Statistical analysis of noise for highly-reliable fringe search
We report a technique for assessing the reliability of the analysis results obtained for astronomical data, including data on the occurrence of periodic signal waves like interferometric fringes. With this technique, the probability of misidentifying noise as a signal (false detection/alarm rate) is very low, and therefore, the detection accuracy is very high.
The false detection rate is often calculated from the probability distribution of the maximum value of the fringe and noise amplitude with a Rice and Rayleigh distribution (Thompson et al. 1986). In this calculation, however, the time taken for the amplitude to reach the maximum value, i.e., signal duration, is not considered.
In our technique, we take into account the duration and count the occurrences of noise-induced periodic waves over a given signal duration in a spectrogram. We then record the peak amplitude for each of the detected noise-induced (i.e., false-signal-induced) waves, and define the false-signal-to-noise ratio. Finally, we plot the histogram of the false-signal-to-noise ratios and estimate the probability density by non-parametric kernel density estimation. From the probability density, we calculate the false detection rate and the objective confidence level of the detection results, on the basis of which we conclude whether a detected fringe originates from an astronomical objects or not. Thus, we can carry out an accurate assessment of the reliability of the detection results.
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