Abstract: In order to improve the accuracy of borehole survey systems utilizing probes with inertial components including inclinometers, two ring laser gyro units are included to provide rotation information to the system. When the probe is moving in a borehole, inclinometer iformation is used to produce a synthetic rotation signal to take the piece of a third gyro and the earth's rotation is used for a similar purpose in combination with signals from the two ring laser gyros when the probe is stopped. Wire line velocity is used in combination with the inclinometer and gyro information to provide signals representing the probe velocity and position. Coordinate transformations are provided in the probe to transform the inertial signals and wire line velocity signals into earth reference coordinate system. Kalman filtering incorporates noninertial velocity data to reduce the effect of errors inherent in the generation of various input signals to the system.