Robust Estimation Problem Research Articles

Robust Scheduling Filter Design for a Class of Nonlinear Stochastic Poisson Signal Systems

Nonlinear dynamic systems may suffer from both continuous Wiener noise and discontinuous Poisson noise. This paper studies a robust filter design for a class of nonlinear stochastic Poisson signal systems with external disturbances. Currently, there are no good filtering design methods to treat the discontinuous Poisson noise filter problem. Based on the Ito-Levy formula, a robust $H_{\infty}$ filter design is proposed for nonlinear stochastic Poisson signal systems by solving a Hamilton-Jacobi inequality (HJI) for the robust filter design of a nonlinear stochastic Poisson signal system. However, such an HJI is difficult to solve. Hence, this study employs the Polytopic Linear Model(PLM) scheduling scheme to approximate this HJI by a set of linear matrix inequalities(LMIs) so that the $H_{\infty}$ robust filter design problem for a nonlinear stochastic Poisson signal system can be simplified. The optimal $H_{\infty}$ robust scheduling filter design problem for the nonlinear stochastic Poisson signal system is also discussed. Since the PLM interpolation method transforms the HJI-constrained optimization problem into an LMI-constrained optimization problem which can be efficiently solved using the LMI toolbox in MATLAB, an optimal filtering level $\gamma^{\ast}$ (the minimum value of the filtering error-to-noise ratio in a mean square sense) can be achieved. Finally, a simulation example of a robust trajectory estimation problem in an anti-tactical ballistic missile radar system with discontinuous random maneuvering jets is given to illustrate the design procedure and to confirm the estimation performance of the proposed $H_{\infty}$ robust scheduling filter.

Simple robust parameter estimation for the Birnbaum-Saunders distribution

We study the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution. It is well known that the maximum likelihood estimator (MLE) is efficient when the underlying model is true but at the same time it is quite sensitive to data contamination that is often encountered in practice. In this paper, we propose several estimators which have simple closed forms and are also robust to data contamination. We study the breakdown points and asymptotic properties of the proposed estimators. These estimators are then applied to both simulated and real datasets. Numerical results show that the proposed estimators are attractive alternative to the MLE in that they are quite robust to data contamination and also highly efficient when the underlying model is true.

Robust dissipativity and passivity based state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays

In this paper, the problem of robust state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays is investigated based on dissipativity and passivity theory. The parameters of the neural networks are subject to the switching from one mode to another according to a Markov chain. By using the Lyapunov---Krasovskii functional together with linear matrix inequality approach, a new set of sufficient conditions are derived for the existence of state estimator such that the error state system is strictly $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma $$(Q,S,R)-?-dissipative. Finally, numerical examples are addressed to show the effectiveness of the proposed design method .

A Polynomial Approach to Robust Estimation of Uncertain Discrete-Time Systems

The robust estimation problem for uncertain discrete-time systems is treated in this paper considering parametric uncertainties in the polynomial framework. The estimator is the minimiser of a cost function written in a $\epsilon$ -contaminated form. Uncertainties are not formally modelled. It is shown that, in the present context, the proposed approach can be connected to stochastic modelling of uncertainties. The optimal robust estimator is obtained by computing a spectral factorisation and by solving a single Diophantine equation. An example shows the efficiency of the proposed method.

Identification of asymmetric conditional heteroscedasticity in the presence of outliers

The identification of asymmetric conditional heteroscedasticity is often based on sample cross-correlations between past and squared observations. In this paper we analyse the effects of outliers on these cross-correlations and, consequently, on the identification of asymmetric volatilities. We show that, as expected, one isolated big outlier biases the sample cross-correlations towards zero and hence could hide true leverage effect. Unlike, the presence of two or more big consecutive outliers could lead to detecting spurious asymmetries or asymmetries of the wrong sign. We also address the problem of robust estimation of the cross-correlations by extending some popular robust estimators of pairwise correlations and autocorrelations. Their finite sample resistance against outliers is compared through Monte Carlo experiments. Situations with isolated and patchy outliers of different sizes are examined. It is shown that a modified Ramsay-weighted estimator of the cross-correlations outperforms other estimators in identifying asymmetric conditionally heteroscedastic models. Finally, the results are illustrated with an empirical application.

