Abstract
Standard methods of determining the time of arrival (ToA) of an unknown pulse are adaptive thresholding (ATH) and double differentiation (DD). The former first finds the amplitude of the pulse, and uses a fraction, say 1/2, of the amplitude as a threshold (TH). The ToA estimate is the time when the leading edge of the pulse exceeds TH. In DD, the ToA estimate is the time at which the maximum slope of the leading edge occurs. In ATH, there is the requirement of storing measurements, until slightly past the pulse center, and of a peak detection. Due to differentiation, DD is unreliable at even moderate noise situations. By using the ratio of pulse samples as a detection statistic, the ratio thresholding (RTH) scheme requires only a constant TH. Simplicity in implementation is its main advantage over ATH. Its theoretical variance is derived and corroborated by simulation. The performance of RTH is superior to DD and close to ATH.
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