Publication

Kalman Filtering for a Generalized Class of Nonlinear Systems and a New Gaussian Quadrature Technique

2012
Journal Articles

Abstract

The class of nonlinear systems treated in this technical note consists of the discrete time nonlinear systems that are formed by the interconnection of linear systems through static nonlinearities with few inputs. This special structure is exploited to reduce the dimension of the integrals involved in the propagation of mean values and covariances, thus permitting accurate calculations. Furthermore, a new quadrature scheme suitable for nonlinear Kalman filtering is introduced. The proposed techniques are applied to a seven-dimensional numerical example. The results show that they can increase the performance significantly.

Official source

https://infoscience.epfl.ch/entities/publication/1199399f-0894-4d24-a097-8bc37a0bf3d1

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2012
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1199399f-0894-4d24-a097-8bc37a0bf3d1

About this result

Related concepts (31)

Nonlinear system

In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.

Nonlinear optics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear.

Kalman filter

For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.

Related publications (32)

Kalman Filtering for a Generalized Class of Nonlinear Systems and a New Gaussian Quadrature Technique

Chat with Graph Search

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks