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Analytic example of a Schweppe likelihood-ratio detector

机译：Schweppe似然比检测器的解析示例

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摘要

A low-dimensional test problem with a known solution is used to verify various computer implementations of F.C. Schweppe's likelihood detector (1965). In this case a closed-form solution is provided for a Schweppe likelihood detector in terms of an intermediate Kalman filter, as utilized in its implementation, for detecting the presence of a two-state signal model in Gaussian white noise. The associated error probabilities are also evaluated following a procedure that utilizes optimized Chernoff-like bounds for a tight approximation. A methodology is demonstrated for appropriately setting the decision threshold for this example as a tradeoff against allowable observation time. By using this or similar examples, certain qualitative and quantitative aspects of the software implementation can be checked for conformance to anticipated behavior as an intermediate benchmark, prior to modular replacement of the various high-order matrices appropriate to the particular application.
机译：具有已知解决方案的低维测试问题用于验证F.C.的各种计算机实现。 Schweppe的似然检测器（1965）。在这种情况下，为施韦普似然检测器提供了一种中间形式的卡尔文滤波器的封闭形式的解决方案，如在其实现中所采用的那样，用于检测高斯白噪声中二态信号模型的存在。在利用优化的类似于切尔诺夫边界的过程进行严格逼近的过程之后，也将评估相关的错误概率。演示了一种方法，该方法可适当设置此示例的决策阈值，以作为对允许观察时间的折衷。通过使用此示例或类似示例，可以在模块化替换适合特定应用的各种高阶矩阵之前，检查软件实现的某些定性和定量方面是否符合作为中间基准的预期行为。

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