{"title":"A numerically stable unscented transformation with optimal tuning parameters for high-dimensional systems","authors":"H.A. Krog, J. Jäschke","doi":"10.1016/j.jprocont.2025.103406","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents a new formulation for an unscented transformation for high-dimensional systems using the optimal tuning parameter for a symmetric random variable. The standard unscented transformation with optimal tuning parameters is known to be numerically unstable for high-dimensional systems. In this contribution, we show how to reformulate a high-dimensional (unstable) unscented transformation to a sum of one-dimensional (stable) unscented transformations. Our reformulation increases estimation accuracy since it allows for using the optimal tuning parameters. These benefits are shown theoretically and on several examples, where one example has a state dimension of <span><math><msup><mrow><mn>10</mn></mrow><mrow><mn>5</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"150 ","pages":"Article 103406"},"PeriodicalIF":3.9000,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Process Control","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0959152425000344","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents a new formulation for an unscented transformation for high-dimensional systems using the optimal tuning parameter for a symmetric random variable. The standard unscented transformation with optimal tuning parameters is known to be numerically unstable for high-dimensional systems. In this contribution, we show how to reformulate a high-dimensional (unstable) unscented transformation to a sum of one-dimensional (stable) unscented transformations. Our reformulation increases estimation accuracy since it allows for using the optimal tuning parameters. These benefits are shown theoretically and on several examples, where one example has a state dimension of .
期刊介绍：
This international journal covers the application of control theory, operations research, computer science and engineering principles to the solution of process control problems. In addition to the traditional chemical processing and manufacturing applications, the scope of process control problems involves a wide range of applications that includes energy processes, nano-technology, systems biology, bio-medical engineering, pharmaceutical processing technology, energy storage and conversion, smart grid, and data analytics among others.
Papers on the theory in these areas will also be accepted provided the theoretical contribution is aimed at the application and the development of process control techniques.
Topics covered include:
• Control applications• Process monitoring• Plant-wide control• Process control systems• Control techniques and algorithms• Process modelling and simulation• Design methods
Advanced design methods exclude well established and widely studied traditional design techniques such as PID tuning and its many variants. Applications in fields such as control of automotive engines, machinery and robotics are not deemed suitable unless a clear motivation for the relevance to process control is provided.
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