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首页> 外文期刊>IEEE Transactions on Aerospace and Electronic Systems >Asymptotically optimal bias for a general nonlinearity in Page's test
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Asymptotically optimal bias for a general nonlinearity in Page's test

机译：Page测试中一般非线性的渐近最优偏差

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摘要

Page's test for the quick detection of a change in distribution is optimized by utilizing the log-likelihood ratio (LLR) as a detector nonlinearity. For signal detection applications, locally optimal nonlinearities are optimal as the signal strength /spl gamma/ goes to zero, however, for non-zero values of /spl gamma/, the performance of Page's test may be improved by applying a subtractive bias. The bias that maximizes an asymptotic (i.e. as the average time between false alarms goes to infinity) performance measure for Page's test for a fixed signal strength is derived for a general detector nonlinearity. Additionally, the bias is derived to minimize the signal strength required to achieve a desired asymptotic performance. These two methods for choosing the bias are shown to be equivalent The asymptotically optimal bias for the LLR nonlinearity is shown to be zero, which is consistent with the optimality of the LLR. Subject to a first order approximation, it is shown that the proposed asymptotically optimal bias is equivalent to an extension of the bias derived by Dyson (1986) which approximately maximizes the relative efficiency between Page's test with the biased locally optimal nonlinearity and Page's test with the LLR nonlinearity. The use of the asymptotically optimal bias is illustrated through an example.
机译：通过利用对数似然比（LLR）作为检测器非线性来优化Page的快速检测分布变化的测试。对于信号检测应用，当信号强度/ spl gamma /变为零时，局部最优非线性是最佳的，但是，对于/ spl gamma /的非零值，可以通过应用减法偏差来改善Page测试的性能。对于一般的检测器非线性，得出了针对固定信号强度的Page测试的渐进性最大化（即，虚假警报之间的平均时间达到无穷大）的偏差。另外，导出偏置以最小化实现所需渐近性能所需的信号强度。这两种选择偏差的方法显示为等效。LLR非线性的渐近最优偏差显示为零，这与LLR的最优性相一致。服从一阶近似，表明拟议的渐近最优偏置等效于Dyson（1986）推导的偏置的扩展，该偏置近似最大化了带有偏局部最优非线性的Page检验与带有σ的Page检验之间的相对效率。 LLR非线性。通过示例说明了渐近最佳偏置的使用。

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