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This paper aims to develop a novel attitude determination system aided by polarization sensor. An improved heading angle function is derived using the perpendicular relationship between directions of E-vector of linearly polarized light and solar vector in the atmospheric polarization distribution model. The Extended Kalman filter (EKF) with quaternion differential equation as a dynamic model is applied to fuse the data from sensors. The covariance functions of filter process and measurement noises are deduced in detail. The indoor and outdoor tests are conducted to verify the validity and feasibility of proposed attitude determination system. The test results showed that polarization sensor is not affected by magnetic field, thus the proposed system can work properly in environments containing the magnetic interference. The results also showed that proposed system has higher measurement accuracy than common attitude determination system and can provide precise parameters for Unmanned Aerial Vehicle (UAV) flight control. The main contribution of this paper is implementation of the EKF for incorporating the self-developed polarization sensor into the conventional attitude determination system. The real-world experiment with the quad-rotor proved that proposed system can work in a magnetic interference environment and provide sufficient accuracy in attitude determination for autonomous navigation of vehicle.

Accurate flood forecasting is crucial for flood prevention and mitigation, safeguarding the lives and properties of residents, as well as the rational use of water resources. The study proposes a model of long and short-term memory (LSTM) combined with the vector direction (VD) of the flood process. The Jingle and Lushi basins were selected as the research objects, and the model was trained and validated using 50 and 49 measured flood rainfall-runoff data in a 7:3 division ratio, respectively. The results indicate that the VD-LSTM model has more advantages than the LSTM model, with increased NSE, and reduced RMSE and bias to varying degrees. The flow simulation results of VD-LSTM better match the observed flow hydrographs, improving the underestimation of peak flows and the lag issue of the model. Under the same task and dataset, with the same hyperparameter settings, VD-LSTM can more quickly reduce the loss function value and achieve a better fit compared to LSTM. The proposed VD-LSTM model couples the vectorization process of flood runoff with the LSTM neural network, which contributes to the model better exploring the change characteristics of rising and receding water in flood runoff processes, reducing the training gradient error of input–output data for the LSTM model, and more effectively simulating flood process.

Despite empirical mode decomposition (EMD) becoming a de facto standard for time-frequency analysis of nonlinear and non-stationary signals, its multivariate extensions are only emerging; yet, they are a prerequisite for direct multichannel data analysis. An important step in this direction is the computation of the local mean, as the concept of local extrema is not well defined for multivariate signals. To this end, we propose to use real-valued projections along multiple directions on hyperspheres (n-spheres) in order to calculate the envelopes and the local mean of multivariate signals, leading to multivariate extension of EMD. To generate a suitable set of direction vectors, unit hyperspheres (n-spheres) are sampled based on both uniform angular sampling methods and quasi-Monte Carlo-based low-discrepancy sequences. The potential of the proposed algorithm to find common oscillatory modes within multivariate data is demonstrated by simulations performed on both hexavariate synthetic and real-world human motion signals.

This paper proposes a new pose and focal length estimation method using two vanishing points and a known camera position. A vanishing point can determine the unit direction vector of the corresponding parallel lines in the camera frame, and as input, the unit direction vector of the corresponding parallel lines in the world frame is also known. Hence, the two units of direction vectors in camera and world frames, respectively, can be transformed into each other only through the rotation matrix that contains all the information of the camera pose. Then, two transformations can be obtained because there are two vanishing points. The two transformations of the unit direction vectors can be regarded as transformations of 3D points whose coordinates are the values of the corresponding unit direction vectors. The key point in this paper is that our problem with vanishing points is converted to rigid body transformation with 3D–3D point correspondences, which is the usual form in the PnP (perspective-n-point) problem. Additionally, this point simplifies our problem of pose estimation. In addition, in the camera frame, the camera position and two vanishing points can form two lines, respectively, and the angle between the two lines is equal to the angle between the corresponding two sets of parallel lines in the world frame. When using this geometric constraint, the focal length can be estimated quickly. The solutions of pose and focal length are both unique. The experiments show that our proposed method has good performances in numerical stability, noise sensitivity and computational speed with synthetic data and real scenarios and also has strong robustness to camera position noise.

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data.

