# Sigma-point Kalman Filter with Nonlinear Unknown Input Estimation via Optimization and Data-driven Approach for Dynamic Systems

arXiv: https://arxiv.org/abs/2306.12361 · HTML: https://mlsanity.com/paper/2306.12361/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 38 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Robust Unscented Kalman Filtering via Recurrent Meta-Adaptation of Sigma-Point Weights](https://mlsanity.com/paper/2603.04360/) (2026)
- [Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators](https://mlsanity.com/paper/2606.14195/) (2026)

## Abstract (arXiv)

Most works on joint state and unknown input (UI) estimation require the assumption that the UIs are linear; this is potentially restrictive as it does not hold in many intelligent autonomous systems. To overcome this restriction and circumvent the need to linearize the system, we propose a derivative-free Unknown Input Sigma-point Kalman Filter (SPKF-nUI) where the SPKF is interconnected with a general nonlinear UI estimator that can be implemented via nonlinear optimization and data-driven approaches. The nonlinear UI estimator uses the posterior state estimate which is less susceptible to state prediction error. In addition, we introduce a joint sigma-point transformation scheme to incorporate both the state and UI uncertainties in the estimation of SPKF-nUI. An in-depth stochastic stability analysis proves that the proposed SPKF-nUI yields exponentially converging estimation error bounds under reasonable assumptions. Finally, two case studies are carried out on a simulation-based rigid robot and a physical soft robot, i.e., robots made of soft materials with complex dynamics to validate effectiveness of the proposed filter on nonlinear dynamic systems. Our results demonstrate that the proposed SPKF-nUI achieves the lowest state and UI estimation errors when compared to the existing nonlinear state-UI filters.