A high resolution method and apparatus for measuring the depth of a tool suspended from a cable inside a borehole are described. The tool includes accelerometers for measuring its acceleration and this measurement is combined with a cable depth measurement with which the amount of cable in the borehole is determined. A Kalman filter is employed to continually provide estimates of the velocity and depth of the tool from the accelerometer and cable depth measurements. A filter modifier alters operation of the filter during discontinuous motions of the tool such as when it is stuck and slips. A tool sticking detector senses when the tool is stuck and for how long to correspondingly modify the filter by forcing it to more strongly rely upon accelerometer measurements when the tool is stuck and gradually return to normal filter operation when the tool resumes movement after having been stuck.
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