TUTCRIS - Tampereen teknillinen yliopisto

TUTCRIS

On the convergence of the Gaussian mixture filter

Tutkimustuotos

Standard

On the convergence of the Gaussian mixture filter. / Ali-Löytty, S.

Tampere : Unknown Publisher, 2008. 16 s. (Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti; Vuosikerta 89).

Tutkimustuotos

Harvard

Ali-Löytty, S 2008, On the convergence of the Gaussian mixture filter. Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti, Vuosikerta. 89, Unknown Publisher, Tampere.

APA

Ali-Löytty, S. (2008). On the convergence of the Gaussian mixture filter. (Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti; Vuosikerta 89). Tampere: Unknown Publisher.

Vancouver

Ali-Löytty S. On the convergence of the Gaussian mixture filter. Tampere: Unknown Publisher, 2008. 16 s. (Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti).

Author

Ali-Löytty, S. / On the convergence of the Gaussian mixture filter. Tampere : Unknown Publisher, 2008. 16 Sivumäärä (Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti).

Bibtex - Lataa

@book{e0d3b74d79a646fc9110c06406925e44,
title = "On the convergence of the Gaussian mixture filter",
abstract = "This paper presents convergence results for the Box Gaussian Mixture Filter (BGMF). BGMF is a Gaussian Mixture Filter (GMF) that is based on a bank of Extended Kalman Filters. The critical part of GMF is the approximation of probability density function (pdf) as pdf of Gaussian mixture such that its components have small enough covariance matrices. Because GMF approximates prior and posterior as Gaussian mixture it is enough if we have a method to approximate arbitrary Gaussian (mixture) as a Gaussian mixture such that the components have small enough covariance matrices. In this paper, we present the Box Gaussian Mixture Approximation (BGMA) that partitions the state space into specific boxes and matches weights, means and covariances of the original Gaussian in each box to a GM approximation. If the original distribution is Gaussian mixture, BGMA does this approximation separately for each component of the Gaussian mixture. We show that BGMA converges weakly to the original Gaussian (mixture). When we apply BGMA in a Gaussian mixture filtering framework we get BGMF. We show that GMF, and also BGMF, converges weakly to the correct/exact posterior distribution.",
author = "S. Ali-L{\"o}ytty",
note = "Contribution: organisation=mat,FACT1=1",
year = "2008",
language = "English",
isbn = "978-952-15-2097-6",
series = "Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti",
publisher = "Unknown Publisher",

}

RIS (suitable for import to EndNote) - Lataa

TY - BOOK

T1 - On the convergence of the Gaussian mixture filter

AU - Ali-Löytty, S.

N1 - Contribution: organisation=mat,FACT1=1

PY - 2008

Y1 - 2008

N2 - This paper presents convergence results for the Box Gaussian Mixture Filter (BGMF). BGMF is a Gaussian Mixture Filter (GMF) that is based on a bank of Extended Kalman Filters. The critical part of GMF is the approximation of probability density function (pdf) as pdf of Gaussian mixture such that its components have small enough covariance matrices. Because GMF approximates prior and posterior as Gaussian mixture it is enough if we have a method to approximate arbitrary Gaussian (mixture) as a Gaussian mixture such that the components have small enough covariance matrices. In this paper, we present the Box Gaussian Mixture Approximation (BGMA) that partitions the state space into specific boxes and matches weights, means and covariances of the original Gaussian in each box to a GM approximation. If the original distribution is Gaussian mixture, BGMA does this approximation separately for each component of the Gaussian mixture. We show that BGMA converges weakly to the original Gaussian (mixture). When we apply BGMA in a Gaussian mixture filtering framework we get BGMF. We show that GMF, and also BGMF, converges weakly to the correct/exact posterior distribution.

AB - This paper presents convergence results for the Box Gaussian Mixture Filter (BGMF). BGMF is a Gaussian Mixture Filter (GMF) that is based on a bank of Extended Kalman Filters. The critical part of GMF is the approximation of probability density function (pdf) as pdf of Gaussian mixture such that its components have small enough covariance matrices. Because GMF approximates prior and posterior as Gaussian mixture it is enough if we have a method to approximate arbitrary Gaussian (mixture) as a Gaussian mixture such that the components have small enough covariance matrices. In this paper, we present the Box Gaussian Mixture Approximation (BGMA) that partitions the state space into specific boxes and matches weights, means and covariances of the original Gaussian in each box to a GM approximation. If the original distribution is Gaussian mixture, BGMA does this approximation separately for each component of the Gaussian mixture. We show that BGMA converges weakly to the original Gaussian (mixture). When we apply BGMA in a Gaussian mixture filtering framework we get BGMF. We show that GMF, and also BGMF, converges weakly to the correct/exact posterior distribution.

M3 - Commissioned report

SN - 978-952-15-2097-6

T3 - Tampereen teknillinen yliopisto. Matematiikan laitos. Tutkimusraportti

BT - On the convergence of the Gaussian mixture filter

PB - Unknown Publisher

CY - Tampere

ER -