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This paper aims to present a pipeline to progressively deal with the online external parameter calibration and estimator initialization of the Stereo-inertial measurement unit (IMU) system, which does not require any prior information and is suitable for system initialization in a variety of environments.

Before calibration and initialization, a modified stereo tracking method is adopted to obtain a motion pose, which provides prerequisites for the next three steps. Firstly, the authors align the pose obtained with the IMU measurements and linearly calculate the rough external parameters and gravity vector to provide initial values for the next optimization. Secondly, the authors fix the pose obtained by the vision and restore the external and inertial parameters of the system by optimizing the pre-integration of the IMU. Thirdly, the result of the previous step is used to perform visual-inertial joint optimization to further refine the external and inertial parameters.

The results of public data set experiments and actual experiments show that this method has better accuracy and robustness compared with the state of-the-art.

This method improves the accuracy of external parameters calibration and initialization and prevents the system from falling into a local minimum. Different from the traditional method of solving inertial navigation parameters separately, in this paper, all inertial navigation parameters are solved at one time, and the results of the previous step are used as the seed for the next optimization, and gradually solve the external inertial navigation parameters from coarse to fine, which avoids falling into a local minimum, reduces the number of iterations during optimization and improves the efficiency of the system.

This study aims to provide the best estimate of a stock's next day's closing price for a given day with the help of the hidden Markov model–Gaussian mixture model (HMM-GMM). The results were compared with Hassan and Nath’s (2005) study using HMM and artificial neural network (ANN).

The study adopted an initialization approach wherein the hidden states of the HMM are modelled as GMM using two different approaches. Training of the HMM-GMM model is carried out using two methods. The prediction was performed by taking the closest closing price (having a log-likelihood within the tolerance range) to that of the present one as the closing price for the next day. Mean absolute percentage error (MAPE) has been used to compare the proposed GMM-HMM model against the models of the research study (Hassan and Nath, 2005).

Comparing this study with Hassan and Nath (2005) reveals that the proposed model outperformed in 66 out of the 72 different test cases. The results affirm that the model can be used for more accurate time series prediction. Further, compared with the results of the ANN model from Hassan's study, the proposed HMM model outperformed 24 of the 36 test cases.

The study introduced a novel initialization and two training/prediction approaches for the HMM-GMM model. It is to be noted that the study has introduced a GMM-HMM-based closing price estimator for stock price prediction. The proposed method of forecasting the stock prices using GMM-HMM is explainable and has a solid statistical foundation.

This chapter examines the limit properties of information criteria (such as AIC, BIC, and HQIC) for distinguishing between the unit-root (UR) model and the various kinds of explosive models. The explosive models include the local-to-unit-root model from the explosive side the mildly explosive (ME) model, and the regular explosive model. Initial conditions with different orders of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the UR model when data come from the UR model. When data come from the local-to-unit-root model from the explosive side, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the ME model in the form of 1 + n^α/n with α ∈ (0, 1), all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample.

The K-means (KM) clustering algorithm is extremely responsive to the selection of initial centroids since the initial centroid of clusters determines computational effectiveness, efficiency and local optima issues. Numerous initialization strategies are to overcome these problems through the random and deterministic selection of initial centroids. The random initialization strategy suffers from local optimization issues with the worst clustering performance, while the deterministic initialization strategy achieves high computational cost. Big data clustering aims to reduce computation costs and improve cluster efficiency. The objective of this study is to achieve a better initial centroid for big data clustering on business management data without using random and deterministic initialization that avoids local optima and improves clustering efficiency with effectiveness in terms of cluster quality, computation cost, data comparisons and iterations on a single machine.

This study presents the Normal Distribution Probability Density (NDPD) algorithm for big data clustering on a single machine to solve business management-related clustering issues. The NDPDKM algorithm resolves the KM clustering problem by probability density of each data point. The NDPDKM algorithm first identifies the most probable density data points by using the mean and standard deviation of the datasets through normal probability density. Thereafter, the NDPDKM determines K initial centroid by using sorting and linear systematic sampling heuristics.

