ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration

Abstract

The invention relates to an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration, and the method comprises the steps: carrying out the initialization of an antenna position through employing K-means clustering according to a BAS algorithm, and coping with the change of a target function in a multi-dimensional space through combining with a self-adaptive learning rate; meanwhile, by introducing a temperature parameter, the random exploration capability of the algorithm is enhanced, and a search strategy can be flexibly adjusted in different stages, so that effective balance between global and local solutions is realized. And the algorithm has good stability. Besides, in consideration of the significant advantage of ensemble learning in the aspect of improving the generalization ability of the model, the basic prediction subsets, basic prediction submodel parameters and corresponding weights are dynamically adjusted according to the prediction performance and target maneuvering characteristics of the basic prediction subsets, an online learning framework suitable for target maneuvering trajectory prediction is constructed, training data are fully utilized, and the prediction efficiency of the target maneuvering trajectory is improved. And the target maneuvering trajectory prediction precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of target trajectory prediction methods, and particularly relates to an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration. Background Art

[0002] Trajectory prediction is a process of reasonably predicting the future motion trend of a target by extracting and analyzing the inherent information contained in the historical motion trajectory of the target. The accurate prediction of the target maneuver trajectory provides a key basis for damage effect evaluation and decision-making. Therefore, the research on the target maneuver trajectory prediction problem has important practical significance and application value.

[0003] In recent years, the research directions of target maneuver trajectory prediction methods have mainly been divided into two categories: model-driven methods and data-driven methods. Model-driven methods are based on physical motion models and kinematic principles, combined with the dynamic characteristics of the target and environmental influencing factors, to establish mathematical and physical models, and then to achieve accurate prediction of the target's future trajectory. In the references, a trajectory prediction model for aircraft climb and descent motions was constructed based on a genetic algorithm. Zhang et al. aimed to improve the safety of in-flight by developing a deep learning model for trajectory prediction, where the uncertainty of the model prediction was characterized using a Bayesian method. Wang et al. proposed an extended Kalman filter trajectory prediction algorithm based on a constant angular velocity and speed kinematic model, which can effectively predict the future trajectory of the target. Zhang et al. mainly studied trajectory prediction algorithms and their error analysis in trajectory prediction. We collected a large amount of flight trajectory data as samples, processed the sample data using a geographic information system, established a flight motion model based on the data, and predicted the sample data using the Kalman filter algorithm.

[0004] The data-driven target maneuver trajectory prediction method takes intelligent algorithms as the core and combines big data to establish a target maneuver trajectory prediction model. The research on data-driven target maneuver trajectory prediction methods generally regards it as a time series prediction problem. Xi et al. proposed an air combat target maneuver recognition model based on an online ensemble semi-supervised classification framework of online learning, ensemble learning, semi-supervised learning, and Tri-training algorithm, improving the accuracy and adaptability under high-dynamic air combat conditions. Compared with land transportation, sparse waypoints and shared flight paths pose difficulties for flight trajectory prediction. Shi et al. proposed a constrained long short-term memory network for flight trajectory prediction. According to the dynamic characteristics of the aircraft, three constraint conditions are proposed for the climb, cruise, and descent / approach phases, namely climb altitude, waypoint, and runway direction. This model can maintain long-term dependencies through dynamic physical constraints. To improve the optimization performance of the differential evolution algorithm (DE), Zhong et al. proposed a hybrid optimization trajectory prediction algorithm based on the differential evolution algorithm and the Harris hawk optimization algorithm. Under the same conditions, the performance of this hybrid optimization algorithm is better than other methods. Regarding the target maneuver trajectory prediction as a time series prediction problem. The above methods do not require the establishment of an accurate target motion model, and the model structure is simple, but the process of adjusting the model parameters is complex, and the requirements for data samples are relatively high. The target motion trajectory prediction methods based on time series also include the Volterra model, Gaussian mixture model, fuzzy time series prediction, RNN, echo state neural network, and long short-term memory neural network. In LSTM, the LSTM is improved using the stochastic gradient descent method, and the target position, attitude information, and relative situation information between the friendly and enemy sides are collected to construct an end-to-end mapping, thus achieving accurate prediction of the target maneuver trajectory. SHI et al. constructed some new dimensional features based on existing historical trajectory data. By analyzing the statistical features of three-dimensional data of longitude, latitude, and altitude, a combined prediction model based on LSTM and ARIMA was proposed, and this combined model improved the accuracy of trajectory prediction.

[0005] The Volterra series is a series of functions, called the Taylor series, where the memory function was proposed by an Italian mathematician in 1880. The essence of the Volterra series is the expansion of a sequence of functions. It can approximate the continuous function represented by any nonlinear system with arbitrary accuracy and can achieve accurate prediction of time series. However, the prediction effect of the Volterra series is easily affected by data quality. In the confrontation process, due to the complexity of the electromagnetic environment, the accuracy and anti-interference limitations of detection equipment, the accuracy and robustness of trajectory prediction are not high. Summary of the Invention

[0006] Aiming at the above problems, the present invention proposes an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration.

[0007] The present invention adopts the following technical solutions:

[0008] An ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration, comprising the following steps:

[0009] Step 1: Input the shipborne detection parameters of the target at each moment within a period of time and construct an input matrix D;

[0010] Step 2: Select multiple prediction models as basic predictors, adopt a model weight adaptive update strategy, initialize the weights of all basic predictors to the same value, then adaptively update according to real-time data, calculate the dynamic cumulative prediction error, adaptively update the weights, and determine the weight vectors of each basic predictor through normalization. The adaptive update weight of basic predictor i at time t is w1;

[0011] According to the preset performance index, set a threshold T to screen the features in the input matrix D, and reconstruct the input matrix according to the importance of the features:

[0012]

[0013] where, d ij represents the element in the i-th row and j-th column of the input matrix D, D′ is the reconstructed input matrix, and β is a parameter for controlling the adjustment intensity.

