A central topic in active microwave remote sensing is the measurement of polarimet-ric scattering matrix time series. At least two successive measurements, employing orthogonal transmitter polarisations, are necessary to determine the full S-matrix of an object. In many remote sensing applications, however, the observed targets experience small but non-negligible variations even in the small time interval which is required to perform the S-matrix measurement. In order to cope with this problem, a Doppler phase correction scheme can be applied which compensates for the deterministic mean target motion. The possible internal variation of a composite target due to the random motion of the target's individual scattering centres of particles, however, results in decorrelation of the consecutively measured S-matrix columns and leaves significant statistical errors uncorrected. In the present paper the mean Doppler phase correction method and the related estimation errors are studied in greater detail, employing a quite general model of time-variant random targets. It turns out that the critical quantity which determines the statistical accuracy of the Doppler correction is given by the ratio of the pulse repetition interval and the decorrelation time of the observed random target. The pulse repetition frequency of the radar measurement, hence, has to be chosen carefully in order to avoid large estimation errors in the S-matrix determination. Matching the pulse repetition frequency properly to the decorrelation time of the observed target, on the other hand, allows the measurement and processing of polarimetric S-matrix series with maximum information content on the target. The present statistical studies, this way, are of fundamental interest in many polarimetric remote sensing applications.