A convergence result for the unscented Kalman-Bucy filter using contraction theory

This paper applies contraction theory to establish necessary conditions for contraction, hence, exponential convergence of the unscented Kalman-Bucy Filter. It follows that regions of contraction can subsequently be defined, given such necessary conditions. Both state and measurement models are Itô-type stochastic differential equations. By employing a virtual/actual system framework, a special relation is established between sigma-point dynamics, and observed process states, with respect to contraction and convergence. The proposed theory is illustrated on an isothermal, non-linear CSTR process.