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This study provides a comprehensive theoretical analysis of a modified maximum likelihood signal-to-noise ratio (SNR) estimator and quantifies the minimum coherent integration time required to achieve a predefined level of accuracy. The SNR estimator is derived under the assumptions of perfect frequency synchronisation, data bit aiding and constant signal phase during the observation window. The probability density function (pdf) of the SNR estimator in logarithmic units is derived and used to quantify the bias and error bounds associated with the considered SNR estimator. The minimum coherent integration time is determined by requiring a desired level of accuracy with a given probability level, that is the integration time is chosen in order to make the SNR estimate lie in a predefined confidence interval. Theoretical results have been validated using GNSS software and hardware simulations. The agreement between theoretical and experimental results supports the validity of the developed theory.