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

A zero-mean Ornstein-Uhlenbeck (first-order Gauss-Markov) process on each coordinate of the block named by Path, such as a slowly varying sensor bias. More...

#include <EmrysFilter/Models/ProcessModel.h>

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

Public Types
using	Scalar = Scalar_
	the scalar type of the parameters

Public Member Functions
	OrnsteinUhlenbeck (TimeConstant< Scalar_ > timeConstant, StationaryVariance< Scalar_ > variance)
	Time constant timeConstant and stationary variance variance.
Scalar_	timeConstant () const
Scalar_	variance () const

Detailed Description

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

A zero-mean Ornstein-Uhlenbeck (first-order Gauss-Markov) process on each coordinate of the block named by Path, such as a slowly varying sensor bias.

With time constant \( \tau \) and stationary variance \( \sigma^2 \), a step \( \Delta t \) gives \( x' = \phi x \) with \( \phi = e^{-\Delta t / \tau} \) and noise \( \sigma^2 (1 - \phi^2) \) on each coordinate, the exact discretization of the Ornstein-Uhlenbeck process, the first-order Gauss-Markov process of Gelb (1974), that models slowly varying sensor errors. The model is affine in its block and returns its Jacobian.

Scalar_ is the type of \( \tau \) and \( \sigma^2 \). The step computes in the scalar of the step it is given, as Kinematic's does. The two are given by name, OrnsteinUhlenbeck<Bias>{TimeConstant{60.0}, StationaryVariance{0.25}}, since as two numbers of one type they would swap silently. Each coordinate of the block takes the same \( \tau \) and \( \sigma^2 \); coordinates that differ are blocks of their own (decisions.md [continuous-time-noise]).

Member Function Documentation

timeConstant()

template<typename Path, RealScalar Scalar_ = double>

Scalar_ Emrys::OrnsteinUhlenbeck< Path, Scalar_ >::timeConstant ( ) const

inlinenodiscard

Returns

the time constant \( \tau \)

variance()

template<typename Path, RealScalar Scalar_ = double>

Scalar_ Emrys::OrnsteinUhlenbeck< Path, Scalar_ >::variance ( ) const

inlinenodiscard

Returns

the stationary variance \( \sigma^2 \)

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

• EmrysFilter/Models/ProcessModel.h