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The purpose of this paper is to propose an uncertain regression model with an intrinsic error structure facilitated by an uncertain canonical process.

This model is suitable for dealing with expert's knowledge ranging from small to medium size data of impreciseness. In order to have a rigorous mathematical treatment on the new regression model, this paper establishes a series of new uncertainty concepts sequentially, such as uncertainty joint multivariate distribution, the uncertainty distribution of uncertainty product variables and uncertain covariance and correlation based on the axiomatic uncertainty theoretical foundation. Two examples are given for illustrating a small data regression analysis.

The uncertain regression model is formulated and the estimation of the model coefficients is developed.

The paper is devoted to a regression model to handle a small amount of data with mathematical rigor.

The theory and the methodology of the uncertain canonical process regression is proposed for the first time. It addresses the practical challenges of small data size modelling.

The successful use of the standard extended Kalman filter (EKF) is restricted by the requirement on the statistics information of the measurement noise. The covariance of the measurement noise may deviate from its nominal value in practical environment, and the filtering performance may decline because of the statistical uncertainty. Although the adaptive EKF (AEKF) is available for recursive covariance estimation, it is often less accurate than the EKF with accurate noise statistics.

Aiming at this problem, this paper develops a parallel adaptive EKF (PAEKF) by combining the EKF and the AEKF with an adaptive law, such that the final state estimate is dominated by the EKF when the prior noise covariance is accurate, while the AEKF is activated when the actual noise covariance deviates from its nominal value.

The PAEKF can reduce the sensitivity of the algorithm to the model uncertainty and ensure the estimation accuracy in the normal case. The simulation results demonstrate that the PAEKF has the advantage of both the AEKF and the EKF.

The presented algorithm is applicable for spacecraft relative attitude and position estimation.

The PAEKF is presented for a kind of nonlinear uncertain systems. Stability analysis is provided to show that the error of the estimator is bounded under certain assumptions.

This paper aims to improve the performance of the autonomous optical navigation using relativistic perturbation of starlight, which is a promising technique for future space missions. Through measuring the change in inter-star angle due to the stellar aberration and the gravitational deflection of light with space-based optical instruments, the position and velocity vectors of the spacecraft can be estimated iteratively.

To enhance the navigation performance, an integrated optical navigation (ION) method based on the fusion of both the inter-star angle and the inter-satellite line-of-sight measurements is presented. A Q-learning extended Kalman filter (QLEKF) is designed to optimize the state estimate.

Simulations illustrate that the integrated optical navigation outperforms the existing method using only inter-star angle measurement. Moreover, the QLEKF is superior to the traditional extended Kalman filter in navigation accuracy.

A novel ION method is presented, and an effective QLEKF algorithm is designed for information fusion.

The purpose of this work is to obtain an overbounded broadcast sigma from actual (non-Gaussian) correction error distribution under the stringent navigation integrity requirements for aircraft precision approach and landing.

Approach is statistically to overbound satellite pseudorange correction error distribution with the use of numerical solution of Fisher-Z transformation. Inflation factors for overbounding broadcast sigma are extracted from Fisher-Z transformation based on measured correlation and counted independent identically distributed (iid) sample sizes of true empirical data.

New overbounded broadcast sigma values for eight long-pass satellites were obtained based on measured actual empirical data and ensured integrity risk at 10⁻⁸ probability level. Proposed methodology successfully overbounds ground reflection multipath-type systematic and temporal errors sources.

This paper introduced a new method of accounting for ground reflection multipath for local area augmentation system/ground-based augmentation system navigation integrity. The method is also applicable to statistically overbound any other serially correlated temporal variation in measured data if both correlation values and finite iid sample sizes are known.

The purpose of this paper is to propose a new computational approach for parameter estimation in the Bayesian framework. A posteriori probability density functions are obtained using the polynomial chaos theory for propagating uncertainties through system dynamics. The new method has the advantage of being able to deal with large parametric uncertainties, non‐Gaussian probability densities and nonlinear dynamics.

The maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. Direct stochastic collocation is used as a less computationally expensive alternative to the traditional Galerkin approach to propagate the uncertainties through the system in the polynomial chaos framework.

The new approach is explained and is applied to very simple mechanical systems in order to illustrate how the Bayesian cost function can be affected by the noise level in the measurements, by undersampling, non‐identifiablily of the system, non‐observability and by excitation signals that are not rich enough. When the system is non‐identifiable and an a priori knowledge of the parameter uncertainties is available, regularization techniques can still yield most likely values among the possible combinations of uncertain parameters resulting in the same time responses than the ones observed.

The polynomial chaos method has been shown to be considerably more efficient than Monte Carlo in the simulation of systems with a small number of uncertain parameters. This is believed to be the first time the polynomial chaos theory has been applied to Bayesian estimation.

The purpose of this paper is to estimate aerodynamic parameters accurately from flight data in the presence of unknown noise characteristics.

