8,674 research outputs found
Nonlinear Attitude Filtering: A Comparison Study
This paper contains a concise comparison of a number of nonlinear attitude
filtering methods that have attracted attention in the robotics and aviation
literature. With the help of previously published surveys and comparison
studies, the vast literature on the subject is narrowed down to a small pool of
competitive attitude filters. Amongst these filters is a second-order optimal
minimum-energy filter recently proposed by the authors. Easily comparable
discretized unit quaternion implementations of the selected filters are
provided. We conduct a simulation study and compare the transient behaviour and
asymptotic convergence of these filters in two scenarios with different
initialization and measurement errors inspired by applications in unmanned
aerial robotics and space flight. The second-order optimal minimum-energy
filter is shown to have the best performance of all filters, including the
industry standard multiplicative extended Kalman filter (MEKF)
A Direct D-Bar Method for Partial Boundary Data Electrical Impedance Tomography With a Priori Information
Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges due to a nonlinear low-pass filtering of the measured data, and this problem becomes especially marked in the case of partial boundary data. Including a priori data directly into the D-bar solution method greatly enhances the spatial resolution, allowing for detection of underlying pathologies or defects, even with no assumption of their presence in the prior. This work combines partial data D-bar with a priori data, allowing for noise-robust conductivity reconstructions with greatly improved spatial resolution. The method is demonstrated to be effective on noisy simulated EIT measurement data simulating both medical and industrial imaging scenarios
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
Reconstruction subgrid models for nonpremixed combustion
Large-eddy simulation of combustion problems involves highly nonlinear terms that, when filtered, result in a contribution from subgrid fluctuations of scalars, Z, to the dynamics of the filtered value. This subgrid contribution requires modeling. Reconstruction models try to recover as much information as possible from the resolved field Z, based on a deconvolution procedure to obtain an intermediate field ZM. The approximate reconstruction using moments (ARM) method combines approximate reconstruction, a purely mathematical procedure, with additional physics-based information required to match specific scalar moments, in the simplest case, the Reynolds-averaged value of the subgrid variance. Here, results from the analysis of the ARM model in the case of a spatially evolving turbulent plane jet are presented. A priori and a posteriori evaluations using data from direct numerical simulation are carried out. The nonlinearities considered are representative of reacting flows: power functions, the dependence of the density on the mixture fraction (relevant for conserved scalar approaches) and the Arrhenius nonlinearity (very localized in Z space). Comparisons are made against the more popular beta probability density function (PDF) approach in the a priori analysis, trying to define ranges of validity for each approach. The results show that the ARM model is able to capture the subgrid part of the variance accurately over a wide range of filter sizes and performs well for the different nonlinearities, giving uniformly better predictions than the beta PDF for the polynomial case. In the case of the density and Arrhenius nonlinearities, the relative performance of the ARM and traditional PDF approaches depends on the size of the subgrid variance with respect to a characteristic scale of each function. Furthermore, the sources of error associated with the ARM method are considered and analytical bounds on that error are obtained
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