In this paper, the mean square error (MSE) of the new technique, the shifted scaled least squares (SSLS), and the minimum MSE (MMSE) estimator is analysed in the Rician distributed flat fading multiple-input–multiple-output (MIMO) channels. First, the closed form expressions are obtained for MSE of the estimators using the estimated and the actual mathematical expectation matrix of the channel and the matrix of channel covariances. It is analytically and numerically shown that the performance of the estimators is less sensitive to the erroneous estimation of the Rice factor at the receiver. On the other hand, it is shown that the performance of the MMSE estimator is quite sensitive to the erroneous estimation of the channel correlation coefficient. In order to estimate the channel Rice factor, two algorithms are also proposed in this paper. These algorithms work based on the optimal training signal and least squares (LS) technique. Finally, the estimated Rice factor is used in the SSLS and MMSE estimators. Simulation results confirm the efficiency of the algorithms and the robustness of the above-mentioned estimators to the erroneous estimation of Rice factor.