Abstract: This invention provides a measurement-while-drilling (MWD) downhole assembly for use in drilling boreholes which utilizes gyroscopes, magnetometers and accelerometers for determining the borehole inclination and azimuth during the drilling of the borehole. The downhole assembly includes at least one gyroscope that is rotatably mounted in a tool housing to provide signals relating to the earth's rotation. A device in the tool can rotate the gyroscope and other sensors on the tool at any desired degree. A processor in the tool combines measurements from the sensors taken at a plurality of positions at the same depth to determine the systematic bias in the sensors before further processing. Accelerometers in the MWD tool provide gravity measurements from which the toolface and inclination are determined. The unbiased gyroscopic measurements are used in conjunction with the tool face and inclination measurements to determine the azimuth and tool face with respect to true north.