Emrys::methods::FourthMomentUnscented Struct Reference

Unscented method with \( \alpha = 1 \), \( \beta = 0 \), and \( \kappa = 3 - L \) over \( L \) coordinates, so that \( L + \lambda = 3 \): the points sit at \( \sqrt 3 \) standard deviations along each column of the root whatever \( L \) is, and their fourth moment along each column is a Gaussian's, 3. More...

#include <EmrysFilter/Models/Methods.h>

Static Public Member Functions
template<typename Scalar>
static constexpr UnscentedParams< Scalar >	params (Eigen::Index n)

Detailed Description

Unscented method with \( \alpha = 1 \), \( \beta = 0 \), and \( \kappa = 3 - L \) over \( L \) coordinates, so that \( L + \lambda = 3 \): the points sit at \( \sqrt 3 \) standard deviations along each column of the root whatever \( L \) is, and their fourth moment along each column is a Gaussian's, 3.

The choice of \( \kappa \) for a Gaussian input of Julier and Uhlmann (2004) (Särkkä (2013), §6.5, at equation (6.45)). The center point's weight is \( 1 - L / 3 \), negative over more than three coordinates, so the covariance is a difference of positive terms there and can be indefinite; a square-root form downdates by the center's column. \( \beta = 0 \) because the points already carry the fourth moment that \( \beta = 2 \) makes up for. An UnscentedRule, as Unscented is, whose parameters depend on the number of coordinates: over a fixed number, the compiler computes its weights as it does Unscented's.

Member Function Documentation

params()

template<typename Scalar>

constexpr UnscentedParams< Scalar > Emrys::methods::FourthMomentUnscented::params ( Eigen::Index n )

inlinestaticnodiscardconstexpr

Returns

\( \alpha = 1 \), \( \beta = 0 \), and \( \kappa = 3 - n \) in Scalar

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The documentation for this struct was generated from the following file:

• EmrysFilter/Models/Methods.h