Adaptive Quasi-Monte Carlo method for nonlinear function error propagation and its application in geodetic measurement

Abstract

The standard deviation of the nonlinear functional value can be obtained by the law of covariance propagation. Existing covariance propagation methods of the nonlinear model contain the following problems: the approximate function method requires complicated derivative operation; the Monte Carlo method has a high simulated burden and low convergence effectiveness. To overcome these disadvantages, we introduce the Quasi-Monte Carlo (QMC) method and design the implementation process of the QMC method for covariance propagation with independent or correlated observations. Considering that the QMC method cannot balance the number of simulations and the accuracy of the results, a novel QMC algorithm for small numbers of batches simulation is proposed, namely, Adaptive Quasi-Monte Carlo (AQMC). The QMC method and the AQMC algorithm are applied in the forward intersection and covariance propagation of the GNSS baseline vector in geodetic measurement. The results verify the effectiveness of the QMC method and the AQMC algorithm. Compared with the adaptive Monte Carlo method, the AQMC method can improve the computational efficiency by almost 84.4%. The proposed approach provides a new idea for the covariance propagation of the nonlinear model.