Effect of redundancy on estimation accuracy in process data reconciliation

SummaryThis paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single‐input–single‐output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple‐input–multiple‐output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

For Time-varying, Time-invariant, and steady-state systems, Kalman Filter can be implemented as a prediction algorithm, since it produces the state prediction and the corresponding prediction error covariance matrix via the state estimation and the corresponding estimation error covariance matrix. Lainiotis Filter is equivalent to Kalman Filter and can be used to compute the prediction. In this paper, for Time-varying, Time-invariant and steady state systems, estimation-free Prediction Algorithms are derived via Kalman and Lainiotis filters; they are equivalent and compute iteratively the prediction and the corresponding prediction error covariance matrix. The estimation and the corresponding estimation error covariance matrix are not needed and are not computed. The proposed estimation-free prediction algorithms are faster than the Kalman filter.

In a distributed estimation system, the local sensor estimates are transferred to fusion center and fused to be an optimal estimation according to some criterion. The well-known best linear unbiased estimation (BLUE) fusion optimally combines the local estimates by minimising the covariance matrix of estimation errors. However, the BLUE fusion need know the cross-covariances of sensor estimation errors exactly, which are not attainable in most of practical applications. In this article, the random matrix is employed to describe the uncertainty of the estimation error covariance among the sensors. By minimising the estimation error covariance only for the most favorable realisations of the random matrix, we model it as an optimisation problem with chance constraint. With appropriate relaxation method, a robust linear unbiased estimation fusion is proposed analytically. Furthermore, an upper bound on the relaxation gap is proposed. Finally, we demonstrate through some numerical simulations that the presented estimation fusion always has smaller absolute estimation error than that of the covariance intersection filter.

In the processing of radar data, target estimation states fusion is an important problem. Especially under the decentralized model, various estimations of target state which come from local filters with Kalman filter may be fused in order to obtain a more accurate target estimation state. There are two problems to be solved. The first is the fusion criterion, different fusion criteria bring out different results. Three fusion criteria are discussed; one is based on the covariance matrix of estimation error, the second is dependent on the infinite normal number, and the last is related to the element of the state vector. The second problem is the tracking algorithm; it affects the accuracy of the state fusion result. The three criteria and their corresponding algorithms are presented. The algorithms estimating target state are set up with a strong tracking filter other than Kalman or extended Kalman filter; they have better tracking performance so that they can overcome the deficiencies related to Kalman or extended Kalman filters. The reason for this is explained. Comparison results are given.

Covariance intersection fusion steady-state Kalman estimator for discrete time stochastic linear systems with system errors and sensor errors is presented in this paper. Gevers-Wouters (G-W) algorithm is used in this paper. Steady-state Kalman estimator is presented in this paper avoids the complex Diophantine equation, and it is based on the ARMA model to compute the steady-state Kalman estimators gain, further the Lyapunov equation is used to estimate the variance matrix and covariance matrix of estimation error. So this algorithm can obviously reduce the computational burden. The information fusion algorithm presented in this paper is covariance intersection fusion. Compared with the single sensor case, the accuracy of the fused filter is greatly improved. A simulation example of the target tracking controllable system with two sensors shows its effectiveness and correctness.

В работе рассматривается математическая модель комплекса обнаружения воздушных целей с комплексированием данных от различных источников информации - средств обнаружения. В составе комплекса обнаружения рассматриваются средства обнаружения трех типов: радиолокационная станция, радиопеленгатор и оптико-электронная система. Приводятся математические модели каждого средства обнаружения и динамики цели, заданной в виде материальной точки. Обработка информации строится с использованием селективного метода комплексирования на основе федеративного фильтра Калмана. При использовании которого на каждом такте моделирования работы комплекса обнаружения выбирается наиболее достоверный источник информации о координатах цели (между всеми средствами обнаружения) с наименьшим следом ковариационной матрицы ошибок оценивания. Результаты моделирования показывают принципиальную применимость предложенной математической модели комплекса обнаружения воздушных целей. The paper considers a mathematical model of an air target detection system with data integration from various information sources - detection means. The detection system includes three types of detection means: a radar station, a radio direction finder, and an optical-electronic system. Mathematical models of each detection means and the dynamics of a target specified as a material point are given. Information processing is built using a selective integration method based on the federated Kalman filter. When using it, at each simulation cycle of the detection system operation, the most reliable source of information on the target coordinates (between all detection means) with the smallest trace of the covariance matrix of estimation errors is selected. The modeling results show the fundamental applicability of the proposed mathematical model of the air target detection system.

