{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T18:34:50Z","timestamp":1779042890348,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T00:00:00Z","timestamp":1422835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014809","name":"TACR","doi-asserted-by":"publisher","award":["TA02011092"],"award-info":[{"award-number":["TA02011092"]}],"id":[{"id":"10.13039\/100014809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Grant Agency of the Czech Technical University in Prague","award":["SGS13\/144\/OHK3\/2T\/13"],"award-info":[{"award-number":["SGS13\/144\/OHK3\/2T\/13"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>MEMS (micro-electro-mechanical system)-based inertial sensors, i.e., accelerometers and angular rate sensors, are commonly used as a cost-effective solution for the purposes of navigation in a broad spectrum of terrestrial and aerospace applications. These tri-axial inertial sensors form an inertial measurement unit (IMU), which is a core unit of navigation systems. Even if MEMS sensors have an advantage in their size, cost, weight and power consumption, they suffer from bias instability, noisy output and insufficient resolution. Furthermore, the sensor\u2019s behavior can be significantly affected by strong vibration when it operates in harsh environments. All of these constitute conditions require treatment through data processing. As long as the navigation solution is primarily based on using only inertial data, this paper proposes a novel concept in adaptive data pre-processing by using a variable bandwidth filtering. This approach utilizes sinusoidal estimation to continuously adapt the filtering bandwidth of the accelerometer\u2019s data in order to reduce the effects of vibration and sensor noise before attitude estimation is processed. Low frequency vibration generally limits the conditions under which the accelerometers can be used to aid the attitude estimation process, which is primarily based on angular rate data and, thus, decreases its accuracy. In contrast, the proposed pre-processing technique enables using accelerometers as an aiding source by effective data smoothing, even when they are affected by low frequency vibration. Verification of the proposed concept is performed on simulation and real-flight data obtained on an ultra-light aircraft. The results of both types of experiments confirm the suitability of the concept for inertial data pre-processing.<\/jats:p>","DOI":"10.3390\/s150203282","type":"journal-article","created":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T10:27:36Z","timestamp":1422872856000},"page":"3282-3298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Adaptive Data Filtering of Inertial Sensors with  Variable Bandwidth"],"prefix":"10.3390","volume":"15","author":[{"given":"Mushfiqul","family":"Alam","sequence":"first","affiliation":[{"name":"Department of Measurement, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Prague 16627, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Rohac","sequence":"additional","affiliation":[{"name":"Department of Measurement, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Prague 16627, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,2]]},"reference":[{"key":"ref_1","unstructured":"Gebre-Egziabher, D., Hayward, R.C., and Powell, J.D. (1998, January 20\u201323). A low-cost GPS\/inertial attitude heading reference system (AHRS) for general aviation applications. Palm Springs, CA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2514\/2.4228","article-title":"Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms","volume":"21","author":"Savage","year":"1998","journal-title":"J. Guid. Control Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"208","DOI":"10.2514\/2.4242","article-title":"Strapdown inertial navigation integration algorithm design part 2: Velocity and position algorithms","volume":"21","author":"Savage","year":"1998","journal-title":"J. Guid. Control Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sipos, M., Paces, P., Reinstein, M., and Rohac, J. (2009, January 25\u201328). Flight attitude track reconstruction using two AHRS units under laboratory conditions. Christchurch, New Zealand.","DOI":"10.1109\/ICSENS.2009.5398341"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Euston, M., Coote, P., Mahony, R., and Jonghyuk, K. (2008, January 22\u201326). A complementary filter for attitude estimation of a fixed-wing UAV. Nice, France.","DOI":"10.1109\/IROS.2008.4650766"},{"key":"ref_6","unstructured":"Bristeau, P.-J., and Petit, N. Navigation System for Ground Vehicles using Temporally."},{"key":"ref_7","unstructured":"Reinstein, M., and Kubelka, V. (2012, January 14\u201318). Complementary filtering approach to orientation estimation using inertial sensors only. Prague, Czech Republic."},{"key":"ref_8","unstructured":"Farrell, J. (2008). Aided Navigation: GPS with High Rate Sensors, McGraw Hill Education."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1109\/TMECH.2014.2311416","article-title":"Evaluation of the EKF-Based Estimation Architectures for Data Fusion in Mobile Robots","volume":"20","author":"Simanek","year":"2014","journal-title":"IEEE-Asme T. Mech."},{"key":"ref_10","unstructured":"Moorhouse, D.J., and Woodcock, R.J. (1982). Background Information and User Guide for MIL-F-8785C, Military Specification-Flying Qualities of Piloted Airplanes, Air Force Wright Aeronautical Labs Wright-Patterson Air Force Base."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pratt, R.W. (2000). Flight Control Systems: Practical Issues in Design and Implementation, The Institute of Electrical Engineers.","DOI":"10.1049\/PBCE057E"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Harris, F. (2009, January 17\u201320). Fixed length FIR filters with continuously variable bandwidth. Aalborg, Denmark.","DOI":"10.1109\/WIRELESSVITAE.2009.5172575"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Harris, F., and Lowdermilk, W. (2007, January 4\u20137). Implementation Considerations and Performance Comparison of Variable Bandwidth FIR Filter and Phase Equalized IIR Filter. Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2007.4487401"},{"key":"ref_14","unstructured":"IEEE Standard for Digitizing Waveform Recorders, 1994. Available online: http:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=469117."},{"key":"ref_15","unstructured":"IEEE Standard for Terminology and Test. Methods for Analog-To-Digital Converters, 2001. Available online: http:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=929859."},{"key":"ref_16","unstructured":"Kay, S.M. (1998). Fundamentals of statistical signal processing, Prentice Hall."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Rohac, J., Reinstein, M., and Draxler, K. Data processing of inertial sensors in strong-vibration environment. 15\u201317 September 2011.","DOI":"10.1109\/IDAACS.2011.6072713"},{"key":"ref_18","first-page":"19","article-title":"Impact of Environmental Vibration on Inertial Sensor's Output","volume":"24","author":"Rohac","year":"2013","journal-title":"Sens. Transducers J."},{"key":"ref_19","unstructured":"Fugal, D.L. (2009). Conceptual Wavelets In Digital Signal Processing, Space & Signals Technologies LLC."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rajmic, P., Vlach, J., and Vyoral, J. (2008, January 14\u201317). Real-time wavelet transform with overlap of signal segments. Krakow, Poland.","DOI":"10.1109\/ICSES.2008.4673351"},{"key":"ref_21","unstructured":"Weeks, M. (2010). Digital Signal Processing Using MATLAB & Wavelets, Jones & Bartlett Learning."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wojtaszczyk, P. (1997). A Mathematical Introduction to Wavelets, Cambridge University Press.","DOI":"10.1017\/CBO9780511623790"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/2\/3282\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:42:13Z","timestamp":1760215333000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/2\/3282"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,2]]},"references-count":22,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,2]]}},"alternative-id":["s150203282"],"URL":"https:\/\/doi.org\/10.3390\/s150203282","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,2]]}}}