Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer

Precise inertial navigation depends on external aiding to remove various systematic errors in the sensed accelerations and rotations that cause an accumulation of position error up to many hundreds of meters per hour. Technological developments in inertial sensors are underway to eliminate this dependence at the level of a few meters uncertainty over one hour of unaided inertial navigation. However, no matter how precise the inertial measurement units are, the systematic effect of unknown gravitation can cause navigation errors up to several hundred meters per hour. Compensation for this effect can take several forms, but always requires updates or information from systems external to the inertial navigator. This report analyzes the unique capabilities provided by an onboard integrated gravity gradiometer that senses the gravitational gradients, thus enabling in situ compensation. Particular attention is given to the coupling of observed gradients with angular rates and accelerations. It is shown that errors from conventional precision gyros negate the effect of gradiometer aiding on the cross-track position error if only the essential gradients are measured [accuracy of 0.1 Eotvos (E)]. With additional measurements of appropriate symmetric gradient components, both along-track and cross-track errors caused by gravitation can be controlled at the 5-m level after one hour of free-inertial navigation.