Improved beetle antennae search dynamic integrated ADIBAS-Volterra aircraft trajectory prediction method

Abstract

The application relates to an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamics integration. The BAS algorithm of the application firstly performs K-means clustering to initialize the antenna position, and combines an adaptive learning rate to cope with the change of a target function in a multidimensional space. Meanwhile, 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 that an effective balance between global and local solutions is realized, and the algorithm has good stability. In addition, considering the significant advantage of ensemble learning in improving the generalization ability of a model, according to the prediction performance of each basic predictor set and the target maneuvering characteristics, the basic predictor set, the basic predictor model parameters and the corresponding weight are dynamically adjusted, an online learning framework suitable for target maneuvering trajectory prediction is constructed, the training data is fully utilized, and the target maneuvering trajectory prediction precision is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of target trajectory prediction methods, and particularly relates to an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antennae search dynamic integration. BACKGROUND

[0002] Trajectory prediction is a process of extracting and analyzing the inherent information contained in the historical motion trajectory of a target to reasonably predict its future motion trend. Accurate prediction of the target maneuvering trajectory provides a key basis for damage assessment and decision-making. Therefore, the study of target maneuvering trajectory prediction has important practical significance and application value.

[0003] In recent years, the research direction of target maneuvering trajectory prediction methods mainly falls into two categories: model-driven method and data-driven method. The model-driven method is based on physical motion models and kinematic principles, combined with the dynamic characteristics of the target and environmental impact factors, to establish mathematical physical models, and then realize accurate prediction of the future trajectory of the target. In the reference, a trajectory prediction model for aircraft climbing and descending motion is constructed based on genetic algorithm. Zhang et al. aimed to improve the safety of en route flight by developing a deep learning model for trajectory prediction, in which the uncertainty of the model prediction was characterized by the Bayesian method. Wang et al. proposed an extended Kalman filter trajectory prediction algorithm based on constant angular velocity and velocity kinematic model, which can effectively predict the future trajectory of the target. Zhang et al. mainly studied the trajectory prediction algorithm and its error analysis in trajectory prediction. We collected a large amount of flight trajectory data as samples, processed the sample data using geographic information system, established a flight motion model according to the data, and predicted the sample data using Kalman filter algorithm.

[0004] Data-driven target maneuver trajectory prediction methods take intelligent algorithms as the core and establish target maneuver trajectory prediction models combined with big data. 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 identification model based on online learning, ensemble learning, semi-supervised learning and online ensemble semi-supervised classification framework of Tri-training algorithm, which improves the accuracy and adaptability under high dynamic air combat conditions. Compared with land traffic, sparse waypoints and shared airways bring difficulties to flight trajectory prediction, and Shi et al. proposed a restricted 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, which are the climb height, waypoint and runway direction respectively, and the model can maintain long-term dependencies through dynamic physical constraints. In order to improve the optimization performance of differential evolution algorithm (DE), Zhong et al. proposed a hybrid optimization trajectory prediction algorithm based on differential evolution algorithm and Harris eagle optimization algorithm, and the performance of the hybrid optimization algorithm is better than that of other methods under the same conditions. The target maneuver trajectory prediction is regarded as a time series prediction problem. The above methods do not need to establish an accurate target motion model, and the model structure is simple, but the parameter adjustment process of the model is complex, and the requirement for data samples is high. The time series-based target motion trajectory prediction methods also include Volterra model, Gaussian hybrid model, fuzzy time series prediction, RNN, echo state neural network and long short-term memory neural network. In the LSTM, the random gradient descent method is used to improve the LSTM, the target position, attitude information and enemy and friendly relative situation information are collected to construct an end-to-end mapping, so as to realize 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 characteristics of the longitude, latitude and height three-dimensional data, a combination prediction model based on LSTM and ARIMA is proposed, which improves the accuracy of trajectory prediction.

[0005] Volterra series is a function series, called Talyor series, which is a memory function proposed by an Italian mathematician in 1880. The essence of Volterra series is the expansion of function sequence, which can approximate the continuous function represented by any nonlinear system with arbitrary precision, and can realize accurate prediction of time series, but the prediction effect of Volterra series is easily affected by data quality. In the process of confrontation, due to the complexity of electromagnetic environment, the precision and anti-interference limitation of detection equipment, the accuracy and robustness of trajectory prediction are not high. SUMMARY

[0006] In view of the above problems, the application provides an ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration.

[0007] The application adopts the following technical solutions:

[0008] The ADIBAS-Volterra aircraft trajectory prediction method based on the improved beetle antennae search dynamic integration includes the following steps:

[0009] Step 1, input the shipborne detection parameters of a target at each time in 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 updating strategy, initialize the weights of all basic predictors to the same value, then perform adaptive updating according to real-time data, calculate a dynamic cumulative prediction error, adaptively update the weights, determine a weight vector of each basic predictor through normalization, and the adaptive updating weight of the basic predictor i at time t is w1;

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

[0012]

[0013] wherein d ij represents an element in the ith row and jth column of the input matrix D, D' is the reconstructed input matrix, and β is a parameter for controlling the adjustment strength.

