Abstract: The Global navigation satellite systems use a part of the L band.The part is within 1.1GHz to 1.6GHz and has a width of about 150MHz.This severely interferes with radio astronomy observations in the frequency range of the part.In this paper, we discuss applying adaptive filtering methods designed for radio communication and radar technology to reduction of radio frequency interferences (RFIs) caused by a Beidou satellite in observations of neutral hydrogen (HI) 21cm spectral line.In order to improve the performance of the LMS adaptive filtering algorithm, we have derived a new type of functions relating step sizes and error signals based on our study of a class of conventional LMS algorithms of variable step sizes.Using functions of the new type improves the performance of adaptive filtering.The improvement is either in faster convergence or in smaller steady-state deviation.Our numerical simulation results are consistent with our theoretical analysis of the application of new functions in adaptive filtering for reducing RFI in radio astronomy, which validates the performance improvement.