This paper proposes a novel accurate position estimation method for switched reluctance machine (SRM). The method requires only the flux-linkage characteristics at two particular rotor positions, which can be conveniently measured by the torque-balanced method. The interval which takes these two positions as endpoints is selected as the optimal interval due to the good linearity between the flux linkage and position and the low sensitivity to the errors of the flux linkage. The positions in the optimal interval are obtained by the linear flux-linkage model, and the positions that do not lie in this interval are estimated by the monadic linear regression analysis (MLRA). Furthermore, the rotational speed is also estimated based on MLRA. The accuracy of the proposed method is verified by detailed simulation and experiment under different operating conditions such as angle position control and current chopping control.