Comparison of methods for covariance estimation for factor graph optimization of the Bayesian estimation problem

Abstract

Factor graphs optimization is becoming a common approach to states and parameters estimation in navigation tasks due to the simplicity of the system description and combining various measurement sources, as well as the high accuracy of estimates. To obtain the best estimate, it is necessary that the noise covariance matrices of the corresponding measurements are known a priori. However, in practice, this is very difficult to achieve due to the complexity of methods for estimating noise parameters and the non-stationarity of these parameters, which may require the evaluation or correction of the covariance matrices used. Recently, several approaches have been presented to obtain an estimate of the covariance matrix in relation to factor graph optimization, but no comparison has been made with other approaches. This paper is devoted to comparing two methods for estimating measurement and system noise covariance matrices. First is a factor graph method where both covariances and state vector are estimated using algorithms based on factor graph, second is a combined Bayesian – factor graph method where a sequential nonlinear Bayesian algorithm is used to estimate covariances and factor graph is used to estimate the state vector. The following metrics were used for comparison: the mathematical expectation and the standard deviation of the estimates of covariance, and a coefficient of accuracy of the system state estimates with the obtained estimates of covariance.