Generalized Kalman smoothing: Modeling and algorithms
Generalized Kalman smoothing: Modeling and algorithms
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DOI：
10.1016/j.automatica.2017.08.011
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发表时间：
2017-12-01
期刊：
影响因子：
6.4
通讯作者：
Pillonetto, Gianluigi
中科院分区：
文献类型：
--
作者：
Aravkin, Aleksandr;Burke, James V.;Pillonetto, Gianluigi
状态空间平滑在科学和工程中有着广泛的应用。在线性和高斯假设下，可以使用有效的递归来获得平滑的估计，例如Rauchong Striebel和Mayne Fraser算法。这类方案等价于线性代数技术，即最小化由动态模型诱导的具有结构的凸二次目标函数。这些经典公式在许多重要情况下是不合适的。例如，当数据中存在异常值时，使用二次惩罚获得的平滑器可能会失效，并且无法跟踪脉冲输入和突然的状态变化。由于这些缺点，最近几年提出了广义卡尔曼平滑公式，用更合适的(通常是非光滑的)凸函数来代替二次模型。与经典模型相比，这些一般估计器需要使用迭代算法，这些算法越来越受到控制、信号处理、机器学习和优化领域的关注。在这篇综述中，我们表明，优化观点为控制和信号处理领域提供了很大的自由，可以为动态系统开发新的建模和推理框架。我们讨论了动态系统的一般统计模型，充分利用了非光滑凸罚和约束，并提供了到信号处理和机器学习中的重要模型的链接。我们还综述了这些公式的优化技术，密切关注动态问题结构。通过数值算例说明了建模的概念和算法。(C)2017爱思唯尔有限公司。保留所有权利。
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.