Application of Polynomial Filtering Algorithms to Nonlinear Discrete Dynamical Systems in Navigation Data Processing

The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior proba-bility density function of the estimated vector at the previous step and minimization of estimation error covariance matrix using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and secondorder Kalman filters are discussed. The procedure for estimating the performance and comparing the algorithms is presented.

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Relationship between time-invariant and time-variant filtering algorithms for a class of problems of navigation data processing

2012 IEEE 51st IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2012.6426716 ◽

2012 ◽

Author(s):

Alexei V. Loparev ◽

Oleg A. Stepanov ◽

Igor B. Chelpanov

Keyword(s):

Data Processing ◽

Filtering Algorithms ◽

Navigation Data ◽

Variant Filtering ◽

Time Invariant

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Hidden Attractors in Discrete Dynamical Systems

Entropy ◽

10.3390/e23050616 ◽

2021 ◽

Vol 23 (5) ◽

pp. 616

Author(s):

Marek Berezowski ◽

Marcin Lawnik

Keyword(s):

Dynamical Systems ◽

Chaos Theory ◽

Scientific Literature ◽

Discrete Systems ◽

Discrete Dynamical Systems ◽

Continuous Systems ◽

Hidden Attractors ◽

Negative Effects ◽

Chemical Reactors ◽

Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

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Internal Model Control Design based on Approximation of Linear Discrete Dynamical Systems

Applied Mathematical Modelling ◽

10.1016/j.apm.2021.04.017 ◽

2021 ◽

Author(s):

G. Vasu ◽

M. Siva Kumar ◽

M. Ramalinga Raju

Keyword(s):

Dynamical Systems ◽

Internal Model ◽

Control Design ◽

Discrete Dynamical Systems ◽

Internal Model Control ◽

Model Control

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A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127493000234 ◽

1993 ◽

Vol 03 (02) ◽

pp. 293-321 ◽

Cited By ~ 1

Author(s):

JÜRGEN WEITKÄMPER

Keyword(s):

Hopf Bifurcation ◽

Dynamical Systems ◽

Cellular Automata ◽

Cellular Automaton ◽

Parallel Computers ◽

Discrete Dynamical Systems ◽

Two Dimensional ◽

Bifurcation Structure ◽

Logistic Mapping ◽

Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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