I would first try with a hierarchical normal model with the target location model as a latent mean \mu, and each observation (from one user) model as \mu_{user} \sim \text{Normal}(\mu, \sigma). If you take multiple measurements from each user you can model individual \sigma for each user (e.g., \sigma_{user} \sim \text{HalfNormal()}), otherwise either a fixed value or scaler parameter for \sigma will do.