Although the Global Positioning System (GPS) is used widely in car navigation systems, cell phones, surveying, and other areas, several issues still exist. We focus on the continuous data received in public use of GPS, and propose a new positioning algorithm that uses time series analysis. By fitting an autoregressive model to the time series model of the pseudorange, we propose an appropriate state-space model. We apply the Kalman filter to the state-space model and use the pseudorange estimated by the filter in our positioning calculations. The results of our positioning experiment show that the accuracy of our proposed method is much better than that of the standard method. In addition, as we can obtain valid values estimated by time series analysis using the state-space model, the proposed state-space model can be applied in several other fields.