Open Access

Multilevel Mixture Kalman Filter

EURASIP Journal on Advances in Signal Processing20042004:413780

Received: 30 April 2003

Published: 7 November 2004


The mixture Kalman filter is a general sequential Monte Carlo technique for conditional linear dynamic systems. It generates samples of some indicator variables recursively based on sequential importance sampling (SIS) and integrates out the linear and Gaussian state variables conditioned on these indicators. Due to the marginalization process, the complexity of the mixture Kalman filter is quite high if the dimension of the indicator sampling space is high. In this paper, we address this difficulty by developing a new Monte Carlo sampling scheme, namely, the multilevel mixture Kalman filter. The basic idea is to make use of the multilevel or hierarchical structure of the space from which the indicator variables take values. That is, we draw samples in a multilevel fashion, beginning with sampling from the highest-level sampling space and then draw samples from the associate subspace of the newly drawn samples in a lower-level sampling space, until reaching the desired sampling space. Such a multilevel sampling scheme can be used in conjunction with the delayed estimation method, such as the delayed-sample method, resulting in delayed multilevel mixture Kalman filter. Examples in wireless communication, specifically the coherent and noncoherent 16-QAM over flat-fading channels, are provided to demonstrate the performance of the proposed multilevel mixture Kalman filter.

Keywords and phrases

sequential Monte Carlomixture Kalman filtermultilevel mixture Kalman filterdelayed-sample method

Authors’ Affiliations

Department of Electrical Engineering, Columbia University, New York, USA
Department of Information and Decision Sciences, University of Illinois at Chicago, Chicago, USA
Department of Business Statistics & Econometrics, Peking University, Beijing, China


© Guo et al. 2004