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Systems comprised of a number of computing nodes all supporting a common mission. All nodes can be given the same task or asked to support the mission through a subset of tasks. Decentalized systems offer several advantages over their centralized counterparts including:
- Each node does not require intrinsic knowledge of the system topology
- Topology is variable. Nodes can be added or subtracted without significantly impacting the overall system
- Less vulnerable to single-point failures
- Computational load can be spread amongst nodes for efficiency
Decentralized systems also suffer from some disadvantages:
- All nodes may not have access to all information contained within the system
- Multiple nodes have access to the same information
Examples of decentralized systems include robotic swarms, cooperative UAVs, formation flying spacecraft and formation of synthetic apertures using multiple smaller sensors.
Another elegant property of the CI algorithm is that, while being derived from a geometric viewpoint, it can also be derived from a matrix- and scalar-weighted optimization problem. This property allows the CI algorithm to be extended to the fusion of higher dimensional state vectors and an arbitrary number of estimates.
Covariance Intersection for Attitude Estimation
While the CI algorithm provides a meaningful and elegant solution for the problem of fusion under unknown correlations, the fusion of attitude states is not trivial. The main difficulty with fusing attitude estimates is the choice of attitude parametrization. The traditional attitude parametrization of choice for space applications, the quaternion, must satisfy a unit norm constraint. This leads the CI fused estimate to be the solution of a constrained optimization problem. For state vectors including only a single quaternion there are several solutions to the resulting optimization problem. For fusion of state vectors containing more than a single quaternion iterative solution methods are required which also seek to mitigate the increasing numeric instability of the problem statement.
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Julier, S. J., and Uhlmann, J., K., General Decentralized Data Fusion with Covariance Intersection (CI) in Handbook of Multisensor Data Fusion. CRC Press. Boca Raton, FL., 2001, Chap. 12.
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Crassidis, J. L., Cheng, Y., Nebelecky, C. K., and Fosbury, A. M., “Decentralized Attitude Estimation Using a Quaternion Covariance Intersection Approach”, Journal of the Astronautical Sciences, Vol. 57, Nos. 1& 2, Jan.-June 2009, pp. 113 – 128.
Nebelecky, C. K., Crassidis, J. L., Fosbury, A. M., and Cheng, Y., “Efficient Covariance Intersection of Attitude Estimates Using a Local-Error Representation”, Journal of Guidance, Control, and Dynamics Vol. 35, No. 2, Mar.-Apr. 2012, pp 692 –696.
Nebelecky, C. K., Crassidis, J. L., Banas, W. D., Cheng, Y., and Fosbury, A. M., “Decentralized Relative Attitude Estimation for Three-Spacecraft Formation Flying Applications”, AIAA Guidance, Navigation and Control Conference AIAA Paper 2009-6313, Chicago, IL, Aug. 2009.