Improved Calibration of Numerical Integration Error in Sigma-Point Filters

11/28/2018
by   Jakub Prüher, et al.
10

The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in the sigma-point filters are motivated via polynomial approximation of the integrand, however in the applied context these assumptions cannot always be justified. As a result, quadrature error can introduce bias into estimated moments, for which there is no compensatory mechanism in the classical sigma-point filters. This can lead in turn to estimates and predictions that are poorly calibrated. In this article, we investigate the Bayes-Sard quadrature method in the context of sigma-point filters, which enables uncertainty due to quadrature error to be formalised within a probabilistic model. Our first contribution is to derive the well-known classical quadratures as special cases of the Bayes-Sard quadrature method. Then a general-purpose moment transform is developed and utilised in the design of novel sigma-point filters, so that uncertainty due to quadrature error is explicitly quantified. Numerical experiments on a challenging tracking example with misspecified initial conditions show that the additional uncertainty quantification built into our method leads to better-calibrated state estimates with improved RMSE.

READ FULL TEXT

Authors

page 1

page 13

05/16/2021

A Realizable Filtered Intrusive Polynomial Moment Method

Intrusive uncertainty quantification methods for hyperbolic problems exh...
10/30/2019

Heteroscedastic Calibration of Uncertainty Estimators in Deep Learning

The role of uncertainty quantification (UQ) in deep learning has become ...
01/05/2017

Gaussian Process Quadrature Moment Transform

Computation of moments of transformed random variables is a problem appe...
08/18/2020

Moment Multicalibration for Uncertainty Estimation

We show how to achieve the notion of "multicalibration" from Hébert-John...
12/15/2020

Calibrated Adaptive Probabilistic ODE Solvers

Probabilistic solvers for ordinary differential equations (ODEs) assign ...
11/18/2017

The Bayes Lepski's Method and Credible Bands through Volume of Tubular Neighborhoods

For a general class of priors based on random series basis expansion, we...
06/21/2021

Self-Calibrating Neural-Probabilistic Model for Authorship Verification Under Covariate Shift

We are addressing two fundamental problems in authorship verification (A...

Code Repositories

SSMToybox

Nonlinear Sigma-Point Kalman Filters based on Bayesian Quadrature


view repo
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.