  In this paper we propose a new sequential data assimilation method for
non-linear ordinary differential equations with compact state space. The method
is designed so that the Lyapunov exponents of the corresponding estimation
error dynamics are negative, i.e. the estimation error decays exponentially
fast. The latter is shown to be the case for generic regular flow maps if and
only if the observation matrix H satisfies detectability conditions: the rank
of H must be at least as great as the number of nonnegative Lyapunov exponents
of the underlying attractor. Numerical experiments illustrate the exponential
convergence of the method and the sharpness of the theory for the case of
Lorenz96 and Burgers equations with incomplete and noisy observations.
