Regularized Optimal Transport Based on an Adaptive Adjustment Method for Selecting the Scaling Parameters of Unscented Kalman Filters

Abstract

In this paper, an adaptation method for adjusting the scaling parameters of an unscented Kalman filter (UKF) is proposed to improve the estimation performance of the filter in dynamic conditions. The proposed adaptation method is based on a sequential algorithm that selects the scaling parameter using the user-defined distribution of discrete sets to more effectively deal with the changing measurement distribution over time and avoid the additional process for training a filter model. The adaptation method employs regularized optimal transport (ROT), which compensates for the error of the predicted measurement with the current measurement values to select the proper scaling parameter. In addition, the Sinkhorn–Knopp algorithm is used to minimize the cost function of ROT due to its fast convergence rate, and the convergence of the proposed ROT-based adaptive adjustment method is also analyzed. According to the analysis results of Monte Carlo simulations, it is confirmed that the proposed algorithm shows better performance than the conventional algorithms in terms of the scaling parameter selection in the UKF.