Emrys::RandomWalk< Path, Scalar_ > Class Template Reference

A model driven by white noise alone: \( x' = x \), with noise \( Q_c \, \Delta t \) on its differences. More...

#include <EmrysFilter/Models/ProcessModel.h>

Inheritance diagram for Emrys::RandomWalk< Path, Scalar_ >:

Public Types
using	Scalar = Scalar_
	the scalar type of the spectral density
using	SpectralDensityMatrix = Eigen::Matrix<Scalar_, Dimension, Dimension>
	The spectral density's type: \( d \times d \) over the block's differences.

Public Member Functions
	RandomWalk (Scalar_ spectralDensity)
	Spectral density spectralDensity on every axis, independently.
	RandomWalk (SpectralDensityMatrix const &spectralDensity)
	Spectral density matrix spectralDensity.
SpectralDensityMatrix const &	spectralDensity () const

Static Public Attributes
static constexpr int	Dimension = Differences::FixedValueDimension
	Dimension of the block's differences.

Detailed Description

template<typename Path, RealScalar Scalar_ = double>
class Emrys::RandomWalk< Path, Scalar_ >

A model driven by white noise alone: \( x' = x \), with noise \( Q_c \, \Delta t \) on its differences.

Path is a tag or a TagPath to a fixed-size block, such as a sensor bias. The spectral density \( Q_c \) is a \( d \times d \) matrix over the block's differences, so it applies as well to a block whose differences have another size than its values: a random walk on a UnitQuaternion attitude holds the attitude and adds the noise to its rotation vector (decisions.md [continuous-time-noise]). It is the exact discretization of a Wiener process. The model is affine in its block and returns its Jacobian, the identity, so Linearized predicts it exactly without differentiating.

Scalar_ is the type of \( Q_c \). The step computes in the scalar of the step it is given, the filter's, converting \( Q_c \) to it where the two differ.

Member Function Documentation

spectralDensity()

template<typename Path, RealScalar Scalar_ = double>

SpectralDensityMatrix const & Emrys::RandomWalk< Path, Scalar_ >::spectralDensity ( ) const

inlinenodiscard

Returns

the spectral density \( Q_c \) of the white noise on the block

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

• EmrysFilter/Models/ProcessModel.h