To estimate parameters of chaotic dynamical systems a
measure to quantify the likelihood function of chaotic variability
(the ’distance’ between different trajectories) is
needed. We review problems encountered by previously
used methods and propose a method related to fractal dimension
concepts. The methodology is demonstrated using
classical chaotic examples, the Lorenz 63 and Lorenz 95
systems, and the Shallow Water Equation as a high dimensional example .