Testing for a Signal with Unknown Location and Scale in a Stationary Gaussian Random Field
平稳高斯随机场中位置与尺度未知的信号检验
We suppose that our observations can be decomposed into a fixed signal plus random noise, where the noise is modelled as a particular stationary Gaussian random field in $N$-dimensional Euclidean space. The signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude, and we are primarily interested in a test to detect such a signal. There are many examples where the signal scale or width is assumed known, and the test is…