Combining a Genetic Algorithm and Simulated Annealing to Design a Fixed-Order MixedH2/H∞Deconvolution Filter with Missing Observations

Jui-Chung Hung

doi:10.1155/2008/530803

Abstract

We introduce a new combination approach to a fixed-order mixedH2/H∞deconvolution filter with missing observations. The missing observations model is based on a probabilistic structure with the probability of the occurrence of missing data modeled as the unknown prior. The aim of the mixedH2/H∞criterion is to achieveH2optimal reconstruction and subject theH∞norm constraint to the transfer function from the channel input to the filter error. For simplicity of implementation, the fixed-order model is interesting for engineers in signal processing and in practical applications. In this situation, the deconvolution filter design becomes a complicated nonlinear estimation problem. In this paper, we combine a genetic algorithm (GA) and simulated annealing (SA) to treat the signal reconstruction problem with missing observations. Finally, a numerical example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.

Highlights

A deconvolution filter is used to remove the distortion of a channel and suppress the influence of additive noise in the transmission path
The proposed mixed H2/H∞ optimal deconvolution filter design minimizes H2 reconstruction performance subject to a robustness requirement based on the H∞ norm to attenuate the performance degradation due to the system’s uncertainty [8]
We describe the genetic algorithm in the subsection [14]

Summary

Introduction

A deconvolution filter is used to remove the distortion of a channel and suppress the influence of additive noise in the transmission path. The proposed mixed H2/H∞ optimal deconvolution filter design minimizes H2 reconstruction performance subject to a robustness requirement based on the H∞ norm to attenuate the performance degradation due to the system’s uncertainty [8]. Kirkpatrick et al [16] found the analogy between minimizing the cost function of a combinatorial optimization problem and the slow cooling of a solid until it reaches its low-energy ground state. They found that the optimization process can be realized by applying the metropolis algorithm, by substituting cost for energy, configuration for state and viewing temperature as a control parameter. The statistical distribution of energies allows the system to escape from a local energy minimum

Objectives

Methods

Conclusion