a24f01d3-4349-4e66-9870-5a41f304a0c720220320041406861wseas:wseasmdt@crossref.orgMDT DepositEQUATIONS10.37394/232021https://wseas.com/journals/equations/112021112021110.37394/232021.2021.1https://wseas.com/journals/equations/2021.phpSnunyiZhaoJiangnan University Institute of Automation 214122, Wuxi P.R.CHINAYuriyShmaliyUniversidad de Guanajuato Electronics Engineering Dept. 36885, Salamanca MEXICOSanowarKhanCity University London Electronics Engineering Dept. EC1V 0HB, London UKIn this paper, we give an analysis of the embedded unbiasedness (EU) on optimal finite impulse response (OFIR) estimates. By minimizing the mean square error (MSE) constrained by the unbiasedness condition, a new OFIR-EU filter is derived. We show that the OFIR-EU filter does not require the initial conditions, and occupies an intermediate place between the UFIR and OFIR filters. It is also shown that the MSEs of the OFIR-EU and OFIR filters diminish with the estimation horizon. 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