[0014] Step 3, real-time identification of target maneuvering mode, segmentation of the target maneuvering trajectory into continuous maneuvering actions, determination of boundary points, real-time identification of the aircraft maneuvering mode, determination of corresponding flight trajectory constraint conditions according to the maneuvering mode;

[0015] Step 4, determination of the optimal kernel coefficient of the Volterra series model by using the improved beetle antennae search algorithm, obtaining of the optimized Volterra series model, input of the reconstructed input matrix D' obtained in step 2 into the optimized Volterra series model, and input of the flight trajectory constraint conditions obtained in step 3 as constraint conditions, and output of the trajectory prediction result by the optimized Volterra series model.

[0016] Further, in step 4, the method for determining the optimal kernel coefficient of the Volterra series by using the improved beetle antennae search algorithm includes the following steps:

[0017] Step 1, intelligent initialization of initial antennae positions by using a K-means clustering algorithm, each antennae position corresponding to a candidate kernel coefficient matrix value, and the fitness of each antennae position being evaluated by the following formula:

[0018]

[0019] In the formula, each parameter represents the following meaning:

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

[0021] f(x i ): fitness value of the current antenna position x i , the lower the fitness, the smaller the prediction error; L(x i ): function of fitness evaluation, representing the loss or error measure calculated for the current x i , corresponding to the fitness f(x i ), reflecting the performance of the model;

[0022] M: sample size, representing the total number of data points used to evaluate the performance of the model;

[0023] Y j is the actual target position value corresponding to the jth sample;

[0024] At the jth sample, the position prediction result of the output of the model after bringing the kernel coefficient corresponding to x i into the Volterra series model;

[0025] After obtaining the fitness values of all antenna positions, select the one with the lowest fitness as the best position of this round;

[0026] Step 2, determine whether the maximum number of iterations is reached, if yes, output the best position of this round obtained in the last iteration as the optimal kernel coefficient, otherwise go to step 3;

[0027] Step 3, increment the iteration number by 1, and update all antenna positions using the antenna position update formula:

[0028] x i (t+1) = x i (t) + α·Δ + r·D

[0029] x i (t): position of the ith antenna at the tth round.

[0030] x i (t+1): position of the ith antenna at the t+1th round.

[0031] α: adaptive learning rate, dynamically adjusted according to fitness

[0032] Δ: difference between the current best antenna position and x i (t).

[0033]

[0034] r: random disturbance factor.

[0035] x t * : the best position in the t-th round among all the tentacles;

[0036] r=rand(0,1)

[0037] where r is a random number from 0 to 1, used to introduce randomness to expand the search space, and D is a disturbance vector defined as:

[0038] D=U·(x max -x min )

[0039] U: a random number generated in the range of [-1, 1], ensuring the uncertainty of the direction of disturbance.

[0040] x max and x min represent the upper and lower limits of the tentacle position, respectively, ensuring that the tentacle searches within the effective range;

[0041] The fitness values of all tentacle positions updated in this iteration are calculated according to the fitness calculation formula in step 1, and the one with the lowest fitness is selected as the best position in this round, then go to step 2.

[0042] Further, in step 2, the calculation method of w1 is as follows:

[0043]

[0044]

[0045] where e 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 of historical error in the current prediction error, K is the historical window size, representing the number of past prediction steps considered in calculating the current error, γ is the decay factor, controlling the influence of past errors on the current prediction error, 0 < γ < 1, N is the number of basic predictors;

[0046] 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;

[0047] σMSEt is the standard deviation of the dynamic cumulative prediction error of all basic predictors at present, used to quantify the stability of the prediction performance, is a preset constant added to avoid division by zero error, and is a historical error feedback factor, controlling the influence degree of the current prediction error on the weight update, is the prediction error of the basic predictor at the current time point;

[0048] ω t is the normalized weight of the basic predictor i at time t, is the sum of all basic predictor weights.

[0049] Compared with the prior art, the present application has the following advantages:

[0050] The ADIBAS-Volterra aircraft trajectory prediction model based on the Beetle Antennae Search (BAS) adaptive dynamic integration (ADI) of the present application inherits the basic idea of sequence learning of the online prediction model. In the online learning process, the BAS algorithm uses K-means clustering to initialize the antenna position, and combines the adaptive learning rate to cope with the changes of the objective function in the multi-dimensional space. At the same time, by introducing the 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 realize effective balance between global and local solutions. The algorithm has 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 predictor set and the target maneuvering characteristics, the basic predictor set, the basic predictor model parameters and the corresponding weight are dynamically adjusted, a new ADIBAS-Volterra prediction model is proposed, and an online learning framework suitable for target maneuvering trajectory prediction is constructed, which fully utilizes the training data and improves the sea-to-air target maneuvering trajectory prediction accuracy.

