# Longwall mining automation an application of minimum-variance smoothing [Applications of Control]

@article{Einicke2008LongwallMA,
title={Longwall mining automation an application of minimum-variance smoothing [Applications of Control]},
author={Garry A. Einicke and Johnathon C. Ralston and Chad O. Hargrave and D. Reid and David W. Hainsworth},
journal={IEEE Control Systems},
year={2008},
volume={28}
}
• Published 17 November 2008
• Mathematics
• IEEE Control Systems
This article reviews the development of the minimum-variance smoother and describes its use in longwall automation. We describe both continuous- and discrete-time smoother solutions. It is shown, under suitable assumptions, that the two-norm of the smoother estimation error is less than that for the Kalman filter. A simulation study is presented to compare the performance of the minimum-variance smoother with the methods of H.E. Rauch et al. (1965), and D.C. Fraser and J.E. Potter (1969).
47 Citations

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## References

SHOWING 1-10 OF 11 REFERENCES
Optimal and robust noncausal filter formulations
• G. Einicke
• Mathematics
IEEE Transactions on Signal Processing
• 2006
The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother that involves a cascade of a KalMan predictor and an adjoint Kalman predictor and demonstrates that optimal, robust, and extended Kalman smoothers can provide performance benefits.
An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise
• Mathematics
• 1968
The innovations approach to linear least-squares approximation problems is first to "whiten" the observed data by a causal and invertible operation, and then to treat the resulting simpler
Asymptotic Optimality of the Minimum-Variance Fixed-Interval Smoother
• G. Einicke
• Mathematics
IEEE Transactions on Signal Processing
• 2007
This correspondence investigates the asymptotic performance of the discrete-time and continuous-time, time-varying, minimum-variance, fixed-interval smoothers. Comparison theorems are generalized to
Optimal Filtering
• Computer Science
IEEE Transactions on Systems, Man, and Cybernetics
• 1982
This book helps to fill the void in the market and does that in a superb manner by covering the standard topics such as Kalman filtering, innovations processes, smoothing, and adaptive and nonlinear estimation.
The optimum linear smoother as a combination of two optimum linear filters
• Mathematics
• 1969
A solution to the optimum linear smoothing problem is presented in which the smoother is interpreted as a combination of two optimum linear filters. This result is obtained from the well-known
A New Approach to Linear Filtering and Prediction Problems
The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result
A schur method for solving algebraic Riccati equations
• A. Laub
• Mathematics, Computer Science
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes
• 1978
A new algorithm for solving algebraic Riccati equations (both continuous-time and discrete-time versions) is presented, a variant of the classical eigenvector approach and uses instead an appropriate set of Schur vectors thereby gaining substantial numerical advantages.
Two filter smoothing formulae by diagonalization of the Hamiltonian equations
• Mathematics
• 1982
We present a new approach to two filter smoothing formulae via diagonalization of the general time variant hamiltonian equations of the linear estimation problem. This approach shows the special role
On the maximum likelihood estimates for linear dynamic systems
• Mathematics, Materials Science
• 1963
A steel slab or bloom containing 0.3 DIFFERENCE 0.15% by weight of C, 0.05 DIFFERENCE 0.60% by weight of Si, 0.60 DIFFERENCE 2.5% by weight of Mn, 0.010 DIFFERENCE 0.15% by weight of Nb, 0.005