A parameter determination method of unscented transformation and its approximate ability analysis in the precision estimation of nonlinear measurement adjustment

Abstract

Unscented transformation (UT) is the key technology of unscented Kalman filter, which can approximate probability distribution to estimate second-order approximate mean and covariance matrix of nonlinear function. In parameter selection of various sampling strategies in the framework of the unscented transformation (UT), there are few studies on the determination method of sampling parameters. In this study, the particle swarm optimization (PSO) algorithm is introduced into UT for high convergence efficiency and few control parameters. The parameter selection of several commonly used sampling strategies is analyzed from the numerical point of view, and a method to determine the sampling parameters is proposed. Furthermore, the higher-order information ignored by the recommended parameters of UT is considered, and the approximation ability of UT is tapped and improved by the obtained parameters. For the first time, the minimal skew simplex sampling (MSS) and the scaled minimal skew simplex sampling (SMSS) are applied to the precision estimation of nonlinear measurement adjustment. Considering the influence of non-normal distribution data on nonlinear error propagation in geodetic measurement, this study analyzes the PSO-UT model in a case study from the geodetic field. Experiments show that PSO can effectively determine the parameters of UT and improve its approximation ability, which enriches UT theory.