[0051] The present application will be described in detail below in conjunction with the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a flowchart of the present application;

[0053] Figure 2 is a schematic diagram of the segmentation result of an aircraft flight trajectory;

[0054] Figure 3is the comparison of different time recognition methods on a single aircraft flight maneuver dataset, including the segmentation and recognition of a long-distance flight maneuver dataset containing 12 action units, the black line represents the boundary of the action. Different methods use different colors to correspond to different maneuver actions, and the written bold labels correspond to the labels of the maneuver actions;

[0055] Figure 4 is a single-step prediction result graph of X coordinates, where (a) is a single-step prediction error comparison of the basic predictor; (b) is a single-step prediction error comparison of each independent component; (c) is a single-step prediction error comparison of the ensemble prediction algorithm.

[0056] Figure 5 is a single-step prediction result graph of Y coordinates, where (a) is a single-step prediction error comparison of the basic predictor; (b) is a single-step prediction error comparison of each independent component; (c) is a single-step prediction error comparison of the ensemble prediction algorithm. DETAILED DESCRIPTION

[0057] The principles and features of the present application are described below in conjunction with the accompanying drawings, which are only used to explain the present application and are not intended to limit the scope of the present application.

[0058] 1. Beetle antenna search algorithm

[0059] BAS is an optimization algorithm based on the foraging behavior of insects in nature. By simulating the antenna detection mechanism of insects during the search for food, a multi-dimensional search space is constructed to find the optimal solution. First, the algorithm randomly initializes a group of "insect" individuals representing different solutions, and then these individuals adjust their positions and velocities to explore the search space. In this process, each insect updates its position based on its own experience and the information of its peers, thereby constantly approaching better solutions. When an insect finds a better solution, it will pass this information to other insects, prompting the entire group to move closer to the better solution. This collective intelligence effectively avoids the algorithm from falling into local optimum, increasing the probability of finding the global optimal solution. The basic steps of BAS include initialization, position update, information transmission and termination condition judgment, which are suitable for solving complex problems such as function optimization, combinatorial optimization and constraint optimization. Its advantages lie in its ability to adaptively adjust the search strategy, strong global search ability, simple implementation and good practical application effect.

[0060] 2. Adaptive reconstruction method

[0061] Adaptive Reconstruction Method (ARM) is a theory and method that effectively solves the problem of complex system analysis and optimization. It adjusts the model structure and parameters dynamically to improve the performance and response ability of the system. The core of this method is the dynamic adjustment mechanism: the system monitors and collects data in real time, analyzes the performance of the current model, and evaluates its effectiveness and reveals potential problems. This process involves model updating, feature selection, data processing, and other aspects, enabling the system to better respond to complex environments and sudden changes. The key to ARM is its adaptive ability, which enhances flexibility in dynamic or complex environments through intelligent algorithms such as genetic algorithms, particle swarm optimization, or fuzzy logic. The operation steps include data collection and analysis, model evaluation, reconstruction strategy development, and model updating, forming a continuous optimization feedback loop. In summary, ARM is an important tool in modern scientific research and engineering practice, which analyzes running data in depth and adjusts the model in real time to adapt to changing environments.

[0062] 3. Time series prediction model based on BAS-Volterra algorithm

[0063] 3.1 Basic principles

[0064] The BAS-Volterra algorithm aims to use the state information of the aircraft (speed, height, azimuth angle, and pitch angle) and the state information of the ship (position, heading, and speed) transmitted by the ship detection equipment to predict the flight trajectory of the aircraft in real time.

[0065] Firstly, when facing the threat of aircraft, the ship can obtain the state information of the aircraft in real time, including speed, height, azimuth and pitch angle, etc. In addition, the state information of the ship itself, such as position, heading and speed, is also important for trajectory prediction. Second, in the process of building the BAS-Volterra model, the adaptive reconstruction method optimizes the input data by selecting the features that have a significant impact on the prediction results, and simplifies the data matrix used by the model, thereby improving the efficiency and accuracy of the calculation when dealing with real-time data. Third, using Volterra series modeling can handle complex nonlinear relationships between aircraft and ship states. The motion trajectory of the aircraft is not only affected by the motion law of the aircraft itself, but also by environmental factors and ship states and other factors. After introducing high-order time functions, the Volterra model can deeply explore these complex relationships to achieve higher accuracy trajectory prediction. Fourth, the improved BAS algorithm is used to optimize the kernel coefficients, and through continuous iteration evaluation, the model quickly converges to the optimal parameter configuration. This fast adaptive ability enables the prediction model to adjust in time to adapt to the dynamic changes of aircraft and ship states in the changing tactical environment. Fifth, according to the BAS-Volterra time series prediction algorithm, it can quickly take measures to deal with complex environments. In summary, we propose a combination of improved BAS-Volterra aircraft maneuver trajectory prediction model.

[0066] 3.2BAS-Volterra algorithm time series prediction model flow

[0067] To improve the prediction accuracy and computational efficiency of the Volterra time series model, we introduce the improved moth antennae search algorithm into the Volterra model. The moth antennae search algorithm simulates the foraging behavior of moths in nature and has global search ability, which can effectively avoid local optimal solutions, thereby optimizing the parameter settings of the Volterra model and accurately capturing the nonlinear and time-varying characteristics in the time series. The simultaneous optimization process can adjust the model parameters in real time, making the model more adaptable and robust, especially when dealing with complex data with large aircraft trajectory noise, the prediction results are more reliable.

