高斯因子结构变分推断的导弹轨迹学习与估计

Missile trajectory learning and estimation based on variational inference of Gaussian factor structure

针对具有非线性批量状态的弹道导弹的状态难以预测和高斯变分推断估计方法存在迭代误差大、估计时间久等缺点,提出一种具有因子结构协方差的高斯变分推断方法.通过对协方差进行分解,将所有参数之间的协方差关系转化为矩阵中部分主要参数之间的联系.同时采用随机梯度上升方法、重参数化技巧以及自适应学习率方法对变分下界以及变分参数进行迭代优化,获取最优参数.通过该算法对导弹状态估计实例分析,并与基于高斯变分推断的状态估计算法进行了比较.结果表明,提出的具有因子协方差结构的高斯变分推断方法,仿真计算时间平均缩减了23.6%,能够有效地提高导弹状态估计的计算效率,降低了计算误差.

Aiming at the problem that the state of ballistic missiles with nonlinear batch state is difficult to predict,the Gaussian variational inference estimation method has the disadvantages of large iteration error and long estimation time.Based on this,a Gaussian variational inference method with factor structure covariance is proposed.By decomposing the covariance,the covariance relationship between all parameters is transformed into the connection between some main parameters in the matrix.At the same time,the stochastic gradient ascent method,reparameterization technique and adaptive learning rate method are used to iteratively optimize the variational lower bound and variational parameters to obtain the optimal parameters.Finally,the algorithm is used to analyze the example of missile state estimation,and compared with the state estimation algorithm based on Gaussian variational inference,its simulation calculation time is reduced by 23.6%on average.Accordingly,the proposed Gaussian variational inference method with factor covariance structure can effectively improve the computational efficiency of missile state estimation and reduce computational errors.