In the process of robust Kalman filtering, in order to avoid the problem of gross error transfer due to the correlation among Global Navigation Satellite System (GNSS) observations, a partial gross error robust filtering algorithm for GNSS observations based on chisquare test is proposed. Firstly, the correlation among observations is analyzed based on the anomaly test of the observation model, and aiming at the problem of gross error misjudgment caused by the correlation among observations, a partial gross error robust filtering algorithm is proposed. According to the hypothesis testing theory, the overall test of the filtering model is constructed, which judges whether there exists an abnormality in the overall model based on chisquare test, and the overall flow framework of the partial gross error robust filtering algorithm for GNSS observations based on chisquare test is given. Finally, two sets of experiments are designed, and three methods are used for comparative analysis to verify the performance of the proposed algorithm. The experiment results show that the proposed algorithm greatly reduces the influence of correlation among observations, can accurately identify the location of gross errors, significantly reduces the false alarm rate of gross error detection and ensures the robustness of positioning.