[0068] Firstly, the trajectory prediction system is established by inputting the dynamic state parameters of aircraft and ship. The dynamic state of aircraft includes speed, height, azimuth angle, pitch angle and position information, while the state of ship contains 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 results are retained, and the input features are adjusted based on the current prediction error to enhance the prediction ability of the model. Thirdly, Volterra series modeling is adopted to effectively capture the nonlinear dynamic behavior of aircraft, further improving the complexity and adaptability of the model. At the same time, the kernel coefficients are optimized by the improved moth-flame optimization algorithm to find the best 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 output.

[0069] Specifically as follows:

[0070] (1) Input the detection parameters of the ship, the model involves the following dynamic state parameters of aircraft and ship:

[0071] Aircraft dynamic state parameters:

[0072] Speed v d (t): the flight speed of the aircraft at time t, unit: m / s.

[0073] Height h d (t): the flight height of the aircraft at time t, unit: m.

[0074] Azimuth angle θ d (t): the azimuth angle of the aircraft at time t, unit: degree (°).

[0075] Pitch angle φ d (t): the pitch angle of the aircraft at time t, unit: degree (°).

[0076] Position (latitude lat d (t), longitude lon b (t)): the geographical position of the aircraft at time t, unit: degree (°).

[0077] Ship dynamic state parameters:

[0078] Position (latitude lat b (t), longitude lon b (t)): the position of the ship at time t, unit: degree (°).

[0079] Heading ψ b : the heading angle of the ship at time t, unit: degree (°).

[0080] Speed vb : the sailing speed of the ship at time t, in m / s.

[0081] : the heading angle of the ship b (t) :

[0082] : the pitch angle of the target d (t) :

[0083] : the yaw angle of the target d (t) : ψ d (t) = θ d (t) - ψ b (t)

[0084] where h d is the height of the target, h b is the height of the ship, which is set to 0.

[0085] (2) Input matrix construction, construct the input matrix D, whose elements are the state parameters of the aircraft and the ship:

[0086] Here M represents the number of samples.

[0087] (3) Select important features according to the preset performance indicators, such as prediction error. Set a threshold T to select features:

[0088] If the feature has a significant impact on prediction (error less than threshold), the feature is retained.

[0089] After each prediction, adjust the input features based on the current prediction error. Let the prediction output of the current model be The true value is Y(t), and the error is

[0090]

[0091] Reconstruct the input matrix according to the importance of the features:

[0092] D' = D + β · E(t) · W

[0093] where D' is the reconstructed input matrix, β is a parameter that controls the adjustment strength, and W is an importance weight vector that reflects the importance of each feature to input adjustment.

[0094] (4) Volterra series modeling, use Volterra series to capture the nonlinear dynamic behavior of the aircraft, and the output equation can be represented as:

[0095]

[0096] y(t) is the output of the system at time t (predicted aircraft trajectory).

[0097] d(t) is the input feature matrix. In Volterra series modeling, d(t) is an abstract representation of the input feature at time t. Here, d(t) is actually a reference to a state parameter at time t in D (input matrix after adaptive reconstruction). That is, d(t) can be regarded as data from the t-th row in the input matrix D.

[0098] First-order kernel coefficient h k Reflects the direct influence of each feature on the output.

[0099] Second-order kernel coefficient Describes the interaction between multiple inputs, thereby capturing the nonlinear characteristics of the model.

[0100] The final output formula is:

[0101]

[0102] (5) Improved beetle antennae search algorithm, in the optimization framework, the improved beetle antennae search algorithm is used for optimization of kernel coefficient.

[0103] Step 1: Use the K-means clustering algorithm to intelligently initialize the initial antenna position:

[0104] x i (0) = KMeans(data, clusters)

[0105] x i (0): initialized antenna position.

[0106] Step 2: The fitness of each antenna position is evaluated by the following formula:

[0107]

[0108] Y j : actual observation value.

[0109] Predicted value through the current antenna position.

[0110] Step 3: Use adaptive learning rate and multi-scale search strategy to optimize the antenna position, where the adaptive learning rate is

[0111]

[0112] Antenna position update

[0113] x i (t+1) = xi (t) + a(t) - (r(t) - (x * -x i (t)) + s(t) - n)

[0114] r(t) is a random disturbance factor, x * is the current best antenna position, s(t) is the disturbance intensity.

[0115] In the multi-scale search strategy, the temperature parameter T(t)

[0116] T(t) = T0- exp(- l t)

[0117] In order to enhance the global exploration ability of the search algorithm and avoid falling into local optimal solution, a larger random disturbance is performed at high temperature period

[0118]

[0119] where x i (t) is the state of the antenna position at time t, a(t) is the learning rate at time t, r(t) is a random disturbance factor, rand is used to determine whether to adopt the first or second update rule, and the value is less than T(t) The antenna will adopt random disturbance update, T(t) is the temperature parameter at time t, which is used to measure the openness of the search in the execution process 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 d is a local adjustment vector randomly sampled from the neighborhood.

[0120] (6) Trajectory prediction

[0121] The model optimized by the beetle antenna search algorithm uses the optimized kernel coefficient matrix H* for prediction.

[0122]

[0123] H' is the kernel coefficient matrix optimized by ABS algorithm, D' is the input matrix adjusted by adaptive reconstruction method, is the predicted aircraft trajectory output vector.

[0124] (7) Complete steps of prediction model:

[0125] Step 1: Collect the speed, height, azimuth angle, pitch angle, position and distance of the aircraft, and the speed, heading and position of the ship, as well as state information and detection data.

[0126] Step 2: Create input matrix D and perform feature selection and reconstruction.

[0127] Step3: Use Volterra series to express the aircraft motion model, and add ship state information.

[0128] Step4: Optimize kernel coefficients using the improved moth antennae search algorithm to find the best parameter configuration to minimize the loss function.

[0129] Step5: Perform target trajectory prediction using the optimized kernel coefficient matrix.

[0130] In summary, the BAS-Volterra trajectory prediction model we propose aims to improve the prediction accuracy and computational efficiency of aircraft maneuvering trajectory prediction. The improved BAS algorithm has strong global search capability and can effectively optimize the parameter settings of the Volterra model, accurately capturing the nonlinear and time-varying characteristics of time series data.

[0131] 4. Target maneuvering trajectory prediction model based on BAS-Volterra and adaptive ensemble learning strategy

[0132] Ensemble learning is a machine learning method that uses a series of basic learners to learn and integrates the learning results of each basic learner according to certain rules to achieve better learning results than single basic learners. To further improve the performance of the target maneuvering trajectory prediction model based on BAS-Volterra, we introduce ensemble learning theory and combine the target's maneuvering characteristics to propose a target maneuvering trajectory prediction model based on adaptive dynamic ensemble. This model mainly improves the performance of target maneuvering trajectory prediction by implementing adaptive update strategies for basic prediction model set, basic prediction model parameters, and basic prediction model weights to improve the performance of the target maneuvering trajectory prediction model. The process of the ADIBAS-Volterra target maneuvering trajectory prediction model we propose is shown in Figure 1

[0133] 4.1 Boundary point identification model of target maneuvering action

[0134] Real-time identification of aircraft maneuvering mode is a complex and highly dynamic process with obvious time-varying characteristics. To better track the real-time changes in target maneuvering characteristics, we adjust the basic prediction model set in real time based on the identification results of target maneuvering boundary points to improve the performance of target maneuvering trajectory prediction.

[0135] ​The target maneuver trajectory is composed of a series of continuous maneuver actions, so the segmentation of the target maneuver trajectory can be converted into the segmentation between the basic maneuvers. According to the characteristics of different maneuver actions, the target maneuver actions can be divided into three categories: horizontal plane maneuver, vertical plane maneuver and space maneuver. In order to better describe each type of maneuver, the dynamic model and dynamic equation of the target maneuver can be expressed as

[0136]

[0137] Table 2 target maneuver action identification rules

[0138]

[0139]

[0140] where (x t ,y t ,z t ) represents the position in the inertial coordinate. respectively, the rate of change of the trajectory pitch angle and the yaw angle of the aircraft. g represents the acceleration of gravity. respectively, the tangential overload, the normal overload and the roll angle. (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 of the target maneuver trajectory, the state variables and the control variables, the target maneuver trajectory can be divided into 45 maneuver modes. According to the parameter settings of the 45 maneuver modes, the target maneuver identification rules shown in Table 2 can be obtained.

[0141] Generally speaking, the target maneuver trajectory can be composed of a series of action units. According to the target maneuver action identification rules in Table 2, the target maneuver trajectory needs to be further divided. As can be seen from Table 2, the characteristics of each maneuver action unit are summarized as segmentation rules. Due to the diversity of the parameter characteristics of the maneuver action unit, the conditions under which the flight maneuver action cannot be segmented are described. If the parameters do not meet the conditions, the current flight point represents the segmentation point.

[0142] In terms of target maneuver identification, this section proposes 45 maneuver modes and lists the corresponding parameter settings and identification rules in detail. These rules are an important basis for maneuver action division, ensuring that the characteristics of each action unit can be accurately identified and that in some conditions, the flight maneuver action cannot be segmented, but can still be accurately identified.

[0143] 4.2 Model weight adaptive update strategy based on prediction performance

[0144] We construct ADIBAS-Volterra target maneuver trajectory prediction model, in the model initialization phase, the weight of each basic predictor is initialized to the same value, the initial comprehensive prediction system is constructed, in order to ensure the overall performance of the ensemble prediction model, the weight of each basic prediction factor needs to be updated adaptively according to the prediction accuracy of each basic prediction factor in the process of obtaining real-time data, the principle of model weight adaptive update is that the model with superior performance generally has larger weight, for the convenience of description, some related definitions are listed as follows.

