Monte Carlo Method for Nonlinear Filtering

Enachescu, Denis

doi:10.1007/978-94-009-5438-0_9

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Constructing Particle Approximations1

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1997

1999

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Cited by 2 publications

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“…The classical Monte Carlo method [12]: A cloud of particles whose initial positions form a random sample from the initial distribution of the signal moves according to the law of X (particles move independently of the each other). Correction is done by modifying the mass of the particles according to the likelihood function associated to the next piece of observational data.…”

Section: Borel Function When X Is a Markov Process With Generator A mentioning

confidence: 99%

A particle approximation of the solution of the Kushner–Stratonovitch equation

Crisan¹,

Lyons²

1999

Probab Theory Relat Fields

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We construct a sequence of branching particle systems α n convergent in measure to the solution of the Kushner-Stratonovitch equation. The algorithm based on this result can be used to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n 1 4 . This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far. (1991): 93E11, 60G57, 65U05 Mathematics Subject Classification

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Section: Borel Function When X Is a Markov Process With Generator A mentioning

confidence: 99%

A particle approximation of the solution of the Kushner–Stratonovitch equation

Crisan¹,

Lyons²

1999

Probab Theory Relat Fields

View full text Add to dashboard Cite

show abstract

“…We are currently investigating rates of convergence and hope to report on this at a later date. However, if we contrast this approach with the one where particles are weighted with exponentials (the classical Monte Carlo method, see for instance [6], [17], [19]), we would point out two apparent advantages over this (largely disastrous) method. Firstly, all computations done are associated with particles that carry the same weighting ± one never ®nds oneself computing a trajectory that will obviously have a smaller weight than another.…”

Section: Constructing Particle Approximationsmentioning

confidence: 99%