GRU for trajectory prediction. Shi et al. used an LSTM neural network to construct a 4D trajectory prediction model, achieving significant advantages over traditional Markov models. Sekhon et al. used an LSTM network with an attention mechanism for autonomous ship prediction. This model combined spatial and temporal attention mechanisms and spatial and temporal weights to focus on different regions of information. With increasing demands for trajectory prediction length and accuracy, research began to use Transformer models for long-sequence trajectory prediction. Nguyen et al. proposed the TrAISformer model, which obtains more favorable data representations for model learning by embedding trajectory data into a grid, and uses a Transformer network for iterative ship trajectory prediction. Guo et al. proposed the FlightBERT model for civil aviation trajectory prediction tasks. The model proposes a new type of attention block called attribute-related attention to explicitly capture the influence of velocity attributes on the corresponding position dimension, thereby improving the Transformer model's ability to mine trajectory attribute information.

[0004] However, existing technologies only consider the temporal information of trajectory data and ignore the useful frequency domain information in the data. At the same time, these models have weak input representation ability for long trajectories and poor output prediction performance. In the task of predicting longer sequence trajectories, there will still be a large prediction inaccuracy. Summary of the Invention

[0005] One embodiment of this specification provides a state-space vehicle trajectory prediction method based on wavelet transform. The wavelet transform-based state-space vehicle trajectory prediction method includes:

[0006] S1: Obtain the historical observation sequence of the target spacecraft's original trajectory;

[0007] S2: Extract the frequency domain features of the historical observation sequence through discrete wavelet transform;

[0008] S3: Construct and train a state space prediction model. The state space prediction model consists of a Transformer encoder, a Mamba state space module, and a Transformer decoder. Input the frequency domain features of the historical observation sequence into the trained state space trajectory prediction model to generate the frequency domain features of the future predicted trajectory.

[0009] S4: The frequency domain features of the predicted future trajectory are used to reconstruct the trajectory sequence of the aircraft through inverse wavelet transform to determine the prediction result.

[0010] One embodiment of this specification provides a state-space vehicle trajectory prediction system based on wavelet transform, comprising:

[0011] The acquisition module is used to acquire historical observation sequences of the target spacecraft's original trajectory;

[0012] The feature extraction module is used to extract the frequency domain features of the historical observation sequence through discrete wavelet transform;

[0013] The trajectory prediction module is used to construct and train a state-space prediction model. The state-space prediction model consists of a Transformer encoder, a Mamba state-space module, and a Transformer decoder. The frequency domain features of the historical observation sequence are input into the trained state-space trajectory prediction model to generate the frequency domain features of the future predicted trajectory.

[0014] The determination module is used to reconstruct the trajectory sequence of the aircraft by using inverse wavelet transform on the frequency domain features of the predicted future trajectory, and to determine the prediction result.

[0015] One embodiment of this specification provides a state-space vehicle trajectory prediction device based on wavelet transform, including a processor, which is used to execute a state-space vehicle trajectory prediction method based on wavelet transform.

[0016] One embodiment of this specification provides a computer-readable storage medium that stores computer instructions. When a computer reads the computer instructions from the storage medium, the computer executes a state-space vehicle trajectory prediction method based on wavelet transform. Attached Figure Description

[0017] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein:

[0018] Figure 1 This is an exemplary flowchart illustrating wavelet transform-based state-space vehicle trajectory prediction according to some embodiments of this specification;

[0019] Figure 2 This is an exemplary flowchart of training a state-space prediction model according to some embodiments of this specification;

[0020] Figure 3 This is a comparison chart showing the results of predicting the flight trajectory of an aircraft using the state-space trajectory prediction model (WTTr-M) shown in some embodiments of this specification and other models;

[0021] Figure 4 These are example diagrams illustrating the training performance of state-space prediction models according to some embodiments of this specification;

[0022] Figure 5 This is an exemplary block diagram of a state-space vehicle trajectory prediction system based on wavelet transform, as shown in some embodiments of this specification. Detailed Implementation

[0023] To more clearly illustrate the technical solutions of the embodiments in this specification, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this specification. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.

[0024] It should be understood that the terms “system,” “device,” “unit,” and / or “module” used herein are one way to distinguish different components, elements, parts, sections, or assemblies at different levels. However, if other terms can achieve the same purpose, they may be replaced by other expressions.

[0025] As indicated in this specification and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of expressly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0026] Flowcharts are used in this specification to illustrate the operations performed by the system according to embodiments of this specification. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, the steps can be processed in reverse order or simultaneously. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0027] Figure 1 This is an exemplary flowchart illustrating a wavelet transform-based state-space vehicle trajectory prediction method according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps.

[0028] S1: Obtain the historical observation sequence of the target spacecraft's original trajectory.

[0029] The target aircraft can include various types of aircraft, drones, etc., performing flight missions. The raw trajectory of the target aircraft includes multiple data points about the aircraft. Specifically, the raw trajectory data is acquired through the ADS-B system and stored in an SQLite database. The file typically contains the aircraft's serial number, data acquisition time, longitude, latitude, altitude, and speed information during the aircraft's operation.

[0030] In some embodiments, the raw trajectory data will be preprocessed, specifically including outlier removal and time resampling to extract trajectory information. The historical observation sequence includes a 4-dimensional multivariate time series in the format of [longitude, latitude, altitude, velocity].

[0031] S2: Extract the frequency domain features of the historical observation sequence through discrete wavelet transform.

[0032] In some embodiments, the frequency domain features X of the historical observation sequence are obtained through discrete wavelet transform, specifically including: S21: decomposing the historical observation sequence into approximation coefficients and detail coefficients through discrete wavelet transform, wherein the approximation coefficients are the low-frequency part of the transformed signal and the detail coefficients are the high-frequency part of the transformed signal; S22: combining the approximation coefficients and detail coefficients by concatenating the variable dimensions to extract the frequency domain features of the historical observation sequence.

[0033] Historical observation sequence X∈R C×L For each variable, a discrete wavelet transform (DWT) is performed. Through the DWT, the input trajectory sequence can be decomposed into approximation coefficients and detail coefficients. The approximation coefficients are:

[0034] A[n]=∑ k x[2n+k]·g[k],

[0035] Where x[n] is the input signal, and g[k] is the low-pass filter coefficient; the detail coefficients are:

[0036] D[n]=∑ k x[2n+k]·h[k],

[0037] Where h[k] are the coefficients of the high-pass filter.

[0038] The advantages of using discrete wavelet transform are that its approximation coefficients are the low-frequency part of the transformed signal, which can reflect the overall trend of the trajectory motion in the frequency domain space. Understanding this part of the data will help the model characterize the general direction of the trajectory. The detail coefficients are the high-frequency part of the transformed signal, which can reflect the motion details of the trajectory in the frequency domain space. Strengthening the learning of this part of the data will help the model characterize the detailed features of the trajectory in motion.

[0039] In some embodiments, the frequency domain features of historical observation sequences are extracted by concatenating the approximation coefficients with the detail coefficients along the variable dimension. The length of the approximation coefficients and detail coefficients is half the length of the original trajectory, i.e. The frequency domain features of the extracted historical observation sequences are For example, if the input data dimension is (4, N), where N is the length of the input sequence, after discrete wavelet transform and concatenation of low-frequency and high-frequency components, frequency domain data with a dimension of (8, N / 2) is formed. Therefore, x wt The variable dimension doubles, while the sequence dimension decreases by half. Through this change in dimension, the model can implement a "space-for-time" training strategy during training, meaning that the length of the sequence the model needs to memorize becomes shorter, but the sequence dimension increases.

[0040] S3: Construct and train a state-space prediction model. This model consists of a Transformer encoder, a Mamba state-space module, and a Transformer decoder. The frequency domain features of the historical observation sequence are input into the trained state-space trajectory prediction model to generate the frequency domain features of the future predicted trajectory. For details regarding the state-space prediction model training process, please refer to [link to relevant documentation]. Figure 2 And its detailed content. The specific steps for generating the frequency domain features of future predicted trajectories also include the following:

[0041] S31: Input the frequency domain features of the historical observation sequence into the Transformer encoder, and capture the contextual relationships in the frequency dimension through a self-attention mechanism.

[0042] In some embodiments, the frequency domain data x of the historical observation sequence wtFuture trajectory prediction will be performed using an encoder-decoder. In this neural network, the data vector will be characterized by high-dimensional embedding and a Transformer encoder to represent the time-frequency features present in the input trajectory, and a self-attention mechanism will be used to capture the contextual relationships in the frequency dimension.

[0043] H = Encoder(InputEmbedding(x) wt )).

[0044] S32: Based on the Mamba state-space model, selectively process the features passed through the Transformer encoder to obtain selective trajectory features.

[0045] In some embodiments, a state-space model (SSM) is a model used to describe these state representations and predict what their next state might be based on certain inputs; it can represent any cyclic process with potential states. An SSM uses first-order differential equations to represent the state evolution within the model:

[0046] h(t)′=Ah(t)+Bx(t),

[0047] y(t) = Ch(t),

[0048] Where A, B, and C are learnable matrices, x(t) is the sequence input to the Mamba module, specifically the sequence data after passing through the Transformer encoder, y(t) is the output, and h(t) is the hidden state representation. ′ Let be the derivative of the hidden state, indicating how the state is updated.

[0049] For continuous time series, the SSM model discretizes the series by step size. The discrete SSM model is represented as:

[0050]

[0051] y t =Ch t ,

[0052] in, Discretization of its continuous form.

[0053] The Mamba state-space model, by functionalizing matrices B, C, and Δ, allows the model to adaptively adjust its behavior based on the input content, enabling selective attention and filtering of information. Selective state-space models can improve efficiency and performance in long-sequence tasks, and have the potential to enhance long-term trajectory prediction performance.

[0054] S33: Add the selective trajectory features to the features passed through the Transformer encoder to generate the frequency domain features of the future predicted trajectory.

[0055] In some embodiments, the present invention embeds the Mamba model as a module into the main network structure, receives the trajectory embedding H as input, and adds the output to the original embedding to simultaneously capture all trajectory information and selective key information:

[0056] H ′ =MambaBlock(H)+H.

[0057] S4: The frequency domain features of the predicted future trajectory are restored to the time domain trajectory sequence features through inverse wavelet transform to determine the prediction result. For example, the prediction result is input into a state-space Transformer model and output with dimensions (8, L / 2). The time domain trajectory is restored through IDWT with dimensions (4, L), where L is the length of the predicted trajectory.

[0058] Figure 2 This is an exemplary flowchart of training a state-space prediction model according to some embodiments of this specification.

[0059] Obtain a trajectory training dataset, which includes multiple sets of historical trajectory training sequences and future trajectory training sequences.

[0060] The trajectory training dataset can be obtained through the ADS-B system. The data is stored in the form of an SQLite database, and its files usually contain information such as the aircraft number, data acquisition time, longitude, latitude, altitude, and speed during the aircraft's operation.

[0061] In some embodiments, the raw trajectory data will be preprocessed, specifically including outlier removal and time resampling to extract trajectory information. For each trajectory data, the trajectory can be divided into equal-length sliding window trajectories using sliding window processing, and each sliding window trajectory can be divided into two parts: a historical observation sequence and a future trajectory training sequence. The historical observation sequence serves as the model input, and the future trajectory training sequence serves as the model training label.

[0062] The historical trajectory training sequence is used as input to the state-space trajectory prediction model, and the future prediction features of the historical trajectory training sequence are output. The future trajectory training sequence is used as a label, and the future prediction features of the historical trajectory training sequence are trained using the MSE loss function.

[0063] Based on the training results of the loss function, the parameters of the state space trajectory prediction model are adjusted to obtain the optimal state space trajectory prediction model.

