In this paper it is shown that log cos(/spl pi/x/(2C)) is the optimally robust criterion function for prediction error methods with respect to amplitude-bounded stochastic disturbances. This criterion function minimizes the maximum asymptotic covariance matrix of the parameter estimates for the family of innovations of the systems which are amplitude bounded by the constant C. Furthermore, the stochastic worst case performance of the estimate corresponding to the criterion function log cos(/spl pi/x/(2C)) is better than the worst case performance of the least squares estimate even if the constant C is chosen larger than the actual amplitude bound on the innovations. In addition to its favorable properties in a stochastic setting, this criterion function also generates estimates which are unfalsified in a deterministic framework.
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机译：在本文中，证明了log cos（/ spl pi / x /（2C））是关于幅度有界随机扰动的预测误差方法的最优鲁棒标准函数。该标准函数最小化了系统的一系列创新的参数估计值的最大渐近协方差矩阵，该系统的振幅由常数C限制。此外，估计的随机最坏情况性能对应于标准函数log cos（/ spl pi / x /（2C））优于最小二乘估计的最坏情况下的性能，即使选择的常数C大于创新上的实际幅度范围也是如此。除了在随机环境中具有良好的性能外，此标准函数还生成在确定性框架内未经伪造的估计。
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