Determination of the heading and pitch of a ground vehicle are useful for a wide range of land-based applications. For some intelligent transport applications, such as map matching, a heading and pitch solution could be used as the adding information, particularly in the non-flat road or during turns. In addition, in the mobile-mapping system, the heading information could be used to aid the initial alignment of the INS. The vehicle heading and roll information could also be used by the logistic companies to monitor the inclination status of logistic vehicles, especially for these carrying liquids or dangerous goods. Vehicle attitude determination could be mainly obtained from various onboard sensors, including magnetic sensors, inertial sensors, GNSS and their combinations. However, the users may have the stringent requirements of cost performances due to the large quantities may be used in the land-based applications. In order to reduce the cost but with an acceptable heading and pitch accuracy, we have proposed a novel algorithm that determines vehicle dynamic positioning and heading using only one single-frequency GNSS antenna. In particular, the time differenced carrier phase (TDCP) measurement model with the vehicle motion constraint is applied for the vehicle heading and pitch determination. The two assumptions based on the road geometry constraint used in this algorithm are: 1) the heading of the vehicle is approximately equal to its tangent to the trajectory curve when moving on the road and 2) the heading of the vehicle cannot be changed abruptly during the moving, therefore, the secant to the historical trajectory curve can be used to replace the tangent, which is the vehicle heading value. In order to evaluate the feasibility of the proposed algorithm in practical work, we have evaluated the TDCP errors under different frequencies. The sensitively analysis results have shown that the proposed algorithm is applicable even at a measurement frequency of 0.1 Hz, which indicating non-sensitive for the input frequency of the measurements. Two dynamic tests are carried out to verify the performance of the algorithm on highway. The field results show that the proposed single antenna based algorithm is able to provide an economical but feasible solution for the heading and pitch estimation with an error under 1 degree, which is useful for many land-based applications.