Fluid Flow Estimation with Multiscale Ensemble Filters Based on Motion Measurements Under Location Uncertainty

A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

“…for instance (37) and ( 49)). In addition, using (13) or (14) we readily check that Ppp, dqq has a continuous density kpp, qq ą 0 with respect to the variables pp, qq and the Lebesgue measure dq on R `. It is rather well-known that these two properties ensure the existence of a Lyapunov function of the form U pu, vq " up `v such that β U pPq ă 1.…”

“…They were introduced by Evensen in the seminal article [44] published in 1994, see also [45,46] for a more recent overview. In the last three decades the EnKF methodology has become one of the most used numerical techniques for solving high dimensional forecasting and data assimilation problems in a variety of applications including ocean and atmosphere sciences [1,67,68,58,73], fluid mechanics [14,74,78], image inverse problems [15], weather forecasting [3,4,30,49], environmental and ecological statistics [43,52] and oil reservoir simulations [47,72,82,83,94]. To connect these EnKF techniques with particle filtering methodology for solving high dimensional problems arising in fluid mechanics, we also refer to [59].…”

Visual inference of flow flux via free surface PDE model and image sequence assimilation

“…1, pp. [20][21][22][23][24][25][26][27] This is an open access article published by the IET and Zhejiang University Press under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)…”

“…On the other hand, a majority of the literature dealing with the motion estimation problem is focused on reconstructing the flow field via the OFCE where the physical properties of the flow field itself are only regarded as an extra constraint [19,26]. Very few researchers have been trying to achieve such a DA framework using the OFCE and other hydrodynamic equations such as the vorticity equation [27]. Besides, in [27], the authors choose to use the stochastic OFCE alone to estimate the flow field in the first step and then add the resulting flow field into the DA framework along with the predicted state calculated by the vorticity equation.…”

“…Very few researchers have been trying to achieve such a DA framework using the OFCE and other hydrodynamic equations such as the vorticity equation [27]. Besides, in [27], the authors choose to use the stochastic OFCE alone to estimate the flow field in the first step and then add the resulting flow field into the DA framework along with the predicted state calculated by the vorticity equation. This framework processes the motion estimation problem as a relatively independent part and assimilates the resulting velocity field into the vorticity equation.…”