Combining a Genetic Algorithm and Simulated Annealing to Design a Fixed‐Order Mixed H2/H∞ Deconvolution Filter with Missing Observations

We introduce a new combination approach to a fixed-order mixed H2/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 mixed H2/H∞ criterion is to achieve H2 optimal reconstruction and subject the H∞ 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