Algorithm and its parameter settings.

The prediction of aircraft manoeuvre trajectories is an important prerequisite for decision making. However, how to achieve real-time and scientific aircraft manoeuvre trajectory prediction using trajectory data needs to be addressed urgently. To solve this problem, we propose a hybrid algorithm based on Improved Beetle Antennae Search (BAS), Aircraft Manoeuvre Boundary Point Identification algorithm, Adaptive Dynamic Integration (ADI) and Volterra series, called ADIBAS-Volterra. Firstly, a large amount of trajectory sample data is trained to construct the BAS-Volterra algorithm suitable for predicting aircraft manoeuvre trajectories, which achieves a balance between global and local solutions. Secondly, in order to improve the accuracy of the online manoeuvre trajectory prediction of our proposed model in complex environments, the parameters of the whole prediction model based on the BAS-Volterra algorithm are adaptively updated according to the identification results of the aircraft manoeuvre boundary points, including the optimisation of the algorithmic weights and the optimisation of the parameters. Compared with the existing state-of-the-art methods, the newly proposed aircraft manoeuvre trajectory prediction algorithm adopts K-means clustering to initialise the tentacle position, which can flexibly adjust the search strategy at different stages and make the algorithm more reasonable. Four measures, Relative Root Mean Square Error (RRMSE), Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE) and Normalised Mean Square Error (NMSE) were used to assess prediction accuracy. Finally, the scientific validity of the proposed algorithm is verified using Mackey Glass and Rossler datasets.飞行器机动轨迹预测是决策制定的重要前置条件。然而，如何利用轨迹数据实现实时且科学的飞行器机动轨迹预测，仍是亟待解决的问题。针对该问题，本文提出一种融合改进天牛须搜索（Improved Beetle Antennae Search, BAS）、飞行器机动边界点识别算法、自适应动态积分（Adaptive Dynamic Integration, ADI）以及沃尔泰拉级数（Volterra series）的混合算法，命名为ADIBAS-Volterra。首先，通过大量轨迹样本数据训练构建适用于飞行器机动轨迹预测的BAS-Volterra算法，该算法可实现全局解与局部解之间的平衡。其次，为提升所提模型在复杂环境下的在线机动轨迹预测精度，本文基于BAS-Volterra算法，根据飞行器机动边界点的识别结果对整个预测模型的参数进行自适应更新，包括算法权重优化与参数优化两部分。相较于现有主流方法，本文新提出的飞行器机动轨迹预测算法采用K-means聚类初始化天牛须位置，可在不同阶段灵活调整搜索策略，使算法更为合理。本文采用相对均方根误差（Relative Root Mean Square Error, RRMSE）、平均绝对偏差（Mean Absolute Deviation, MAD）、平均绝对百分比误差（Mean Absolute Percentage Error, MAPE）以及归一化均方误差（Normalised Mean Square Error, NMSE）四项指标对预测精度进行评估。最后，通过Mackey Glass与Rossler数据集验证了所提算法的科学有效性。