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1.	Forsling, Robin, 1988-, et al. (author) Conservative Linear Unbiased Estimation Under Partially Known Covariances 2022 In: IEEE Transactions on Signal Processing. - : IEEE. - 1053-587X .- 1941-0476. ; 70, s. 3123-3135 Journal article (peer-reviewed)abstract Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.

Forsling, Robin, 1988-, et al. (author)
Conservative Linear Unbiased Estimation Under Partially Known Covariances
2022
In: IEEE Transactions on Signal Processing. - : IEEE. - 1053-587X .- 1941-0476. ; 70, s. 3123-3135
Journal article (peer-reviewed)abstract
- Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.

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