In recent years, various Portable Navigation Devices (PND) such as smart-phones are becoming popular as a vehicle navigation device. To compare with a conventional built-in navigation system, PND has advantages that it is low cost and easily mounted to the vehicle. On the other hand, PND has also disadvantage that in the most case it cannot obtain the reliable vehicle speed information such as wheel pulse information and that induces degradation of vehicle trajectory estimation (dead-reckoning). The vehicle trajectory estimation is the positioning method using inertial sensors, and generally used when GPS is not available. So in urban area where GPS signals are blocked or reflected by tall buildings, the degradation of vehicle trajectory estimation may cause the severe increase of position error. Accordingly, in this study two approaches are proposed to improve vehicle trajectory estimation with PND. The first one is the accurate speed estimation using time-series tightly coupled integration of accelerometer, gyro, and Doppler shift of GPS. And the second one is the correction of trajectory error using backward refinement that can work even in real-time processing. The experimental result in Shinjuku which is dense urban city shows that the error of vehicle trajectory estimation was reduced to 1/4 compared with the previous method.