Modeling GPS multipath effect based on spherical cap harmonic analysis

Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.

Spherical cap harmonic analysis of regional magnetic anomalies based on CHAMP satellite data

We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over China's Mainland. We assumed satellite points on the same surface （307.69 km） and constructed a spherical cap harmonic model of the satellite magnetic anomalies for elements X, Y, Z, and F over Chinese mainland for 2010.0 （SCH2010） based on selected 498 points. We removed the external field by using the CM4 model. The pole of the spherical cap is 36N° and 104°E, and its half-angle is 30°. After checking and comparing the root mean square （RMS） error of AX, AY, and AZ and X, Y, and Z, we established the truncation level at Kmax = 9. The results suggest that the created China Geomagnetic Referenced Field at the satellite level （CGRF2010） is consistent with the CM4 model. We compared the SCH2010 with other models and found that the intensities and distributions are consistent. In view of the variation off at different altitudes, the SCH2010 model results obey the basics of the geomagnetic field. Moreover, the change rate of X, Y, and Z for SCH2010 and CM4 are consistent. The proposed model can successfully reproduce the geomagnetic data, as other data-fitting models, but the inherent sources of error have to be considered as well.

Obstacle avoidance method of three-dimensional obstacle spherical cap

Focusing on obstacle avoidance in three-dimensional space for unmanned aerial vehicle(UAV), the direct obstacle avoidance method in dynamic space based on three-dimensional velocity obstacle spherical cap is proposed, which quantifies the influence of threatening obstacles through velocity obstacle spherical cap parameters. In addition, the obstacle avoidance schemes of any point on the critical curve during the multi-obstacles avoidance are given. Through prediction, the insertion point for the obstacle avoidance can be obtained and the flight path can be replanned. Taking the Pythagorean Hodograph(PH) curve trajectory re-planning as an example, the three-dimensional direct obstacle avoidance method in dynamic space is tested. Simulation results show that the proposed method can realize the online obstacle avoidance trajectory re-planning, which increases the flexibility of obstacle avoidance greatly.

Modeling and Interpreting CHAMP Magnetic Anomaly Field over China Continent Using Spherical Cap Harmonic Analysis

Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP anomaly fields (latitude φ=25°N to 50°N and longitude λ=78°E to 135°E). The pole of the cap is located at φ=35°N and λ=110°E with half-angle of 30°. The maximum index (K max) of the model is 30 and the total number of model coefficients is 961, which corresponds to the minimum wavelength at the earth's surface about 400 km. The root mean square (RMS) deviations between the calculated and observed values are ～ 4 nT for ΔX, ～ 3 nT for ΔY and ～ 3.5 nT for ΔZ, respectively. Results show that positive anomalies are found mainly at the Tarim basin with ～6- 8 nT, the Yangtze platform and North China platform with ～4 nT, and the Songliao basin with ～4-6 nT. In contrast, negative anomaly is mainly located in the Tibet orogenic belt with the amplitude ～ (-6)-(-8) nT. Upward continuation of magnetic anomalies was used to semi-quantitatively separate the magnetic anomalies in different depths of crust. The magnetic anomalies at the earth's surface are from -6 to 10 nT for upper crust, middle crust -27 to 42 nT and lower crust -12 to 18 nT, respectively. The strikes of the magnetic anomalies for the upper crust are consistent with those for the middle crust, but not for the lower crust. The high positive magnetic anomalies mainly result from the old continental nucleus and diastrophic block (e.g. middle Sichuan continental nucleus, middle Tarim basin continental nucleus, Junggar diastrophic block and Qaidam diastrophic block). The amplitudes of the magnetic anomalies of the old continental nucleus and diastrophic block are related to evolution of deep crust. These results improve our understanding of the crustal structure over China continent.

Buckling Performances of Spherical Caps Under Uniform External Pressure

This study aims to experimentally and numerically examine the buckling performances of stainless steel spherical caps under uniform external pressure.Three laboratory-scale caps were fabricated,measured,and tested.The buckling behaviors of these caps were investigated through experiments and three numerical methods,namely,nonlinear Riks algorithm,nonlinear bifurcation,and linear elastic analysis.The buckling of equal-radius caps was numerically analyzed with different methods to identify their applicability under different wall thicknesses.The results obtained from the nonlinear Riks algorithm are in good agreement with the experimental results,which means the nonlinear Riks algorithm can accurately predict the buckling performances of spherical caps,including the magnitude of critical buckling loads and the deformation of post-buckling modes.The nonlinear bifurcation algorithm is only suitable for predicting the buckling loads of ultra-thin or large-span caps,and the linear buckling method is inappropriate for predicting the buckling of metal spherical caps.

Analysis and improvement of sound radiation performance of spherical cap radiator

A spherical cap radiator is one of the important parts of an underwater wide-beam imaging system. The back radiation of a traditional spherical cap radiator, which is composed of a vibrating cap and a rigid baffle, is strong and its far-field directivity function may fluctuate in big amplitude in the vicinity of the polar axis. These shortcomings complicate the processing of the reflective waves received for imaging the targets. In this study, the back radiation is weakened by adding an acoustic soft material belt between the vibrating cap and the rigid baffle. And the fluctuation mentioned above is lowered remarkably by dividing the spherical cap radiator into many annuluses and a relatively smaller spherical cap, and by controlling the phase retardations of all elements appropriately. Furthermore, the numerical experiments are carried out by the finite element method （FEM） to prove the validity of the above methods.

The Nonlinear Analysis of Spherical Caps under Centrally Distributed Pressures

in this paper, the nonlinear response of spherical caps under centrally distributed pressures isstudied by the hybrid changeable basis Galerkin techmique. The influence of the boundary conditions and thesize of loaded radius on the nonlinear response of the caps is analyzed. The effectiveness of teclmique isdemonstrated by the numerical examples.

Computation and analysis Computation and analysis of the geomagnetic field model in China and its adjacent area for 2003

Based on the geomagnetic data at 135 stations and 35 observatories in China in 2003, the Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area for 2003 were established. In the model calculation, the truncation order of the model and the influences of the boundary restriction on the model calculation were carefully analyzed. The results show that the geomagnetic data used are precise and reliable, and the selection of the truncation order is reasonable. The Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area established in this paper are consistent very well.

A high resolution lithospheric magnetic field model over China

CHAMP satellite data and ground-based magnetic observations are used and combined to map the lithospheric magnetic field over China by means of the revised spherical cap harmonic analysis(R-SHCA)modeling technique.The magnetic field is described to a spatial resolution of 150 km at the mean Earth’s radius,which represents a good compromise between the resolutions afforded by surface and satellite data.We compare the magnetic anomalies modeled at the regional scale with composite regions containing large-scale of tectonic structures.These regions,including the Tarim Basin and the Tibetan Plateau,are correlated with regional magnetic anomalies at satellite altitude but contain a significant number of small-scale and complex magnetic structures at the mean Earth’s radius.These magnetic anomalies are globally consistent with the known geological features in China but also offer a way to delineate the contours of the geological blocks and to discuss the connection between magnetic anomalies and the heat flow distribution in this region.