Angular random walk and rate random walk are two dominant random noise components which are inherent in almost gyroscopes. Therefore, modelling these noise components accurately is very important. Here, a modified algorithm is proposed for estimating the two random noise components accurately. Up to now, the statistical modelling of the two random noise components has been conducted by the best linear unbiased estimator, which is based on the formulae for mean, variance and covariance of non‐overlapping Allan variance of them, that is, angular random walk and rate random walk. The modified algorithm is developed by using the best linear unbiased estimator, based on formulae for mean, variance and covariance of fully‐overlapping Allan variance which are newly derived in this paper. Efficiency of the algorithm is evaluated by simulation and experiment.