The calculating formulas was deduced for the surface area of the triaxial ellipsoid.Compared with the former formulas,the formulas not only have simple form,but also avoid the calculation of the elliptic integral which is very difficult to solve.The advantage of the deducing course is that the expanding order of the power series can be changed to meet different precision requirements.Finally,through calculating the different formulas with same parameters of the earth ellipsoid,the result was obtained,which shows this method is correct.
The effect of six different harvest time on yield and output of maize in cold-humid region of Jilin province was studied using'Jidan 27'with mid-early maturity,'Xianyu 335' with middle maturity,'Jidan 618'with mid-late maturity as materials.The results showed that the optimum harvest time are October 5 to October 15 for'Jidan 27',September 30 to October 15 for'Xianyu 335',October 5 to October 15 for'Jidan 618',the yield and output value would be the best during this time.
Nowadays, synergetics was being applied in more and more fields. Using the satellite positioning technology to realize the multiple points cooperative positioning has become a hottest research direction. Aimed at the problem in which if the unknown nodes can't received signal from sufficient satellites then the node can't be located in the single point positioning, this article constructed a multipoint cooperative positioning model based on the method of satellite pseudo-range positioning principle of BDS II. It also analyzed the judgment conditions and location feasibility when the unknown node received different number satellites, especially explained the positioning arithmetic about how to get the coordinate values of unknown nodes when each node can only receive three or two satellite in detail. This research provides a new way to solve the cooperative positioning for a terminal node in a complied scenic spot and obtain the location information for providing LBS under complicated and harsh environment which can't receive enough satellites. The output could be as a reference to guide the construction of information service platform for LBS in mobile environment, promote the positioning technology and method based on BDS applying to informationization construction and further the intersection and development of related disciplines.
Integer ambiguity resolution plays a key role in applications related to GNSS precise positioning. This contribution focuses on three commonly used integer estimators (IEs), i.e., integer rounding (IR), integer bootstrapping (IB) and integer least-squares (ILS). Contributions are mainly of four aspects. First, the objective function of IR and IB is given, respectively. Second, an upper bound for ILS is proposed. Third, a sorting technique is introduced to tighten the upper bound of IR/ILS after decorrelation. Fourth, the success-rate approximation for IR and ILS with bounded error is developed, respectively. Finally, real-collected data in PPP validate the following arguments. (i) Applying sorting technique after decorrelation can improve the tightness of IR upper bound a lot, but can only slightly tighten the ILS upper bound. (ii) The proposed ILS upper bound is almost as the same tight as the one in PS-LAMBDA software, much tighter than other known upper bounds. Unlike the PS-LAMBDA upper bound, the proposed ILS upper bound has the advantage of time efficiency for real-time applications. (iii) The proposed approximations produce more accuracy approximated success-rate than the frequently-used ambiguity dilution of precision (ADOP) based approximation.
GNSS is now affecting in various aspects of human life, while it is susceptible to interference including jamming and spoofing, which will make itself be caught in serious risk. Therefore, reliable safeguards are urgently necessary to ensure the safety of GNSS applications. Array signals received by different array sensors contain the spatial characteristics of GNSS signals from different directions, which offer possible approaches to spoofing mitigation based on the general assumption that all spoofing pseudorandom noises are from the same direction. Given this, a novel array signal processing method is proposed in this paper, which can adaptively suppress jamming and spoofing and enhance the useful signals simultaneously. This proposed method can be compatible with the traditional GPS receiver without the need of adjusting the GPS receiver hardware. The effectiveness of this proposed method is verified by simulation results.
SUMMARY The functional analysis of the least-squares collocation (LSC) for gravity potential modelling using m measurements is revisited starting from an explicit spherical harmonic expansion. A spherical harmonic representer theorem (SHRT) is given: the model of the potential is a linear combination of m kernels or covariances. This theorem is independent of the specific forms of the data-fitting loss and the regularizer, showing that it is a stronger result than the LSC theory. The corresponding reproducing kernel Hilbert space is explicitly specified. When the least-squares data-fitting loss and the quadratic regularizer are employed, the SHRT gives exactly the LSC method for variable prediction. The nominal prediction precision assessment of the SHRT and that of the LSC are also explicitly compared; this contributes to the unification of the deterministic and stochastic analyses of the LSC theory.
High-accuracy seabed surface modelling provides multi-source high-precision fundamental geographic datasets for marine visual computing, seabed topography detection, marine biology, marine engineering and other fields. Proposed in this paper is a high-precision seabed surface model, which combines B-spline functions and Fourier-series, referred to as the Spline-Fourier-series (S-FS) method. Firstly, the mathematical relationship between the B-spline functions and Fourier-series in the modelling process is explored in depth, deducing the non-recursive basis functions of the pth Spline-Fourier-series model and the specific representation of the two dimensional pth Spline-Fourier-series model. Furthermore, using a publicly available Large-area bathymetric dataset, extensive experiments are conducted for comparisons with traditional methods (nearest-neighbor, bilinear, bicubic) and traditional Fourier-series, which generally shows the S-FS method has higher accuracy, better convergence and stronger robustness. Finally, based on its mathematically theoretical model, three characteristics (dimensionality reduction, multi-resolution expression and multi-scale visualization) of the S-FS method for constructing high-precision seabed surface are analyzed visually and deeply. Compared with B-spline function, the basic functions of the S-FS method inherit its prioritized compactly-supported performance and do not need to be recursively calculated anymore, thereby further showing its feasibility and extensibility in the field of high-precision seabed surface modelling.
Based on the characteristic of the Multi-beam bathymetric system,the sound velocity correction technique and the tide correction are analyzed. On the basis of the sound velocity spreaded,the measure of sound velocity is expatiated and the means of the sound correction is discussed. Furthermore,the analyzing for the tide correction is discussed with the influence of the tide. On the basis of the data of the multi-beam bathymetric system which are measured in the test sea area,the sampling depth data which had been processed are developed to form the depth overlay map,isoline map and stereogram,and so the digital map is made.
We have derived and tested several relations between geoid (N) and quasi-geoid (ζ) with model validation. The elevation correction consists of the first-term (Bouguer anomaly) and second-term (vertical gradient of gravity anomaly). The vertical gradient was obtained from direct measurement and terrain calculation. The test results demonstrated that the precision of geoid can reach centimeter-level in mountains less than 5000 meters high.
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