Robustness guarantees for linear control designs with an estimated nonlinear model error model

This paper proposes a twice rapid transfer alignment algorithm based on dual models in order to solve the problems such as long convergence time, poor accuracy, and heavy computation burden resulting from the traditional nonlinear error models. The quaternion matching method based on quaternion error model along with the extended Kalman filter (EKF) is applied to deal with the large misalignment in the first phase. Then in the second transfer alignment phase, velocity plus attitude matching method as well as classical Kalman filter is adopted. The simulation and the results of vehicle tests demonstrate that this method combines the advantages of both nonlinear and linear error models with the guarantee of accuracy and fastness.

Recognition that measurement error in the independent (predictor) variable of data used for regression modeling necessitates special methods of model fitting dates back to the late 1800s. In the ensuing 100 years attention was devoted almost entirely to measurement error in linear regression models, at which time advances in computing opened the door to the nonlinear statistical modeling generally, and to the study of measurement error in nonlinear regression modeling in particular. This article contains an introduction to the problem of measurement error in regression using linear regression measurement error models to illustrate key ideas. It includes a discussion of the types of measurement error commonly studied (classical and Berkson, differential and nondifferential) and how those types arise in practice. A summary of the consequences of ignoring measurement error when analyzing data measured with error is presented, with detailed results given for simple and multiple linear measurement error models. Pointers to the literature on both linear and nonlinear measurement error models are provided.

A new calibration model of a radio telescope that includes pointing error is presented, which considers nonlinear errors in the azimuth axis. For a large radio telescope, in particular for a telescope with a turntable, it is difficult to correct pointing errors using a traditional linear calibration model, because errors produced by the wheel-on-rail or center bearing structures are generally nonlinear. Fourier expansion is made for the oblique error and parameters describing the inclination direction along the azimuth axis based on the linear calibration model, and a new calibration model for pointing is derived. The new pointing model is applied to the 40m radio telescope administered by Yunnan Observatories, which is a telescope that uses a turntable. The results show that this model can significantly reduce the residual systematic errors due to nonlinearity in the azimuth axis compared with the linear model.

In recent years, quantum computing has been applied in optimizing different challenging systems in the domains of science and engineering. This work reflects the identification of the input nonlinear output error (I-NOE) model by using the Quantum-based avian navigation optimizer algorithm (QANA). QANA is an evolutionary method inspired by the precision navigation of migratory birds. The assessment of QANA is achieved on various iterations, population, and noise levels. The complexity, statistical, and convergence investigation of QANA with arithmetic optimization algorithm (AOA), coati optimization algorithm (COA), grey wolf optimizer (GWO), particle swarm optimization (PSO), synergistic swarm optimization algorithm (SSOA), and velocity pausing particle swarm optimization (VPPSO) approves the robustness of QANA for I-NOE model identification.

Abstract: In this paper, a method for determination of refractive index in membrane of fuel cell on basis of three-longitudinal-mode laser heterodyne interferometer is presented. The optical path difference between the target and reference paths is fixed and phase shift is then calculated in terms of refractive index shift. The measurement accuracy of this system is limited by nonlinearity error. In this study, nonlinearity error is modeled by multi-layer perceptrons (MLPs) and stacked generalization method (Stacking), using two learning methods; back propagation (BP) and genetic algorithm. Training neural networks with genetic algorithm, improves modeling of nonlinearity error in this system. In the proposed technique, a real code version of genetic algorithm is used. Parameters and genetic operators are set and designed accurately. The results indicate that the nonlinearity error can be effectively modeled by training the stacking with the genetic algorithm which has minimum mean square error (MSE). Keywords: Fuel cell, Genetic algorithm, Heterodyne interferometer, Multi-layer perceptrons, Nonlinearity error, Refractive index, Stacked Generalization.

We consider the assessment of outliers and influential observation in non-linear measurement error models. Residuals, leverage measures and case-deletiondiagonostics are examined. The method of local influence is also applied to the models. In particular, the perturbation of measurement error variances has been found useful in assessing the adequancy of the model assumptions. A numerical example is given to illustrate the application of the diagonostics.

A novel nonlinear attitude error model based on square root cubature information filter (SR-CIF) is proposed aiming to speed up the convergence rate of DVL-aided strapdown inertial navigation system (SINS) in-motion initial alignment for autonomous underwater vehicle (AUV) when both large initial heading error and large initial level attitude errors exist The new nonlinear attitude error model and measurement model are applicable for initial alignment after a short-time coarse alignment with large attitude errors exist. The SR-CIF embeds the whole iterative process into the data structure framework of the information filtering, replacing the covariance matrix in the square root cubature Kalman filter (SR-CKF) with an information matrix which simplifies the filter initialization. The square root technology ensures the symmetry and positive definiteness of the information matrix with enhanced stability of the filter. The simulation and experimental results indicate that the proposed DVL-aided alignment filter is effective with large initial attitude errors. The rate of convergence and estimation accuracy of the SR-CIF is higher than that of the conventional SR-CKF with large attitude misalignments.