[0145]

[0146] In the formula, The prediction error of basic predictor i at time t, y t The actual target value at time t, λ is the historical error weighting factor, which controls the influence degree of historical error in the current prediction error, K is the historical window size, which represents the number of past prediction steps considered in calculating the current error, γ is the decay factor, which controls the influence degree of past error on the current prediction error, usually 0 < γ < 1.

[0147] Dynamic cumulative prediction error

[0148]

[0149] The adaptive update weight of basic predictor i at time t is The weight of basic predictor i at time t-1, α is the learning rate, which controls the sensitivity of weight update, larger value may lead to instability, AMSE t The average dynamic cumulative prediction error of all basic predictors.

[0150] σMSE t The standard deviation of the dynamic cumulative prediction error 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 error, usually take very small value, δ is the historical error feedback factor, which controls the influence degree of current prediction error on weight update, The prediction error of basic predictor at current time point.

[0151]

[0152] The normalized weight of basic predictor i at time t is The sum of all basic predictor weights, which ensures the overall weight normalization to 1.

[0153] Therefore, the adaptive updating method of model weights can reduce the influence of the model with poor prediction performance on the integrated system to a certain extent. When calculating , we not only consider the prediction error of the model for the ith newly arrived data, but also consider the prediction performance of the model in the historical data, so as to comprehensively evaluate the integrated performance of the model on the newly arrived data and the historical data.

[0154] 5. Simulation verification and analysis

[0155] The experiment was carried out in the Matlab2021 environment, and was run on a PC equipped with a 4-core Intel Core i7 3 GHz processor and 8 GB of memory. We used the adversarial training data extracted from the simulated aircraft system as the experimental data.

[0156] In order 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 experiments, as follows:

[0157]

[0158] where, is the actual value, y is the predicted value, and y is the average value. In order to evaluate the performance of the target maneuver trajectory prediction model based on ADIBAS-Volterra algorithm.

[0159] 5.1 Simulation experiment verification of target maneuver trajectory prediction

[0160] According to the ADIBAS-Volterra trajectory prediction model proposed by us, Figure 2 and 3 show the predicted trajectory when the aircraft maneuvers. Target maneuver trajectory prediction is the basis for target damage assessment and maneuver decision-making. The problem of target maneuver prediction is essentially a real-time prediction problem of time series, with nonlinearity and time-varying characteristics. In addition, due to the complexity of the electromagnetic environment, the data obtained by the sensor has certain noise. In order to verify the effectiveness and robustness of the target prediction model proposed by us, the prediction performance of the algorithm is tested based on the target maneuver trajectory data stored in the simulator. The parameter settings of the algorithm are shown in Table 2. The parameter settings of Kmeans, DEHHO, LSTM and Goal Curve Net are consistent with those in the literature.

[0161] Figure 2 ​In Fig. 5, the blue trajectory represents the flight maneuver 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. In order to further verify the effectiveness of the post-segmentation identification, Figure 3 Two comparisons of the aircraft at different times are shown. Figure 3 The main segments are given, and the labels of the segments are shown in bold. In Fig. 5, Figure 3 In Fig. 5(a), ADIBAS-Volterra can correctly display the class labels of all segments except the dependent segments. In the identification of the main segments, ADIBAS-Volterra provides correct class labels for most of the segments except the last segment.

[0162] In the identification of the main segments, ADIBAS-Volterra provides correct class labels for all segments. In other comparative methods, Volterra, TrVolterra, OSVolterra, TrOSVolterra, PCMPA, PSLSTM, OVMD-ICEEMDAN-PE, OVMD-PE, EPL-KGLA, GL-Volterra, IEGL-Volterra, ODL-Volterra, and 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 As can be seen from Fig. 5(b), ADIBAS-Volterra and DW-Volterra can identify all main segments, respectively. At the same time, the other 11 advanced trajectory prediction methods can identify 10, 10, 10, 10, 10, 9, 10, 9, 10, 11, and 11 main segments, respectively. In summary, compared with other advanced methods, ADIBAS-Volterra can achieve better identification effect in terms of segment length and correct identification of boundaries.

[0163] 5.2 Feasibility analysis of target maneuver trajectory prediction method

[0164] The problem of target maneuver trajectory prediction is essentially a time series prediction problem. In order to verify the adaptability of the proposed prediction model, the Mackey Glass and Rossler data sets of typical chaotic time series are used to verify the effectiveness and robustness of the BAS-Volterra prediction model integrated with the improved moth antennae search algorithm.

[0165] To illustrate the necessity of choosing Volterra series as the basic predictor for improving the ensemble prediction model, the prediction performance of this algorithm is compared with 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) algorithms.

[0166] The ADIBAS-Volterra prediction model is an ensemble algorithm, and the improvement of the prediction model performance is the result of improving BAS, Volterra model, online learning and adaptive ensemble learning algorithm. In addition, in order to introduce the role of each part of ADIBAS-Volterra, Volterra, BAS, BAS-Volterra, improved BAS-Volterra and ADIBAS-Volterra are compared.

