The current method to compute the wellbore while drilling is based on stationary surveys at the desired station. This is done by measuring the inclination and the azimuth of the borehole between the current and the previously surveyed stations. Using a mathematical model based on assumptions of the shape of the drilled section, the coordinates of the borehole can be derived. This current method neglects the actual trajectory between the two surveying stations.Exploration and production companies demand cost effective drilling operations. Thus, demand has been rising for a continuous survey that captures the actual trajectory between the stationary surveying stations. This provides an actual estimate of the curvature "dogleg" along the well trajectory. In addition, this allows a better estimation of the casing and cementing of the borehole. Therefore, in this development the wellbore trajectory between the two surveying stations is continuously surveyed using three accelerometers and three MEMS gyroscopes. The computation algorithm is based on strap down Inertial Navigation System mechanization and Kalman filtering.The inputs to the continuous drilling survey system are the accelerometers and gyroscopes measurements, while the outputs are position, tool face, inclination and azimuth of the drill bit. This wellbore survey system will exhibit an unlimited growth of position, and azimuth errors if there are no external observations to update the surveying system. Two external update schemes can limit this error growth while drilling. The first is based on the continuous source of drilled pipe length measurements while the second is the zero velocity update. The Kalman filter continuous surveying system was successfully applied to drilling tests. External updates of the drill pipe length were utilized to reduce measurement error drift. When the drilling process was stopped to connect new drill pipe stands, zero velocity updates were employed by the Kalman filter.