[0014] Step 3: Real-time identify the target maneuver mode, determine the boundary points by segmenting the target maneuver trajectory into continuous maneuver actions, real-time identify the aircraft maneuver mode, and determine the corresponding flight trajectory constraint conditions according to the maneuver mode;

[0015] Step 4: Use the improved beetle antenna search algorithm to determine the optimal kernel coefficients of the Volterra series model, obtain the optimized Volterra series model, input the reconstructed input matrix D′ obtained in Step 2 into the optimized Volterra series model, use the flight trajectory constraint conditions obtained in Step 3 as constraint conditions, and the optimized Volterra series model outputs the trajectory prediction result.

[0016] Furthermore, in Step 4, the method for determining the optimal kernel coefficients of the Volterra series by using the improved beetle antenna search algorithm includes the following steps:

[0017] Step 1: Use the K-means clustering algorithm to intelligently initialize the initial antenna positions. Each antenna position corresponds to a value of the alternative kernel coefficient matrix, and the fitness of each antenna position is evaluated by the following formula:

[0018]

[0019] In the formula, the meanings of the parameters are as follows:

[0020] x i : The current antenna position, representing a set of kernel coefficient configurations;

[0021] f(x i ): The fitness value of the current antenna position x i . The lower the fitness, the smaller the prediction error;

[0022] L(x i ): The function for fitness evaluation, representing the loss or error measure calculated for the current x i , corresponding to the fitness f(x i ) and reflecting the performance of the model;

[0023] M: The number of samples, representing the total number of data points used to evaluate the model performance;

[0024] Y j is the corresponding actual target position value at the j-th sample;

[0025] At the j-th sample, after substituting the kernel coefficients corresponding to x i into the Volterra series model, the position prediction result of the model output;

[0026] After obtaining the fitness values of all antenna positions, select the one with the lowest fitness as the best position for this round;

[0027] Step 2: Determine whether the maximum number of iterations is reached. If so, output the best position for this round obtained in the last iteration as the optimal kernel coefficient. Otherwise, go to Step 3;

[0028] Step 3: Increment the number of iterations by 1, and update all antenna positions using the antenna position update formula. The update formula is:

[0029] x i (t + 1) = x i (t) + α·Δ + r·D

[0030] x i (t): The position of the i-th antenna at the t-th round.

[0031] x i (t + 1): The position of the i-th antenna at the t + 1-th round.

[0032] α: The adaptive learning rate, dynamically adjusted according to the fitness

[0033] Δ: The gap between the current best antenna position and x i (t).

[0034] Δ = x t * -x i (t)

[0035] r: Random perturbation factor.

[0036] x t * : The best position among all antennae in the t-th round;

[0037] r = rand(0, 1)

[0038] In the formula, r is a random number from 0 to 1, used to introduce randomness to augment the search space, D is the perturbation vector, defined as:

[0039] D = U · (x max -x min )

[0040] U: A random number generated within the range [-1, 1], ensuring the uncertainty of the perturbation direction.

[0041] x max and x min represent the upper and lower limits of the antenna position respectively, ensuring that the antenna searches within the effective range;

[0042] Calculate the fitness values of all antenna positions after this iterative update according to the fitness calculation formula in Step 1, select the one with the lowest fitness as the best position in this round, and then go to Step 2.

[0043] Furthermore, in Step 2, the calculation method of w1 is as follows:

[0044]

[0045]

[0046] In the formula, is the prediction error of the basic predictor i at time t, y t is the actual target value at time t, λ is the historical error weighting factor, controlling the influence degree of historical errors on the current prediction error, K is the historical window size, indicating the number of past prediction steps considered when calculating the current error, γ is the decay factor, controlling the influence degree of past errors on the current prediction error, 0 < γ < 1, N is the number of basic predictors;

[0047] is the adaptive update weight of the basic predictor i at time t, is the weight of the basic predictor i at time t - 1, α is the learning rate, controlling the sensitivity of weight update, AMSE tis the average dynamic cumulative prediction error of all basic predictors;

[0048] σMSE t is the standard deviation of the dynamic cumulative prediction errors of all current basic predictors, used to quantify the stability of the prediction performance. ε is a preset constant added to avoid division-by-zero errors, and δ is a historical error feedback factor that controls the degree of influence of the current prediction error on weight updates. is the prediction error of the basic predictor at the current time point;

[0049] ω t is the weight of the basic predictor i at time t after normalization, is the sum of the weights of all basic predictors.

[0050] After the present invention adopts the above technical solutions, compared with the prior art, it has the following advantages:

[0051] The ADIBAS-Volterra aircraft trajectory prediction model of the present invention based on the Beetle Antennae Search (BAS) Adaptive Dynamic Integration (ADI) inherits the basic idea of sequential learning of the online prediction model. During the online learning process, the BAS algorithm uses K-means clustering to initialize the antenna positions and combines an adaptive learning rate to cope with the changes of the objective function in the multi-dimensional space. At the same time, by introducing a temperature parameter, the random exploration ability of the algorithm is enhanced, and the search strategy can be flexibly adjusted at different stages, so as to achieve an effective balance between the global and local solutions, making the algorithm have good stability. In addition, considering the significant advantage of ensemble learning in improving the generalization ability of the model, the ensemble learning theory is further introduced on the basis of the BAS-Volterra prediction model. According to the prediction performance of each basic prediction subset and the target maneuver characteristics, the basic prediction subsets, the parameters of the basic prediction sub-models and the corresponding weights are dynamically adjusted, a new ADIBAS-Volterra prediction model is proposed, and an online learning framework suitable for target maneuver trajectory prediction is constructed, making full use of the training data and improving the prediction accuracy of the sea-to-air target maneuver trajectory.

