We study the existence of ground states of a Schrödinger-Poisson-Slater type equation with pure power nonlinearity. By carrying out the constrained minimization on a special manifold, which is a combination of the Pohozaev manifold and Nehari manifold, we obtain the existence of ground state solutions of this system.
Accurate measurement of position and attitude information has become the basis of application engineering in related fields. Traditional position and attitude measurement schemes, including lasers, infrared light, etc., often place high demands on the measurement environment. The visual image-based measurement scheme needs to be combined with the actual situation to establish a complex pose calculation model. Therefore, exploring a measurement scheme for efficient solution has become an urgent need in related fields. In this paper, we propose a multi-feature fusion position and attitude measurement neural network (MFNN). We effectively introduce the HOG operator as an image feature and combine it with the original image for a specific ratio. At the same time, we draw on the utilization strategy of feature points in traditional measurement methods. By combining the extracted image feature points with the network, the measurement error of the six-dimensional information is effectively reduced. Based on this, we propose a new type of position and attitude measurement network architecture. MFNN has further improved the accuracy of related measurements. INDEX TERMS Position and attitude measurement, MFNN, multi-feature fusion, neural network.
Virtual reality technology, with its continuous development, is gradually applied to healthcare, education, business, and other fields. In the application of the technology, position and attitude estimation, as a space positioning technology, is indispensable. Traditional pose estimation has the problems of high dependence on environment and great complexity. But convolutional neural network (CNN) and other technologies with computational intelligence provide a strong guarantee for the progress of pose estimation. This article, based on the theory of CNN in deep learning, as well as monocular vision system and target sample set with markers, proposes a method for estimation of target position and attitude, and at the same time, describes in detail a general way of making dataset with markers based on simulation environment. In this article, the comparative experiments of different network structures show that this measurement method can avoid manual extraction of complex image features, and realize fast, arbitrary and accurate measurement, which plays a key role in pose and attitude measurement. Moreover, the visual correspondence between the world coordinate system and the pixel coordinate system is proved effectively by quaternion.
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