Results on the filtering problem for linear systems with non-Gaussian initial conditions

1982 ◽  
Author(s):  
Armand Makowski
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
Non Gaussian ◽  
Filtering Problem

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

Adaptive distributed partitioning filters: non-gaussian initial conditions

1999 ◽  
Vol 17 (3) ◽  
pp. 405-419
Author(s):  
Demetrios G. Lainiotis ◽  
Pavlos K. Giannakopoulos ◽  
Sokrates K. Katsikas
Keyword(s):  
Initial Conditions ◽  
Non Gaussian

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

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