Covariance bounds for augmented state Kalman filter application

1999 ◽  
Vol 35 (23) ◽  
pp. 2062 ◽  
Author(s):  
R.H. Deaves
Keyword(s):  
Kalman Filter ◽  
Augmented State

scholarly journals Longwall Shearer Cutting Force Estimation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
A. W. Reid ◽  
P. R. McAree ◽  
P. A. Meehan ◽  
H. Gurgenci
Keyword(s):  
Kalman Filter ◽  
Cutting Forces ◽  
Longwall Mining ◽  
Force Estimation ◽  
Underground Coal Mining ◽  
Indirect Measurements ◽  
Input Estimation ◽  
Internal Model Principle ◽  
Viable Approach ◽  
Augmented State

Longwall mining is an underground coal mining method that is widely used. A shearer traverses the coal panel to cut coal that falls to a conveyor. Operation of the longwall can benefit from knowledge of the cutting forces at the coal/shearer interface, particularly in detecting pick failures and to determine when the shearer may be cutting outside of the coal seam. It is not possible to reliably measure the cutting forces directly. This paper develops a method to estimate the cutting forces from indirect measurements that are practical to make. The structure of the estimator is an extended Kalman filter with augmented states whose associated dynamics encode the character of the cutting forces. The methodology is demonstrated using a simulation of a longwall shearer and the results suggest this is a viable approach for estimating the cutting forces. The contributions of the paper are a formulation of the problem that includes: the development of a dynamic model of the longwall shearer that is suitable for forcing input estimation, the identification of practicable measurements that could be made for implementation and, by numerical simulation, verification of the efficacy of the approach. Inter alia, the paper illustrates the importance of considering the internal model principle of control theory when designing an augmented-state Kalman filter for input estimation.

scholarly journals Using augmented state Kalman filter to localize multi autonomous underwater vehicles

2007 ◽  
Vol 13 (2) ◽  
pp. 61-70
Author(s):  
Silvia Botelho ◽  
Renato Neves ◽  
Lorenzo Taddei ◽  
Vinícius Oliveira
Keyword(s):  
Kalman Filter ◽  
Autonomous Underwater Vehicles ◽  
Underwater Vehicles ◽  
Augmented State

scholarly journals Using Augmented State Kalman filter to localize multi autonomous underwater vehicles

2007 ◽  
Vol 13 (2) ◽  
pp. 61-70 ◽  
Author(s):  
Silvia Botelho ◽  
Renato Neves ◽  
Lorenzo Taddei ◽  
Vinícius Oliveira
Keyword(s):  
Kalman Filter ◽  
Autonomous Underwater Vehicles ◽  
Underwater Vehicles ◽  
Augmented State

scholarly journals Study on the Initial Value Problem for Fractional-order Cubature Kalman Filters of Nonlinear Continuous-time Fractional-order Systems

2021 ◽  
Author(s):  
Chuang Yang ◽  
Zhe Gao ◽  
Yue Miao ◽  
Tao Kan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
The State ◽  
Order System ◽  
Initial Value ◽  
Cubature Kalman Filter ◽  
Augmented State

Abstract To realize the state estimation of a nonlinear continuous-time fractional-order system, two types of fractional-order cubature Kalman filters (FOCKFs) designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system are also regarded as the augmented state, the augmented state equation is constructed to obtain the CKF based on Grünwald-Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter (HECKF) is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can effectively reduce the influence of initial value on the state estimation. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.

Explicit Fractional Model Order Estimation Using Unscented and Ensemble Kalman Filters

2011 ◽  
Author(s):  
Michailas Romanovas ◽  
Lasse Klingbeil ◽  
Martin Traechtler ◽  
Yiannos Manoli
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Computationally Efficient ◽  
Ensemble Kalman Filters ◽  
Model Order ◽  
Order Estimation ◽  
Augmented State

The article presents an approach for combining methods of recursive Bayesian estimation with models of dynamical systems with varying differentiation order. The work addresses the problem of explicit fractional order estimation and tracking by constructing an efficient Unscented Kalman filter, where the model order is directly estimated within an augmented state along with the variables of interest. The feasibility of the estimation method is assessed using a benchmark problem based on a simplified fractional neuron firing rate model and time-dependent differentiation order. The proposed technique is compared to an implicit method based on Interacting Multiple Model filtering and a computationally efficient method using a modification of the Ensemble Kalman filter. The performance with respect to different parameters and filter settings is analyzed and a corresponding discussion is provided.

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