Maximum likelihood recursive state estimation: An incomplete-information based approach

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-08-02 DOI:10.1016/j.automatica.2024.111820

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引用次数: 0

Abstract

This paper revisits classical work of Rauch et al. (1965) and develops a novel statistical method for maximum likelihood (ML) recursive state estimation in general state–space models. The new method is based on statistical estimation theory for incomplete information, which has been well developed primarily for ML parameter estimation (Dempster et al., 1977). Distributional identities for the posterior score function and information matrix of state are established. Using these identities, a fast convergent EM-gradient algorithm is proposed, extending the Lange (1995) algorithm for ML recursive state estimation. It revisits and provides an improvement to the EM-algorithm of Ramadan and Bitmead (2022). An explicit form of the information matrix is developed to provide empirical estimates of the standard errors. Sequential Monte Carlo method is used for the valuation of the score function, information and posterior covariance matrices. Some numerical examples are discussed to exemplify the main results.

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最大似然递归状态估计：基于不完全信息的方法

本文重温了 Rauch 等人（1965 年）的经典工作，并为一般状态空间模型中的最大似然（ML）递归状态估计开发了一种新的统计方法。新方法基于不完全信息统计估计理论，该理论主要针对 ML 参数估计（Dempster 等人，1977 年）。该方法建立了状态的后验得分函数和信息矩阵的分布式等式。利用这些特性，提出了一种快速收敛的 EM 梯度算法，扩展了 Lange（1995 年）的 ML 递归状态估计算法。它重新审视并改进了 Ramadan 和 Bitmead（2022 年）的 EM 算法。开发了信息矩阵的显式形式，以提供标准误差的经验估计值。顺序蒙特卡罗法用于评估得分函数、信息和后验协方差矩阵。讨论了一些数值示例，以举例说明主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.

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