{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T10:03:43Z","timestamp":1767261823612,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T00:00:00Z","timestamp":1737072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces a novel robust Kalman filter designed to leverage symmetrical properties within the Pearson Type VII-Inverse Wishart (PVIW) distribution, enhancing state estimation accuracy in the presence of time-varying biases and non-stationary heavy-tailed (NSHT) noise. The filter includes a shape parameter from the normal distribution and an extra variable from the Gamma distribution, which are used to symmetrically adjust the average and variation measures of the data to fit better under difficult noise conditions. To deal with unknown noise that changes over time, the filter uses the Inverse Wishart distribution to model and estimate the scale matrix deviations, making it easier to adapt to changes. The filter also uses a technique called Variational Bayesian to estimate both the state and the parameters at the same time. The results from simulations show that this new filter greatly improves the accuracy and strength of the estimation compared to the usual Kalman filters that assume a normal distribution, especially when there is non-stationary heavy-tailed noise. The main objective is to improve estimation in signal processing and control systems where heavy-tailed noise is prevalent.<\/jats:p>","DOI":"10.3390\/sym17010135","type":"journal-article","created":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T10:27:58Z","timestamp":1737109678000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Robust Kalman Filter Based on the Pearson Type VII-Inverse Wishart Distribution: Symmetrical Treatment of Time-Varying Measurement Bias and Heavy-Tailed Noise"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0167-5740","authenticated-orcid":false,"given":"Shen","family":"Liang","sequence":"first","affiliation":[{"name":"School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Jiangsu Automation Research Institute, Lianyungang 222000, China"}]},{"given":"Xun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Jiangsu Automation Research Institute, Lianyungang 222000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,17]]},"reference":[{"key":"ref_1","first-page":"41","article-title":"An introduction to the kalman filter","volume":"8","author":"Bishop","year":"2001","journal-title":"Proc. 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