[0064] Figure 3 This is a comparison chart showing the results of predicting the flight trajectory of an aircraft using the state-space trajectory prediction model (WTTr-M) disclosed in this invention, a general Transformer network model, and the TrAISformer model. Figure 4 The figure shows an example of the training effect of the state-space prediction model. In the figure, the input is the historical trajectory training sequence, the ground truth is the future trajectory training sequence, WTTr-M is the future prediction feature of the state-space trajectory prediction model trained according to the embodiment in the specification, and Transformer and TrAISformer represent the future prediction feature results of their respective models.

[0065] Figure 5 This is an exemplary block diagram of a state-space vehicle trajectory prediction system based on wavelet transform, as shown in some embodiments of this specification.

[0066] In some embodiments, the present invention discloses a state-space vehicle trajectory prediction system 500 based on wavelet transform, comprising:

[0067] The acquisition module 510 is used to acquire the historical observation sequence of the original trajectory of the target aircraft;

[0068] The feature extraction module 520 is used to extract the frequency domain features of the historical observation sequence through discrete wavelet transform;

[0069] The trajectory prediction module 530 is used to construct and train a state space prediction model. The state space prediction model consists of a Transformer encoder, a Mamba state space module, and a Transformer decoder. The frequency domain features of the historical observation sequence are input into the trained state space trajectory prediction model to generate the frequency domain features of the future predicted trajectory.

[0070] The determination module 540 is used to reconstruct the trajectory sequence of the aircraft by using the frequency domain features of the predicted future trajectory through inverse wavelet transform, and to determine the prediction result.

[0071] The basic concepts have been described above. Obviously, for those skilled in the art, the detailed disclosure above is merely illustrative and does not constitute a limitation of this specification. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this specification. Such modifications, improvements, and corrections are suggested in this specification and therefore remain within the spirit and scope of the exemplary embodiments described herein.

[0072] Furthermore, this specification uses specific terms to describe embodiments thereof. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic associated with at least one embodiment of this specification. Therefore, it should be emphasized and noted that references to "an embodiment," "one embodiment," or "an alternative embodiment" in different locations throughout this specification do not necessarily refer to the same embodiment. Moreover, certain features, structures, or characteristics in one or more embodiments of this specification can be appropriately combined.

[0073] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this specification are not intended to limit the order of the processes and methods described herein. Although various examples have been discussed in the foregoing disclosure of some embodiments of the invention that are currently considered useful, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the spirit and scope of the embodiments described herein. For example, while the system components described above can be implemented using hardware devices, they can also be implemented solely using software solutions, such as installing the described system on existing servers or mobile devices.

[0074] Similarly, it should be noted that, in order to simplify the description disclosed herein and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of embodiments in this specification may sometimes combine multiple features into a single embodiment, drawing, or description thereof. However, this method of disclosure does not imply that the subject matter of this specification requires more features than those mentioned in the claims. In fact, the embodiments contain fewer features than all the features of a single embodiment disclosed above.

[0075] In some embodiments, numbers describing the quantity of components and attributes are used. It should be understood that such numbers used in the description of embodiments are modified in some examples with the terms "approximately," "approximately," or "generally." Unless otherwise stated, "approximately," "approximately," or "generally" indicates that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the characteristics required by individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of range in some embodiments of this specification are approximate values, in specific embodiments, such values ​​are set as precisely as feasible.

[0076] For each patent, patent application, patent application publication, and other material, such as articles, books, specifications, publications, and documents, referenced in this specification, the entire contents of which are incorporated herein by reference. This excludes historical application documents that are inconsistent with or conflict with the content of this specification, as well as documents that limit the broadest scope of the claims in this specification (currently or subsequently appended to this specification). It should be noted that in the event of any inconsistency or conflict between the descriptions, definitions, and / or terminology used in the supplementary materials to this specification and the content of this specification, the descriptions, definitions, and / or terminology used in this specification shall prevail.

