One prediction step as a joint: the Gaussian the step started from, the Gaussian it predicted, and the cross-covariance between them. More...

#include <EmrysFilter/Models/ProcessModel.h>

Public Types
using	Scalar = Scalar_
	the scalar type
using	SpaceType = Space_
	the state space
using	GaussianType = GaussianParams<Space_, Scalar_>
	the type of either Gaussian
using	MatrixType = typename GaussianType::MatrixType
	the cross-covariance's type, over differences

Public Attributes
GaussianType	filtered
	\( p(x_k \mid z_{1:k}) \), the state the step started from
GaussianType	predicted
	\( p(x_{k+1} \mid z_{1:k}) \), process noise included
MatrixType	cross
	\( C_k \): a row per difference coordinate of \( x_k \), a column per one of \( x_{k+1} \)

Detailed Description

template<Space Space_, RealScalar Scalar_ = double>
struct Emrys::PredictedJoint< Space_, Scalar_ >

One prediction step as a joint: the Gaussian the step started from, the Gaussian it predicted, and the cross-covariance between them.

predictJoint() returns it, and a filter's predictJoint() moves its state as predict() does and returns it too. With \( x_k \) the state before the step and \( x_{k+1} \) after it, given the measurements \( z_{1:k} \) so far, it holds \( p(x_k \mid z_{1:k}) \), \( p(x_{k+1} \mid z_{1:k}) \), and \( C_k = \mathrm{Cov}(x_k, x_{k+1} \mid z_{1:k}) \) in the two tangent spaces, which is everything a Rauch-Tung-Striebel backward step needs from the forward pass (see smoothStep() and GaussianHistory, decisions.md [smoothing]). For an affine step \( x_{k+1} = F x_k + w \), \( C_k = P_{k \mid k} F^T \).

Template Parameters

Space_	the state space
Scalar_	scalar type, `double` by default

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

EmrysFilter/Models/ProcessModel.h

Public Types

Public Attributes

Detailed Description