Autonomous navigation is one of the critical enabling technologies in developing MASS or intelligent ships. This study proposes an autonomous navigation algorithm with INS-aided shipborne GNSS. The proposed algorithm constructs the ship's virtual motion attitude by considering the leeway and drift angle, and takes into account the one-dimensional speed constraints in the virtual ship body reference frame. This approach addresses the issue that the conventional INS and shipborne GNSS integrated navigation scheme can utilize the three-dimensional position information only, without considering the measurement update from the one-dimensional speed obtained by shipborne GNSS. The algorithm is verified by actual ship departure and cruising experiments in natural marine environments. The experimental results show that the proposed algorithm has a higher accuracy than the conventional algorithm when the GNSS speed and position information are available. In the scenario when the GNSS position information is temporarily lost, the proposed algorithm can continue to derive relatively reliable navigation parameters for the safe navigation of ships with only one-dimensional speed measurement.