{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T05:01:54Z","timestamp":1789794114104,"version":"4.0.1"},"reference-count":28,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China under Grant","award":["2023YFB4704000."],"award-info":[{"award-number":["2023YFB4704000."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The conventional Kalman filter operates primarily in the original first-order state-prediction space, which limits the explicit utilization of higher-order state-coupling and predictive statistical structures. To enlarge the candidate prediction space, this study proposes a Prediction-Enhanced Polynomial Kalman Filter (PEPKF). Through Kronecker augmentation, the original one-step prediction is extended to second-, third-, and higher-order polynomial representation spaces, introducing nonlinear internal predictive transformations while preserving the linear physical state-space model. The resulting higher-order quantities are formulated as equivalent predictive pseudo-observations and fused with the original prediction through weighted least squares to construct an enhanced prior, followed by the standard Kalman measurement update. Numerical simulation results show that PEPKF achieves better state-estimation performance than the conventional KF, thereby demonstrating the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s26185871","type":"journal-article","created":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T13:50:27Z","timestamp":1789566627000},"page":"5871","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Prediction-Enhanced Polynomial Kalman Filter Using Higher-Order Predictive Representations for State Estimation"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-5554-8746","authenticated-orcid":false,"given":"Jing","family":"Long","sequence":"first","affiliation":[{"name":"College of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation and Intelligence, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenglin","family":"Wen","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Petrochemical Equipment Fault Diagnosis, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5246","DOI":"10.1109\/TVT.2019.2907696","article-title":"MME-EKF-based path-tracking control of autonomous vehicles considering input saturation","volume":"68","author":"Hu","year":"2019","journal-title":"IEEE Trans. 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