Parameter Estimation Issues Research Articles

A modular approach to addressing model design, scale, and parameter estimation issues in distributed hydrological modelling

AbstractA modular approach to model design and construction provides a flexible framework in which to focus the multidisciplinary research and operational efforts needed to facilitate the development, selection, and application of the most robust distributed modelling methods. A variety of modular approaches have been developed, but with little consideration for compatibility among systems and concepts. Several systems are proprietary, limiting any user interaction. The US Geological Survey modular modelling system (MMS) is a modular modelling framework that uses an open source software approach to enable all members of the scientific community to address collaboratively the many complex issues associated with the design, development, and application of distributed hydrological and environmental models. Implementation of a common modular concept is not a trivial task. However, it brings the resources of a larger community to bear on the problems of distributed modelling, provides a framework in which to compare alternative modelling approaches objectively, and provides a means of sharing the latest modelling advances. The concepts and components of the MMS are described and an example application of the MMS, in a decision‐support system context, is presented to demonstrate current system capabilities. Copyright © 2002 John Wiley & Sons, Ltd.

Identification of black-box nonlinear models for lower limb movement control using functional electrical stimulation

In this work, the problem of identification of nonlinear models for the functional electrical stimulation (FES) process is considered. In particular, experiments of stimulation of the quadriceps muscle group and the subsequent movement (or torque release) of the knee-joint will be examined. Both isometric and isotonic experimental conditions are described and NARX models will be identified from data, considering polynomial and neural network structures. For both model families, the issues of parameter estimation, structural identification and model validation will be discussed and effective solutions are proposed.

Estimation of multicomponent polynomial phase signals of mixed orders

This paper addresses the issue of detection and parameter estimation of multicomponent polynomial phase signals (mc-PPS) embedded in noise. We focus on analyzing a general class of mc-PPS in the sense that we allow the PPS to have (i) very different amplitudes, (ii) unknown phase orders, and (iii) unknown number of components. We first show how existing techniques are inadequate in providing reliable estimates for such a broad class of mc-PPS. High-order ambiguity function (HAF) and its product multi-lag variant (PHAF) are the basic tools that we use here. The main contribution of this paper is that we present a recursive algorithm that always starts with the lowest order HAF (or PHAF) to successively detect, estimate, and remove the PPS components. This is contrasted with prevailing mc-PPS estimation techniques where the highest order HAF is first used and the PPS components are often assumed to have the same phase orders and like amplitudes. Computer simulations are carried out to illustrate the advantage of the proposed algorithm over existing techniques.

A Model-Based Inversion of Rough Soil Surface Parameters From Radar Measurements

In this paper, a model-based retrieval algorithm is developed for the remote sensing of rough surfaces. The probabilistic and sensitive issues of parameter estimation for soil surfaces are discussed and modeled. A geophysical model function (GMF) that relates the input (observation space) and output vectors (parameter space) includes both an electromagnetic scattering model and a dielectric model; the electromagnetic scattering model describes the relationship between the radar echoes and the target parameters (geometrical and electrical), while the dielectric model connects the electrical parameter (permittivity) to the geophysical parameter of interest (soil moisture). Within the framework of an integral equation model, a scattering model is devised and used as part of the GMF. To estimate the parameters from finite sets of measurements, a good approximation of an GMF inverse function of GMF is required. We apply a neural technique to do this, by exploring its many merits, including not needing an explicit function. The necessary training data sets are generated using the GMF within a pre-defined domain. In order to alleviate an ill-posed problem, in which more than one set of parameters may be mapped onto a single backscattering coefficient, (i.e, non-unique), the range of parameters must be properly selected through a sensitivity analysis. In practice, the measured data are unavoidably contaminated by inherent noise. It turns out that the measurement uncertainty becomes quite large making the inversion accuracy even worse. By properly taking the noise components into account in the training data, the noise-tolerant capability of the inversion system can be increased. A reasonably good estimation of the surface correlation length, the roughness, and the soil moisture parameters may be obtained from laboratory-controlled measurements and AIRSAR data in this study.