[0052] The present invention will be described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0053] Figure 1 is the flowchart of the present invention;

[0054] Figure 2 is the schematic diagram of the segmentation result of an aircraft's flight trajectory once;

[0055] Figure 3It is a comparison of different time recognition methods on a dataset of aircraft flight maneuvers, including the segmentation and recognition of a long-distance flight maneuver dataset with 12 action units. The black lines represent the boundaries of the actions. Different colors used by different methods correspond to different maneuver actions, and the bold labels written correspond to the labels of the maneuver actions;

[0056] Figure 4 It is a graph of the single-step prediction results of the X coordinate, where (a) is a comparison of the single-step prediction errors of the basic predictor; (b) is a comparison of the single-step prediction errors of each independent component; (c) is a comparison of the single-step prediction errors of the ensemble prediction algorithm.

[0057] Figure 5 It is a graph of the single-step prediction results of the Y coordinate, where (a) is a comparison of the single-step prediction errors of the basic predictor; (b) is a comparison of the single-step prediction errors of each independent component; (c) is a comparison of the single-step prediction errors of the ensemble prediction algorithm. Specific implementation manner

[0058] The principles and features of the present invention will be described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0059] 1. Beetle Antenna Search Algorithm

[0060] BAS is an optimization algorithm based on the foraging behavior of beetles in nature. This algorithm constructs a multi-dimensional search space by simulating the antenna detection mechanism of beetles during the process of finding food, aiming to find the optimal solution. First, the algorithm randomly initializes a group of "beetle" individuals representing different solutions, and then these individuals explore in the search space by adjusting their positions and speeds. During this process, each beetle updates its position based on its own experience and the information of its companions, thus continuously approaching a better solution. When a beetle discovers a better solution, it will pass this information to other beetles, prompting the entire group to move closer to the better solution. This characteristic of collective intelligence effectively avoids the algorithm from falling into local optima and increases the probability of finding the global optimal solution. The basic steps of BAS include initialization, position update, information transmission, and termination condition judgment, and it is applicable to solving complex problems such as function optimization, combinatorial optimization, and constraint optimization. Its advantages lie in its ability to adaptively adjust the search strategy, having strong global search capabilities, and being simple to implement, showing good practical application effects.

[0061] 2. Adaptive Reconstruction Method

[0062] The Adaptive Reconstruction Method (ARM) is a theory and method for effectively solving the analysis and optimization problems of complex systems. This method improves the performance and response ability of the system by dynamically adjusting the model structure and parameters. Its core lies in the dynamic adjustment mechanism: the system analyzes the performance of the current model through real-time monitoring and data collection to evaluate its effectiveness and reveal potential problems. This process involves model updates, feature selection, data processing, etc., enabling the system to better cope with complex environments and sudden changes. The key to the Adaptive Reconstruction Method lies in its adaptability. Through intelligent algorithms such as genetic algorithms, particle swarm optimization, or fuzzy logic, its flexibility in dynamic or complex environments is enhanced. The operation steps include data collection and analysis, model evaluation, reconstruction strategy formulation, and model update, forming a continuously optimized feedback loop. In summary, the Adaptive Reconstruction Method deeply analyzes the operation data and adjusts the model in real time to adapt to the changing environment, making it an important tool in modern scientific research and engineering practice.

[0063] 3. Time Series Prediction Model Based on BAS-Volterra Algorithm

[0064] 3.1 Basic Principle

[0065] The BAS-Volterra algorithm aims to use the ship detection equipment to transmit the state information of the aircraft (speed, altitude, azimuth angle, and pitch angle) and the state information of the ship (position, heading, and speed) to predict the flight trajectory of the aircraft in real time.

[0066] First, when facing the threat of aircraft, the ship can obtain the status information of the aircraft in real time, including speed, altitude, azimuth angle, pitch angle, etc. In addition, the status information of the ship itself, such as position, heading, and speed, is also of great significance for trajectory prediction. Second, in the process of constructing the BAS-Volterra model, the adaptive reconstruction method optimizes the input data. By screening out the features that have a significant impact on the prediction results and streamlining the data matrix used by the model, the computational efficiency and accuracy are improved when processing real-time data. Third, using Volterra series modeling can handle the complex non-linear relationship between the states of the aircraft and the ship. The movement trajectory of the aircraft is affected not only by its own movement laws but also by various factors such as environmental factors and the ship's state. After introducing the high-order time series function, the Volterra model can deeply explore these complex relationships to achieve higher-precision trajectory prediction. Fourth, the improved BAS algorithm is used to optimize the kernel coefficients. Through continuous iterative evaluation, the model quickly converges to the optimal parameter configuration. This rapid adaptation ability enables the prediction model to adjust in a timely manner in a changing tactical environment to adapt to the dynamic changes in the states of the aircraft and the ship. Fifth, according to the BAS-Volterra time series prediction algorithm, countermeasures can be quickly taken in a complex environment. In summary, we propose a maneuvering trajectory prediction model of the aircraft combined with the improved BAS-Volterra.

[0067] 3.2 Flowchart of the time series prediction model of the BAS-Volterra algorithm

[0068] To improve the prediction accuracy and computational efficiency of the Volterra time series model, we introduce the improved beetle antenna search algorithm into the Volterra model. The beetle antenna search algorithm can effectively avoid local optimal solutions through its global search ability by simulating the foraging behavior of beetles in nature, thereby optimizing the parameter settings of the Volterra model and accurately capturing the non-linear and time-varying characteristics in the time series. The synchronous optimization process can adjust the model parameters in real time, making the model more adaptable and robust. Especially when dealing with complex data with high noise in the aircraft trajectory, the prediction results are more reliable.