The performance of the proposed algorithm is compared with KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms through Davies Bouldin score, Silhouette coefficient, SD Validity, S_Dbw Validity, Number of Iterations and CPU time validation indices on eight real business datasets. The experimental evaluation demonstrates that the NDPDKM algorithm reduces iterations, local optima, computing costs, and improves cluster performance, effectiveness, efficiency with stable convergence as compared to other algorithms. The NDPDKM algorithm minimizes the average computing time up to 34.83%, 90.28%, 71.83%, 92.67%, 69.53% and 76.03%, and reduces the average iterations up to 40.32%, 44.06%, 32.02%, 62.78%, 19.07% and 36.74% with reference to KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms.

The KM algorithm is the most widely used partitional clustering approach in data mining techniques that extract hidden knowledge, patterns and trends for decision-making strategies in business data. Business analytics is one of the applications of big data clustering where KM clustering is useful for the various subcategories of business analytics such as customer segmentation analysis, employee salary and performance analysis, document searching, delivery optimization, discount and offer analysis, chaplain management, manufacturing analysis, productivity analysis, specialized employee and investor searching and other decision-making strategies in business.

The purpose of the paper is to present an approach to detect and isolate the sensor failures, using a bank of extended Kalman filters (EKF) using an innovative initialization of covariance matrix using system dynamics.

The EKF is developed for nonlinear flight dynamic estimation of a spacecraft and the effects of the sensor failures using a bank of Kalman filters is investigated. The approach is to develop a fast convergence Kalman filter algorithm based on covariance matrix computation for rapid sensor fault detection. The proposed nonlinear filter has been tested and compared with the classical Kalman filter schemes via simulations performed on the model of a space vehicle; this simulation activity has shown the benefits of the novel approach.

In the simulations, the rotational dynamics of a spacecraft dynamic model are considered, and the sensor failures are detected and isolated.

A novel fast convergence Kalman filter for detection and isolation of faulty sensors applied to the three‐axis spacecraft attitude control problem is examined and an effective approach to isolate the faulty sensor measurements is proposed. Advantages of using innovative initialization of covariance matrix are presented in the paper. The proposed scheme enhances the improvement in estimation accuracy. The proposed method takes advantage of both the fast convergence capability and the robustness of numerical stability. Quaternion‐based initialization of the covariance matrix is not considered in this paper.

A new fast converging Kalman filter for sensor fault detection and isolation by innovative initialization of covariance matrix applied to a nonlinear spacecraft dynamic model is examined and an effective approach to isolate the measurements from failed sensors is proposed. An EKF is developed for the nonlinear dynamic estimation of an orbiting spacecraft. The proposed methodology detects and decides if and where a sensor fault has occurred, isolates the faulty sensor, and outputs the corresponding healthy sensor measurement.

The passive source localization (PSL) problem using angles of arrival (AOA), time differences of arrival (TDOA) or gain ratios of arrival (GROA) is generally nonlinear and nontrival. In this research, the purpose of this paper is to design an accurate hybrid source localization approach to solve the PSL problem. The inspiration is drawn from the fact that the bearings, TDOAs and GROAs are complementary in terms of their geometry properties.

The maximum-likelihood (ML) method is reexamined by using hybrid measurements. Being assisted by the bearings, a new hybrid weighted least-squares (WLS) method is then proposed by jointly utilizing the bearing, TDOA and GROA measurements.

Theoretical performance analysis illustrates that the mean-square error of the ML or WLS method can attain the Cramér-Rao lower bound for Gaussian noise over small error region. However, the WLS method has much lower computational complexity than the ML algorithm. Compared with the AOA-only, TDOA-only, AOA-TDOA, TDOA-GROA methods, the localization accuracy can be greatly improved by combining the AOAs, TDOAs and GROAs, especially for some specific geometries.

