# Online Joint State Inference and Learning of Partially Unknown State-Space Models

arXiv: https://arxiv.org/abs/2102.07418 · HTML: https://mlsanity.com/paper/2102.07418/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2021.

## Built on by (most cited first, 9 of 9)

- [Evaluation of Differentially Constrained Motion Models for Graph-Based Trajectory Prediction](https://mlsanity.com/paper/2304.05116/) (2023)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions](https://mlsanity.com/paper/2210.09168/) (2022)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Robust online joint state/input/parameter estimation of linear systems](https://mlsanity.com/paper/2204.05663/) (2022)
- [Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking over Wireless Sensor Networks](https://mlsanity.com/paper/2409.07652/) (2024)
- [Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices](https://mlsanity.com/paper/2408.02346/) (2024)
- [Adaptive Basis Function Selection for Computationally Efficient Predictions](https://mlsanity.com/paper/2408.07480/) (2024)

## Abstract (arXiv)

A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion representing unknown system dynamics and inherits properties from both physical and data-driven modeling. The method uses an extended Kalman filter approach to jointly estimate the state of the system and learn the unknown system dynamics, via the parameters of the basis function expansion. The key contribution is a computational complexity reduction compared to a similar approach with globally supported basis functions. By using compactly supported radial basis functions and an approximate Kalman gain, the computational complexity is considerably reduced and is essentially determined by the support of the basis functions. The approximation works well when the system dynamics exhibit limited correlation between points well separated in the state-space domain. The method is exemplified via two intelligent vehicle applications where it is shown to: (i) have competitive system dynamics estimation performance compared to the globally supported basis function method, and (ii) be real-time applicable to problems with a large-scale state-space.