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This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems.

The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems.

The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis.

An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results.

The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

This paper aims to propose a method to solve the problem of localization and mapping of a two-wheeled inverted pendulum (TWIP) robot on the ground using the Stereo–inertial measurement unit (IMU) system. This method reparametrizes the pose according to the motion characteristics of TWIP and considers the impact of uneven ground on vision and IMU, which is more adaptable to the real environment.

When TWIP moves, it is constrained by the ground and swings back and forth to maintain balance. Therefore, the authors parameterize the robot pose as SE(2) pose plus pitch according to the motion characteristics of TWIP. However, the authors do not omit disturbances in other directions but perform error modeling, which is integrated into the visual constraints and IMU pre-integration constraints as an error term. Finally, the authors analyze the influence of the error term on the vision and IMU constraints during the optimization process. Compared to traditional algorithms, the algorithm is simpler and better adapt to the real environment.

The results of indoor and outdoor experiments show that, for the TWIP robot, the method has better positioning accuracy and robustness compared with the state-of-the-art.

The algorithm in this paper is proposed for the localization and mapping of a TWIP robot. Different from the traditional positioning method on SE(3), this paper parameterizes the robot pose as SE(2) pose plus pitch according to the motion of TWIP and the motion disturbances in other directions are integrated into visual constraints and IMU pre-integration constraints as error terms, which simplifies the optimization parameters, better adapts to the real environment and improves the accuracy of positioning.

This paper aims to propose a fast and robust 3D point set registration method for pose estimation of assembly features with few distinctive local features in the manufacturing process.

The distance between the two 3D objects is analytically approximated by the implicit representation of the target model. Specifically, the implicit B-spline surface is adopted as an interface to derive the distance metric. With the distance metric, the point set registration problem is formulated into an unconstrained nonlinear least-squares optimization problem. Simulated annealing nested Gauss-Newton method is designed to solve the non-convex problem. This integration of gradient-based optimization and heuristic searching strategy guarantees both global robustness and sufficient efficiency.

The proposed method improves the registration efficiency while maintaining high accuracy compared with several commonly used approaches. Convergence can be guaranteed even with critical initial poses or in partial overlapping conditions. The multiple flanges pose estimation experiment validates the effectiveness of the proposed method in real-world applications.

The proposed registration method is much more efficient because no feature estimation or point-wise correspondences update are performed. At each iteration of the Gauss–Newton optimization, the poses are updated in a singularity-free format without taking the derivatives of a bunch of scalar trigonometric functions. The advantage of the simulated annealing searching strategy is combined to improve global robustness. The implementation is relatively straightforward, which can be easily integrated to realize automatic pose estimation to guide the assembly process.

The purpose of this paper is to propose a high-precision attitude solution to solve the attitude drift problem caused by the dispersion of low-cost micro-electro-mechanical system devices in strap-down inertial navigation attitude solution of micro-quadrotor.

In this study, a three-stage attitude estimation scheme that combines data preprocessing, gyro drifts prediction and enhanced unscented Kalman filtering (UKF) is proposed. By introducing a preprocessing model, the quaternion orientation is calculated as the composition of two algebraic quaternions, and the decoupling feature of the two quaternions makes the roll and pitch components independent of magnetic interference. A novel real-time based on differential value (DV) estimation algorithm is proposed for gyro drift. This novel solution prevents the impact of quartic characteristics and uses the iterative method to meet the requirement of real-time applications. A novel attitude determination algorithm, the pre-process DV-UKF algorithm, is proposed in combination with UKF based on the above solution and its characteristics.

Compared to UKF, both simulation and experimental results demonstrate that the pre-process DV-UKF algorithm has higher reliability in attitude determination. The dynamic errors in the three directions of the attitude are below 2.0°, the static errors are all less than 0.2° and the absolute attitude errors tailored by average are about 47.98% compared to the UKF.

This paper fulfils an identified need to achieve high-precision attitude estimation when using low-cost inertial devices in micro-quadrotor. The accuracy of the pre-process DV-UKF algorithm is superior to other products in the market.

A crucial stage in the formulation of operations strategy is the derivation of a ranked (or rated) list of competitive factors such as quality, flexibility, cost. This list is used either to infer an appropriate set of strategic operations decisions or alternatively it is used in conjunction with an independently derived list of the organization′s performance to prioritize each of the competitive factors. Martilla and James take the latter approach to derive an importance‐performance matrix. Examines how the matrix can be modified to reflect managers′ perceived relationships between “importance”, “performance” and “priority for improvement”. Reports two investigations, one dealing with operations improvement at the level of the whole operations function, the other at the level of the department or micro‐operation. Proposes a different zoning of the importance‐performance matrix from that used by Martilla and James.

The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics.

This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively.

This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups.

The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.

To achieve a full understanding of the role of marketing from plan to profit requires a knowledge of the basic building blocks. This textbook introduces the key concepts in the art or science of marketing to practising managers. Understanding your customers and consumers, the 4 Ps (Product, Place, Price and Promotion) provides the basic tools for effective marketing. Deploying your resources and informing your managerial decision making is dealt with in Unit VII introducing marketing intelligence, competition, budgeting and organisational issues. The logical conclusion of this effort is achieving sales and the particular techniques involved are explored in the final section.

Kids get exposed to advertising on social media platforms when they visit them to perform various goals. The purpose of this study is to find out the factors which affect kids' behaviour when the kids encounter advertising on social media and also to establish causal relationships amongst the factors of social media advertising (SMA).

A total of 11 factors of SMA have been identified with the help of experts and the causal relationships amongst the SMA factors have been constructed by the implementation of decision-making trail and laboratory evaluation (DEMATEL). Based on the established relationships, a causal diagram has been also developed to understand the structural nature of interdependence amongst the factors.

DEMATEL technique is based on logical steps, which have assisted in categorising the identified factors into two groups: cause group and effect group. Cause group factors are the reasons for the effect group factors to occur. Customisation, entertainment, information and interactivity have been observed as cause factors whereas, relevance, engagement with SMA, purchase intention, product involvement, advertising value, attitude towards SMA and irritation have been observed as effect factors. Product involvement is found to have the highest level of interaction with all other factors. Information and interactivity are observed to influence all other factors.

Kids possess a limited understanding of the selling intent of advertisers which makes kids vulnerable to advertising. This study supports that the content of the advertisement should be kept in accordance with the need of kids and also suggests that marketers should emphasise cause group factors which derive subsequent consequences on effect group factors. The foremost limitation of this study lies in the process of identifying the factors through expert opinions. The sets of contextual relationships may vary when different experts are considered.

This study strives to identify the factors which affect kids' understanding of SMA and also establishes causal relationships amongst them. This kind of study is unique in state of the art and to the authors' knowledge no significant research has been conducted in India which involves establishment of inter-relationships amongst SMA factors that affect kids' behaviour.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.