Abstract: In this paper, we deal with the problem of tracking smoothly time-varying parameters of linear regression channel models occurring in mobile radio communications. The system under consideration is subjected to time-varying coefficient uncertainties with bounded covariances and noises with inexplicit statistical characteristics. The objective of the tracking problem is to find the filter parameters such that the tracking performance, defined as the least mean square of the tracking error, is optimized. The key to the addressed problem is that the tracking problem is transformed into a filtering one and using a projection formula. A polynomial approach based solution for the tracking will be developed. The robust filter design proposed in this paper may have slightly highercomputational complexity than the standard optimal filter designed for systems without random coefficient uncertainties. However, the tracking performance is improved.