Improved Parameter Estimation by Noise Compensation in the Time-Scale Domain

2009 ◽  
Author(s):  
James R. McCusker ◽  
Todd Currier ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Dynamic Model ◽  
Time Scale ◽  
Prediction Error ◽  
Noise Suppression ◽  
Model Parameters ◽  
Individual Parameter ◽  
Noise Compensation ◽  
Confidence Factor ◽  
Estimated Parameters

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter attributions of the prediction error, individual parameter errors can be estimated for iterative parameter estimation. A benefit of relying entirely on the time-scale domain for parameter estimation is the added capacity for noise suppression. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates it as a confidence factor when estimating individual parameter errors. This method is shown to further improve the estimated parameters beyond the time-filtering and denoising techniques developed for time-based estimation.

Parameter Adaptation by Parameter Signature Isolation in the Time-Scale Domain

2008 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker
Keyword(s):  
Error Estimates ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Noise Suppression ◽  
Model Parameters ◽  
Isolation Method ◽  
Parameter Adaptation ◽  
Single Output ◽  
Parameter Error

It is shown that delineation of output sensitivities with respect to model parameters in dynamic models can be enhanced in the time-scale domain. This enhanced differentiation of output sensitivities then provides the capacity to isolate regions of the time-scale plane wherein a single output sensitivity dominates the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at these regions so as to estimate each model parameter error separately. The proposed Parameter Signature Isolation Method (PARSIM) that uses these parameter error estimates for parameter adaptation has been found to have an adaptation precision comparable to that of the Gauss-Newton method for noise-free cases. PARSIM, however, appears to be less sensitive to input conditions, while offering the promise of more effective noise suppression by the capabilities available in the time-scale domain.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker
Keyword(s):  
Parameter Estimation ◽  
Error Estimates ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Noise Suppression ◽  
Isolation Method ◽  
Estimation Precision ◽  
Parameter Error

It is shown that output sensitivities of dynamic models can be better delineated in the time-scale domain. This enhanced delineation provides the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at each parameter signature so as to enable estimation of each model parameter error separately. As a test of fidelity, the estimated parameter errors are evaluated in iterative parameter estimation in this paper. The proposed parameter signature isolation method (PARSIM) that uses the parameter error estimates for parameter estimation is shown to have an estimation precision comparable to that of the Gauss–Newton method. The transparency afforded by the parameter signatures, however, extends PARSIM’s features beyond rudimentary parameter estimation. One such potential feature is noise suppression by discounting the parameter error estimates obtained in the finer-scale (higher-frequency) regions of the time-scale plane. Another is the capacity to assess the observability of each output through the quality of parameter signatures it provides.

Mutual Identifiability Analysis for Parameter Signature Isolation in the Time-Scale Plane

2008 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker ◽  
C. V. Hollot
Keyword(s):  
Time Scale ◽  
Prediction Error ◽  
Linear Models ◽  
Necessary Condition ◽  
Model Parameters ◽  
Identifiability Analysis ◽  
Individual Model ◽  
Model Parameter

It was shown recently that regions in the time-scale plane can be isolated wherein the prediction error can be attributed to the error of an individual model parameter. A necessary condition for this isolation capacity is the mutual (pairwise) identifiability of the model parameters. This paper presents conditions for mutual identifiability of parameters of linear models and refines these conditions for models that exhibit rank-1 dependency on the parameters.

Design of Experiments Using Uncertainty Information

1996 ◽  
Vol 118 (3) ◽  
pp. 532-538 ◽  
Author(s):  
A. F. Emery ◽  
T. D. Fadale
Keyword(s):  
Inverse Problem ◽  
Parameter Estimation ◽  
Design Of Experiments ◽  
Measurement Noise ◽  
Model Parameters ◽  
Maximum Information ◽  
Estimated Parameters ◽  
Uncertainty Information

The process of parameter estimation and the estimated parameters are affected not only by measurement noise, which is present during any experiment, but also by uncertainties in the parameters of the model used to describe the system. This paper describes a method to optimize the design of an experiment to deduce the maximum information during the inverse problem of parameter estimation in the presence of uncertainties in the model parameters. It is shown that accounting for these uncertainties affects the optimal locations of the sensors.

