Table of Content

25 December 2011, Volume 40 Issue 6

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学术论文

A new method to calculate the vertical derivatives of total field magnetic anomaly

², ²

2011, 40(6):  671-678. 

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The vertical derivatives of the total field magnetic anomaly (TMA) plays an important role in the interpretation process of magnetic objects. Owing to the filter characteristic of vertical derivative operator, the conversion of vertical derivative is inherently unstable and any high-frequency noise present in the surveying data gets strongly magnified in the transformed map in such a way to mask any useful signal. Based on the harmonic properties of the vertical integral and derivatives of TMA which are confirmed theoretically in this paper, an algorithm is presented to perform calculation of vertical derivatives using both frequency and space domain transformations. The algorithm involves following steps: vertically integrating the field by using a frequency domain operator; and then, according to the Laplace equation, computing its second vertical derivative by means of the sum of its second horizontal derivatives which is approximated with three-point finite-differences or bicubic splines method; finally, all the other vertical derivatives are again computed by the Laplace equation starting from the TMA (even derivatives) and its first vertical derivative (odd derivatives). The effectiveness of the suggested techniques had been illustrated by synthetic sphere magnetic model whose total field magnetic anomaly’s first and second vertical derivative expressions are deduced for the first time when the geomagnetic direction is different from magnetization direction. The conclusion indicates that the presented vertical derivatives calculation method provides better results and allows a lower degrading of the signal-to-noise ratio than the standard Fourier method, especially when the order of computed derivatives increases, as the vertical integration filter is a smoothing filter.

Improved two-dimensional moment method for positioning sub-pixel of CCD star image in digital zenith camera

2011, 40(6):  679-683. 

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Precise star-centroid determination of digital star image screened with CCD is important to estimate the precise astronomical location of observing station in the surveying of vertical deflection based on GPS and CCD with the astro-geodetic method. The sub-pixel center of CCD star image should be positioned to improve the precision of station astronomical latitude and longitude with the digital zenith camera. A program is developed with MATLAB to read CCD image in FITS format in the paper. Based on the analysis of CCD star image, the two-dimensional moment method is improved to process the real CCD star image. The threshold value selected in the moment method in common use can affect the positioning precisions of star images with different brightness. So a iterative method to calculate the optimal threshold is put forward. Comparing this method with the two-dimensional modified moment method, we find that the improved two-dimensional moment method is of more efficiency and reliability. We get more precise positioning results for faint stars with the improved method and the positioning precision for faint stars is up to 0.1-0.15 pixel.

Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity

2011, 40(6):  684-689. 

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Generalized ridge estimate was suggested for solving the ill-posed problem in downward continuation (DWC) of airborne gravity, three regularization methods were studied to solve the inverse Poisson problem, which are Tikhonov regularization, ridge estimate and generalized ridge estimate. By conducting a simulated numerical experiment designed based on EGM2008 Earth gravitational model, the 2.5′×2.5′gravity disturbances with white noise at the flight levels were downward continued to the Geoid, the accuracy and stability of the DWC methods were tested and compared, the numerical results show that, in terms of continued accuracy, stability and robustness, the generalized ridge estimate based on multiple optimal regularization parameters performs significantly better than Tikhonov regularization and ridge estimate which based on single regularization parameter.

Tikhonov Two-Parameter Regulation Algorithm in Downward Continuation of Airborne Gravity Data

2011, 40(6):  690-696. 

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In order to avoid the correct effect provided by regulation parameter on the downward continuation credible portion, in this paper Tikhonov two-parameter regulation algorithm was presented. Using the truncation parameter, the singular values of the normal matrix were divided into the relative large singular values (the credible portion) and the relative small singular values (the incredible portion); using regulation parameter, only the relative small singular values were corrected, and the effect induced by the high frequency error was suppressed. The truncation parameter and the regulation parameter were determined by GCV method. Using the simulative airborne gravity data based on the EGM2008, as true values of the gravity field, the results of numerical calculation examples have clearly demonstrated that this method for downward continuation of airborne gravity data is fairly efficient, and shown significant advantages.

Simulation Study for Recovering GOCE Satellite Gravity Model Based on Space-Wise LS Method

2011, 40(6):  697-702,. 