A novel bearing-assisted TDOA-GROA method is proposed for source localization, and a new hybrid WLS estimator is presented inspired from the fact that the bearings, TDOAs and GROAs are complementary in terms of their geometry properties.

This paper aims to give the centralized and distributed fusion estimator for nonlinear multi-sensor networked systems with packet loss compensation and correlated noises and give the corresponding square-root cubature Kalman filter.

Based on the Gaussian approximation recursive filter framework, the authors derive the centralized fusion filter and using the projection theorem, the authors derive the centralized fusion smoother. Then, based on the fast batch covariance intersection fusion algorithm, the authors give the corresponding results for distributed fusion estimators.

Designing the fusion estimators for nonlinear multi-sensor networked systems with packet loss compensation and correlated noises is necessary. It is useful for general nonlinear systems.

Throughout the whole study, the main highlights of this paper are as follows: packet loss compensation and correlated noises are considered in nonlinear multi-sensor networked systems. There are no relevant conclusions in the existing literature; centralized and distributed fusion estimators are derived based on the above system; for the posterior covariance with compensation factor and correlated noises, a new square-root factor of the error covariance is derived; and the new square-root factor of the error covariance is used to replace the numerical implementation of the covariance in cubature Kalman filter (CKF), which simplified the problem in calculating the posterior covariance in CKF.

The purpose of this paper is to consider the process of design and implementation of an enhanced fuzzy H_∞ (EFH_∞) estimation algorithm to determine the attitude and heading angles of ground vehicles, which are frequently affected by considerable exogenous disturbances. To detect the changes of disturbances, a fuzzy system is designed based on expert knowledge and experiences of a navigation engineer. In the EFH_∞ estimator, the intensity bounds of disturbances affecting the measurements are updated using a heuristic combination of three change‐detection indices. Performance of the proposed estimator is evaluated by Monte‐Carlo simulations and field tests of three kinds of vehicles using a manufactured attitude‐heading reference system (AHRS). In both simulations and real tests, the proposed estimator results in a superior performance compared to those of the recently developed and standard H_∞ estimators.

Design, implementation and real tests of the EFH_∞ estimator are considered for an AHRS specialized for vehicular applications. In the AHRS, three‐axis accelerometers (TAA) and three‐axis magnetometers (TAM) may be affected by large disturbances due to non‐gravitational accelerations and local magnetic fields. Therefore, the design parameters of EFH_∞ estimator including the theoretic bound of disturbance intensity and the attenuation level are adaptively tuned using a fuzzy combination of three change‐detection indices. Once a sensor is affected by an exogenous disturbance, the fuzzy system will increase the scale factor of the corresponding measurement disturbance to place more confidence on the data of the AHRS dynamics including measurements of gyros with respect to the data coming from the TAA and TAM.

An intelligent fault detector is proposed for considering changes of disturbances to adjust the upper bounds of the estimator's disturbances and the length of data to update the fuzzy system inputs. The EFH_∞ estimator is suitable to attenuate the effects of disturbances changes on accurate estimation of the attitude and heading angles, intelligently.

The paper provides a fuzzy state estimator for adaptively adjusting the theoretic disturbance matrices according to the actual intensity of the disturbances affecting the AHRS dynamics and the measurement sensors.

This paper compares alternative estimation procedures for multi-level factor models which imply blocks of zero restrictions on the associated matrix of factor loadings. We suggest a sequential least squares algorithm for minimizing the total sum of squared residuals and a two-step approach based on canonical correlations that are much simpler and faster than Bayesian approaches previously employed in the literature. An additional advantage is that our approaches can be used to estimate more complex multi-level factor structures where the number of levels is greater than two. Monte Carlo simulations suggest that the estimators perform well in typical sample sizes encountered in the factor analysis of macroeconomic data sets. We apply the methodologies to study international comovements of business and financial cycles.