[0167] To verify the performance superiority of the proposed improved ensemble learning algorithm based on target maneuver characteristics, the improved adaptive ensemble prediction model is compared with (the grey Lotka-Volterra model, GL-Volterra, (information-enhanced Grey Lotka-Volterra model, IEGL-Volterra), (onedimensional linear Volterra-Fredholm, ODL-Volterra)

[31] (Daubechies wavelets-Volterra, DW-Volterra) to verify the performance superiority of the proposed improved ensemble learning algorithm based on target maneuver characteristics. The target maneuver trajectory prediction based on a single learning model belongs to a global modeling method, and the model is complex and easy to fall into local optimization. Compared with a single learning algorithm, an ensemble of multiple learning algorithms often achieves higher prediction accuracy. In recent years, ensemble learning has been increasingly applied to time series prediction problems.

[0168] To better compare the effectiveness and superiority of the BAS-Volterra algorithm, simulations were used to compare its robustness to noisy data. Chaotic systems are commonly used to test the performance of nonlinear systems. We used the typical chaotic time series datasets Mackey and Rossler as training and testing samples to verify the algorithm's effectiveness. The data generation conditions were completely consistent with those in the references. To verify the effectiveness and advancement of our proposed algorithm, we adopted (The paper culminates in presenting an enhanced version of the Marine Predator Algorithm, PCMPA). [ A comparison is made between the following algorithms: (Apartial least squares based pruning algorithm is proposed hereby for a simplified LSTM, PSLSTM), (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), and (Kernel general loss algorithm based on onevolving participatory learning, EPL-KGLA). 15% noise is added to all samples in all three datasets. 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 onto the corresponding dimensions of the sample data.

[0169] The prediction results of the Mackey and Rossler chaotic time series are listed in Table 3. It can be seen that the RRMSE, MAD, MAPE and NMSE of ADIBAS-Volterra are much lower than those of other methods in terms of prediction accuracy, and the prediction accuracy of ADIBAS-Volterra is significantly better than that of other prediction algorithms. Under the same test data set, hardware platform and initial parameter setting of the algorithm, the prediction accuracy of the algorithm is significantly better than that of other prediction algorithms in the literature. In terms of algorithm running time, compared with the other five prediction algorithms, ADIBAS-Volterra is more time-saving than the other methods. This is because Volterra processes the relationship between time variable and 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, so that the model can achieve better prediction performance in a shorter time. The model also introduces an online learning mechanism that allows 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 model adjustment when new situations arise. As can be seen from the running time of the single-step prediction of the algorithm, the single-step running time of the improved ADIBAS-Volterra prediction algorithm can meet the real-time requirements of time series prediction problems.

[0170] Table 3 Single-step prediction results of time series data set with added noise

[0171]

[0172] Table 3 lists the prediction results of the Mackey and Rossler chaotic time series with noise. It can be seen that the BAS-Volterra prediction algorithm can still maintain high prediction accuracy when noise is added, and its performance is significantly better than that of other prediction methods. The robustness of our proposed algorithm is verified. By comparing the prediction results of PCMPA, PSLSTM, OVMD-ICEEMDAN-PE, OVMD-PE and EPL-KGLA algorithms, it can be seen that the original method can effectively perform trajectory prediction under noise conditions, thereby improving the prediction performance of the algorithm.

[0173] In order to verify the effectiveness and robustness of the target prediction model proposed in this paper, the prediction performance of the algorithm is tested based on the target maneuver trajectory data stored in the simulator. The parameter settings of the algorithm are shown in Table 4, and the parameter settings of other comparison algorithms are consistent with those in the literature. In order to reduce the accidental error of the prediction algorithm, the prediction results of each algorithm are the average results of 100 repeated experiments. The single-step prediction results of different algorithms for the target maneuver trajectory are shown in Tables 4-6. In order to more intuitively compare the prediction performance of different algorithms for the target maneuver trajectory, the single-step prediction absolute error values of X, Y and Z coordinates of different algorithms are represented in the form of charts, as shown in Figure 4 andFigure 5

[0174] Table 4 Algorithm and its parameter setting

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[0176] Table 5 Single step prediction results of X coordinate

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[0178]

[0179] 4.5 Conclusion

[0180] We propose an adaptive hybrid algorithm based on beetle antennae search algorithm, target maneuver boundary point identification algorithm and Volterra series, called ADIBAS-Volterra, for time series prediction of target maneuver trajectory. Through the Volterra model, the nonlinear and time-varying characteristics are captured, and the complex relationship between time variable and system state is handled using convolution form, which improves the prediction accuracy. At the same time, the improved beetle antennae search algorithm (ABS) is used to enhance the global search ability of the model, avoiding the problem of local optimal solution, thereby improving the robustness and real-time response ability in complex environment. The innovation points of the trajectory prediction model can be summarized as follows:

[0181] (1) Since the prediction of aircraft maneuver trajectory is a time series problem, it is affected by various nonlinear factors and dynamic environment, so the Volterra model is introduced. The Volterra model can effectively capture the nonlinear characteristics of the system and is suitable for behavior prediction of complex dynamic systems. Through the convolution form of the polynomial, the model can handle the changes of time variable and adapt to the dynamic characteristics of different time points. This method can more comprehensively consider various interference factors and improve the prediction reliability.

