# Bayesian Approach for Linear Optics Correction

## TL;DR

This paper introduces a Bayesian framework for linear optics correction in storage rings, enhancing existing algorithms with probabilistic modeling, regularization, and a novel method to resolve degenerated errors using select BPMs.

## Contribution

It presents a Bayesian-based correction algorithm with regularization and a new technique for resolving degenerated errors at specific BPMs, improving accuracy and robustness.

## Key findings

- The Bayesian approach can re-derive traditional correction algorithms.
- Regularization prevents overfitting in the correction process.
- A new method resolves degenerated errors using near-orthogonal response vectors.

## Abstract

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions". Under some assumptions, the least square algorithm and then the Jacobian matrix approach can be re-derived. The coherence of the correction algorithm is ensured through specifying a self-consistent regularization coefficient to prevent overfitting. Optimal weights for different correction objectives are obtained based on their measurement noise level. A new technique has been developed to resolve degenerated quadrupole errors when observed at a few select BPMs. A necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near-orthogonal.