[0069] First, a trajectory prediction system is established by inputting the dynamic state parameters of the aircraft and the ship. The dynamic state of the aircraft includes speed, altitude, azimuth angle, pitch angle, and position information, while the state of the ship includes position, heading, and speed, etc. Secondly, the input features are screened according to the preset performance indicators. By calculating the prediction error and comparing it with the set threshold, the features that have a significant impact on the prediction result are retained, and the input features are adjusted based on the current prediction error to enhance the prediction ability of the model. Thirdly, the Volterra series modeling is adopted to effectively capture the nonlinear dynamic behavior of the aircraft, further improving the complexity and adaptability of the model. At the same time, the kernel coefficient is optimized by an improved beetle antenna search algorithm to find the optimal parameter configuration and minimize the loss function of the model. Finally, the optimized kernel coefficient matrix is used for target trajectory prediction, and the predicted trajectory of the aircraft is finally output.

[0070] The details are as follows:

[0071] (1) Input the shipborne detection parameters. The model involves the following dynamic state parameters of the aircraft and the ship:

[0072] Dynamic state parameters of the aircraft:

[0073] Speed v d (t): The flight speed of the aircraft at time t, with the unit of m / s.

[0074] Altitude h d (t): The flight altitude of the aircraft at time t, with the unit of m.

[0075] Azimuth angle θ d (t): The azimuth angle of the aircraft at time t, with the unit of degree (°).

[0076] Pitch angle φ d (t): The pitch angle of the aircraft at time t, with the unit of degree (°).

[0077] Position (latitude lat d (t), longitude lon d (t)): The geographical location of the aircraft at time t, with the unit of degree (°).

[0078] Dynamic state parameters of the ship:

[0079] Position (latitude lat b (t), longitude lon b (t)): The position of the ship at time t, with the unit of degree (°).

[0080] Heading ψ b : The heading angle of the ship at time t, with the unit of degree (°).

[0081] Speed vb : The navigation speed of the ship at time t, with the unit of m / s.

[0082] The course angle ψ of the ship b (t):

[0083] The elevation angle φ of the target d (t):

[0084] The yaw angle ψ of the target d (t): ψ d (t) = θ d (t) - ψ b (t)

[0085] In the formula, h d is the height of the target, and h b is the height of the ship, which is set to 0.

[0086] (2) Input matrix construction: Construct the input matrix D, whose elements are the state parameters of the aircraft and the ship:

[0087] Here, M represents the number of samples.

[0088] (3) According to the preset performance indicators, such as prediction error, select important features. Set the threshold T to select features:

[0089] If the feature has a significant impact on the prediction (the error is less than the threshold), then retain the feature.

[0090] After each prediction, adjust the input features based on the current prediction error. Let the predicted output of the current model be The true value is Y(t), and the error is

[0091]

[0092] Reconstruct the input matrix according to the importance of features:

[0093] D′ = D + β·E(t)·W

[0094] In the formula, D′ is the reconstructed input matrix, β is the parameter controlling the adjustment intensity, and W is the importance weight vector, which reflects the importance of each feature to the input adjustment.

[0095] (4) Volterra series modeling: Use the Volterra series to capture the nonlinear dynamic behavior of the aircraft, and the output equation can be expressed as:

[0096]

[0097] y(t) is the output of the system at time t (predicted aircraft trajectory).

[0098] d(t) is the input feature matrix. In Volterra series modeling, d(t) is an abstract representation of the input feature matrix, representing the input features at time t. Here, d(t) is actually a reference to the state parameters at a certain time in D (the input matrix processed by the adaptive reconstruction method). That is, d(t) can be regarded as the data from the t-th row of the input matrix D.

[0099] The first-order kernel coefficient h k reflects the direct influence of each feature on the output.

[0100] The second-order kernel coefficient describes the interaction effects among multiple inputs, thereby capturing the non-linear characteristics of the model.

[0101] The final output formula is:[[]]

[0102]

[0103] (5) Improved beetle antenna search algorithm. In the optimization framework, the improved beetle antenna search algorithm is used for the optimization of kernel coefficients.

[0104] Step1: Use the K-means clustering algorithm to intelligently initialize the initial antenna positions:

[0105] x i (0) = KMeans(data, clusters)

[0106] x i (0): The initialized antenna positions.

[0107] Step2: The fitness of each antenna position is evaluated by the following formula:

[0108]

[0109] Y j : The actual observed value.

[0110] The value predicted by the current antenna position.

[0111] Step3: Optimize the antenna positions using the adaptive learning rate and multi-scale search strategy, where the adaptive learning rate is

[0112]

[0113] Antenna position update

[0114] x i (t + 1) = xi (t) + α(t)·(r(t)·(x * - x i (t)) + σ(t)·n)

[0115] r(t) is a random perturbation factor, x * is the current best antenna position, and σ(t) is the perturbation intensity.

[0116] In the multi-scale search strategy, the temperature parameter T(t) is introduced

[0117] T(t) = T0·exp(-λt)

[0118] To enhance the global exploration ability of the search algorithm and avoid falling into local optimal solutions, a larger random perturbation is performed during the high-temperature period

[0119]

[0120] where x i (t) is the state of the antenna position at time t, α(t) is the learning rate at time t, r(t) is the random perturbation factor, rand is used to determine whether to adopt the first update rule or the second update. When its value is less than T(t), the antenna will be updated by random perturbation. The temperature parameter T(t) at time t is used to measure the openness of the search during the execution of the algorithm. The higher the degree, the more inclined to random exploration; when the temperature is low, the update of the antenna position depends more on the current optimal solution x*, and δ is a local adjustment vector randomly sampled from the neighborhood.

[0121] (6) Trajectory prediction

[0122] The model optimized by the beetle antenna search algorithm uses the optimized kernel coefficient matrix H* for prediction.

[0123]

[0124] H′ is the kernel coefficient matrix optimized by the ABS algorithm, and D' is the input matrix adjusted by the adaptive reconstruction method, is the predicted flight trajectory output vector.