Performance Analysis of the Pisarenko Harmonic Decomposition Method

Abstract. In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemistry transport model MOCAGE (Modèle de Chimie Atmosphérique à Grande Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in many numerical weather prediction centres. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm−1 to estimate the observation-error covariance matrix. This spectral range includes ozone-sensitive and atmospheric window channels. We computed hourly 3D-Var analyses and compared the resulting O3 fields against ozonesondes and the measurements provided by the Microwave Limb Sounder (MLS) and by the Ozone Monitoring Instrument (OMI). The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement, especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance matrix is employed in the assimilation system, by reducing the number of iterations needed for the minimizer to converge.

In this paper, we propose a new design method of RKF via l1 regression for multi output systems. Parameters of conventional RKF are designed by heuristic methods, so the parameters have no physical meanings. It is shown that statistics of Gaussian measurement noise determine the parameters of RKF via a primal and dual problem of l1 optimization problem. We discuss a covariance matrix of updated state estimation error. The proposed parameters can design the parameters systematically. In addition, the parameters have physical meanings, and we need no prior information except Gaussian measurement noise. RKF with the proposed design method is applied to a two-wheeled vehicle control with outliers, and the effectiveness is demonstrated by numerical simulations.

In this paper the Kalman filter equations are re- derived for systems with mobile sensors. The motion of the sensor impacts the measurement noise statistical properties through the measurement covariance matrix and, consequently, the estimation error covariance matrix. Moreover, since the sensors are mobile, their motion has an associated control cost. Minimizing the control effort expended during the measurement process is of critical importance in many applications, in particular where fuel and energy resources scarce. With this realization, the Kalman filter equations are re-derived in this paper to include sensor dynamics and their impact on the estimation error. While the classical Kalman filter seeks to minimize a measure of the estimation error, in this paper the goal is to minimize both the estimation error as well as control energy expended during the estimation process. Necessary optimality conditions are derived, and are further simplified for the case where the process to be estimated is composed of a set of decoupled and uncorrelated processes. A mathematical continuation approach is proposed to solve the resulting nonlinear two-point value problem. A numerical example is provided to illustrate the work of this paper.

A switched SDRE filter for state of charge estimation of lithium-ion batteries

Landscape ecology links landscape pattern to ecological function. Achieving this goal hinges on accurate depiction and quantification of pattern, which is frequently done by visually interpreting remotely sensed imagery. Therefore, understanding both the accuracy of that interpretation and what influences its accuracy is crucial. In addition, imagery is pixel-based but landscape pattern exists, more realistically, as irregularly shaped patches. Patches may contain only one feature type such as trees, but, in some landscapes, patches may contain several different types of features such as trees and buildings. Using a patch-based approach, this paper investigates two types of variables—whole-patch and within-patch—that are hypothesized to influence the accuracy of visually estimating the cover of features within patches. A highly accurate reference map, obtained from object-based classification, was used to evaluate the accuracy of visual estimates of cover within patches. The effects of the variables on the accuracy of these estimates were tested using logistic regressions and multimodel inferential procedures. Though all variables significantly affected the accuracy, the within-patch configuration of features is the most significant factor. In general, errors of cover estimates are more likely to occur when patches are smaller or have more complex shapes, and features within a patch are (1) more diverse; (2) more fragmented; (3) more complex in shape; and (4) physically less connected. These results provide an important first step towards a quantitative, spatially explicit model for predicting error of cover estimates and determining under what circumstances estimation error is most likely to occur.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

The authors consider the worst-case transceiver design problem under spectrum bounded channel uncertainty matrices. Their design aims to minimise the trace and the determinant of the estimate error covariance matrix, respectively. The authors relax the formulated problem into an optimisation problem with bilinear matrix inequality constraints (i.e. BMI problem), from which a local optimal solution is obtained by applying semi-definite programming. Furthermore, the authors consider norm bounded source symbols and extend their approach to design the worst-case transceiver with respect to both channel uncertainties and norm bounded source symbols.

Image reconstruction algorithm of electromagnetic tomography based on fractional Kalman filter