The invention described herein is directed to a method and apparatus for estimating an onset time t0 of a noisy waveform by producing a time t1 that a magnitude of the noisy waveform crosses a positive threshold T which is as small as possible while keeping the probability of false crossings due to noise at an acceptable level. The estimate of the onset time t0 uses an initial portion of a noisy waveform magnitude leading edge to avoid errors due to later-occurring multipath components. The invention also produces a derivative of the noisy waveform magnitude at time t1, which is used to normalize against errors due to variations to power level without having to use any portion of the noisy waveform beyond time t1. The waveform to which the invention applies can be a received signal, the cross-correlation function derived from a received signal, or another waveform where onset time needs to be estimated.