The introduced adaptive filter scheme is composed of two parallel UKFs. At every time‐step, the master UKF estimates the states and parameters using the noise covariance obtained by the slave UKF, while the slave UKF estimates the noise covariance using the innovations generated by the master UKF. This real time innovation‐based adaptive unscented Kalman filter (UKF) is used to estimate aerodynamic parameters of aircraft in uncertain environment where noise characteristics are drastically changing.

The investigations are initially made on simulated flight data with moderate to high level of process noise and it is shown that all the aerodynamic parameter estimates are accurate. Results are analyzed based on Monte Carlo simulation with 4000 realizations. The efficacy of adaptive UKF in comparison with the other standard Kalman filters on the estimation of accurate flight stability and control derivatives from flight test data in the presence of noise, are also evaluated. It is found that adaptive UKF successfully attains better aerodynamic parameter estimation under the same condition of process noise intensity changes.

The presence of process noise complicates parameter estimation severely. Since the non‐measurable process noise makes the system stochastic, consequently, it requires a suitable state estimator to propagate the states for online estimation of aircraft aerodynamic parameters from flight data.

This is the first paper highlighting the process noise intensity change on real time estimation of flight stability and control parameters using adaptive unscented Kalman filter.

This paper is concerned with an online parameter estimation algorithm for nonlinear uncertain time‐varying systems for which no stochastic information is available.

The estimation procedure, called nonlinear learning rate adaptation (NLRA), computes an individual adaptive learning rate for each parameter instead of using a single adaptive learning rate for all the parameters as done in stochastic approximation, each individual learning rate being controlled by a meta‐learning rate rule for the sake of minimizing the measurement prediction error. The method does not require stochastic information about the system model and the measurement noise covariance matrices contrarily to the Kalman filtering. Numerical results about aircraft navigation trajectory tracking show that the method is able to estimate reliably time‐varying parameters even in presence of measurement noise.

The proposed algorithm is practically insensitive to changes in the meta‐learning rate. Therefore, the performance of the method is stable with respect to the tuning parameter of the algorithm.

The proposed NLRA method may be adopted for recursive parameter estimation of uncertain systems when no stochastic information is available. It may also be used for process regulation and dynamic system stabilization in feedback control applications.

Provides a method for fast and practical computation of parameter estimates without requiring to know the model and measurement noise covariance matrices contrarily to existing stochastic estimation methods.

In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics‐based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations.

The purpose of this paper is to set up a two‐stage stochastic integer‐programming model (TSM) for the multiperiod scheduling of multiproduct batch plants under demand uncertainty involving the constraints of material balances and inventory constraints, as well as the penalty for production shortfalls and excess.

Scheduling model is formulated as a discrete‐time State Task Network. Given a scheduling horizon consisting of several time‐periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit for a single and multiple product with a given probability level. The stochastic elements of the model are expressed with equivalent deterministic optimization models.

The TSM model not only allows for uncertain product demand correlations, but also gives different processing modes by a range of batch sizes and a task‐dependent processing time. The experimental results show that the TSM model is more appropriate than another model for multiperiod scheduling of multiproduct batch plants under correlated uncertain demand.

The choice of penalty parameter of demand uncertainty is the main limitation.

The paper provides very useful advice for multiperiod scheduling of multiproduct batch plants under demand uncertainty.

A stochastic model for the multiperiod scheduling of multiproduct batch plants under demand uncertainty was set up. A test problem involving 12 correlated uncertain product demands and two alternative models verified the availability of the TSM.

In response to highly volatile and uncertain environments, many firms have implemented flexible strategies and many management researchers have discussed the topic of flexibility. The purpose of this paper is to focus on distribution flexibility, the aspect of flexibility related to a downstream supply chain and to examine the construct of distribution flexibility and how organisations make strategic choices among different distribution flexibility strategies.

This work conducts an exploratory multiple case study which analyses four Chinese manufacturers from different industries (pharmaceutical, solid/liquid separation, electric appliances, and clothing).

The results show that, given different circumstances, firms might choose an appropriate distribution flexibility strategy (one focused on either physical distribution flexibility, demand management flexibility, coordination flexibility, or on distribution flexibility co‐alignment) which fits with their distribution environment in the contingency theory sense of matching. Furthermore, for implementation, they fit a given distribution flexibility strategy to both their distribution networks and their distribution performance outcomes in the sense of gestalts or covariance.

This paper has some limitations common to all case studies, such as the limited generalisability of results (since the sample of firms is not statistically significant) and the potential subjectivity of the analysis.

The paper contributes to the existing literature by empirically investigating the dimensions of distribution flexibility, by considering how an organisation develops a distribution flexibility strategy in order to adapt to a particular environment, and by suggesting that final performance outcomes may arise through a variety of different distribution flexibility strategies.