Optimization Outperforms Unscented Techniques for Nonlinear Smoothing
Payton Howell, Aleksandr Aravkin
TL;DR
The paper addresses nonlinear smoothing by recasting the classic EKF smoother as a Gauss-Newton optimization on a MAP objective, $\min_x \frac{1}{2}\|G(x)\|^2_{Q^{-1}} + \frac{1}{2}\|H(x) - z\|^2_{R^{-1}}$, and compares the Optimized Kalman Smoother (OKS) with Unscented (UKS) and Extended (EKS) approaches. It shows that while all methods perform similarly in linear regimes, OKS delivers notable improvements in highly nonlinear, noisy settings, particularly when multiple GN iterations are employed. The experiments include an oracle-like parameter search over process and measurement noise to assess best-case performance, and demonstrate that OKS can robustly outperform UKS and EKS in nonlinear scenarios. The study highlights the practical value of optimization-based smoothing and points to data-driven tuning and joint state-parameter inference as promising future directions for real-world applications.
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.