Single-replicate longitudinal data analysis in the presence of multiple instrumental measurement errors

•A novel method as a combination of the EM algorithm and Variogram is proposed.•Method decomposes the longitudinal measurement errors in the absence of replication.•Multiple measurements are considered where the units are observed by several gauges.•Proposed model is validated based on simulated longitudinal data and a real case.•The robustness of the proposed method to the missing values is also demonstrated.