Optimal state estimation without the requirement of a priori statistics information of the initial state

Dan-yang, Liu; Xuan-huang, Liu

doi:10.1109/9.328818

Cited by 32 publications

(9 citation statements)

References 10 publications

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“…Consider now the problem of minimizing JFH(X, Ut,t+N-l, N) subject to (1), (2) and when A is nonsingular can be found in [22], [3] . If A is singular, K ZS can be computed by dualizing the filtering results reported in [12]. It is interesting to note that K ZS can be seen as the optimal LQ gain associated with a "fake" cost function…”

Section: The Zero-state Terminal Constraint (Zs)mentioning

confidence: 99%

“…Associated with (11), (12) it is possible to define an RH (Receding Horizon) control strategy in the usual way: at every time instant t, define x = x(t) and compute the optimal solution U~,t+N-l for the FH problem (11) subject to (1), (2), (12); then apply the control u(t) = UO(x) where UO(x) is the first column of U~,t+N-l' Although the F H minimization of (11) has to be performed at each time instant, this is much more viable than solving an I H problem.…”

Section: Nonlinear Rh Controlmentioning

confidence: 99%

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Stability and Robustness of Nonlinear Receding Horizon Control

Nicolao

Magni

Scattolini

2000

Nonlinear Model Predictive Control

109

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Abstract. The main design strategies for ensuring stability and robustness of nonlinear RH (Receding-Horizon) control systems are critically surveyed. In particular, the following algorithms with guaranteed closed-loop stability of the equilibrium are considered: the zero-state terminal constraint, the dualmode RH controller, the infinite-horizon closed-loop costing, the quasi-infinite method, and the contractive constraint. For each algorithm, we analyse and compare feasibility, performance, and implementation issues. For what concerns robustness analysis and design, we consider: monotonicity-based robustness, inverse optimality robustness margins, nonlinear Hoc RH design, and a new nonlinear RH design with local Hoc recovery.

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Section: The Zero-state Terminal Constraint (Zs)mentioning

confidence: 99%

Section: Nonlinear Rh Controlmentioning

confidence: 99%

Stability and Robustness of Nonlinear Receding Horizon Control

Nicolao

Magni

Scattolini

2000

Nonlinear Model Predictive Control

109

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“…If to take into account constraint (18), provide the averaging, and rearrange the terms, (25) can be transformed to…”

Section: The Gain For Ofir-eu Filtermentioning

confidence: 99%

“…Nowadays, the interest to FIR estimators has grown owing to the tremendous progress in the computational resources. Accordingly, we find a number of new solutions on FIR filtering [16][17][18][19][20][21], smoothing [22][23][24], and prediction [25][26][27] as well as efficient applications [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Effect of embedded unbiasedness on discrete-time optimal FIR filtering estimates

Zhao

Shmaliy

Liu

et al. 2015

EURASIP J. Adv. Signal Process.

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Unbiased estimation is an efficient alternative to optimal estimation when the noise statistics are not fully known and/or the model undergoes temporary uncertainties. In this paper, we investigate the effect of embedded unbiasedness (EU) on optimal finite impulse response (OFIR) filtering estimates of linear discrete time-invariant statespace models. A new OFIR-EU filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint. We show that the OFIR-UE filter is equivalent to the minimum variance unbiased FIR (UFIR) filter. Unlike the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. Contrary to the UFIR filter which MSE is minimized by the optimal horizon of N opt points, the MSEs in the OFIR-EU and OFIR filters diminish with N and these filters are thus full-horizon. Based upon several examples, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

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“…The computational burden associated with large dimensions of vectors and matrices [7,8], which cause slow operation, makes the batch FIR estimator highly unattractive for engineering applications, that is, in spite of its inherent bounded input/bounded output stability [9], better robustness [7,10], and lower sensitivity to noise [11] against the Kalman filter (KF). The tremendous progress in the computational resources did not bring about essential change, and the batch FIR estimators [12][13][14][15][16][17][18][19][20][21] still remain mostly on a theoretical level.…”

Section: Introductionmentioning

confidence: 99%

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

Zhao

Shmaliy

et al. 2016

Adaptive Control & Signal

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link SUMMARYThis paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias-constrained optimal finite impulse response filtering algorithm for linear discrete time-invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite-horizon and full-horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade-off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full-horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate.

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Optimal state estimation without the requirement of a priori statistics information of the initial state

Cited by 32 publications

References 10 publications

Stability and Robustness of Nonlinear Receding Horizon Control

Stability and Robustness of Nonlinear Receding Horizon Control

Effect of embedded unbiasedness on discrete-time optimal FIR filtering estimates

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

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