The Story of Gradiometer Map Matching

. The key to this work was developing spatially distributed stochastic micro models for the gravity characteristics, where hundreds of states could be used , based on physical laws, and optimal estimation , to imply macroscopic phenomena. It is assumed that the gravity field can be represented by horizontal planes of mascons at assumed known positions, but of unknown magnitude. Each mascon becomes a “bias” state in the filter, to be estimated using the 6 independent gravity gradient measurements available from a Bell Gradiometer at each time interval. There are several planes of mascons. Each mascon, as it affects the measurements, can be accurately modeled

Although there is a great deal of uncertainty associated with the magnitude of each mascon after estimation, estimates of the gravity field ( e.g. the gravity vector, and gradients at locations of the vicinity of, but not on the survey ) will be very accurate. Estimates of each gravity component are nothing but known linear transformations (based on gauss’ law ) of the mascon value estimates (at assumed known locations). In other words the mascon estimated values and their known position represent the survey generated gravity map. This concept was first used as an approach to estimating vertical deflections ( if uncompensated cause error in inertial navigation) . It was quite successful.

Then we took the inductive leap and developed, and demonstrated via at sea tests gravity gradiometer map matching capable of meeting precise navigation needs of Trident (nuclear submarine). The Idea is when precise navigation is available , create a position registered field “map”( mascon values and their positions) generated via Bell Gradiometer measurements. Tracks in the measurement survey do not need to be terribly dense. This creates a permanent position fix area when precise radio navigation is not available. Upon return ( perhaps 30 years later) , when a fix is required by the Trident or its descendant, the onboard gradiometer measurements can be used, though map matching techniques using all six gradients in conjunction with the ships inertial system (for dead reckoning) to fix position within specs and completely passively!

The Concept was tested.. (Performing the survey , then return to the vicinity for a fix). It worked as advertised.

But then the cold war ended.