Based on tensor theory, three Invariants of the Gravitational Gradient Tensor (IGGT) are independent of the Gradiometer Reference Frame (GRF). Compared to traditional methods for calculation of gravity field models based on the Gravity field and steady-state Ocean Circulation Explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method is obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent Gravitational Gradients (GGs), but the components V xy and V yz of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The Spherical Cap Regularization Approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7 0. With the techniques described above, a degree/order 240 gravity field model called IGGT R1 is computed. Since the synthetic components of V xy and V yz are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT R1's accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/Leveling data.
In this paper, according to the characteristics of nonlinear equations. An improve Cuckoo Search Algorithm was used to solve the systems of nonlinear equations, the algorithm was experimented and the experimental results show that the new algorithm to be successful in locating multiple solutions and better accuracy. At the end the paper made a simple comparison with the bat algorithms.
In this paper, we introduce a new hybrid model called probabilistic hesitant N-soft sets by a suitable combination of probability with hesitant N-soft sets, a model that extends hesitant N-soft sets. Our novel concept extends the ability of hesitant N-soft set by considering the occurrence probability of hesitant grades, which could effectively avoid the loss of decision-making information. Moreover, we investigate some basic properties of probabilistic hesitant N-soft sets and construct fundamental operations on them. Then we describe group decision-making methods including TOPSIS, VIKOR, choice value and weighted choice value based on probabilistic hesitant N-soft sets. The corresponding algorithms are put forward and their validity is proved by examples.
CG-5 is new automatic land relative gravimeter developed by Canada Scintrex Company. Gravity vertical gradient can be measured by CG-5. This article mainly aims at precision analysis of the gravity vertical gradient measurement based on CG-5.This paper analyzes the error sources and error propagation formulae. In the end, it shows relation between altitude differences and observation sets in certain accuracy requirement. Results show that the precision of CG-5 vertical gradient measurement is improved when altitude difference and observation set increase. In vertical gradient measurement, 13 observation sets are needed with altitude difference at 2m to obtain the precision of ±20E.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.