arXiv subjects

Gregor Robinson

Publications and source records attributed to Gregor Robinson.

3 recordsLinked to original sources

arXiv2021

A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity

A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-`96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-`96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.

stat.ME↗

arXiv2020

A fast tunable blurring algorithm for scattered data

A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data, and then convolving the interpolant with a multiresolution Gaussian approximation of the Green's function to a differential operator whose spectrum can be tuned for problem-specific considerations. Like conventional blurring algorithms, which the new algorithm generalizes to data measured at locations other than a uniform grid, applications include deblurring and separation of spatial scales. An example illustrates a possible application toward enabling importance sampling approaches to data assimilation of geophysical observations, which are often scattered over a spatial domain, since blurring observations can make particle filters more effective at state estimation of large scales. Another example, motivated by data analysis of dynamics like ocean eddies that have strong separation of spatial scales, uses the algorithm to decompose scattered oceanographic float measurements into large-scale and small-scale components.

stat.CO↗

arXiv2018

Improving particle filter performance by smoothing observations

This article shows that increasing the observation variance at small scales can reduce the ensemble size required to avoid collapse in particle filtering of spatially-extended dynamics and improve the resulting uncertainty quantification at large scales. Particle filter weights depend on how well ensemble members agree with observations, and collapse occurs when a few ensemble members receive most of the weight. Collapse causes catastrophic variance underestimation. Increasing small-scale variance in the observation error model reduces the incidence of collapse by de-emphasizing small-scale differences between the ensemble members and the observations. Doing so smooths the posterior mean, though it does not smooth the individual ensemble members. Two options for implementing the proposed observation error model are described. Taking discretized elliptic differential operators as an observation error covariance matrix provides the desired property of a spectrum that grows in the approach to small scales. This choice also introduces structure exploitable by scalable computation techniques, including multigrid solvers and multiresolution approximations to the corresponding integral operator. Alternatively the observations can be smoothed and then assimilated under the assumption of independent errors, which is equivalent to assuming large errors at small scales. The method is demonstrated on a linear stochastic partial differential equation, where it significantly reduces the occurrence of particle filter collapse while maintaining accuracy. It also improves continuous ranked probability scores by as much as 25%, indicating that the weighted ensemble more accurately represents the true distribution. The method is compatible with other techniques for improving the performance of particle filters.

stat.AP↗