6 research outputs found
Recommended from our members
Editorial.
RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are
Lookahead Strategies for Sequential Monte Carlo
Based on the principles of importance sampling and resampling, sequential
Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with
complex stochastic dynamic systems. Many of these systems possess strong
memory, with which future information can help sharpen the inference about the
current state. By providing theoretical justification of several existing
algorithms and introducing several new ones, we study systematically how to
construct efficient SMC algorithms to take advantage of the "future"
information without creating a substantially high computational burden. The
main idea is to allow for lookahead in the Monte Carlo process so that future
information can be utilized in weighting and generating Monte Carlo samples, or
resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multilevel Mixture Kalman Filter
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