Aerodynamic Parameter Estimation for High-Performance Aircraft Using Extended Kalman Filtering

1997 ◽  
Vol 20 (6) ◽  
pp. 1257-1260 ◽  
Author(s):  
Juan Garcia-Velo ◽  
Bruce K. Walker
Keyword(s):  
Parameter Estimation ◽  
Kalman Filtering ◽  
High Performance ◽  
Extended Kalman Filtering ◽  
Aerodynamic Parameter ◽  
High Performance Aircraft

Hierarchical Bayesian Models for Regularization in Sequential Learning

2000 ◽  
Vol 12 (4) ◽  
pp. 933-953 ◽  
Author(s):  
J. F. G. de Freitas ◽  
M. Niranjan ◽  
A. H. Gee
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Kalman Filtering ◽  
Adaptive Learning ◽  
Minimum Variance ◽  
Noise Estimation ◽  
Sequential Learning ◽  
Hierarchical Bayesian ◽  
Extended Kalman Filtering ◽  
Adaptive Noise

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise estimation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not possible. The Bayesian approach, with extended Kalman filtering at the parameter estimation level, allows for regularization within a minimum variance framework. A multilayer perceptron is used to generate the extended Kalman filter nonlinear measurements mapping. We describe several algorithms at the noise estimation level that allow us to implement on-line regularization. We also show the theoretical links between adaptive noise estimation in extended Kalman filtering, multiple adaptive learning rates, and multiple smoothing regularization coefficients.

scholarly journals Observer Design for Nonlinear Systems with Equivariance

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Robert Mahony ◽  
Pieter van Goor ◽  
Tarek Hamel
Keyword(s):  
State Space ◽  
Kalman Filtering ◽  
High Performance ◽  
Autonomous Systems ◽  
Observer Design ◽  
Annual Review ◽  
Publication Date ◽  
Navigation Systems ◽  
Extended Kalman Filtering ◽  
Wide Range

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high-performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a global intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model, we show that the error dynamics have a particularly nice form. Applying the methodology of extended Kalman filtering to the equivariant error state yields a filter we term the equivariant filter. The geometry of the state-space manifold appears naturally as a curvature modification to the classical Riccati equation for extended Kalman filtering. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model, and thus yields high-performance, robust filters for a wide range of mechatronic and navigation systems. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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