Gravity gradiometers (or gravity gradient instrument, GGI) measure one or more components of the gradient of gravity which is expressed as the gradient of a gravity vector. One or more feedback loops extend from the instrument output to one or more of the accelerometers (1–4) to compensate for errors. The feedback loops include one or more inputs in addition to the instrument output. The additional inputs include signals representing one or more of: components of attitude, velocity and acceleration, the physical environment and flight conditions, taken alone or in combination.