Covariance Fusion of Multiple Positioning Systems for Minimizing Uncertainty through Innovation

Redundant outputs from multiple positioning systems are not typically fused together on moving vehicles, resulting in unrealized opportunities in minimizing any combined position error and uncertainty. Satellite navigation is commonly used in timing and positioning applications, and combined with complementary inertial information to generate a more complete solution. However, the use of multiple Global Positioning System outputs has not been thoroughly explored within a decentralized fusion context for reducing the uncertainty and position error. To prospect any such improvements, a federated architecture using the position outputs of multiple GPS with an inertial measurement unit are considered for a ground vehicle. The innovations are derived from extended Kalman filters and used in weighting the combination of outputs, under conditions of independence, estimated correlations, and unknown cross covariance. Detailed statistical and high fidelity simulations, along with multiple field experiments, provide data for evaluating the covariance fusion methods in both stationary and moving positioning scenarios.;From simulation and experiment data, the fusion methods of averaging, Maximum Likelihood Estimation, joint covariance trace optimization, and covariance intersection are studied. As the number of systems grows, the results show that the root mean squared (horizontal) position error decreases between 20 to 80% over the mean performance of the individual systems. The results are consistent between static and dynamic applications, as well as with the various simulations and experiments. In general, the covariance fusion methods that account for non-zero correlations provide the most improved fused mean position error. When considering the complementary nature of satellite and inertial-based navigation being used together, the covariance fusion techniques become much more effective and consistent. Both the experiments and detailed simulations showed an improvement of 70% to 80% when fusing GPS-aided inertial navigation solutions together. This is about double what standard averaging techniques would provide (that do not consider any system uncertainties in the fusion process).;In addition, combinatorial mathematic analysis is used to identify the incremental gains in position errors when using larger number of systems together. Experiments considered up to 17 systems being fused on a moving ship and found that the benefits effectively diminish after 8 systems are combined. Similar conclusions were also identified from the statistical-based and physics-based simulations. Overall, as redundant position data becomes more ubiquitous, the proposed decentralized systems approach with a federated scheme can be used to improve the combined position of an arbitrary number of systems with both precision and uncertainty, while further increasing overall robustness to system failures and performance degradations.