[0125] (7) Complete steps of the prediction model:

[0126] Step1: Collect the state information such as the speed, altitude, azimuth angle, pitch angle, position and distance of the aircraft, as well as the speed, heading and position of the ship, and the detection data.

[0127] Step2: Create the input matrix D and perform feature selection and reconstruction.

[0128] Step 3: Express the aircraft motion model using the Volterra series and incorporate the ship state information.

[0129] Step 4: Optimize the kernel coefficients through an improved beetle antenna search algorithm to find the optimal parameter configuration to minimize the loss function.

[0130] Step 5: Conduct target trajectory prediction using the optimized kernel coefficient matrix.

[0131] In summary, the proposed BAS-Volterra trajectory prediction model aims to improve the prediction accuracy and computational efficiency of the aircraft's maneuvering trajectory. The improved BAS algorithm has a powerful global search ability and can effectively optimize the parameter settings of the Volterra model, thereby accurately capturing the non-linear and time-varying characteristics in time series data.

[0132] 4. Target Maneuvering Trajectory Prediction Model Based on BAS-Volterra and Adaptive Ensemble Learning Strategy

[0133] Ensemble learning is a machine learning method that uses a series of basic learners for learning and integrates the learning results of each basic learner according to certain rules to obtain better learning effects than a single basic learner. To further improve the performance of the target maneuvering trajectory prediction model based on BAS-Volterra, by introducing the ensemble learning theory and combining the maneuvering characteristics of the target, a target maneuvering trajectory prediction model based on adaptive dynamic ensemble is proposed. This model mainly improves the performance of target maneuvering trajectory prediction by implementing an adaptive update strategy for the basic prediction model set, an adaptive update strategy for the parameters of the basic prediction model, and an adaptive strategy for the weights of the basic prediction model. The process of the proposed ADIBAS-Volterra target maneuvering trajectory prediction model is as Figure 1 shown.

[0134] 4.1 Boundary Point Identification Model for Target Maneuvering Actions

[0135] Real-time identification of the aircraft's maneuvering mode is a complex and highly dynamic process with obvious time-varying characteristics. To better track the real-time changes in the target's maneuvering characteristics, combined with the identification results of the target maneuvering boundary points, we adjust the basic prediction model set in real time according to the identification results of the target maneuvering boundary points, thereby improving the prediction performance of the target maneuvering trajectory.

[0136] The maneuvering trajectory of the target consists of a series of consecutive maneuvering actions. Therefore, the segmentation of the target maneuvering trajectory can be transformed into the segmentation between basic maneuvers. According to the characteristics of different maneuvering actions, the maneuvering actions of the target can be divided into three categories: horizontal plane maneuver, vertical plane maneuver, and spatial maneuver. To better describe various maneuvers, the dynamic model and dynamic equations of target maneuvers can be expressed as follows.

[0137]

[0138] Table 2 Target Maneuvering Action Recognition Rules

[0139]

[0140]

[0141]

[0142] Among them, (x t , y t , z t ) represents the position in the inertial coordinate. are the rates of change of the aircraft's speed, trajectory pitch angle, and yaw angle respectively. g represents the acceleration due to gravity. are the tangential overload, normal overload, and roll angle respectively. (x t , y t , z t , ν t , γ t , ψ t ) and represent the state variables and control variables. According to the kinematic model, state variables, and control variables of the target maneuvering trajectory, the target maneuvering trajectory can be divided into 45 maneuvering modes. According to the parameter settings of the 45 maneuvering modes, the target maneuvering recognition rules shown in Table 2 can be obtained.

[0143] Generally speaking, the maneuvering trajectory of the target can be composed of a series of action units. According to the target maneuvering action recognition rules in Table 2, the target maneuvering trajectory needs to be further segmented. It can be seen from Table 2 that the characteristics of each maneuvering action unit are summarized into segmentation rules. Due to the diversity of the parameter characteristics of the maneuvering action units, the conditions for the non-segmentability of flight maneuvering actions are described. If the parameters do not meet the conditions, the current flight point represents the segmentation point.

[0144] In terms of target maneuvering recognition, this section proposes 45 maneuvering modes and details the corresponding parameter settings and recognition rules. These rules are important bases for the segmentation of maneuvering actions, ensuring that the characteristics of each action unit can be accurately recognized and guaranteeing that in certain conditions, the situations where flight maneuvering actions cannot be segmented can still be accurately recognized.

[0145] 4.2 Model Weight Adaptive Update Strategy Based on Prediction Performance

[0146] We constructed the ADIBAS-Volterra target maneuver trajectory prediction model. In the model initialization stage, the weights of each basic predictor were initialized to the same value to construct the initial integrated prediction system. To ensure the overall performance of the ensemble prediction model, during the process of obtaining real-time data, it is necessary to adaptively update the weights according to the prediction accuracy corresponding to each basic predictor. The principle of model weight adaptive update is that a model with superior performance generally has a larger weight. For ease of explanation, some related definitions are listed as follows.

[0147]

[0148] In the formula, is the prediction error of the basic predictor i at time t, y t is the actual target value at time t, λ is the historical error weighting factor, which controls the influence degree of historical errors on the current prediction error, K is the historical window size, indicating the number of past prediction steps considered when calculating the current error, and γ is the decay factor, which controls the influence degree of past errors on the current prediction error. Usually, 0 < γ < 1.

[0149] Dynamic Cumulative Prediction Error

[0150]

[0151] is the adaptive update weight of the basic predictor i at time t, is the weight of the basic predictor i at time t - 1, α is the learning rate, which controls the sensitivity of weight update. A larger value may lead to instability. AMSE t The average dynamic cumulative prediction error of all basic predictors.

