A method for computing the orientation of a MWD system in a borehole comprising: providing a MWD system (107, 207, 307, 407), the MWD system (107, 207, 307, 407) including multiple sensors (209, 211, 213, 309, 313), the data collected by the sensors interpreted by sensor models having adjustable sensor model parameters, the MWD system (107, 207, 307, 407) having an orientation, the orientation including azimuth and inclination; positioning the MWD system (107, 207, 307, 407) on a drill string; positioning the drill string at a depth within a borehole drilled from a surface location, the depth measured from the location of the MWD system (107, 207, 307, 407) to the surface location, the direction of the borehole generally being represented by the orientation of the MWD system (107, 207, 307, 407); moving, by a motion of the drill string, the location of the MWD system (107, 207, 307, 407),within the borehole from a first depth to a second depth; sensing changes in the orientation of the MWD system (107, 207, 307, 407) using one or more sensors of the multiple sensors (209, 211, 213, 309, 313) as the MWD system (107, 207, 307, 407) is moved from the first depth to the second depth; calculating the change in orientation of the MWD system (107, 207, 307, 407) between the first and second depths using the sensed changes in the orientation of the MWD system (107, 207, 307, 407); combining the readings from two or more sets of sensors measuring different quantities using two or more sensors of the multiple sensors (209, 211, 213, 309, 313) at the first depth to determine an estimated orientation of the MWD system (107, 207, 307, 407) at the first depth; combining the readings from two or more sets of sensors measuring different quantities using two or more sensors of the multiple sensors (209, 211, 213, 309, 313) at the second depth to determine an estimated orientation of the MWD system (107, 207, 307, 407) at the second depth; computing a computed orientation of the MWD system (107, 207, 307, 407) at the second depth using the calculated change in orientation between the first and second depths and estimated orientation of the MWD system (107, 207, 307, 407) at the first depth; comparing the computed orientation of the MWD system (107, 207, 307, 407) at the second depth to the estimated orientation of the MWD system (107, 207, 307, 407) at the second depth to calculate an offset error; and adjusting one or more of the adjustable sensor model parameters of one or more sensors of the multiple sensors (209, 211, 213, 309, 313) in response to the offset error. providing a MWD system (107, 207, 307, 407), the MWD system (107, 207, 307, 407) including multiple sensors (209, 211, 213, 309, 313), the data collected by the sensors interpreted by sensor models having adjustable sensor model parameters, the MWD system (107, 207, 307, 407) having an orientation, the orientation including azimuth and inclination; positioning the MWD system (107, 207, 307, 407) on a drill string; positioning the drill string at a depth within a borehole drilled from a surface location, the depth measured from the location of the MWD system (107, 207, 307, 407) to the surface location, the direction of the borehole generally being represented by the orientation of the MWD system (107, 207, 307, 407); moving, by a motion of the drill string, the location of the MWD system (107, 207, 307, 407),within the borehole from a first depth to a second depth; sensing changes in the orientation of the MWD system (107, 207, 307, 407) using one or more sensors of the multiple sensors (209, 211, 213, 309, 313) as the MWD system (107, 207, 307, 407) is moved from the first depth to the second depth; calculating the change in orientation of the MWD system (107, 207, 307, 407) between the first and second depths using the sensed changes in the orientation of the MWD system (107, 207, 307, 407); combining the readings from two or more sets of sensors measuring different quantities using two or more sensors of the multiple sensors (209, 211, 213, 309, 313) at the first depth to determine an estimated orientation of the MWD system (107, 207, 307, 407) at the first depth; combining the readings from two or more sets of sensors measuring different quantities using two or more sensors of the multiple sensors (209, 211, 213, 309, 313) at the second depth to determine an estimated orientation of the MWD system (107, 207, 307, 407) at the second depth; computing a computed orientation of the MWD system (107, 207, 307, 407) at the second depth using the calculated change in orientation between the first and second depths and estimated orientation of the MWD system (107, 207, 307, 407) at the first depth; comparing the computed orientation of the MWD system (107, 207, 307, 407) at the second depth to the estimated orientation of the MWD system (107, 207, 307, 407) at the second depth to calculate an offset error; and adjusting one or more of the adjustable sensor model parameters of one or more sensors of the multiple sensors (209, 211, 213, 309, 313) in response to the offset error.