{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:22:48Z","timestamp":1777656168319,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2012,6,25]],"date-time":"2012-06-25T00:00:00Z","timestamp":1340582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper a quaternion-based Variable-State-Dimension Extended Kalman Filter (VSD-EKF) is developed for estimating the three-dimensional orientation of a rigid body using the measurements from an Inertial Measurement Unit (IMU) integrated with a triaxial magnetic sensor. Gyro bias and magnetic disturbances are modeled and compensated by including them in the filter state vector. The VSD-EKF switches between a quiescent EKF, where the magnetic disturbance is modeled as a first-order Gauss-Markov stochastic process (GM-1), and a higher-order EKF where extra state components are introduced to model the time-rate of change of the magnetic field as a GM-1 stochastic process, namely the magnetic disturbance is modeled as a second-order Gauss-Markov stochastic process (GM-2). Experimental validation tests show the effectiveness of the VSD-EKF, as compared to either the quiescent EKF or the higher-order EKF when they run separately.<\/jats:p>","DOI":"10.3390\/s120708491","type":"journal-article","created":{"date-parts":[[2012,6,25]],"date-time":"2012-06-25T16:55:20Z","timestamp":1340643320000},"page":"8491-8506","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Variable-State-Dimension Kalman-Based Filter for Orientation Determination Using Inertial and Magnetic Sensors"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3306-6498","authenticated-orcid":false,"given":"Angelo Maria","family":"Sabatini","sequence":"first","affiliation":[{"name":"The BioRobotics Institute, Scuola Superiore Sant\u2019Anna, Piazza Martiri della Libert\u00e0 33, Pisa 56127, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,6,25]]},"reference":[{"key":"ref_1","unstructured":"Stanney, K.M. 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