With the increasing penetration of renewable energy, stability issues have become more prominent. Grid-connected converters can improve the stability of systems through adaptive control when grid impedance information is known. Therefore, the grid impedance estimation (GIE) is essential. When it comes to GIE, accuracy and its impact on power quality need to be considered, which can be affected by the injected perturbation period and amplitude of grid-connected converters. In this regard, this paper proposes an impedance sensing method based on the Recursive Least Squares (RLS) algorithm to decrease the impact of continuous converters' injection perturbations on power quality. The method is not affected by variations in grid current, effectively decreasing the possibility of false triggering. Additionally, an amplitude calculation strategy based on the target response is employed to enhance the accuracy of impedance estimation. Finally, the effectiveness of the proposed method is verified in MATLAB/Simulink.