Minimization Problems Based on Relative <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> ) were studied. Such minimizers were called forward ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> -projections. Here, a complementary class of minimization problems leading to the so-called reverse ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> -projections are studied. Reverse ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> -projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (α > 1) and in constrained compression settings (α <; 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> -projection into a forward ℐ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sub> -projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

Agostinelli, Leung, Yohai and Zamar (Agostinelli et al. in the remainder) consider the difficult problem of robust estimation based on high-dimensional data. If outlying values can appear independently in the variables, then it can easily occur that the majority of the observations in high-dimensional data is contaminated, as pointed out in Alqallaf et al (2009). Consequently, standard robust methods fail in this case, and new methods need to be developed that can handle this type of contamination. Moreover, next to independent contamination also casewise or structural outliers can still appear in the data. This situation was formalized as the partially spoiled independent contamination model (PSICM) in Alqallaf et al (2009). In their paper Agostinelli et al. are the first to introduce a consistent estimator of multivariate location and scatter that is highly robust against both cellwise and casewise outliers. The 2SGS is a strongly consistent estimator of the location and shape of general elliptical distributions. Similarly to other proposals, the estimator proceeds in two steps. In the first step an outlier detection rule is used to identify potential cellwise outliers. A first improvement is the use of a data adaptive cutoff instead of a fixed cutoff value when filtering cellwise outliers. The second novelty is to replace flagged outliers by missing values as first proposed in Danilov (2010) and Farcomeni (2013), while earlier proposals tried to reduce their effect through some form of Winsorization, see e.g. Alqallaf et al. (2002), Van Aelst et al. (2011,2012), Van Aelst (2015). In the second step, the location and scatter are estimated based on the data set with missing values by using the GSE estimator of Danilov et al (2012). GSE

A fast and robust homography scheme for real-time planar target detection

The present paper is concerned with the problem of robust pose estimation for planar targets in the context of real-time mobile vision. For robust recognition of targets at very low computational costs, we employ feature-based methods which are based on local binary descriptors allowing fast feature matching at run time. The matching set is then fed to a robust parameter estimation algorithm to obtain a reliable estimate of homography. The robust estimation of model parameters, which in our case is a 2D homographic transformation, constitutes an essential part of the whole recognition process. We present a highly optimized and device-friendly implementation of homography estimation through a unified hypothesize-and-verify framework. This framework is specifically designed to meet the growing demand for fast and robust estimation on power-constrained platforms. The focus of the approach described in this paper is not only on developing fast algorithms for the recognition framework, but also on the optimized implementation of such algorithms by accounting for the computing capacity of modern CPUs. The experimentations show that the resulting homography estimation implementation proposed in this paper brings a speedup of 25 $$\times$$ over the regular OpenCV RANSAC homography estimation function.

Robust finite-time state estimation of uncertain neural networks with Markovian jump parameters

In this paper, the robust finite-time state estimation problem of the uncertain Markovian jump neural networks with partly unknown transition probabilities is investigated. In the neural networks, there are a set of modes, which are determined by Markov chain. First, we design a state observer to estimate the neuron states. Second, based on Lyapunov stability theory, a robust stability sufficient condition is derived such that the uncertain Markovian jump neural networks with partly unknown transition probabilities are robust finite-time stable. Then, the robust stability condition is expressed in terms of linear matrix inequalities (LMIs), which can be easily solved by standard software. Finally, a numerical example is given to demonstrate the effectiveness of the proposed new design techniques.

Robust stability and evaluation of the quality functional for nonlinear control systems

We develop new methods of robust stability analysis for equilibrium states and optimization of nonlinear feedback control systems. For a family of nonlinear systems with uncertain matrices of coefficients and measurable output feedback we formulate sufficient stability conditions for the zero state with a general quadratic Lyapunov function. We propose a solution for the general robust stabilization and estimation problem for a quadratic performance index for a family of nonlinear systems. We show an example of a stabilization system for a single-link robot manipulator.

Robust state estimation for Markov jump genetic regulatory networks based on passivity theory

In this article, the robust state estimation problem for Markov jump genetic regulatory networks (GRNs) based on passivity theory is investigated. Moreover, the effect of time‐varying delays is taken into account. The focus is on designing a linear state estimator to estimate the concentrations of the mRNAs and the proteins of the GRNs, such that the dynamics of the state estimation error can be stochastically stable while achieving the prescribed passivity performance. By applying the Lyapunov–Krasovskii functional method, delay‐dependent criteria are established to ensure the existence of the mode‐dependent estimator in the form of linear matrix inequalities. Based on the obtained results, the parameters of the desired estimator gains can be further calculated. Finally, a numerical example is given to illustrate the effectiveness of our proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 214–223, 2016

Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach

This paper is concerned with the problem of robust fault estimation and fault-tolerant control for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and actuator faults. Based on the ( $k-1$ )th fault estimation information, a novel $k$ -step fault-estimation observer is proposed to construct the $k$ th fault error dynamics. The obtained fault estimates via $k$ -step fault-estimation can practically better depict the size and shape of the faults. Then, based on the information of online $k$ -step fault-estimation, a dynamic output feedback fault tolerant controller is designed to compensate the fault effects on the closed-loop fuzzy system. Furthermore, some less conservative delay dependent sufficient conditions for the existence of fault estimation observers and fault tolerant controllers are given in terms of solution to a set of linear matrix inequalities. Finally, simulation results of two numerical examples are presented to show the effectiveness and merits of the proposed methods.

