# Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systems

arXiv: https://arxiv.org/abs/1504.06173 · HTML: https://mlsanity.com/paper/1504.06173/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2015.

## Built on by (most cited first, 6 of 6)

- [Reactive Message Passing for Scalable Bayesian Inference](https://mlsanity.com/paper/2112.13251/) (2021)
- [Projective Integral Updates for High-Dimensional Variational Inference](https://mlsanity.com/paper/2301.08374/) (2023)
- [The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling](https://mlsanity.com/paper/2605.31547/) (2026)
- [Uncertainty-Aware Task Allocation for Distributed Autonomous Robots](https://mlsanity.com/paper/2107.10350/) (2021)
- [Coordinate ascent neural Kalman-MLE for state estimation](https://mlsanity.com/paper/2511.01855/) (2025)
- [A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements](https://mlsanity.com/paper/2606.31137/) (2026)

## Abstract (arXiv)

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the maximization step in a class of models that are linear in parameters and have additive noise. To obtain approximations to the filtering and smoothing distributions needed in the likelihood-maximization methods, we focus on using Gaussian filtering and smoothing algorithms that employ sigma-points to approximate the required integrals. We discuss different sigma-point schemes based on the third, fifth, seventh, and ninth order unscented transforms and the Gauss--Hermite quadrature rule. We compare the performance of the methods in two simulated experiments: a univariate nonlinear growth model as well as tracking of a maneuvering target. In the experiments, we also compare against approximate likelihood estimates obtained by particle filtering and extended Kalman filtering based methods. The experiments suggest that the higher-order unscented transforms may in some cases provide more accurate estimates