We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with unit variances. For a given false alarm (1st-kind error) probability, the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation horizon. We explore the maximal set of means and covariance matrices (composite hypothesis) such that its minimax testing can be replaced with testing a single particular pair consisting of a mean and a covariance matrix (simple hypothesis) without degrading the detection exponent. We completely describe this maximal set.
翻译:我们考虑用不确切已知的手段和共变矩阵探测(测试)高斯随机序列(信号)的问题。 替代的方法是独立的, 均匀分布为零位高斯随机变量, 且有单位差异 。 对于给定的假警报( 一次误差) 概率, 迷你Max 检测的质量是由在日益增长的观测地平线上最差的概率( 两次误差概率) 给出的。 我们探索了一套最大手段和共变矩阵( 复合假设 ), 以便用测试由平均和共变矩阵( 简单假设 ) 组成的单一一对特定组合( 共同假设 ) 来取代它。 我们完整地描述这个最大数据集 。</s>