A Statistical Model of Gross Errors and Model Parameters Estimation

Abstract

Abstract This contribution introduces a statistical model of gross errors, which is called the Bernoulli-Gaussian (BG) model, where the gross error consists of the product of a Bernoulli variable and a Gaussian variable. First, with the BG model, different causes of outliers can be interpreted from the perspective of gross errors. As well, the commonly used observation models, such as the mean shift model and variance inflation model, can be unified by the BG model, via choosing different values range of model parameters. Second, based on the EM (expectation maximization) algorithm, the estimation method of BG model parameters for linear observation equations is proposed. With this method, the BG model parameters can be estimated in both a static observation system and a dynamic observation system. Finally, normal sample examples and GNSS examples proved that it is effective in estimating the BG model parameters via the the EM algorithm.