Modeling Term Structure Dynamics: An Infinite Dimensional Approach

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

Product high-order ambiguity function for multicomponent polynomial-phase signal modeling

Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPSs) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results.

Parameter estimation in Extended Kalman Filters for quality control in polymerization reactors

The issue of parameter estimation in Extended Kalman Filters is addressed in this paper. It is shown that the use of parameters as additional system states is appropriate whenever there are systematic errors in the model of the process. Such is the case of the filters which are used to estimate quality properties of polymers which are not measured on-line in polymerization reactors. Criteria for the choice of the parameters to be updated are suggested. Moreover, in order to realize the possibility of obtaining offset free response, the effect of errors on both updated and not updated parameters, both on the observable and on the unobservable system states is analysed. Applications to the polymerization of methylmethacrylate (MMA) in a continuous stirred tank reactor confirm the theoretical results.

An empirical study of the simulation of various models used for images

Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation. >

Statistical models for PET and SPECT data.

This article outlines the statistical developments that have taken place in emission tomography during the past decade or so. We discuss the statistical aspects of the modelling of the projection data and define the additive Poisson regression model. This leads to the use of the method of maximum likelihood as a means of estimating the underlying isotope concentration within a given region of a patient's body, and to the use of the EM algorithm to compute the reconstruction. The need for the regulation of the maximum likelihood solution is tackled using Bayesian techniques. A number of algorithms for the computation of regularized solutions are outlined. The issue of parameter estimation is discussed and some open issues are mentioned.

Correct and Incorrect Error Specifications in Statistical Cost Models

A functional form often employed in cost-estimating relationships is Y = otYP, where Y and X are the cost and predictor variables, respectively, and a and (3 are parameters to be estimated from empirical data. Logarithmic transformation of either side of this intrinsically linear relationship leads to 7* a* + fL¥*, with the asterisks denoting logs. What typically happens in practice is that ordinary least squares (OLS) regression is applied to a set of observations on Y* and X*, generating estimates of a* and p. From a statistical point of view, however, justification of this process requires the presence of a multiplicative random error term in the untransformed model. In addition, the multiplicative structure gives rise to variance in cost that changes systematically with X. If the error term is additive, the variance in cost will be constant, but the parameters in that model must be estimated by nonlinear least squares (NLS) applied to the untransformed variables. In general, OLS and NLS lead to different parameter estimates and different cost predictions, and frequently analysts are unsure as to which method is correct. This paper reports on a Monte Carlo study of the accuracy of each estimation method under correct and incorrect error specifications. The multi-predictor model that serves as the basis of the study is representative of models with which cost analysts frequently deal. Results suggest that OLS, applied to the logs of the variables, may be the preferred method under either specification, provided the estimate of a is properly developed. This finding, however, is applicable strictly to the issue of parameter estimation. Accuracy of cost prediction requires further analysis.

Parameter estimations of normal fuzzy variables

Although fairly much attention has been paid to theoretical applications of Nahmias' fuzzy variables, little effort has been focused on the related parameter estimation issues. This keeps down the practical use of fuzzy variables. In this note we make a preliminary discussion on parameter estimation of normal fuzzy variables with parameters ( a , b ) and distinguish three situations: estimation of a with b known, estimation of b with a known, and estimation of unknown a and b . Formulae for calculating parameter estimates by use of practical collected data are presented.

Computational issues in parameter estimation and feedback control problems for partial differential equation systems

We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems,(ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. Sufficient conditions for convergence of algorithms for these problems are discussed; in both cases, some type of adjoint or costate system convergence is required in addition to the expected system convergence. Examples are discussed that illustrate computational difficulties which may arise if only convergence of the approximate system holds (i.e., in the event costate convergence does not hold).