# On Kernel Design for Regularized Non-Causal System Identification

arXiv: https://arxiv.org/abs/2307.13999 · HTML: https://mlsanity.com/paper/2307.13999/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator](https://mlsanity.com/paper/2503.11854/) (2025)

## Abstract (arXiv)

Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its application in the non-causal system identification, and the key issue lies in the design and analysis of kernels for non-causal systems. In this paper, we develop systematic ways to deal with this issue. In particular, we first introduce the guidelines for kernel design and then extend the system theoretic framework to design the so-called non-causal simulation-induced (NCSI) kernel, and we also study its structural properties, including stability and semiseparability. Finally, we consider some special cases of the NCSI kernel and show their advantage over the existing kernels through numerical simulations.