[0152] σMSE t is the standard deviation of the dynamic cumulative prediction errors of all current basic predictors, which is used to quantify the stability of prediction performance. ε is a small constant added to avoid division-by-zero errors. Usually, a very small value is taken. δ is the historical error feedback factor, which controls the influence degree of the current prediction error on weight update. is the prediction error of the basic predictor at the current time point.

[0153]

[0154] is the normalized weight of the basic predictor i at time t, is the sum of the weights of all basic predictors, ensuring that the overall weight is normalized to 1.

[0155] Therefore, the adaptive update method of model weights can, to a certain extent, reduce the impact of models with poor prediction performance on the integrated system. When calculating , we not only consider the prediction error of the model for the i-th newly arrived data but also the prediction performance of the model in historical data, so as to comprehensively evaluate the comprehensive performance of the model on newly arrived data and historical data.

[0156] 5. Simulation Verification and Analysis

[0157] The experiment was carried out in the Matlab 2021 environment and run on a PC equipped with a 4-core Intel Core i7 3.0 GHz processor and 8 GB of memory. We used the adversarial training data extracted from the simulated aircraft system as the experimental data.

[0158] To better compare the performance of different algorithms, we adopted four measurement methods, namely Relative Root Mean Square Error (RRMSE), Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), and Normalized Mean Square Error (NMSE), to evaluate the prediction accuracy. The simulation results of each group are the average results of 100 independent trials, as follows:

[0159]

[0160] Among them, is the actual value, y is the predicted value, and y is the average value of . To evaluate the performance of the target maneuver trajectory prediction model based on the ADIBAS-Volterra algorithm.

[0161] 5.1 Verification of Target Maneuver Trajectory Prediction Simulation Experiment

[0162] According to the ADIBAS-Volterra trajectory prediction model we proposed, Figure 2 and 3 show the predicted trajectories during aircraft maneuvers. Target maneuver trajectory prediction is the basis for target damage assessment and maneuver decision-making. The target maneuver prediction problem is essentially a time-series real-time prediction problem, with non-linear and time-varying characteristics. In addition, due to the complexity of the electromagnetic environment, the data obtained by sensors has certain noise. To verify the effectiveness and robustness of the target prediction model we proposed, based on the target maneuver trajectory data stored in the simulator, the prediction performance of the algorithm was tested. The parameter settings of the algorithm are shown in Table 2, and the parameter settings of Kmeans, DEHHO, LSTM, and Goal Curve Net are the same as those in the literature.

[0163] Figure 2Among them, the blue trajectory represents the flight actions of the aircraft, and the orange rectangular points represent the segmentation points. According to the comparison between the original segmentation and the proposed segmentation, the main segmentation points correspond to the original segmentation points in terms of quantity and length. To further verify the effectiveness of the recognition after segmentation, Figure 3 shows two comparisons of the recognition methods of the aircraft at different times. Figure 3 gives the main segments, and the labels of the segments are in bold. In Figure 3 Figure (a), ADIBAS-Volterra can correctly display the class labels of all segments except the subordinate segments. In the recognition of the main segments, ADIBAS-Volterra provides the correct class labels for most segments except the last segment.

[0164] In the recognition of the main segments, ADIBAS-Volterra provides the correct class labels for all segments. Among the other comparison methods, Volterra, TrVolterra, OSVolterra, TrOSVolterra, PCMPA, PSLSTM, OVMD-ICEEMDAN-PE, OVMD-PE, EPL-KGLA, GL-Volterra, IEGL-Volterra, ODL-Volterra, DW-Volterra can provide 7, 7, 6, 6, 7, 6, 5, 7, 6, 7, 6, 7 and 8 correct main segments respectively. From Figure 3 Figure (b), it can be seen that ADIBAS-Volterra and DW-Volterra can respectively recognize all the main segments. At the same time, the other 11 advanced trajectory prediction methods can respectively recognize 10, 10, 10, 10, 10, 9, 10, 9, 10, 11 and 11 main segments. In general, compared with other advanced methods, ADIBAS-Volterra can achieve better recognition results in terms of segment length and correct recognition of boundaries.

[0165] 5.2 Feasibility Analysis of the Target Maneuvering Trajectory Prediction Method

[0166] The problem of target maneuvering trajectory prediction is essentially a time series prediction problem. To verify the adaptability of the prediction model we proposed, the typical chaotic time series Mackey Glass and Rossler datasets are used to verify the effectiveness and robustness of the BAS-Volterra prediction model integrated with the improved beetle antenna search algorithm.

[0167] To illustrate the necessity of selecting the Volterra sequence as the basic predictor for improving the integrated prediction model, the prediction performance of this algorithm was compared with that of the shallow machine learning algorithms K-means, (differential evolution, DE, based on DE and Harris hawks optimization, DEHHO), LSTM, and (a multimodal trajectory prediction network combining heterogeneous graph attention goal prediction and curve fitting, Goal-Curve Net).

[0168] The ADIBAS-Volterra prediction model is an ensemble algorithm, and the improvement in the performance of the prediction model is the result of improving the BAS, Volterra model, online learning, and adaptive ensemble learning algorithms. In addition, to introduce the roles of each part of ADIBAS-Volterra, comparisons were made with Volterra, BAS, BAS-Volterra, improved BAS-Volterra, and ADIBAS-Volterra.

[0169] To verify the performance superiority of the proposed improved ensemble learning algorithm based on target maneuver characteristics, the improved adaptive ensemble prediction model was compared with (the grey Lotka-Volterra model, GL-Volterra, (information-enhanced Grey Lotka-Volterra model, IEGL-Volterra), (one-dimensional linear Volterra-Fredholm, ODL-Volterra)

[31] (Daubechies wavelets-Volterra, DW-Volterra). The target maneuver trajectory prediction based on a single learning model belongs to the global modeling method, with a complex model and being prone to falling into local optima. Compared with a single learning algorithm, integrating multiple learning algorithms can often achieve higher prediction accuracy. In recent years, ensemble learning has been increasingly applied to time series prediction problems.

