{"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/generalized-kalman-smoothing-modeling-and","title":"Generalized Kalman Smoothing: Modeling and Algorithms","arxiv_id":"1609.06369","date":"2016-09-20","proceeding":null,"authors":["A. Y. Aravkin","J. V. Burke","L. Ljung","A. Lozano","G. Pillonetto"],"abstract":"State-space smoothing has found many applications in science and engineering.\nUnder linear and Gaussian assumptions, smoothed estimates can be obtained using\nefficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser\nalgorithms. Such schemes are equivalent to linear algebraic techniques that\nminimize a convex quadratic objective function with structure induced by the\ndynamic model.\n  These classical formulations fall short in many important circumstances. For\ninstance, smoothers obtained using quadratic penalties can fail when outliers\nare present in the data, and cannot track impulsive inputs and abrupt state\nchanges. Motivated by these shortcomings, generalized Kalman smoothing\nformulations have been proposed in the last few years, replacing quadratic\nmodels with more suitable, often nonsmooth, convex functions. In contrast to\nclassical models, these general estimators require use of iterated algorithms,\nand these have received increased attention from control, signal processing,\nmachine learning, and optimization communities.\n  In this survey we show that the optimization viewpoint provides the control\nand signal processing community great freedom in the development of novel\nmodeling and inference frameworks for dynamical systems. We discuss general\nstatistical models for dynamic systems, making full use of nonsmooth convex\npenalties and constraints, and providing links to important models in signal\nprocessing and machine learning. We also survey optimization techniques for\nthese formulations, paying close attention to dynamic problem structure.\nModeling concepts and algorithms are illustrated with numerical examples.","url_abs":"http://arxiv.org/abs/1609.06369v2","url_pdf":"http://arxiv.org/pdf/1609.06369v2.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":"generalized-kalman-smoothing-modeling-and","repo_url":"https://github.com/UW-AMO/TimeSeriesES-Cell","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"survey","task_name":"Survey"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1609.06369","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}