Receding Horizon Recursive State Estimation

Muske, Kenneth R.; Rawlings, James B.; Lee, Jay H.

doi:10.23919/acc.1993.4792993

Cited by 118 publications

(63 citation statements)

References 2 publications

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“…MHE was developed [18], [22], [27], [28] to avoid the computational burden encountered by full-information estimators. This so called "curse of dimensionality" arises from the need to solve optimization problems of ever increasing dimension as more measurements become available.…”

Section: Introductionmentioning

confidence: 99%

“…This so called "curse of dimensionality" arises from the need to solve optimization problems of ever increasing dimension as more measurements become available. Although restricted by this computational difficulty, full-information estimators have well developed convergence properties [22], [26], i.e., under certain conditions the estimated state is guaranteed to converge asymptotically to the true state of the system. A fundamental question, therefore, is to ask what convergence properties still hold for a given MHE scheme.…”

Section: Introductionmentioning

confidence: 99%

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Convergence Guarantees for Moving Horizon Estimation Based on the Real-Time Iteration Scheme

Wynn

Vukov

Diehl

2014

IEEE Trans. Automat. Contr.

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Abstract-In this note, conditions are proven under which a realtime implementable moving horizon estimation (MHE) scheme is locally convergent. Specifically, the real-time iteration scheme of [17] is studied in which a single Gauss-Newton iteration is applied to approximate the solution to the respective MHE optimization problem at each timestep. Convergence is illustrated by a challenging small scale example, the Lorenz attractor with an unknown parameter. It is shown that the performance of the proposed real-time MHE algorithm is nearly identical to a fully converged MHE solution, while its fixed execution time per sample would allow one to solve 30 000 MHE problems per second on current hardware.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convergence Guarantees for Moving Horizon Estimation Based on the Real-Time Iteration Scheme

Wynn

Vukov

Diehl

2014

IEEE Trans. Automat. Contr.

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“…The fixed-size estimation window is necessary to bound the size of the quadratic program. Most previous works assume that the noise among the system is mutually independent and the initial state and noise have (truncated) Gaussian distributions with zero means, where the posterior probability can be easily derived (Muske and Rawlings, 1993;Goodwin and Hernan, 2004), while in the CTA case as proposed in Equations (18) and (19), we take the varying means Gaussian distributions into account. That is:…”

Section: P Ro B L E M Fomentioning

confidence: 99%

“…When it comes to the constrained estimation problem, various filters other than traditional Kalman filtering have been presented (Simon, 2010), such as projecting methods, unscented filtering and truncated particle filtering, etc. To maintain a trade-off between accuracy and calculating costs, the MHE (Muske and Rawlings, 1993), which stems from the Bayesian Maximum a Posterior (MAP), is modified to better suit the proposed framework. The Bayesian MAP estimation of x given y essentially means the most likely value of x, given y is:…”

Section: P Ro B L E M Fomentioning

confidence: 99%

Performance Enhancement of Large-Ship Transfer Alignment: A Moving Horizon Approach

Yang

Wang

et al. 2012

J. Navigation

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In shipborne Transfer Alignment (TA) applications, partial observability is one of the most important factors limiting convergence velocity. This paper proposes a new method of attributing weak observable states and lever-arm variables to a group of constraints in order to improve the observability of TA model. This yields the so-called Constrained Transfer Alignment (CTA) model which is uniformly observable even under zero-manoeuvre conditions. Within this framework, the Moving Horizon Estimation (MHE) and its stability analysis are also addressed. Finally, comparative simulation results are given to demonstrate the advantages of the proposed approach.

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“…Thus the problem size grows without bound as more measurements are taken into account. To counteract the growing complexity, moving horizon estimation (MHE) schemes have been proposed and investigated by many authors, e.g., Muske et al (1993), Robertson et al (1996), Rao et al (2001).…”

Section: Introductionmentioning

confidence: 99%

Explicit Solution to Constrained Linear Estimation

Zhuo

Doná

Serón

2005

IFAC Proceedings Volumes

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This paper investigates the structure present in constrained linear state estimation problems formulated as a quadratic optimization program subject to linear inequality constraints. Polyhedral constraints on the system disturbance, the measurement noise, and the initial state are considered. The result interprets the measurement data and prior estimate as parameters and the parameter space is partitioned into multiple regions. Within each region the state estimate can be calculated as a piece-wise affine function of the measurement data and prior estimate. The parameterized regions and coefficients of the piece-wise affine function can be precomputed offline allowing a simplified approach in implementing a moving horizon estimation scheme. Copyright

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Receding Horizon Recursive State Estimation

Cited by 118 publications

References 2 publications

Convergence Guarantees for Moving Horizon Estimation Based on the Real-Time Iteration Scheme

Convergence Guarantees for Moving Horizon Estimation Based on the Real-Time Iteration Scheme

Performance Enhancement of Large-Ship Transfer Alignment: A Moving Horizon Approach

Explicit Solution to Constrained Linear Estimation

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