[0170] To better compare the effectiveness and superiority of the BAS-Volterra algorithm, the robustness of the algorithm to noisy data was compared through simulation. Chaotic systems are usually used to test the performance of nonlinear systems. We used the typical chaotic time series Mackey and Rossler datasets as the training and test samples of the algorithm to verify the effectiveness of the algorithm. The data generation conditions were exactly the same as those in the reference. To verify the effectiveness and advancement of the proposed algorithm, we adopted (The paper culminates in presenting an enhanced version of the Marine Predator Algorithm, PCMPA) [ , (a partial least squares based pruning algorithm is hereby proposed for a simplified LSTM, PSLSTM), (the optimal variational mode decomposition, improved complete ensemble empirical mode decomposition and permutation entropy, OVMD-ICEEMDAN-PE), (optimal variational mode decomposition with permutation entropy, OVMD-PE), (kernel general loss algorithm based on evolving participatory learning, EPL-KGLA) for comparison. 15% noise was added to all samples of the three groups of data. The noise addition method is as follows: Calculate the standard deviation σ of each dimension of the test sample data, generate random numbers that satisfy the N(0,σ) distribution and superimpose them on the corresponding dimensions of the sample data.

[0171] Table 3 lists the prediction results of the chaotic time series Mackey and Rossler. It can be seen that in terms of the prediction accuracy of the algorithm, the RRMSE, MAD, MAPE, and NMSE of ADIBAS-Volterra are much lower than those of other methods, and its prediction accuracy is significantly better than that of other prediction algorithms. Under the conditions of the same test data set, hardware platform, and algorithm initial parameter settings, the prediction accuracy of this algorithm is significantly better than that of other prediction algorithms in the literature. In terms of the running time of the algorithm, compared with the other five prediction algorithms, ADIBAS-Volterra is more time-saving than other methods. This is because Volterra processes the relationship between the time variable and the system state in the form of convolution, which can reduce the time required for model creation and adjustment. BAS can accelerate the convergence of parameters, enabling the model to achieve better prediction performance in a shorter time. This model also introduces an online learning mechanism, allowing the model to adjust its parameters in real time after receiving new data. This adaptive ability can automatically optimize the model according to the changes in real-time data, thereby reducing the time required for the model to adjust when new situations occur. It can be seen from the running time of the single-step prediction of this algorithm that the single-step running time of the improved ADIBAS-Volterra prediction algorithm can meet the real-time requirements of time series prediction problems.

[0172] Single-step prediction results of the time series data set with added noise in Table 3

[0173]

[0174] Table 3 lists the prediction results of the noisy Mackey and Rossler chaotic time series. It can be seen that the BAS-Volterra prediction algorithm can still maintain a high prediction accuracy when adding noise, and its performance is significantly better than that of other prediction methods. The robustness of the algorithm we proposed has been verified. By comparing the prediction results of the PCMPA, PSLSTM, OVMD-ICEEMDAN-PE, OVMD-PE, and EPL-KGLA algorithms, under noise conditions, the original method can effectively perform trajectory prediction, thereby improving the prediction performance of the algorithm.

[0175] To verify the effectiveness and robustness of the target prediction model we proposed, the prediction performance of the algorithm was tested based on the target maneuver trajectory data stored in the simulator. The parameter settings of the algorithm are shown in Table 4. The parameter settings of other comparison algorithms are the same as those in the literature. To reduce the accidental error of the prediction algorithm, the prediction results of each algorithm are the average results of 100 repeated trials. The single-step prediction results of different algorithms for the target maneuver trajectory are shown in Tables 4-6. To more intuitively compare the prediction performance of different algorithms for the target maneuver trajectory, the single-step prediction absolute error values of the X coordinate, Y coordinate, and Z coordinate of different algorithms are presented in the form of a graph, such as Figure 4 andFigure 5 as shown

[0176] Table 4 Algorithm and Its Parameter Settings

[0177]

[0178] Table 5 Single-Step Prediction Results of X Coordinates

[0179]

[0180]

[0181] 4.5 Conclusion

[0182] We proposed an adaptive hybrid algorithm based on the beetle antenna search algorithm, target maneuver boundary point recognition algorithm, and Volterra series, called ADIBAS-Volterra, for time series prediction of target maneuver trajectories. Through the Volterra model, the nonlinear and time-varying characteristics are captured, and the complex relationship between the time variable and the system state is processed in a convolutional form, improving the prediction accuracy. At the same time, the improved beetle antenna search algorithm (ABS) is adopted to enhance the global search ability of the model, avoid the problem of local optimal solutions, and thus improve the robustness and real-time response ability in complex environments. The innovation points of the trajectory prediction model can be summarized as follows:

[0183] (1) Since the maneuver trajectory prediction of the aircraft is a time series problem affected by various nonlinear factors and dynamic environments, the Volterra model is introduced. The Volterra model can effectively capture the nonlinear characteristics of the system and is suitable for the behavior prediction of complex dynamic systems. Through the convolutional form of polynomials, this model can handle the changes of time variables and adapt to the dynamic characteristics at different time points. This method can consider various interference factors more comprehensively and improve the prediction reliability.

[0184] (2) To make up for the limitations of a single Volterra model in capturing the nonlinear dynamic characteristics of target maneuver trajectories, a beetle antenna search framework suitable for target maneuver trajectory prediction is constructed. This method optimizes the model parameters through ABS, uses intelligent initialization and multi-scale search strategies, effectively improves the global search ability, avoids the problem of local optimal solutions, and improves the real-time online prediction performance of the model.