[0077] Finally, it should be understood that the embodiments described in this specification are merely illustrative of the principles of the embodiments described herein. Other variations may also fall within the scope of this specification. Therefore, alternative configurations of the embodiments described herein are intended to be illustrative rather than limiting, and should be considered consistent with the teachings of this specification. Accordingly, the embodiments described herein are not limited to those explicitly introduced and described herein.

Claims

1. A state-space vehicle trajectory prediction method based on wavelet transform, characterized in that, include: S1: Obtain the historical observation sequence of the target spacecraft's original trajectory; S2: Extract the frequency domain features of the historical observation sequence through discrete wavelet transform; S3: Construct and train a state space prediction model. The state space prediction model consists of a Transformer encoder, a Mamba state space module, and a Transformer decoder. Input the frequency domain features of the historical observation sequence into the trained state space trajectory prediction model to generate the frequency domain features of the future predicted trajectory. S4: Reconstruct the trajectory sequence of the aircraft by using inverse wavelet transform based on the frequency domain features of the predicted future trajectory, and determine the prediction result; The specific steps for generating the frequency domain features of the future predicted trajectory include: S31: Input the frequency domain features of the historical observation sequence into the Transformer encoder, and capture the contextual relationships in the frequency dimension through a self-attention mechanism; S32: Based on the state-space model of Mamba, selectively process the features of the Transformer encoder to obtain selective trajectory features; S33: Add the selective trajectory features to the features passed through the Transformer encoder to generate the frequency domain features of the future predicted trajectory.

2. The state-space vehicle trajectory prediction method based on wavelet transform as described in claim 1, characterized in that, S2 extracts the frequency domain features of the historical observation sequence through discrete wavelet transform, and also includes: S21: The historical observation sequence is decomposed into approximation coefficients and detail coefficients by discrete wavelet transform, wherein the approximation coefficients are the low-frequency part of the transformed signal and the detail coefficients are the high-frequency part of the transformed signal; S22: By concatenating the approximation coefficients and detail coefficients along the variable dimension, the frequency domain features of the historical observation sequence are extracted.

3. The state-space vehicle trajectory prediction method based on wavelet transform as described in claim 1, characterized in that, Training the state-space prediction model includes: Obtain a trajectory training dataset, which includes multiple sets of historical trajectory training sequences and future trajectory training sequences; The historical trajectory training sequence is used as input to the state-space trajectory prediction model, and the future prediction features of the historical trajectory training sequence are output. The future trajectory training sequence is used as a label, and the future prediction features of the historical trajectory training sequence are used for training using the MSE loss function; Obtain a well-trained state-space trajectory prediction model.

4. A state-space vehicle trajectory prediction system based on wavelet transform, characterized in that, include: The acquisition module is used to acquire historical observation sequences of the target spacecraft's original trajectory; The feature extraction module is used to extract the frequency domain features of the historical observation sequence through discrete wavelet transform; The trajectory prediction module is used to construct and train a state-space prediction model. The state-space prediction model consists of a Transformer encoder, a Mamba state-space module, and a Transformer decoder. The frequency domain features of the historical observation sequence are input into the trained state-space trajectory prediction model to generate the frequency domain features of the future predicted trajectory. The prediction module is used to reconstruct the trajectory sequence of the aircraft by using inverse wavelet transform to extract the frequency domain features of the predicted future trajectory and determine the prediction result. The trajectory prediction module is configured as follows: The frequency domain features of the historical observation sequence are input into the Transformer encoder, and the contextual relationships in the frequency dimension are captured through a self-attention mechanism. Selective trajectory features are obtained by selectively processing the features passed through the Transformer encoder based on the Mamba state-space model. The selective trajectory features are added to the features passed through the Transformer encoder to generate the frequency domain features of the future predicted trajectory.

5. A state-space vehicle trajectory prediction device based on wavelet transform, comprising a processor, the processor being configured to execute the state-space vehicle trajectory prediction method based on wavelet transform as described in any one of claims 1 to 3.

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