Guaranteed Fast Implementation of the Split Covariance Intersection Filter: Nested Newton Method Thanks to the Fourth-Order Convexity of w-Optimization

Abstract

The split covariance intersection filter (Split CIF) is a useful tool for general data fusion and has the potential to be applied in a variety of engineering tasks. The w-optimization problem involved in the Split CIF concerns the performance and implementation efficiency of the Split CIF. It is known that the w-optimization problem enjoys the desirable property of convexity (or more clearly, the second-order convexity in this paper's context). This paper proves that the w-optimization problem further enjoys a more desirable property namely the fourth-order convexity, thanks to which a guaranteed fast implementation of the Split CIF can be realized. The new implementation is coined as the nested Newton method, which is also presented in this paper.