This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the second-order ensemble Kalman filter and the singular extended interpolated filter. The aim is to study ...

<p style='text-indent:20px;'>We study the problem of diffeomorphometric geodesic landmark matching where objective is to find a diffeomorphism that, via its group action, maps between two sets landmarks. It well-known that motion landmarks, and thereby diffeomorphism, can be encoded by an initial momentum leading formulation solved as optimisation over such momenta. The novelty our work l...

Two types of filtering failure are the well known filter divergence where errors may exceed the size of the corresponding true chaotic attractor and the much more severe catastrophic filter divergence where solutions diverge to machine infinity in finite time. In this paper, we demonstrate that these failures occur in filtering the L-96 model, a nonlinear chaotic dissipative dynamical system wi...