基于改进粒子群算法辨识Volterra级数的目标机动轨迹预测

目标机动轨迹预测是空战态势感知和目标威胁评估的重要前提。针对传统目标机动轨迹预测模型复杂度大、预测精度低等问题，结合目标机动轨迹时间序列的混沌特性，提出一种基于相空间重构理论和Volterra泛函级数的目标机动轨迹预测模型。该模型首先采用0-1检测法验证了目标机动轨迹时间序列具有混沌特性；其次，利用C-C法确定嵌入维数和时间延迟，对目标机动轨迹时间序列进行了相空间重构；然后，引入Volterra泛函级数预测模型，为了克服高阶Volterra核函数求解复杂的难题，提出一种混沌变异自适应粒子群算法，构建一种基于改进粒子群算法辨识的Volterra级数预测模型，并将其应用于目标机动轨迹预测；最后，将所提算法与卡尔曼滤波算法以及机器学习算法进行单步和多步预测对比，同时将改进粒子群算法与其他智能算法进行性能比较。仿真结果表明：所提预测模型具有良好的单步和多步预测性能，改进的粒子群算法具有参数辨识精度高、收敛速度快的优点。

Target maneuver trajectory prediction based on Volterra series identified by improved particle swarm algorithm

Target maneuver trajectory prediction plays an important role in air combat situation awareness and target threat assessment. Aiming at the problems of high complexity and low prediction accuracy in the traditional method, this paper proposes a target maneuvering trajectory prediction model based on the phase space reconstruction theory and Volterra functional series, combining the chaotic characteristics of the target maneuvering trajectory time series. The 0-1 test method is firstly used to verify the chaotic characteristics of the target maneuvering trajectory time series, followed by determination of the embedding dimension and time delay by the C-C method. The target maneuvering trajectory time series is further reconstructed. The Volterra functional series prediction model is introduced. However, the identification of higher-order Volterra kernel function is difficult. To solve this problem, we propose a Modified Particle Swarm Optimization algorithm (MPSO) combining the chaotic strategy and adaptive strategy, construct a Volterra series prediction model identified by the MPSO, and apply the model to target maneuvering trajectory prediction. Finally, the algorithm proposed in this paper is compared with the Kalman filter and machine learning algorithm for single-step and multi-step prediction. Meanwhile, the performance of MPSO is compared with that of other intelligent algorithms. The simulation results show good performance of the proposed prediction model in both single-step and multi-step prediction, and fast, accurate identification of the Volterra series model parameters by the MPSO.