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The approach to deal with the colored noise in Space-Wise LS was discussed in this paper. The AR filter was proposed to process the colored noise in the GOCE satellite gravity gradiometry, which was validated by the numerical results. The PCCG approach method and the direct inverse for solving the large normal equation are also verified by the numerical analysis. And the former approach is much faster than the latter one. Combing the radial component Vzz of the simulated gravity gradient tensor with colored noise and SST observation with white noise, the global gravity field model up to degree and order 180 was estimated by the Space-Wise LS method and the SA approach respectively. The accuracies of geoid and gravity anomaly of the global gravity field model estimated from the Space-Wise LS method are 3.01cm and 0.75mGal respectively, which are better than them from the SA approach.

Rupture Characteristic and Slip Constrained by GPS Coseismic Deformation Induced by the Wenchuan Earthquake

2011, 40(6):  703-709. 

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In order to study the Wenchuan Mw7.9 earthquake rupture characteristic and slip,we model the dense GPS coseismic deformation using simulated annealing algorithm based on uniform elastic half-space model. We find the GPS coseismic deformation can be modeled well using five rupture segments from Yingxiu to Beichuan combined with one rupture segment from Guanxian to Jiangyou, and the result is better than one which is inferred from seismic wave data or InSAR data. The rupture along Yingxiu-Beichuan is 255-294 km length. The south segment can be separated into upper and lower two layers, and is 30 km depth characterized by dip-slip reverse faulting. The mid-segment characterized by right 1ateral oblique faulting and dip-slip reverse faulting, and the north segment characterized by right 1ateral oblique faulting. The shortest earthquake recurrence interval is 3000-year at Yingxiu segment. The rupture depth 14 km of upper layer is probably the locking depth along the Longmenshan fault. The Wenchuan earthquake maybe arised from block relatively moving and extrusion, sliping at depth or locking at shallow,and break out at weakness.

Unified scheme for integer ambiguity resolution in precise point positioning

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2011, 40(6):  710-716. 

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The un-differenced GPS observations are usually adopted by precise point positioning (PPP), of which the initial phase biases (IPBs) underlying the phase observables are inseparable with the integer ambiguities, leading to ambiguity-float PPP-based solutions. Currently, the satellite IPBs as retrieved from regional or global GPS networks can be used for correcting PPP user’s phase observable and restoring the integer nature of the ambiguities. After successful ambiguity resolution, improving accuracy and convergence behavior of PPP-based solutions can be expected. The commonly used methods for estimating satellite IPBs include estimation of decoupled satellite clock or fractional phase biases. Starting from the original GPS observations, the full-rank mathematical model for satellite IPBs estimation is derived and used for comparatively analysis of the characteristics and implementation of both methods. It is concluded from the analysis that full utilization of information from GPS observations can be expected for the former method, and the process of generating decoupled satellite clocks is consistent with the standard satellite clocks estimation, but doesn’t make good use of the stable temporal behaviors of satellite IPBs. In contrast, the latter method doesn’t fully account for the stochastic correlations between the linear combinations of GPS observations, which would lead to a sub-optimal satellite IPBs, besides, the real-time implementation of this method is more troublesome than the former, and the GPS code observations of high-accuracy are always required. The strategy presented in this paper can avoid the shortcomings in both methods, and reasonable constraints due to the stability of several unknowns can be easily imposed upon during parameter estimation to generate more reliable satellite IPBs.

Real-time Cycle-slip Detection and Repair Based on Code-Phase Combinations for GNSS Triple-frequency Un-differenced Observations

2011, 40(6):  717-722,. 

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In case of triple-frequency signals, there are many combination observations with longer wavelength, smaller noise, smaller ionosphere effect, which may improve the precision of cycle-slip detection and repair. The threshold for cycle-slip detection is deduced, and the success probability of cycle-slip determination is proposed. Criterions and methods for selecting code-phase combination are presented from the viewpoint of enhancing the success probability of cycle-slip determination. At last, experiments are carried out to test the performance of the method using GPS triple-frequency observations. The result shows that optimal code-phase combinations selected by proposed criterions can detect and repair all cycle-slips of triple-frequency un-differenced observations, when ionosphere error between-epoch can be ignored in case of high data rate.

The New Generation of Global Mean Sea Surface Height Model Based on Multi-altimetric Data

2011, 40(6):  723-729. 

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The high precision and resolution global mean sea surface height (MSSH) model is the basis of research on variation of ocean dynamic environment. Based on multi-satellite altimetric data, including Geosat/GM、Geosat/ERM、ERS-1/168、ERS-2、Envisat-1、T/P and Jason-1, this paper improves and re-computes their geophysical corrections by unified accurate models and methods. Then, by assuming the dataset combing the T/P and Jason-1 measurements which are collinear adjusted as reference, the radial orbit error and time-variation affect of sea surface height are reduced through the developed whole combination crossover adjustment. Furthermore, global MSSH model named WHU2009 with the boundary from 80°S to 82°N and resolution of 2′×2′ is achieved by remove-restore method and least square collocation grid method with EGM2008 high degree gravitation model. Compared with CLS01 model that commonly used internationally and the dataset that collinear adjusted with 2 year Jason-1 measurements, it is concluded that WHU2009 has better integrated accuracy than CLS01.

