<p>The Fourier filter is a classical technique for extracting components within desired frequency bands from noisy time series. However, it cannot be directly applied to process GNSS (Global Navigation Satellite System) position time series, due to the inevitable data gaps, and varying precision levels over time, which the ordinary Fourier filter (OFF) does not account for. To address these challenges, we propose a least squares-based Fourier filter (LSFF) approach, which solves for the missing values based on the least squares criterion of optimal temporal filtering. The proposed method can directly process incomplete time series without prior interpolation while simultaneously accounting for the formal errors of time series to further improve the filtering performance. The effectiveness of the proposed LSFF method is validated through the analysis of vertical position time series from 27 GNSS permanent stations located in the Chinese mainland from 1999 to 2019. Results demonstrate that the LSFF method outperforms OFF with previous interpolations and least squares spectrum analysis (LSSA), as evidenced by a significant reduction in the fitting error of the extracted signals. Furthermore, after subtracting signals within the frequency bands of interest from the raw time series, the power associated with these components in the residuals filtered by the LSFF method is significantly lower than those filtered by OFF with interpolations and LSSA, indicating a more effective extraction of signals. Repeated simulations confirm that LSFF retrieves signals closer to the true values than OFF and LSSA, regardless of gap sizes (10 to 60% of data missing) or the distribution pattern of gaps (short sporadic or long consecutive). As a bonus, LSFF also enables multi-mode analysis of time series across different frequency bands.</p>