<p>The article presents an investigation of non-parametric SG statistics as an objective function for estimating the probability of delay-based resolution of wideband pulsed signals distorted by multiplicative noise. It is assumed that no a priori information about the probability density function of the multiplicative noise is available. The noise is modeled as a random process with independent and identically distributed (IID) random variables. The problem of delay measurement and resolution of signals distorted by multiplicative noise is addressed. A nonparametric approach to solving this problem is based on the use of an objective function constructed from SG statistics. A comparative analysis of the proposed signal measurement and resolution method with the maximum likelihood method is performed. Dependencies of the estimated signal resolution probability obtained using non-parametric SG statistics are presented for different values of delay separation and signal-to-noise ratio. The results of statistical simulation of the signal measurement and resolution problem show that, in contrast to the maximum likelihood method, the SG statistics-based approach provides efficient signal resolution in the absence of a priori information about the noise distribution density. Recommendations for selecting simulation parameters of the non-parametric signal measurement and resolution algorithm based on SG statistics are provided. The Kullback–Leibler information measure is used as a diagnostic indicator of the correctness of the proposed method since it shares a common conceptual foundation with SG statistics. The correctness of the proposed method is demonstrated by cross-validation.</p>