{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:17:59Z","timestamp":1760235479679,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T00:00:00Z","timestamp":1629849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NASA","award":["80NSSC19P1369"],"award-info":[{"award-number":["80NSSC19P1369"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are affected by zero-mean Gaussian errors. These tools consist of: (1) the analytical derivation of the gravity direction expectation and its covariance matrix, and (2) a continuous description of the geoid model correction as a linear combination of a set of orthogonal surfaces. The accuracy of the statistical quantities is validated by extensive Monte Carlo tests and the application in an Extended Kalman Filter (EKF) has been included. The continuous geoid description is needed as the geoid represents the true gravity direction. These tools can be implemented in any problem requiring high-precision estimates of the local gravity direction.<\/jats:p>","DOI":"10.3390\/s21175727","type":"journal-article","created":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T23:25:50Z","timestamp":1629933950000},"page":"5727","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0787-4547","authenticated-orcid":false,"given":"Daniele","family":"Mortari","sequence":"first","affiliation":[{"name":"Aerospace Engineering, Texas A&M University, 746C H.R. Bright Building, 3141 TAMU, College Station, TX 77843-3141, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anthony","family":"Gardner","sequence":"additional","affiliation":[{"name":"Aerospace Engineering, Texas A&M University, 746C H.R. Bright Building, 3141 TAMU, College Station, TX 77843-3141, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"\u0141uczak, S., and Ekwi\u0144ska, M. (2021). Electric-Contact Tilt Sensors: A Review. Sensors, 21.","DOI":"10.3390\/s21041097"},{"key":"ref_2","unstructured":"Sun, H., and Deng, X. (2015). Accuracy analysis of inclinometer in slope monitoring. Hydropower Autom. Dam. 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