# Asymptotic Optimality of the Minimum-Variance Fixed-Interval Smoother

@article{Einicke2007AsymptoticOO, title={Asymptotic Optimality of the Minimum-Variance Fixed-Interval Smoother}, author={Garry A. Einicke}, journal={IEEE Transactions on Signal Processing}, year={2007}, volume={55}, pages={1543-1547} }

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 provide sufficient conditions for the monotonic convergence of the underlying Riccati equations. Under these conditions, the energy of the estimation errors asymptotically approach a lower bound and attain lscr2 /L2 stability

## 33 Citations

Asymptotic convergence of Riccati equation and smoother solutions

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

It is shown that when the Riccati equation solutions converge, the time-varying, minimum-variance, fixed-interval smoothers provide optimal performance.

Properties of a continuous-time H∞ fixed-interval smoother

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the Hinfin filter.

A Solution to the Continuous-Time H ∞ Fixed-Interval Smoother Problem

- Mathematics

—The minimum-variance fixed-interval smoother is a state-space realization of the Wiener solution generalized for time-varying problems. It involves forward and adjoint Wiener-Hopf factor inverses in…

A Solution to the Continuous-Time ${\rm H}_{\infty}$ Fixed-Interval Smoother Problem

- MathematicsIEEE Transactions on Automatic Control
- 2009

It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the H∞ filter.

About the true type of smoothers

- MathematicsArXiv
- 2008

The variational formulation and the Euler-Lagrange equations are used to study the steady-state error in linear non-causal estimators (smoothers) and reveal a significant advantage of smoothing over filtering with respect to robustness to model uncertainty.

Iterative Smoother-Based Variance Estimation

- MathematicsIEEE Signal Processing Letters
- 2012

The minimum-variance smoother solution for input estimation is described and it is shown that the resulting estimates are unbiased. The smoothed input and state estimates are used to iteratively…

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

- MathematicsIEEE Control Systems
- 2008

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,…

Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment

- MathematicsIEEE Transactions on Signal Processing
- 2009

This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error…

The use of energy constraints within filtering and smoothing

- MathematicsIEEE Conference on Decision and Control and European Control Conference
- 2011

A low-cost filtering procedure is proposed in which the input measurements are constrained by nonlinear censuring functions and the resulting estimates are unbiased, and the estimation errors are bounded.

EM algorithm convergence for inertial navigation system alignment

- Mathematics2008 47th IEEE Conference on Decision and Control
- 2008

The convergence of a Kalman filter-based EM algorithm for estimating variances is investigated. It is established that if the variance estimates and the error covariances are initialized…

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