A Unified Framework for Solving a General Class of Conditional and Robust Set-Membership Estimation Problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.

Optimize Preview Model Parameters Evaluation of RANSAC

The Random Sample Consensus (RANSAC) algorithm is a popular tool for robust estimation problems in computer vision, primarily due to its ability to tolerate a tremendous fraction of outliers. In this paper, we propose an approach for optimizing the preview model parameters evaluation of RANSAC that has the benefit of offering fast and accurate RANSAC. With guaranteeing the same confidence of the solution as RANSAC, a very large number of erroneous model parameters obtained from the contaminated samples are discarded in the preview evaluation selection. And use local optimization step apply to selected models. The combination of these two strategies results in a robust estimation procedure that provides a significant speed and accuracy RANSAC techniques, while requiring no prior information to guide the sampling process.

Robust Fault Estimation for Takagi–Sugeno Nonlinear Systems with Time-Varying State Delay

This paper addresses the problem of robust fault estimation for Takagi---Sugeno (T---S) nonlinear systems with time-varying state delay. Under $$H_{\infty }$$ H ? performance constraint, a fuzzy-augmented fault estimation observer (AFEO) design is proposed to enhance the performance of fault estimation for T---S nonlinear state delay models with actuator and sensor faults simultaneously. Based on Lyapunov function and improved free-weighting approach, some less conservative sufficient conditions for the existence of AFEO are given in terms of linear matrix inequalities, and the obtained fault estimates via AFEO can practically better depict the size and shape of the faults. Finally, three illustrative examples are given to illustrate the validity of the proposed design procedures.

Model-based robust estimation and fault detection for MEMS-INS/GPS integrated navigation systems

In micro-electro-mechanical system based inertial navigation system (MEMS-INS)/global position system (GPS) integrated navigation systems, there exist unknown disturbances and abnormal measurements. In order to obtain high estimation accuracy and enhance detection sensitivity to faults in measurements, this paper deals with the problem of model-based robust estimation (RE) and fault detection (FD). A filter gain matrix and a post-filter are designed to obtain a RE and FD algorithm with current measurements, which is different from most of the existing priori filters using measurements in one-step delay. With the designed filter gain matrix, the H-infinity norm of the transfer function from noise inputs to estimation error outputs is limited within a certain range; with the designed post-filter, the residual signal is robust to disturbances but sensitive to faults. Therefore, the algorithm can guarantee small estimation errors in the presence of disturbances and have high sensitivity to faults. The proposed method is evaluated in an integrated navigation system, and the simulation results show that it is more effective in position estimation and fault signal detection than priori RE and FD algorithms.

Bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors

We consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error-prone surrogates for the unobserved covariate are available for each sampled unit. Existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors, for example, normality and, for the latter two, also homoscedasticity and thus independence from the covariate. In this article we describe Bayesian semiparametric methodology based on mixtures of B-splines and mixtures induced by Dirichlet processes that relaxes these restrictive assumptions. In particular, our models for the aforementioned densities adapt to asymmetry, heavy tails and multimodality. The models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity. In simulation experiments, our method vastly outperforms existing methods. We apply our method to data from nutritional epidemiology.

On Outliers and Interventions in Count Time Series following GLMs

We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided.

Carrier Aircraft Urgent Takeoff In-Flight Alignment Extended Set-Membership Estimation

This paper considers the nolinear system robust estimation problem with measurement time delay. The purpose is to provide algorithm for inertial navigation system nonlinear error model in transmittion delay case. Considering that innovation regroup method can treat the measurement delay problem better with no addition of system state dimension, and decrease the system computation, therefore, that algorithm is combined with extended set-membership estimation and deduce the distrete nonlinear system extended set-membership estimation algorithm with measurement delay, realize nonlinear system varying state estimation and the treatment of measurement delay. At last, apply the algorithm to carrier aircraft in-flight alignment and validate the effecitiveness.

A Round-Robin type protocol for distributed estimation with [formula omitted] consensus

The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a Round-Robin rule, at discrete time instances. The results of the paper are sufficient conditions which guarantee a suboptimal H∞ level of consensus between observers with sampled interconnections.