Although the emergence of new satellite systems offers considerable opportunities, the integration of Global Navigation Satellite System (GNSS) multi-constellation entails more complicated approaches, especially for stochastic modeling. This study proposes a filtering approach that combines robust Kalman filtering and variance component estimation to specify the weights of multi-GNSS observations in single-frequency positioning. In this approach, robust Kalman filter resists the impact of unexpected outliers by introducing the equivalent covariance matrix, while multi-GNSS observation variances are determined adaptively in each epoch by using variance component estimation. The study demonstrated that the proposed filtering approach determines the variances of multi-GNSS observations more rigorously as a result of the assessment of the observation residuals. The results also showed that the positioning accuracy of single-frequency multi-GNSS positioning that depends on the conventional weighting approaches is improved by 18.5% on average with the employment of the proposed filtering approach and its improvement ratio can exceed 30% in some stations.