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.
关键词
鲁棒估计/贝叶斯理论/不可达系统/极大极小博弈
Key words
robust estimation/Bayesian theory/unreachable system/minimax game
维普
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