[0185] (3) Combining the target maneuver boundary point recognition algorithm and prediction performance, an adaptive update comprehensive prediction model is constructed. To better adapt to the target maneuver trajectory prediction problem, the ADIBAS-Volterra prediction model combines the target maneuver boundary point recognition algorithm with prediction performance, and dynamically updates the integrated model in real time. At the same time, according to the prediction performance indicators of the basic predictors, weights are dynamically allocated to ensure the effectiveness and accuracy of the integrated model.

[0186] The ADIBAS-Volterra algorithm enhances the global search ability of the model by effectively capturing non-linear and time-varying characteristics and avoids the problem of local optimal solutions. At the same time, with the help of the dynamic update strategy and adaptive weight allocation, ADIBAS-Volterra significantly improves the prediction accuracy and robustness to meet the trajectory prediction requirements in complex dynamic environments.

[0187] The above are examples of the best implementation modes of the present invention, and the parts not described in detail are the common general knowledge of those of ordinary skill in the art. The protection scope of the present invention shall be subject to the content of the claims, and any equivalent transformation based on the technical inspiration of the present invention shall also be within the protection scope of the present invention.

Claims

1. An ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration, characterized in that, It includes the following steps: Step 1: Input the shipborne detection parameters of the target at each moment within a period of time and construct the input matrix D; Step 2: Select multiple prediction models as basic predictors, adopt the model weight adaptive update strategy, initialize the weights of all basic predictors to the same value, then adaptively update according to real-time data, calculate the dynamic cumulative prediction error, adaptively update the weights, and determine the weight vectors of each basic predictor through normalization. The adaptive update weight of basic predictor i at time t is w1; According to the preset performance index, set the threshold T to screen the features in the input matrix D, and reconstruct the input matrix according to the importance of the features: where d ij represents the element in the i-th row and j-th column of the input matrix D, D' is the reconstructed input matrix, and β is a parameter that controls the adjustment strength. Step 3: Real-time identify the target maneuver mode. By segmenting the target maneuver trajectory into continuous maneuver actions, determine the boundary points, real-time identify the aircraft maneuver mode, and determine the corresponding flight trajectory constraint conditions according to the maneuver mode; Step 4: Use the improved beetle antenna search algorithm to determine the optimal kernel coefficients of the Volterra series model, obtain the optimized Volterra series model, input the reconstructed input matrix D' obtained in Step 2 into the optimized Volterra series model, and use the flight trajectory constraint conditions obtained in Step 3 as constraint conditions. The optimized Volterra series model outputs the trajectory prediction result.

2. The ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration according to claim 1, characterized in that, In Step 4, the method for using the improved beetle antenna search algorithm to determine the optimal kernel coefficients of the Volterra series includes the following steps: Step 1: Use the K-means clustering algorithm to intelligently initialize the initial antenna positions. Each antenna position corresponds to a candidate kernel coefficient matrix value, and the fitness of each antenna position is evaluated by the following formula: In the formula, the meanings of the parameters are as follows: x i : The current antenna position, corresponding to a set of kernel coefficient configurations; f(x i ): The fitness value of the current antenna position x i . The lower the fitness, the smaller the prediction error; L(x i ):The function for fitness evaluation, representing the loss or error metric calculated for the current x i , corresponding to the fitness f(x i ) and reflecting the performance of the model; M: The number of samples, representing the total number of data points used to evaluate the model performance; Y j is the corresponding actual target position value at the j-th sample; At the j-th sample, after substituting the corresponding kernel coefficient of x i into the Volterra series model, the position prediction result of the output of the model; After obtaining the fitness values of all antenna positions, select the one with the lowest fitness as the best position for this iteration; Step 2: Judge whether the maximum number of iterations is reached. If so, output the best position obtained in the last iteration as the optimal kernel coefficient, otherwise go to Step 3; Step 3: Increment the iteration number by 1, and update all antenna positions using the antenna position update formula. The update formula is: x i (t + 1)=x i (t)+α·Δ + r·D x i (t): The position of the i-th antenna at the t-th iteration. x i (t + 1): The position of the i-th antenna at the (t + 1)-th iteration. α: Adaptive learning rate, dynamically adjusted according to fitness Δ: The difference between the current best antenna position and x i (t). Δ = x t * -x i (t) r: Random perturbation factor. x t * : The best position among all the antennae in the t-th round; r = rand(0,1) In the formula, r is a random number from 0 to 1, used to introduce randomness to augment the search space, D is the perturbation vector, defined as: D = U·(x max - x min ) U: A random number generated within [-1,1] to ensure that the direction of the perturbation is uncertain. x max and x min represent the upper and lower limits of the antenna position respectively, ensuring that the antenna searches within the effective range; Calculate the fitness values of all antenna positions updated in this iteration according to the fitness calculation formula in Step 1, select the one with the lowest fitness as the best position for this iteration, and then go to Step 2.

3. The ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antennae search dynamic integration according to claim 1, characterized in that, In Step 2, the calculation method of w1 is as follows: In the formula, is the prediction error of the basic predictor i at time t, and y t is the actual target value at time t, λ is the historical error weighting factor that controls the influence degree of the historical error on the current prediction error, K is the historical window size that represents the number of past prediction steps considered when calculating the current error, γ is the decay factor that controls the influence degree of the past error on the current prediction error, 0 < γ < 1, and N is the number of basic predictors; is the adaptive update weight of the basic predictor i at time t, is the weight of the basic predictor i at time t-1, α is the learning rate, controlling the sensitivity of weight update, AMSE t is the average dynamic cumulative prediction error of all basic predictors; σMSE t is the standard deviation of the dynamic cumulative prediction errors of all current basic predictors, which is used to quantify the stability of the prediction performance. ε is a preset constant added to avoid division-by-zero errors, and δ is a historical error feedback factor that controls the degree of influence of the current prediction error on the weight update. is the prediction error of the basic predictor at the current time point; ω t is the weight of the normalized base predictor i at time t, which is the sum of all base predictor weights.

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