Inverse covariance intersection: New insights and properties

Decentralized Tracking in Sensor Networks with Varying Coverage

“…Covariance Intersection (ICI, [10,11]): The relatively recent ICI method is designed to overestimate and remove any common information from the fused estimate. Assumptions are made about correlations, which allows ICI to be less conservative than CI.…”

“…, where all the components λ 1 , λ 2 , γ 1 , and γ 2 are mutually independent, except for the pair γ 1 γ 2 , and an α > 0 exists such that αΓ −1 1 P −1 2 and 1 α Γ −1 2 P −1 1 . This includes the cases, but is not limited to, both estimates sharing the same common information and estimates with common process noise [10].…”

“…It also provides the same covariance matrix as the largest ellipsoid method [1], but gives a different mean estimate. A recent and promising method is the inverse covariance intersection (ICI, [10,11]) method, which provides a middle way, providing a less conservative estimate than CI, while being able to guarantee consistency under quite general assumptions.…”

Heterogeneous sensor fusion based on Copula theory and importance sampling

“…The representative example of such kind of fusion techniques is the covariance intersection (CI) method [21], which is able to yield a convex combination of the means and covariances of the local estimates with an unknown degree of cross‐correlation based on some optimisation methods. In recent works, the ellipsoidal intersection method [22] and the inverse CI method [23] have been developed to reduce the conservative property of CI by including additional parameters to maximise the common information contained in the local estimates. At the same time, the performance improvement of these intersection‐based fusion algorithms [24] is still limited due to their ignorance of the internal correlation structure between the local tracks.…”

Optimally Distributed Kalman Filtering with Data-Driven Communication

“…In general, the correlations required to fuse the local estimates optimally are difficult to reconstruct [ 11 , 12 ]. In the case of unknown correlations, conservative fusion algorithms, like Covariance Intersection [ 13 , 14 ] or Ellipsoidal Intersection [ 15 , 16 , 17 ] and its further development Inverse Covariance Intersection [ 18 , 19 ], can be employed to obtain consistent fusion results. However, these algorithms often provide too conservative assessments of the actual estimation error.…”