The Improved Method of Calculating the Geoid Innermost Area Effects Using Deflections of the Vertical

,Shaofeng Bian

2011, 40(6):  730-735. 

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In order to improve the precision of the innermost area effects in altimetry geoid computed by the Molodensky formula, deflections of the vertical were expressed as double quadratic polynomials regarding the innermost area as a rectangular one, and the formulae to calculate gravity anomaly of this area were derived after the non-singular transformation was introduced. The analysis based on the theoretical model of deflections of the vertical shows that these formulae’s errors are zero, and traditional formulae’s erros depend on the latitude and the ratio of the north-south deflection component to the west-east deflection component. A practical calculation was done based on deflections of the vetical data with a resolution of 2'*2' in the middle latitude area. The results indicate that the RMS differences between the contributions of the grid including the calculation point calculated by traditional formulae and this paper’s formulae are several centimeters. The formulae derived in this paper could provide theoretical basis for the recovery of altimetry geoid with high precision.

Comparison of Gravity Gradient Reference Map Composition for Navigation

2011, 40(6):  736-744. 

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Reference database is inevitable problem in the research of gravity gradient aided navigation system (GGANS). Since complete gravity gradient measurement still needs a long time, gravity gradient approximation using theoretical methods has become a new way to build the reference map. In order to avoid some disadvantages, such as little consideration of existing gravity database, lack of physical meaning of modeled results in present researches, a reference map composition method starting from Free-air anomaly and Bouguer anomaly data is proposed in the paper. On the biases of gravity reduction, the principle of the mapping method is derived, and key algorithms in the computation also introduced. We present critical program flow when the method implement, and then make a detailed analysis on the effect of the method through two application examples. The result shows that most value and characteristics of the acquired reference map agrees well with measured gravity gradient data when high resolution gravity anomaly appears, which embodies practical value of the method. The method and correlative software work above can be referenced for the study of GGANS.

De-noising Method for Gyro Signal Based on EMD

2011, 40(6):  745-750. 

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Gyro random drift is a remarkable factor that can affect the precision of INS(Inertial Navigation System). Wavelet de-noising method is poor in coping with exceptional noise, and it depends greatly on the selection of wavelet base and decomposition scale. Empirical Mode Decomposition (EMD) de-noising method for gyro signal is presented. The signal is decomposed into an Intrinsic Mode Function (IMF) group. Based on this group, IMFs of exceptional noise are first disposed by 2sigma criterion and then the number of IMFs of high frequency noise is determined by correlation coefficient. The de-noising process is finally done by removing the noisy IMFs. Detailed comparison between EMD method and wavelet method is given. Overlapping Allan variance is used to analyze the effect of them, and the applicable ability of EMD method is tested through an INS calculation. It is shown that EMD method outperforms wavelet method in removing exceptional noise and is more efficient in weakening random drift.

Inconsistency Analysis of CE-1 Stereo Camera Images and Laser Altimeter Data

2011, 40(6):  751-755. 

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Optimization of the Rational Function Model of Satellite Imagery

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2011, 40(6):  756-761. 

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To solve the problems of over-parameterization and low geo-referencing accuracy of rational function model (RFM), a novel method of parameter optimization based on scatter matrix and elimination transformation and a new method of remnant systematic error compensation without ground control points are proposed. The proposed parameter optimization method can resolve the ill-posed problem of RFM by rejecting all excess parameters. The systematic error compensation method introduces a new correction model with Fourier coefficients. Experimental results indicate that the performance of the proposed method with less parameters is equal to that of the conventional model which all of the 78 parameters. Moreover, the ill-posed problem is effectively eliminated and thus the stabilities of estimated parameters are improved. The systematic error compensation scheme significantly eliminates the remnant systematic error of RFM and improves the geo-referencing accuracy.

Self-calibration of LiDAR System Mounting Biases Using Virtual Tie Point Model

2011, 40(6):  762-769. 

