Gravity induced position errors in airborne inertial navigation
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Date
1981-12
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Ohio State University. Division of Geodetic Science
Abstract
The report investigates the feasibility of improving airborne inertial navigation by use of gravity field approximations which are more accurate than the normal model presently applied. The effect of the anomalous gravity field on positioning is investigated by using a simplified dynamical error model and by deriving analytical expressions for the steady state error via the state space approach. In this approach, changes in the anomalous gravity field are cast into the form of first-order differential equations which are related to a position dependent covariance representation of the gravity field by way of the vehicle velocity. Different possibilities for a state space model of the anomalous field are discussed. The procedure chosen combines the consistency of the Tscherning-Rapp model with the advantages of a formulation in terms of Gauss-Markov processes by making use of the essential parameters of a covariance function proposed by Moritz. The expressions for the gravity induced position errors resulting from this approach are easy to compute for a wide variety of cases. The assumptions made to derive them are in general justifiable. Based on the available gravity field information a number of approximation models are proposed and expressed in terms of equivalent spherical harmonic expansions. Results show that the use of presently available global models would reduce the gravity induced position errors from σ = 300 m to about σ = 150 m. Improved global models expected in the near future, as for instance those from the GRAVSAT mission, would bring errors below σ = 50 m. However, to reach the meter range, a gravity field approximation equivalent to an expansion of degree and order 1000 would be necessary. This result is not surprising. It demonstrates the well-known fact that the medium and high frequency spectrum contributes considerably to the deflections of the vertical or, in other words, that the relative contribution of local effects is not negligible in this case. Considering the accuracy of present day inertial sensors, gravity field models giving σ = 150 m seem to be adequate and it may take some time before non-gravitational system errors in airborne navigation can be reduced to a level of σ = 50 m.