A contraction theory-based analysis of the stability of the Extended   Kalman Filter
  The contraction properties of the Extended Kalman Filter, viewed as a deterministic observer for nonlinear systems, are analyzed. This yields new conditions under which exponential convergence of the state error can be guaranteed. As contraction analysis studies the evolution of an infinitesimal discrepancy between neighboring trajectories, and thus stems from a differential framework, the sufficient convergence conditions are different from the ones that previously appeared in the literature, which were derived in a Lyapunov framework. This article sheds another light on the theoretical properties of this popular observer. 
Silvere Bonnabel, Jean-Jacques Slotine
cs.SY math.OC