dysii Dynamical Systems Library: ParticleSmootherModel Class Template Reference

~ParticleSmootherModel ( ) [inline, pure virtual]

Destructor.

Definition at line 99 of file ParticleSmootherModel.hpp.

virtual indii::ml::aux::sparse_matrix alpha	(	const indii::ml::aux::DiracMixturePdf &	p_xtn_ytn,
		const indii::ml::aux::DiracMixturePdf &	p_xtnp1_ytnp1,
		const T	start,
		const T	delta
	)			`[pure virtual]`

Calculates the matrix $\alpha(t)$ .

$\alpha^{(j,i)}(t) = p\big(\mathbf{s}^{(j)}(t + \Delta t)\,|\,\mathbf{s}^{(i)}(t)\big)$ , where $\mathbf{s}^{(j)}(t + \Delta t)$ is the $j$ th particle at time $t + \Delta t$ and $\mathbf{s}^{(i)}(t)$ is the $i$ th particle at time $t$ .

Parameters:

	p_xtn_ytn	$P\big(\mathbf{x}(t_n)\, \| \,\mathbf{y}(t_1),\ldots,\mathbf{y}(t_n)\big)$ .
	p_xtnp1_ytnp1	$P\big(\mathbf{x}(t_{n+1})\, \| \,\mathbf{y}(t_1),\ldots,\mathbf{y}(t_{n+1})\big)$ .
	start	; start time.
	delta	$\Delta t = t_{n+1} - t_n$ ; change in time.

Returns:: $\alpha(t)$ .

Particles for the distributions may be obtained with calls to indii::ml::aux::DiracMixturePdf::getComponents().

Note:: The implementation should not assume that there are particles in p_xtn_ytn and p_xtnp1_ytnp1. Instead, use indii::ml::aux::DiracMixturePdf::getNumComponents() to determine this. This is particularly important when working in a parallel environment, where particles are divided up amongst multiple calls to this method.

void alphaPrecalculate	(	const indii::ml::aux::DiracMixturePdf &	p_xtn_ytn,
		const T	start,
		const T	delta
	)			`[inline, virtual]`

Perform precalculations for $\alpha$ matrix.

In a parallel environment, each smoothing step may require multiple calls to the alpha() method of the model with the same first argument. To allow for precalculations based on this first argument, the alphaPrecalculate() method is called before each change to the argument.

For example, in the case of a model with simple Gaussian additive noise, this method could be used to propagate each of the particles at time $t_n$ to time $t_{n+1}$ without noise, obtaining the mean of a Gaussian with covariance equivalent to the system noise. Within the alpha() method, these Gaussians can then be used to quickly calculate densities without having to transition particles again during each call to alpha().

There is no requirement for this method to do anything at all, or even to be implemented in derived classes. It exists purely for optimisation, and is not required for correctness.

Parameters:

	p_xtn_ytn	As p_xtn_ytn of alpha().
	start	As start of alpha().
	delta	As delta of alpha().

Definition at line 104 of file ParticleSmootherModel.hpp.

ParticleSmootherModel Class Template Reference

Detailed Description

template<class T = unsigned int>
class indii::ml::filter::ParticleSmootherModel< T >

Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation