Optimization Outperforms Unscented Techniques for Nonlinear Smoothing

Abstract

We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least squares maximum a posteriori loss, and stabilized with standard globalization techniques. We compare the performance of the Optimized Kalman Smoother (OKS) to Unscented Kalman smoothing techniques, and show that they achieve significant improvement for highly nonlinear systems, particularly in noisy settings. The comparison is performed across standard parameter choices (such as the trade-off between process and measurement terms). To our knowledge, this is the first comparison of these methods in the literature.