The task of inertial sensor calibration has become increasingly important due to the growing use of low-cost inertial measurement units which are however characterized by measurement errors. Being widely employed in a variety of mass-market applications, there is considerable focus on compensating for these errors by taking into account the deterministic and stochastic factors that characterize them. In this paper we focus on the stochastic part of the error signal where it is customary to register the latter and use the observed error signal to identify and estimate the stochastic models, often complex in nature, that underlie this process. However, it is often the case that these error signals are observed through a series of replicates for the same inertial sensor and equally often it can be noticed that these replicates have the same model structure but their parameters appear to be different between replicates. This phenomenon has not been taken into account by current stochastic calibration procedures which therefore can be conditioned by flawed parameter estimation. For this reason, this paper aims at delivering an approach that takes into account the parameter variation between replicates by delivering an estimator that minimizes a loss function that considers each replicate, thereby improving measurement precision on the long run, and allows to build a statistical test to determine the presence of parameter variation between replicates.