Generalized Kalman smoothing: Modeling and algorithms

被引:85
作者
Aravkin, Aleksandr [1 ]
Burke, James V. [2 ]
Ljung, Lennart [3 ]
Lozano, Aurelie [4 ]
Pillonetto, Gianluigi [5 ]
机构
[1] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA
[2] Univ Washington, Dept Math, Seattle, WA 98195 USA
[3] Linkoping Univ, Div Automat Control, Linkoping, Sweden
[4] IBM TJ Watson Res Ctr, Yorktown Hts, NY USA
[5] Univ Padua, Dept Informat Engn, Control & Dynam Syst, Padua, Italy
基金
欧洲研究理事会; 美国国家科学基金会; 瑞典研究理事会;
关键词
SIMULTANEOUS SPARSE APPROXIMATION; VARIABLE SELECTION; REGRESSION; ROBUST; SUM; REGULARIZATION; IDENTIFICATION; COMPUTATION; RECOVERY; MACHINE;
D O I
10.1016/j.automatica.2017.08.011
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch Tung Striebel and Mayne Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a convex quadratic objective function with structure induced by the dynamic model. These classical formulations fall short in many important circumstances. For instance, smoothers obtained using quadratic penalties can fail when outliers are present in the data, and cannot track impulsive inputs and abrupt state changes. Motivated by these shortcomings, generalized Kalman smoothing formulations have been proposed in the last few years, replacing quadratic models with more suitable, often nonsmooth, convex functions. In contrast to classical models, these general estimators require use of iterated algorithms, and these have received increased attention from control, signal processing, machine learning, and optimization communities. In this survey we show that the optimization viewpoint provides the control and signal processing community great freedom in the development of novel modeling and inference frameworks for dynamical systems. We discuss general statistical models for dynamic systems, making full use of nonsmooth convex penalties and constraints, and providing links to important models in signal processing and machine learning. We also survey optimization techniques for these formulations, paying close attention to dynamic problem structure. Modeling concepts and algorithms are illustrated with numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:63 / 86
页数:24
相关论文
共 115 条
[1]  
Agamennoni G, 2011, IEEE INT CONF ROBOT, P1551
[2]  
Angelosante Daniele, 2009, 2009 43rd Asilomar Conference on Signals, Systems and Computers, P181, DOI 10.1109/ACSSC.2009.5470133
[3]  
[Anonymous], 2001, Learning with Kernels |
[4]  
[Anonymous], 2004, Kalman filtering and neural networks
[5]  
[Anonymous], 1999, Athena scientific Belmont
[6]  
[Anonymous], 1997, ADV NEURAL INFORM PR
[7]  
[Anonymous], 2011, INTERIOR POINT ALGOR
[8]  
[Anonymous], 1986, ROBUST STAT
[9]  
[Anonymous], 2006, Journal of the Royal Statistical Society, Series B
[10]  
[Anonymous], 1999, SYSTEM IDENTIFICATIO