In reliability analysis, the probability density function (PDF) of the directional importance sampling method is based on a multi-dimensional vector (i.e., multivariate), thus it is inefficient to obtain the important directional vectors (IDVs) by sampling each dimensional component randomly. In this paper, an efficient solution approach of vector-angle geometric mapping is proposed. Firstly, the angles between IDVs and the design point position vector are set as the important direction angles (IDAs) in the standard Gaussian space. By exploring the geometric relationship between IDVs and IDAs, the PDF of multi-dimensional IDV can be converted into the PDF of one-dimensional IDA, following which, the cumulative distribution function of IDA is derived by integration. Further, the cumulative distribution is sampled uniformly using the Latin hypercube technique, and then the uniform IDAs are generated by inversion. Finally, the IDVs are shown by geometric mapping of the IDAs. The research results show that the PDF of IDA is jointly determined by the two parameters, dimensionality and reliability index. Therefore, the distribution characteristics of IDA can be explored and diagrammatically represented, and the obtained IDVs can be used repeatedly for other reliability analysis with the same mentioned parameters to improve the computational efficiency. The applicability, accuracy, and robustness of the proposed approach are proved on illustrative examples, battery pack and truss structure engineering applications.

In this paper, the graphic representation method is used to study the multiple characteristics of heart sounds from a resting state to a state of motion based on single- and four-channel heart-sound signals. Based on the concept of integration, we explore the representation method of heart sound and blood pressure during motion. To develop a single- and four-channel heart-sound collector, we propose new concepts such as a sound-direction vector of heart sound, a motion–response curve of heart sound, the difference value, and a state-change-trend diagram. Based on the acoustic principle, the reasons for the differences between multiple-channel heart-sound signals are analyzed. Through a comparative analysis of four-channel motion and resting-heart sounds, from a resting state to a state of motion, the maximum and minimum similarity distances in the corresponding state-change-trend graphs were found to be 0.0038 and 0.0006, respectively. In addition, we provide several characteristic parameters that are both sensitive (such as heart sound amplitude, blood pressure, systolic duration, and diastolic duration) and insensitive (such as sound-direction vector, state-change-trend diagram, and difference value) to motion, thus providing a new technique for the diverse analysis of heart sounds in motion.

Due to the inherent periodicity of the angle, the direction of the object detected by the current rotating object detection algorithm is fuzzy. In order to solve this problem, this paper proposes a rotating object direction estimation method based on a neural network, which determines the unique direction of the object by predicting the direction vector of the object. Firstly, we use the two components (sin θ, cos θ) of the direction vector and the length and width parameters of the object to express the object model. Secondly, we construct a neural network model to predict the parameters used to express the object model. However, there is a constraint that the sum of the squares of the two components of the direction vector of the object is equal to 1. Because each output element of the neural network is independent, it is difficult to learn the constrained data between such neurons. Therefore, the function transformation model is designed, and the network transformation layer is added. Finally, affine transformation is used to transform the object parameters and carry out regression calculation, so as to detect the object and determine the direction of the object at the same time. This paper uses three sets of data to carry out the experiment, which are DOTA 1.5, HRSC, and UCAS-AOD data sets. It can be seen from the experimental results that for the object with correct ground truth, the proposed method can not only locate the object but also estimate the direction of the object accurately.

Spatial patterns of movement are fundamental to the ecology of animal populations, influencing their social organization, mating systems, demography, and the spatial distribution of prey and competitors. However, our ability to understand the causes and consequences of animal home range patterns has been limited by the descriptive nature of the statistical models used to analyze them. InMechanistic Home Range Analysis, Paul Moorcroft and Mark Lewis develop a radically new framework for studying animal home range patterns based on the analysis of correlated random work models for individual movement behavior. They use this framework to develop a series of mechanistic home range models for carnivore populations. The authors' analysis illustrates how, in contrast to traditional statistical home range models that merely describe pattern, mechanistic home range models can be used to discover the underlying ecological determinants of home range patterns observed in populations, make accurate predictions about how spatial distributions of home ranges will change following environmental or demographic disturbance, and analyze the functional significance of the movement strategies of individuals that give rise to observed patterns of space use. By providing researchers and graduate students of ecology and wildlife biology with a more illuminating way to analyze animal movement,Mechanistic Home Range Analysiswill be an indispensable reference for years to come.

In response to a question raised by Knox Lovell, we develop a method for estimating directional output distance functions with endogenously determined direction vectors based on exogenous normalization constraints. This is reminiscent of the Russell measure proposed by Färe and Lovell (J Econ Theory 19:150-162, 1978). Moreover it is related to the slacks-based directional distance function introduced by Fare and Grosskopf (Eur J Oper Res 200:320-322, 2010a, Eur J Oper Res 206:702, 2010b). Here we show how to use the slacks-based function to estimate the optimal directions.