Having actual models for power system components, such as generators and loads or auxiliary equipment, is vital for a correct assessment of the power system operating state as well as establishing stability margins. Often, however, a power system operator has limited information about the actual values for power system components' parameters. Even if the model is available, its operating parameters, as well as the control settings, are time-dependent and subject to a real-time identification. Ideally, these parameters should be identified from measurement data, such as PMU signals. However, it is challenging to do this from the ambient measurements in the absence of transient dynamics since the signal to noise ratio (SNR) for such signals is not necessarily big. In this paper, we design a Bayesian framework for on-line identification of power system components' parameters based on ambient phasor measurement unit (PMU) data, that has reliable performance for SNR as low as five and for certain parameters can give good estimations even for unit SNR. Finally, we support the framework by a robust and time-efficient numerical method. We illustrate the approach efficiency on a synchronous generator example.