Bernoulli–Gaussian Model with Model Parameter Estimation

Abstract

First, this paper introduces a statistical model of gross errors, namely the Bernoulli–Gaussian (BG) model, which characterizes the gross error as a product of a Bernoulli variable and a Gaussian variable. The BG model offers a framework to interpret various causes of outliers through the perspective of gross errors. In addition, it unifies commonly used observation models for outliers by adjusting the range of BG model parameters. Second, this paper proposes an estimation method for BG model parameters based on the expectation maximization (EM) algorithm. This approach attributes different gross error parameters for distinct types of observations, facilitating parameter estimation in both single-source and multisource observation systems. Additionally, by organizing equations in the form of individual observations, its applicability can be broadened to both static and dynamic scenarios. Finally, a normal sample example and a Global Navigation Satellite System (GNSS) positioning example verified the effectiveness of the proposed method for estimating the BG model parameters.