Revisiting Split Covariance Intersection: Correlated Components and Optimality

TL;DR

This paper extends the Split Covariance Intersection method to incorporate correlated components, proving it provides optimal conservative bounds for estimator fusion in distributed systems with both correlated and uncorrelated errors.

Contribution

The paper introduces an extended SCI method that accounts for correlated components, establishing its optimality for conservative fusion bounds in complex estimation scenarios.

Findings

Extended SCI effectively utilizes correlated and uncorrelated components.

The new fusion method achieves optimal conservative bounds.

Simulation results demonstrate improved estimation accuracy.

Abstract

Linear fusion is a cornerstone of estimation theory. Implementing optimal linear fusion requires knowledge of the covariance of the vector of errors associated with all the estimators. In distributed or cooperative systems, the cross-covariance terms cannot be computed, and to avoid underestimating the estimation error, conservative fusions must be performed. A conservative fusion provides a fused estimator with a covariance bound that is guaranteed to be larger than the true, but computationally intractable, covariance of the error. Previous research by Reinhardt \textit{et al.} proved that, if no additional assumption is made about the errors of the estimators, the minimal bound for fusing two estimators is given by a fusion called Covariance Intersection (CI). In distributed systems, the estimation errors contain independent and correlated terms induced by the measurement noises and the process noise. In this case, CI is no longer the optimal method. Split Covariance Intersection (SCI) has been developed to take advantage of the uncorrelated components. This paper extends SCI to also take advantage of the correlated components. Then, it is proved that the new fusion provides the optimal conservative fusion bounds for two estimators, generalizing the optimality of CI to a wider class of fusion schemes. The benefits of this extension are demonstrated in simulations.