Optimum measurements for estimation

Herring, Kenneth D.; Melsa, James L.

doi:10.1109/tac.1974.1100568

Cited by 33 publications

(26 citation statements)

References 4 publications

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“…When the process has a finite duration, the steady-state is not achieved (e.g., [11]). Optimizing the performance over a finite time interval is to be considered [6], [13]. The optimal periodic schedule in a model with discrete time is sought in [13] with respect to the performance over a finite time interval.…”

Section: A Previous Workmentioning

confidence: 99%

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Optimal Measurement Times for Observing a Brownian Motion over a Finite Period Using a Kalman Filter

Aksenov

Amblard

Michel

et al. 2017

Latent Variable Analysis and Signal Separation

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The measure timetable plays a critical role for the accuracy of the estimator. This article deals with the optimization of the schedule of measures for observing a random process in time using a Kalman filter, when the length of the process is finite and fixed, and a fixed number of measures are available. The measuring devices are allowed to differ. The mean variance of the estimator is chosen as criterion for optimality. The cases of 1 or 2 measures are studied in detail, and analytical formulas are provided.

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Section: A Previous Workmentioning

confidence: 99%

“…It is supposed that the interval is long enough with respect to the measurement period. No additional assumptions regarding the number of measurements or the duration of the process (which is supposed to be finite) are made in the seminal work [6]. A model, where sensors are active during an interval of time, is considered.…”

Section: A Previous Workmentioning

confidence: 99%

Optimal Measurement Times for Observing a Brownian Motion over a Finite Period Using a Kalman Filter

Aksenov

Amblard

Michel

et al. 2017

Latent Variable Analysis and Signal Separation

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“…The second group, Athans (1972), Herring and Melsa (1974), Sargent (1977, 1978) includes both state excitation and measurement noise. They define the performance index of the estimator to be a sum of measurement costs and the integral square estimation error.…”

Section: Conclusion and Significancementioning

confidence: 99%

Studies in the synthesis of control structures for chemical processes: Part III: Optimal selection of secondary measurements within the framework of state estimation in the presence of persistent unknown disturbances

Morari

Stephanopoulos

1980

AIChE Journal

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When primary control objectives cannot be measured directly, secondary measurements have to be selected and used in conjunction with estimators to infer the value of the unmeasurable variables. Unmeasured process disturbances (state excitation noise) are assumed to be of major importance, dominating the errors caused by measurement noise. Since the white noise assumption is generally insufficient for the persistent disturbances commonly occurring in the chemical engineering environment, a nonstationary noise model has been employed, and is shown to yield superior estimations under these circumstances. New necessary and sufficient conditions have been developed for the observability of the dynamic system augmented to include the noise model.A variety of new measurement selection criteria is presented here, with the goal of minimizing estimation error. One class of criteria aims at minimizing the transient estimation error when a static estimator is used. The other class minimizes the measurement error caused by the unobservable subspace. The design of state reconstruction procedures (which are able to handle persistent unmeasured process disturbances) is explained in a stochastic and a deterministic framework. Finally, the synthesis of reduced order control schemes is discussed. The power of the selection criteria and the superiority of a Kalman filter design employing a nonstationary noise model is demonstrated in many examples. MANFRED MORARI and GEORGE STEPHANOPOULOS SCOPEFrequently, in process control, some important variables are not available for measurement. Secondary measurements have to be selected and used to infer the value of the unmeasurable variables. The proper selection of secondary measurements is a task of paramount importance for the synthesis of control structures. The measurements should be selected to minimize estimation error. The error can be caused by differences between the real system and the process model which forms the basis for the design of the estimator, or by process and measurement noise. Here, the criteria derived consider the influence of those different factors on the error separately: Selection Criterion 1 assumes a steady state model and minimizes the error caused by unmeasurable inputs with normally distributed amplitudes: Selection Criterion 2 (Joseph, Brosilow 1978) minimizes the influence of model inaccuracies.Criteria 3 and 4 minimize the error when a static estimator, which has the advantage of being very simple to implement, is used for the dynamic system. For a linear dynamic system with white state excitation and measurement noise, the Kalman filter is known to be the best estimator-in the sense of minimum variance, maximum likelihood, etc. If a step change in the inputs to the unit occurs which cannot be measured, o r if an unknown change is caused by drifting conditions upstream (so that the process will display a steady state or pseudo steady state behavior under those disturbances), this estimator performs quite poorly. The objective of this article is to prese...

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“…A different numerical approach to solve the problem was provided in [3] which cast the problem as a two-point boundary value problem. This approach was further considered in [11], [14]. A completely general framework for nonlinear systems and general nonlinear diffusion sensor signals was developed in the seminal paper [4].…”

Section: Introductionmentioning

confidence: 99%

Sensor Scheduling using Smart Sensors

Hovareshti

Gupta

Baras

2007

2007 46th IEEE Conference on Decision and Control

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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government.ISR is a permanent institute of the University of Maryland, within the A. James Clark School of Engineering. It is a graduated National Science Foundation Engineering Research Center. Sensor Scheduling using Smart SensorsPedram Hovareshti, Vijay Gupta and John S. BarasAbstract-The sensor selection problem arises when multiple sensors are jointly trying to estimate a process but only a subset of them can take and/or use measurements at any time step. In a networked estimation situation, sensors are typically equipped with some memory and processing capabilities. We illustrate that utilization of these capabilities can lead to significant performance gains in the sensor selection problem for improved inference. Further, it also leads to significant pruning of the search tree that yields the optimum sensor schedule. We also present a periodicity result for the case where the decision is whether the sensor should transmit or not.

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Optimum measurements for estimation

Cited by 33 publications

References 4 publications

Optimal Measurement Times for Observing a Brownian Motion over a Finite Period Using a Kalman Filter

Optimal Measurement Times for Observing a Brownian Motion over a Finite Period Using a Kalman Filter

Studies in the synthesis of control structures for chemical processes: Part III: Optimal selection of secondary measurements within the framework of state estimation in the presence of persistent unknown disturbances

Sensor Scheduling using Smart Sensors

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