不可达系统的鲁棒贝叶斯估计方法

Robust Bayesian estimation method for unreachable systems

中文关键词  鲁棒估计  贝叶斯理论  不可达系统  极大极小博弈

英文关键词  robust estimation  Bayesian theory  unreachable system  minimax game

中文摘要

      本文针对模型扰动下的不可达系统, 提出了一种新的针对退化分布下的极大极小博弈问题的求解和证明方法. 首先, 文章将有相对熵约束的极大极小博弈问题转换成了一个无约束的拉格朗日函数, 并找到其在均值和奇异的方差矩阵方向上都为严格凹函数的条件; 其次, 本文通过求解其均值和方差的极大值, 得到所对应的鲁棒贝叶斯估计器和奇异的扰动状态误差协方差矩阵; 最后, 文章证明存在一个唯一的拉格朗日乘子满足其约束条件. 微机电系统加速度计漂移估计仿真结果表明对所提算法的有效性

英文摘要

      In this paper, a new solution and proof method are proposed for the minimax game problem under degenerate distribution. In particular, the minimax game problem subject to a relative entropy tolerance is first transformed into an unconstrained Lagrangian function. Accordingly, we tend to find the condition in which the unconstrained Lagrangian function is strictly concave along the direction of the singular variance matrix. Next, the robust Bayesian estimator and the disturbed state error covariance matrix are obtained by finding the maximizers of the corresponding mean and variance. Finally, it is shown that there is a unique Lagrange multiplier that satisfies our constraints. In addition, the proposed algorithm is applied to estimate the drift of MEMS accelerometers. The simulation results show that the proposed algorithm outperforms the standard Kalman filter.