{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-level-set-kalman-filter-for-state","title":"The Level Set Kalman Filter for State Estimation of Continuous-discrete Systems","arxiv_id":"2103.11130","date":"2021-03-20","proceeding":null,"authors":["Ningyuan Wang","Daniel B. Forger"],"abstract":"We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set Kalman filter (LSKF). The LSKF assumes the probability distribution can be approximated as a Gaussian, and updates the Gaussian distribution through a time-update step and a measurement-update step. The LSKF improves the time-update step when compared to existing methods, such as the continuous-discrete cubature Kalman filter (CD-CKF) by reformulating the underlying Fokker-Planck equation as an ordinary differential equation for the Gaussian, thereby avoiding expansion in time. Together with a carefully picked measurement-update method, numerical experiments show that the LSKF has a consistent performance improvement over CD-CKF for a range of parameters, while also simplifies the implementation, as no user-defined timestep subdivision between measurements is required, and the spatial derivatives of the drift function are not explicitly needed.","url_abs":"https://arxiv.org/abs/2103.11130v3","url_pdf":"https://arxiv.org/pdf/2103.11130v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-level-set-kalman-filter-for-state","repo_url":"https://github.com/NingyuanWang/level_set_kalman_filter_matlab_demo","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"state-estimation","task_name":"State Estimation"},{"task_slug":"state-space-models","task_name":"State Space Models"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}