scholarly journals The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109752
Author(s):  
Nathan J. Kong ◽  
J. Joe Payne ◽  
George Council ◽  
Aaron M. Johnson
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Kalman Filtering ◽  
Hybrid Dynamical Systems

Noise Reduction of Chaotic Systems by Kalman Filtering and by Shadowing

1997 ◽  
Vol 07 (03) ◽  
pp. 769-779 ◽  
Author(s):  
David M. Walker ◽  
Alistair I. Mees
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Noise Reduction ◽  
Kalman Filtering ◽  
Chaotic Systems ◽  
Reduction Algorithm ◽  
Modified Kalman Filter ◽  
Noise Amplification ◽  
Noise Reduction Algorithm

We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory.

scholarly journals Double hybrid Kalman filtering for state estimation of dynamical systems

2019 ◽  
Vol 28 ◽  
pp. 01051
Author(s):  
Jacek Michalski ◽  
Piotr Kozierski ◽  
Joanna Zietkiewicz
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
State Estimation ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Unscented Kalman Filter ◽  
Variable Number ◽  
Hybrid Filters ◽  
Estimation Quality ◽  
Number Of Particles

In this paper authors present a new approaches to the hybrid Kalman filtering and modified hybrid Kalman filtering, with the changed order of methods inside (Unscented Kalman Filter and Extended Kalman Filter). For these algorithms, the modification based on double use of Hybrid Kalman Filters (Excented and Unscented) has been proposed. This new modification has been checked for Hybrid Kalman Particle Filters too, for the variable number of particles. Based on the obtained results, one can see that duplication of hybrid filters can improve the estimation quality.

scholarly journals Identification of a Class of Hybrid Dynamical Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 875-882
Author(s):  
Stefano Massaroli ◽  
Federico Califano ◽  
Angela Faragasso ◽  
Mattia Risiglione ◽  
Atsushi Yamashita ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Hybrid Dynamical Systems

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

A Rapid Computation Method for Kalman Filtering in Vehicular SINS/GPS Integrated System

2012 ◽  
Vol 182-183 ◽  
pp. 541-545 ◽  
Author(s):  
Qi Ju Zhu ◽  
Gong Min Yan ◽  
Peng Xiang Yang ◽  
Yong Yuan Qin
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Kalman Filtering ◽  
Integrated System ◽  
Computation Method ◽  
System Matrix ◽  
Computational Burden ◽  
Reduced Dimensions ◽  
Classic Method

A new rapid computation method for Kalman filtering is proposed. In this method, the prediction of state covariance matrix is expanded directly rather than computing by a looping program. Sequential filtering for measurement update is also applied. Furthermore, the subsidiary elements in system matrix are set to zero and a reduced-dimensions sub-optimal Kalman filter is presented. The proposed method greatly decreases computational burden and it is only 6.59% of the classic method. In the end, a vehicular test is carried out to prove the feasibility of the filtering.

scholarly journals Theory of hybrid dynamical systems and its applications to biological and medical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4893-4914 ◽  
Author(s):  
Kazuyuki Aihara ◽  
Hideyuki Suzuki
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Systems Theory ◽  
Control Systems ◽  
Hybrid Systems ◽  
Hybrid Dynamical Systems ◽  
Medical Systems ◽  
Theme Issue ◽  
And Control

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on–off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.

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