Transmitter localization in vessel-like molecular communication channels is a fundamental problem with potential applications in healthcare. Existing analytical solutions either assume knowledge of emission time or require multiple closely spaced receivers, which limits their applicability in realistic scenarios. In this letter, we propose a simple closed-form approximation that exploits the temporal variance of the received molecular signal to estimate the distance between the transmitter and the receiver without emission time information. The method is derived from a Gaussian approximation of the received signal near its peak and gives an explicit variance-distance relation. Simulation results in physically relevant capillary vessel scale show that the proposed method achieves distance prediction with error on the order of 1%.

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