非线性函数协方差传播的Stein Monte Carlo方法

Stein Monte Carlo Method for Nonlinear Function Covariance Propagation

基于泰勒级数展开的近似函数法在求解非线性函数的中误差时需要进行复杂的导数计算,已有的Monte Carlo法虽然可以避免导数运算,但在模拟次数的选择上不具有客观性,且无法直接控制模拟结果。因此,将Stein两阶段法融入非线性函数的协方差传播理论中,并与Monte Carlo方法结合,设计了一套非线性函数协方差传播的Stein Monte Carlo算法流程。将该方法用于二维多项式函数和GNSS基线向量的协方差传播计算中,实验结果验证了其有效性,为非线性模型协方差传播的计算提供了一种新思路。

The standard deviations of the observation function can be calculated by the law of covariance propagation. However, the approximate function method based on Taylor series expansion requires complex derivative operations when solving the standard deviation of nonlinear function. The Monte Carlo method can avoid the derivative operation, but it is not objective in the selection of the number of simulations. Moreover, the Monte Carlo method cannot directly control the simulation results. To overcome these disadvantages, we introduce the Stein two-stage method into the covariance propagation theory of nonlinear functions. Combined with the Monte Carlo method, we design the Stein Monte Carlo(SMC) algorithm flow of nonlinear function covariance propagation. We apply the SMC method in the two-dimensional polynomial function and covariance propagation of GNSS baseline vector. Results verify the effectiveness of the SMC method. This method provides a new idea for the covariance propagation of nonlinear models.