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arXiv · 2507.16216

Conservative fusion of unbiased partial state estimates: CI is optimal

Jochen Trumpf·Behzad Zamani·Chris Manzie
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Abstract

We show that Covariance Intersection (CI) is optimal amongst all conservative unbiased linear fusion rules also in the general case of information fusion of two unbiased partial state estimates, significantly generalizing the known optimality result for fusion of full state estimates. In fact, we prove the much stronger result that three different optimization problems are equivalent, namely the abstract optimal conservative unbiased linear information fusion problem with respect to a strictly isotone cost function, the scalar CI problem, and a simple semi-definite program. We provide a general solvability condition for these problems as well as equations characterizing the optimal solutions for the matrix determinant and matrix trace cost functions.

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Jochen Trumpf, Behzad Zamani, Chris Manzie. 2025-07-22. Conservative fusion of unbiased partial state estimates: CI is optimal. https://arxiv.org/abs/2507.16216

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