Decentralised data fusion with exponentials of polynomials

We demonstrate applicability of a general class of multivariate probability density functions of the form e^-P(x), where P(x) is an elliptic polynomial, to decentralised data fusion tasks. In particular, we derive an extension to the covariance Intersect algorithm for this class of distributions and demonstrate the necessary operations - diffusion, multiplication and linear transformation - for Bayesian operations. A simulated target tracking application demonstrates the use of these operations in a decentralised scenario, employing range-only sensing to show their generality beyond Gaussian representations.