不可达系统的鲁棒贝叶斯估计方法

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.