Systematic Estimation of Noise Statistics for Nonlinear Kalman Filters

Abstract

We propose two new systematic and easy-to-implement online tuning strategies for nonlinear Kalman filters with low computational cost. The tuning strategies assume the process and measurement noise are due to parametric uncertainty. We assume nθ uncertain parameters which are translated into noise statistics by either i) generalized unscented transformation with 2nθ extra online model evaluations at every time step or ii) latin hypercube sampling, where the user sets the number of samples. Both approaches are distribution free, hence, the tuning strategies work for all kind of distributions. In the case study, it was found that the two proposed tuning strategies outperform the standard approach of fixed, diagonal noise matrices. In the case study, we further found that tuning based on the generalized unscented transformation seems to be more consistent than the method based on latin hypercube sampling for the same online computational cost. In addition, a Monte Carlo based tuning with modal noise adjustment is tested with promising performance. The modal noise adjustment is interesting as we can estimate the most likely point value of the noise (the mode of the noise distribution) and add this term to the state- and measurement equations at every time step.