The use of linear error correction models based on stationarity and cointegration analysis, typically estimated with least squares regression, is a common technique for financial time series prediction. In this paper, the same formulation is extended to a nonlinear error correction model using the idea of a kernel-based implicit nonlinear mapping to a high-dimensional feature space in which linear model formulations are specified. Practical expressions for the nonlinear regression are obtained in terms of the positive definite kernel function by solving a linear system. The nonlinear least squares support vector machine model is designed within the Bayesian evidence framework that allows us to find appropriate trade-offs between model complexity and in-sample model accuracy. From straightforward primal–dual reasoning, the Bayesian framework allows us to derive error bars on the prediction in a similar way as for linear models and to perform hyperparameter and input selection. Starting from the results of the linear modelling analysis, the Bayesian kernel-based prediction is successfully applied to out-of-sample prediction of an aggregated equity price index for the European chemical sector. Copyright © 2006 John Wiley & Sons, Ltd.

Over the last years miRNA microarray platforms have provided insights in the biological mechanisms underlying onset and development of several diseases and have thus become a very popular instrument for profiling thousands of miRNA simultaneously. However, because of large variety of microarray platforms available, an assessment of their performance in terms of both within-platform reliability and between-platform agreement is needful. In particular, assessment of platform concordance has been a very relevant issue in the past decade. To date, only a few studies have evaluated this problem in the field of miRNA microarray, and mostly by using improper statistical methods such as the Pearson and Spearman correlation coefficients. In this work we suggest to use a recently proposed modified version of the classical Bland-Altman approach for comparing clinical measurement methods. This modified version is useful in that allows not only to evaluate agreement between different miRNA microarray platforms, but also to assess which are the potential sources of disagreement/bias between them.Two samples were profiled using Affymetrix, Agilent and Illumina miRNA platform using three technical replicates each, and pairwise agreement between platforms was evaluated within each sample. Our results suggest that, after bias correction, Illumina and Agilent show the best patterns of agreement for both samples involved in the experiment, whereas Affymetrix is the one which seem to ”disagree” most, suggesting that a linear relationship as that hypothesized by the measurement error model used is not able to capture the complexity of the phenomenon.In the future it will be interesting to apply this method also to the comparison of microarray and NGS platform, a topic which is becoming more and more relevant, also by adopting non-linear measurement error models to depict relationships between platforms.

Analyses of variables measured with error are often flawed when measurement error is ignored. An extensive literature on linear measurement error models is available by [1], and more recently, for non-linear measurement error models by [2] and [3]. We investigate problems encountered in the analysis of longitudinal change, where the difference in some outcome variable is modeled on a set of regressor variables in a linear regression model. This type of analysis has become quite popular in biomedical research, and the results are often biased when the outcome variable is measured with error and its observed baseline value is included as a covariate in the fitted model. [4] demonstrated the effects of measurement error in the analysis of change in wall thickness of the common carotid artery. They showed the naive analysis led to erroneous findings due to the measurement error bias, even when the regressor variables were assumed to be measured precisely. In this paper, we present a method-of-moments correction for measurement error bias, provided the measurement error variance is known or can be estimated. This work extends the work of [4] to include regressor variables that are measured with error.

Disturbance observer based reliable H∞ fuzzy attitude tracking control for Mars entry vehicles with actuator failures

Vehicle state estimation based on Minimum Model Error criterion combining with Extended Kalman Filter

In this paper, a uniform form for the nonlinear error model is proposed for the inertial navigation system (INS). A modified quaternion-based nonlinear error model is derived using the uniform coordinate frame for the INS. Based on the modified quaternion-based nonlinear error model, a uniform form of the nonlinear error model is proposed based on the Gibbs parameter. The uniform form can present the nonlinear error model based on low-order Rodrigues parameters or Rodrigues-like parameters for the INS. Field tests are carried out to assess the performance of the existing typical nonlinear error models.

The large misalignment angle error model of strapdown inertial navigation system (SINS) is a kind of nonlinear Gauss error model. The Gauss Hermite method can approach Gauss integral with any precision, and achieve high precision filtering effect. The number of Gauss Hermite integral points is exponentially related to the dimension of nonlinear system. In the process of real-time filtering, a large number of integral points of multidimensional system may lead to dimension disaster. According to the initial alignment error model of SINS with large misalignment angle, this paper presents a strong tracking reduced dimension sparse grid Gauss Hermite filtering method, which reduces the nonlinear integration dimension through separation of the linear and nonlinear terms, further reduces the number of Gauss hermit filtering integration points by sparse grid method, and ensures the stability of the system by strong tracking method.

In this work, a nonlinear model is developed to simulate the respiratory system of neonatal infants. The nonlinear model is based on a model proposed by other researchers, but with varying parameters based on the oxygen saturation output [1]. The nonlinear model response is compared to the response of a linearized model given small and large step inputs. For small step sizes, the nonlinear and linear models responses are nearly identical. For larger step sizes, the nonlinear model has a higher steady state response. The linear and nonlinear models are also compared to clinical data taken from a bedside monitor. An error model is also developed given known ranges for model parameter variations. Since the varying parameters change performance, a robust controller is designed using the error model and performance specifications using a μ-synthesis optimization. The controller is shown to have robust stability and performance.