{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:18:51Z","timestamp":1760149131061,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NAUSS","award":["NAUSS-23-R23"],"award-info":[{"award-number":["NAUSS-23-R23"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper introduces a novel method for computationally efficient Gaussian estimation of high-dimensional problems such as Simultaneous Localization and Mapping (SLAM) processes and for treating certain Stochastic Partial Differential Equations (SPDEs). The authors have presented the Generalized Compressed Kalman Filter (GCKF) framework to reduce the computational complexity of the filters by partitioning the state vector into local and global and compressing the global state updates. The compressed state update, however, still suffers from high computational costs, making it challenging to implement on embedded processors. We propose a low-precision numerical representation for the global filter, such as 16-bit integer or 32-bit single-precision formats for the global covariance matrix, instead of the expensive double-precision, floating-point representation (64 bits). This truncation can inevitably cause filter instability since the truncated covariance matrix becomes overoptimistic or even turns to be an invalid covariance matrix. We introduce a Minimal Covariance Inflation (MCI) method to make the filter consistent while minimizing the truncation errors. Simulation-based experiments results show significant improvement of the proposed method with a reduction in the processing time with minimal loss of accuracy.<\/jats:p>","DOI":"10.3390\/s23146406","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T08:40:06Z","timestamp":1689324006000},"page":"6406","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Compressed Gaussian Estimation under Low Precision Numerical Representation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8556-8652","authenticated-orcid":false,"given":"Jose","family":"Guivant","sequence":"first","affiliation":[{"name":"School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4763-3230","authenticated-orcid":false,"given":"Karan","family":"Narula","sequence":"additional","affiliation":[{"name":"Independent Researcher, Bangkok 10100, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4505-1103","authenticated-orcid":false,"given":"Jonghyuk","family":"Kim","sequence":"additional","affiliation":[{"name":"Naif Arab University for Security Sciences, Riyadh 14812, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9295-7333","authenticated-orcid":false,"given":"Xuesong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, Australia National University, Canberra, ACT 2601, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0979-3751","authenticated-orcid":false,"given":"Subhan","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, University of Sydney, Camperdown, NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1017\/S0263574716000369","article-title":"The generalized compressed Kalman filter","volume":"35","author":"Guivant","year":"2017","journal-title":"Robotica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.automatica.2018.10.018","article-title":"Switching and information exchange in compressed estimation of coupled high dimensional processes","volume":"99","author":"Narula","year":"2019","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Narula, K., Guivant, J.E., and Li, X. (2018, January 10\u201313). Non-Linear Estimation with Generalised Compressed Kalman Filter. Proceedings of the 2018 21st International Conference on Information Fusion (FUSION), Cambridge, UK.","DOI":"10.23919\/ICIF.2018.8455338"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1109\/70.938382","article-title":"Optimization of the simultaneous localization and map-building algorithm for real-time implementation","volume":"17","author":"Guivant","year":"2001","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1109\/TRA.2003.814500","article-title":"Solving computational and memory requirements of feature-based simultaneous localization and mapping algorithms","volume":"19","author":"Guivant","year":"2003","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cheng, J., Kim, J., Jiang, Z., and Yang, X. (2014, January 5\u201310). Compressed Unscented Kalman Filter-Based Slam. Proceedings of the 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), Bali, Indonesia.","DOI":"10.1109\/ROBIO.2014.7090563"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Narula, K. (2019). Compressed Estimation in Coupled High-Dimensional Processes. [Ph.D. Thesis, The University of New South Wales].","DOI":"10.1016\/j.automatica.2018.10.018"},{"key":"ref_8","unstructured":"Verlaan, M. (1995, January 13\u201317). Reduced Rank Square Root Filters for Large Scale Data Assimilation Problems. Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, Tokyo, Japan."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0924-7963(97)00109-7","article-title":"A singular evolutive extended Kalman filter for data assimilation in oceanography","volume":"16","author":"Pham","year":"1998","journal-title":"J. Mar. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1175\/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2","article-title":"Data assimilation using an ensemble Kalman filter technique","volume":"126","author":"Houtekamer","year":"1998","journal-title":"Mon. Weather. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1988","DOI":"10.1175\/MWR-D-11-00176.1","article-title":"An iterative EnKF for strongly nonlinear systems","volume":"140","author":"Sakov","year":"2012","journal-title":"Mon. Weather. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s10236-003-0036-9","article-title":"The ensemble Kalman filter: Theoretical formulation and practical implementation","volume":"53","author":"Evensen","year":"2003","journal-title":"Ocean. Dyn."},{"key":"ref_13","unstructured":"Olfati-Saber, R. (2005, January 15\u201315). Distributed Kalman Filter with Embedded Consensus Filters. Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Olfati-Saber, R. (2007, January 12\u201314). Distributed Kalman Filtering for Sensor Networks. Proceedings of the 2007 46th IEEE Conference on Decision and Control, New Orleans, LA, USA.","DOI":"10.1109\/CDC.2007.4434303"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kamgarpour, M., and Tomlin, C. (2008, January 9\u201311). Convergence Properties of a Decentralized Kalman Filter. Proceedings of the 2008 47th IEEE Conference on Decision and Control, Cancun, Mexico.","DOI":"10.1109\/CDC.2008.4738989"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4919","DOI":"10.1109\/TSP.2008.927480","article-title":"Distributing the Kalman filter for large-scale systems","volume":"56","author":"Khan","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/MAES.2019.2927898","article-title":"On computational complexity reduction methods for Kalman filter extensions","volume":"34","author":"Raitoharju","year":"2019","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_18","unstructured":"Morelande, M.R., and Ristic, B. (2006, January 14\u201319). Reduced Sigma Point Filtering for Partially Linear Models. Proceedings of the 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, Toulouse, France."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Morelande, M.R., and Moran, B. (2007, January 15\u201320). An Unscented Transformation for Conditionally Linear Models. Proceedings of the 2007 IEEE International Conference on Acoustics, Speech and Signal Processing-ICASSP\u201907, Honolulu, HI, USA.","DOI":"10.1109\/ICASSP.2007.367112"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1109\/TSP.2005.849151","article-title":"Marginalized particle filters for mixed linear\/nonlinear state-space models","volume":"53","author":"Schon","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","unstructured":"Guivant, J.E. (2002). Efficient Simultaneous Localization and Mapping in Large Environments. [Ph.D. Thesis, Australian Centre for Field Robotics, Department of Mechanical and Mechatronic Engineering, University of Sydney]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1029\/2018MS001341","article-title":"Choosing the optimal numerical precision for data assimilation in the presence of model error","volume":"10","author":"Hatfield","year":"2018","journal-title":"J. Adv. Model. Earth Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1175\/MWR-D-17-0132.1","article-title":"Improving weather forecast skill through reduced-precision data assimilation","volume":"146","author":"Hatfield","year":"2018","journal-title":"Mon. Weather. 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