基于ARIMA-UKF算法的最优机动轨迹设计

Optimal Maneuver Trajectory Design Based on ARIMA-UKF Algorithm

摘要: 针对协方差矩阵计算复杂的局限性以及系统中各种测量噪声及误差等非平稳项对定位精度的影响，在EKF和UKF滤波算法的基础上，本文采用一种基于时间序列的ARIMA-UKF算法，能够更快地收敛于后验理论误差下界PCRLB。接着通过目标的运动模型对机载观测平台的机动轨迹进行设计，通过计算机载观测平台在“一步最优”状态下每一时刻的次优航向角，给出基于FIM行列式最大指标的运动轨迹设计方案，仿真和实验结果显示，平台在最优机动时比不机动时有着更高的定位精度，探测距离为200 km时，匀速、匀加速和singer运动模型下的目标测距误差均能达到0.6 km以内，测距误差可达到0.398 km，误差百分比达到0.2%以内。

Abstract: In view of the limitation of complex calculation of covariance matrix and the influence of various non-stationary terms such as measurement noise and error in the system on positioning accuracy, on the basis of EKF and UKF filtering algorithms, this paper adopts an ARIMA-UKF algorithm based on time series, which can converge to the lower bound of posterior theoretical error PCRLB faster. Then the maneuvering trajectory of the airborne observation platform is designed through the motion model of the target, and the motion trajectory design based on the maximum index of the FIM determinant is given by calculating the suboptimal heading angle of the airborne observation platform at each moment in the “one-step optimal” state. The simulation and experimental results show that the platform has higher positioning accuracy when it is optimally maneuvered than when it is not maneuvered. When the detection distance is 200km, the target ranging error under the uniform speed, uniform acceleration, and singer motion models can all reach 0.6 km, the ranging error can reach 0.398 km, and the error percentage is within 0.2%.