In this paper we address the problem of state observation of linear time-varying (LTV) systems with delayed measurements, which has attracted the attention of many researchers—see Sanz et al. (2019) and references therein. We show that, the parameter estimation-based observer (PEBO) design proposed in Ortega et al., 2021, Ortega et al., 2015 provides a very simple solution to the problem with reduced prior knowledge. Moreover, when PEBO is combined with the dynamic regressor extension and mixing (DREM) estimation technique (Aranovskiy et al., 2017, Ortega et al., 2019), the estimated state converges in fixed-time with extremely weak excitation assumptions.