# On kernel design for regularized LTI system identification

arXiv: https://arxiv.org/abs/1612.03542 · HTML: https://mlsanity.com/paper/1612.03542/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2016.

## Built on by (most cited first, 8 of 8)

- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Modelling Non-Smooth Signals with Complex Spectral Structure](https://mlsanity.com/paper/2203.06997/) (2022)
- [Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator](https://mlsanity.com/paper/2503.11854/) (2025)
- [Infinite-Dimensional Sparse Learning in Linear System Identification](https://mlsanity.com/paper/2203.14731/) (2022)
- [Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters](https://mlsanity.com/paper/2303.09842/) (2023)
- [Randomized Atomic Feature Models for Physics-Informed Identification of Dynamic Systems](https://mlsanity.com/paper/2605.14351/) (2026)
- [XMSE-Aware Adaptive Empirical Bayes Estimation](https://mlsanity.com/paper/2606.26975/) (2026)
- [On the Sequentially Semiseparable Structure of SDE-Induced Kernels and Efficient Algorithms for Kernel-Based Estimation Problems](https://mlsanity.com/paper/2610.05856/) (2026)

## Abstract (arXiv)

There are two key issues for the kernel-based regularization method: one is how to design a suitable kernel to embed in the kernel the prior knowledge of the LTI system to be identified, and the other one is how to tune the kernel such that the resulting regularized impulse response estimator can achieve a good bias-variance tradeoff. In this paper, we focus on the issue of kernel design. Depending on the type of the prior knowledge, we propose two methods to design kernels: one is from a machine learning perspective and the other one is from a system theory perspective. We also provide analysis results for both methods, which not only enhances our understanding for the existing kernels but also directs the design of new kernels.