[0182] (2) In order to make up for the limitations of single Volterra model in capturing the nonlinear dynamic characteristics of target maneuver trajectory, a beetle antennae search framework suitable for target maneuver trajectory prediction is constructed. This method optimizes model parameters through ABS, uses intelligent initialization and multi-scale search strategy, effectively improves the global search ability, avoids the problem of local optimal solution, and improves the real-time online prediction performance of the model.

[0183] ​(3) Combined with target maneuvering boundary point identification algorithm and prediction performance, an adaptive updating comprehensive prediction model is constructed, in order to better adapt to the target maneuvering trajectory prediction problem, the ADIBAS-Volterra prediction model combines the target maneuvering boundary point identification algorithm with the prediction performance, and the integrated model is updated in real time, and meanwhile, according to the prediction performance index of the basic predictor, the weight is dynamically allocated, so as to ensure the effectiveness and accuracy of the integrated model.

[0184] The ADIBAS-Volterra algorithm enhances the global search ability of the model by effectively capturing the nonlinear and time-varying characteristics, and avoids the problem of local optimal solution. At the same time, with the help of the dynamic updating strategy and adaptive weight distribution, the ADIBAS-Volterra significantly improves the prediction accuracy and robustness, and adapts to the trajectory prediction demand in complex dynamic environment.

[0185] The above is an example of the best embodiment of the present application, wherein the parts not described in detail are the common knowledge of those skilled in the art. The protection scope of the present application is subject to the content of the claims, and any equivalent transformation based on the technical inspiration of the present application is also within the protection scope of the present application.

Claims

1. An ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration, characterized in that, Includes the following steps: Step 1: Input the shipborne detection parameters of the target at various times within a certain 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, and then perform adaptive updates based on real-time data. Calculate the dynamic cumulative prediction error, adaptively update the weights, and determine the weight vector of each basic predictor through normalization. The adaptive update weight of basic predictor i at time t is w1. Based on preset performance metrics, a threshold T is set to filter the features in the input matrix D, and the input matrix is ​​reconstructed according to the importance of the features: where d ij represents the element of the ith row and jth column in the input matrix D, D' is the reconstructed input matrix, and β is a parameter controlling the adjustment strength. Step 3: Identify the target maneuvering pattern in real time. By segmenting the target maneuvering trajectory into continuous maneuvering actions, determine the boundary points, identify the aircraft maneuvering pattern in real time, and determine the corresponding flight trajectory constraints based on the maneuvering pattern. Step 4: Use the improved beetle antenna search algorithm to determine the optimal kernel coefficients of the Volterra series model, and 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 constraints obtained in Step 3 as constraints. The optimized Volterra series model outputs the trajectory prediction results.

2. The ADIBAS-Volterra aircraft trajectory prediction method based on improved beetle antenna search dynamic integration as described in claim 1, characterized in that, Step 4, the method for determining the optimal kernel coefficients of the Volterra series using the improved beetle antenna search algorithm, 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. The fitness of each antenna position is evaluated using the following formula: In the formula, the meanings of each parameter are as follows: x i : Current antenna position, corresponding to a set of kernel coefficient configurations; f(x i ): Current antenna position x i The fitness value indicates that the lower the fitness, the smaller the prediction error. L(x i ): A function for fitness evaluation, representing the fitness evaluation for the current x. i The calculated loss or error metric, relative to the fitness f(x) i Correspondingly, this reflects the performance of the model; M: Number of samples, representing the total number of data points used to evaluate model performance; Y j It is the actual target location value at the j-th sample; At the j-th sample, x i After substituting the corresponding kernel coefficients into the Volterra series model, the model outputs the location prediction results. After obtaining the fitness values ​​of all tentacle positions, select the position with the lowest fitness as the best position for this iteration; Step 2: Determine if the maximum number of iterations has been reached. If yes, output the best position obtained in the last iteration as the optimal kernel coefficient. Otherwise, go to step 3. Step 3: Increment the iteration count by 1, and update the positions of all tentacles using the tentacles 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 tentacle in the t-th iteration; x i (t+1): The position of the i-th tentacle in the (t+1)-th iteration; α: Adaptive learning rate, dynamically adjusted based on fitness; Δ: Current optimal antenna position relative to x i The difference (t); Δ=x t * -x i (t); r: random perturbation factor; x t * The optimal position of all tentacles in round t; r = rand(0,1) In the formula, r is a random number from 0 to 1, used to introduce randomness to broaden the search space, and D is the perturbation vector, defined as: D=U·(x max -x min ) U: A random number generated in the range [-1, 1], ensuring that the direction of the perturbation is uncertain; x max and x min These represent the upper and lower limits of the antenna position, ensuring that the antennae search within an effective range; The fitness values ​​of all antenna positions after this iteration are calculated according to the fitness calculation formula in step 1. The position with the lowest fitness is selected as the best position for this iteration, and then the process proceeds to step 2.

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

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