Approximate analytical solutions for the weight optimization problems of CI and ICI

Approximate analytical formulae are proposed for the solutions of the weight optimization problems involved in Covariance Intersection (CI) and Inverse Covariance Intersection (ICI). The methodology used for obtaining the analytic approximations boils down to using just two Newton iterations with the initial weight value 1/2. The simulation results show that quite acceptable root-mean-square (RMS) error levels are achievable with the proposed approximate analytical weights with less computations compared to what would be required when numerical optimization with a high termination tolerance is used, which can be critical for applications with very limited computational resources.