Validation of Dynamic Models by Image Distances in the Time-Scale Domain

2009 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker ◽  
Todd Currier ◽  
David O. Kazmer
Keyword(s):  
Time Series ◽  
Dynamic Model ◽  
Model Validation ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Traditional Approaches

Model validation is the procedure whereby the fidelity of a model is evaluated. The traditional approaches to dynamic model validation either rely on the magnitude of the prediction error between the process observations and model outputs or consider the observations and model outputs as time series and use their similarity to assess the closeness of the model to the process. Here, we propose transforming these time series into the time-scale domain, to enhance their delineation, and using image distances between these transformed time series to assess the closeness of the model to the process. It is shown that the image distances provide a more consistent measure of model closeness than available from the magnitude of the prediction error.

Interpretation of Simulation Studies for Efficient Estimation of Population Pharmacokinetic Parameters

1993 ◽  
Vol 27 (9) ◽  
pp. 1034-1039 ◽  
Author(s):  
Ene I. Ette ◽  
Andrew W. Kelman ◽  
Catherine A. Howie ◽  
Brian Whiting
Keyword(s):  
Parameter Estimation ◽  
Efficient Estimation ◽  
Experimental Unit ◽  
Pharmacokinetic Parameters ◽  
Population Pharmacokinetic ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Good Precision ◽  
Simulation Studies ◽  
Individual Parameter

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (Φ) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The Φ approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the Φ for individual parameter estimation and the overall Φ for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.

Improved parameter estimation by noise compensation in the time-scale domain

2011 ◽  
Vol 91 (1) ◽  
pp. 72-84 ◽  
Author(s):  
James R. McCusker ◽  
Todd Currier ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Noise Compensation

Utilizing the Ensemble Kalman Filter and Ensemble Kalman Smoother for Combined State and Parameter Estimation of a Three-Dimensional Towed Underwater Cable Model

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Jan Vidar Grindheim ◽  
Inge Revhaug ◽  
Egil Pedersen
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Three Dimensional ◽  
Ocean Current ◽  
Model Parameters ◽  
State Variables ◽  
Kalman Smoother ◽  
Estimated Parameters ◽  
Underwater Cables

A finite difference method (FDM) solving the coupled partial differential equations governing three-dimensional (3D) motions of a towed underwater cable has been implemented in a combined ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), as a new approach to combined state and parameter estimation for towed underwater cables. A simulation study of the method applied to a seismic streamer has been performed. Cable state variables as well as model parameters are estimated. Parameters estimated are crossline ocean current varying with time as well as cable tangential drag coefficient. The presented results indicate that the method is able to estimate state as well as parameters for seismic streamers.

Reducing Forecast Errors Due to Model Imperfections Using Ensemble Kalman Filtering

2010 ◽  
Vol 138 (8) ◽  
pp. 3316-3332 ◽  
Author(s):  
Hiroshi Koyama ◽  
Masahiro Watanabe
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Lead Time ◽  
General Circulation ◽  
Forecast Error ◽  
Small Scale ◽  
Model Parameters ◽  
Forecast Errors ◽  
Model Ensemble ◽  
Forecast Lead Time

Abstract A method is introduced for reducing forecast errors in an extended-range to one-month forecast based on an ensemble Kalman filter (EnKF). The prediction skill in such a forecast is typically affected not only by the accuracy of initial conditions but also by the model imperfections. Hence, to improve the forecast in imperfect models, the framework of EnKF is modified by using a state augmentation method. The method includes an adaptive parameter estimation that optimizes mismatched model parameters and a model ensemble initialized with the perturbed model parameter. The main features are the combined ensemble forecast of the initial condition and the parameter, and the assimilation for time-varying parameters with a theoretical basis. First, the method is validated in the imperfect Lorenz ’96 model constructed by parameterizing the small-scale variable of the perfect model. The results indicate a reduction in the ensemble-mean forecast error and the optimization of the ensemble spread. It is found that the time-dependent parameter estimation contributes to reduce the forecast error with a lead time shorter than one week, whereas the model ensemble is effective for improving a forecast with a longer lead time. Moreover, the parameter assimilation is useful when model imperfections have a longer time scale than the forecast lead time, and the model ensemble appears to be relevant in any time scale. Preliminary results using a low-resolution atmospheric general circulation model that implements this method support some of the above findings.

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