A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise

2011-01-01
Demirbaş, Kerim
A new suboptimum state filtering and prediction scheme is proposed for nonlinear discrete dynamic systems with Gaussian or non-Gaussian disturbance and observation noises. This scheme is an online estimation scheme for real-time applications. Furthermore, this scheme is very suitable for state estimation under either constraints imposed on estimates or missing observations. State and observation models can be any nonlinear functions of the states, disturbance and observation noises as long as noise samples are independent, and the density functions of noise samples and conditional density functions of the observations given the states are available. State models are used to calculate transition probabilities from gates to gates. If these transition probabilities are known or can be estimated, state models are not needed for estimation. The proposed scheme (PR) is based upon state quantisation and multiple hypothesis testing. Monte Carlo simulations have shown that the performance of the PR, sampling importance resampling (SIR) particle filter and extended Kalman (EK) filter are all model-dependent, and that the performance of the PR is better than both the SIR particle filter and EK filter for some nonlinear models, simulation results of three of which are given in this article.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE

Suggestions

A state prediction scheme for discrete time nonlinear dynamic systems
Demirbaş, Kerim (Informa UK Limited, 2007-01-01)
A state prediction scheme is proposed for discrete time nonlinear dynamic systems with non-Gaussian disturbance and observation noises. This scheme is based upon quantization, multiple hypothesis testing, and dynamic programming. Dynamic models of the proposed scheme are as general as dynamic models of particle predictors, whereas the nonlinear models of the extended Kalman (EK) predictor are linear with respect to the disturbance and observation noises. The performance of the proposed scheme is compared wi...
A Novel Computational Method to Calculate Nonlinear Normal Modes of Complex Structures
Samandarı, Hamed; Ciğeroğlu, Ender (2019-01-31)
In this study, a simple and efficient computational approach to obtain nonlinear normal modes (NNMs) of nonlinear structures is presented. Describing function method (DFM) is used to capture the nonlinear internal forces under periodic motion. DFM has the advantage of expressing the nonlinear internal force as a nonlinear stiffness matrix multiplied by a displacement vector, where the off-diagonal terms of the nonlinear stiffness matrix can provide a comprehensive knowledge about the coupling between the mo...
A novel real-time adaptive suboptimal recursive state estimation scheme for nonlinear discrete dynamic systems with non-Gaussian noise
Demirbaş, Kerim (2012-07-01)
A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state t...
A finite field framework for modeling, analysis and control of finite state automata
Reger, Johann; Schmidt, Klaus Verner (Informa UK Limited, 2004-09-01)
In this paper, we address the modeling, analysis and control of finite state automata, which represent a standard class of discrete event systems. As opposed to graph theoretical methods, we consider an algebraic framework that resides on the finite field F-2 which is defined on a set of two elements with the operations addition and multiplication, both carried out modulo 2. The key characteristic of the model is its functional completeness in the sense that it is capable of describing most of the finite st...
An improved method for inference of piecewise linear systems by detecting jumps using derivative estimation
Selcuk, A. M.; Öktem, Hüseyin Avni (Elsevier BV, 2009-08-01)
Inference of dynamical systems using piecewise linear models is a promising active research area. Most of the investigations in this field have been stimulated by the research in functional genomics. In this article we study the inference problem in piecewise linear systems. We propose first identifying the state transitions by detecting the jumps of the derivative estimates, then finding the guard conditions of the state transitions (thresholds) from the values of the state variables at the state transitio...
Citation Formats
K. Demirbaş, “A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise,” INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, pp. 1789–1799, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/58027.