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To achieve high-precision GNSS positioning of smart devices, it is necessary to correct the pseudorange measurements, especially to reduce time-related errors. Traditional pseudorange smoothing methods fail to cope with measurement anomalies and do not consider the time correlation. Therefore, a time-correlated pseudorange correction (TCPC) method is proposed. The Mann-Kendall trend test and breakpoint detection are used to address data anomalies and pseudorange errors are estimated with an adaptive smoothing method. Using the proposed method, the GNSS receivers can improve the pseudorange accuracy and availability for better single-point positioning performance. The positioning errors are reduced by 10%−45% for different GNSS receivers. Moreover, the circular antenna motion mechanism is used to reduce the measurement correlation and enhance observability. Using the TCPC method in the smartphone antenna motion case, the improvement rates of positioning accuracies are 43%−76% and the horizontal positioning accuracy is improved from meter level to decimeter level.