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

Table 1

Filter style.

Method	Missing probability	Filter style	Deconvolution filter
Proposed method	𝑝=0.9	IIR(2)	𝐷1=0.4446−0.0194𝑧^−1+0.0348𝑧^−21+0.7627𝑧^−1+0.268𝑧^−2
		FIR(10)	𝐷2=0.3718−0.2672𝑧^−1+0.1542𝑧^−2−0.0365𝑧^−3+0.0388𝑧^−4+0.0449𝑧^−5−0.0003𝑧^−6−0.0409𝑧^−7+0.0653𝑧^−8−0.0366𝑧^−9+0.0824𝑧^−10
	𝑝=0.8	IIR(2)	𝐷3=0.3483−0.0108𝑧^−1+0.0609𝑧^−21+0.3667𝑧^−1+0.383𝑧^−2
		FIR(10)	𝐷4=0.2271−0.1437𝑧^−1+0.0027𝑧^−2+0.0588𝑧^−3+0.0203𝑧^−4−0.0693𝑧^−5+0.0308𝑧^−6+0.0422𝑧^−7−0.0297𝑧^−8+0.0719𝑧^−9−0.0161𝑧^−10
	𝑝=0.7	IIR(2)	𝐷5=0.3115−0.01874𝑧^−1+0.0255𝑧^−21+0.2714𝑧^−1+0.091𝑧^−2
		FIR(10)	𝐷6=0.2686−0.0925𝑧^−1−0.098𝑧^−2+0.1106𝑧^−3−0.0337𝑧^−4−0.0081𝑧^−5+0.0976𝑧^−6+0.0208𝑧^−7−0.001𝑧^−8+0.0289𝑧^−9+0.04𝑧^−10
MMSE [4]	Not missing	IIR(3)	𝐷7=1.11+0.7737𝑧^−1−0.0111𝑧^−2−0.77𝑧^−31.1+2.42𝑧^−1+1.727𝑧^−2+0.39𝑧^−3
SA with initial = 1−1𝑧^−1+0.25𝑧^−21−1𝑧^−1+0.25𝑧^−2	𝑝=0.9	IIR(2)	𝐷8=0.4233+0.0269𝑧^−1+0.0393𝑧^−21+0.787𝑧^−1+0.0393𝑧^−2
	𝑝=0.8	IIR(2)	𝐷9=0.2370−0.4954𝑧^−1+0.1406𝑧^−21−0.7008𝑧^−1−0.1758𝑧^−2
	𝑝=0.7	IIR(2)	𝐷10=0.5189−0.5675𝑧^−1−0.0823𝑧^−21−0.5675𝑧^−1−0.0823𝑧^−2