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Airborne LiDAR system calibration estimates a set of parameters to represent biases of LiDAR system. Mounting biases of LiDAR system contain bore-sight angle between laser scanner frame and IMU frame and lever-arm offset between the IMU and laser scanner centers. Each time when LiDAR system is installed or removed within the aircraft, small changes in the mounting parameters may occur, therefore regular calibration of mounting parameters is required. Using the rigorous model of LiDAR direct geo-referencing, quantitative analysis of mounting parameters and their effect on laser footprint location accuracy is described. This paper introduced a rigorous self-calibration method for estimating mounting parameters of LiDAR system, namely the three bore-sight angles and the lever-arm offset. In order to model the differences between strips, tie points are determined by an interactive measurement. As laser footprints are discretely sampled, the selected tie points are almost not real laser footprint. We proposed a Virtual Tie Point Model to integrate the tie point and real laser footprints. Each VTPM contains a tie point and three real laser footprints, and two rules are defined to calculate tie point coordinate from real laser footprints. The flow of self-calibration based on VTPM is detailed described. The practical examples illustrate the feasibility and effectiveness of the proposed self-calibration method.

Application of Chinese Remainder Theorem in Phase Unwrapping for Dual-Baseline InSAR

2011, 40(6):  770-777. 

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The basic formulation of solving congruence equations with Chinese Remainder Theorem (CRT) was introduced. And CRT was applied to phase unwrapping for dual-baseline InSAR. The congruence equations refer to interferometric phase fuzzy numbers were designed, and the phase unwrapping method for dual-baseline InSAR based on Chinese Remainder Theorem was proposed. In this algorithm, the un-fuzzy phase interval of phase unwrapping was extended, which helps to solve the difficult problem of phase unwrapping in sub-sampling area. The phase unwrapping experiments were done with simulated interferograms from different areas DEMs. The satisfying phase unwrapping results were gotten, as validated the phase unwrapping ability for the proposed algorithm in sub-sampling area.

Maximal Coverage Spatial Optimization based on Diagrams Heuristic and Swarm Intelligence

2011, 40(6):  778-784. 

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A maximal coverage location model based on network Voronoi area diagrams and particle swam optimization are proposed, which have been applied to spatial optimization for time sensibility public service facilities in city. In this paper we take that facilities function radiate to the areas along traffic network and variable demands continuous distribution into account, the sites of facilities optimized can be located in continuous network space. The network Voronoi area diagrams were used to simulate the service areas of facilities in the maximal coverage location model, which has heuristic to minimize overlap coverage in spatial optimization. The model proposed maximizes comprehensive utilization of facilities, which formulates that the demands within a certain distance from at least one facility are provided complete service coverage and the demands beyond the distance from at least one facility are provided partial coverage. An improved Particle Swam spatial Optimization algorithm based on genetic mechanism and generalized Voronoi diagram in this paper, which can improve the performance of POS. The computational experiment for spatial optimization of fire stations in Nanjing shows that the proposed location model and optimization algorithm have achieved ideal result, the approaches can be applied to spatial optimization of maximal covering location for emergency facilities in urbanized area.

Indexing Schema of the Aperture 4 Hexagonal Discrete Global Grid System

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2011, 40(6):  785-789,. 

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The paper describes the Octahedron-based Aperture 4 Hexagonal DGGS (OA4HDGGS) using the set theory. By defining two basic operations, the dual and the central subdivision, recursive relation, nested relation and hierarchical relation between the set of hexagonal grids and the set of triangular grids are established. Location of the hexagonal cell on triangular face is described in the three-axes integral grid coordinate system, and meanwhile, essential problems of index schema, including the calculation of Cartesian coordinates of the cell, the determination of neighbors, children and parents of the cell, are solved by a few theorems. According to the theorems, indexing algorithms are proposed and validated by contrastive experiments. The experimental results show that our indexing schema is 600 times faster than similar schema, which proves it is more suitable for computer processing.

Research on Incremental and Dynamic Image Update and Fusion Technology

2011, 40(6):  790-795. 

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Based on the analysis of the existing methods of image update, this paper proposes a new method for image update and fusion in an incremental and dynamic way. The method firstly locates the changing map sheets and areas with grid index maps and incrementally updates the local parts of original data with images of different phrases through mosaic technique. Then it conducts color balance manipulation to reduce color variation of different images. The image smooth process based on convolution and distance-inverse weighted method is also applied to solve the pixel mutation effects existed in the transition zone. This paper illustrates the method with a case study and corresponding analysis. The result shows that the method has high computational efficiency and good mosaic effect. The method exhibits satisfied practicability in local scope incremental image updating and successfully solves the dynamic update problems caused by limitation of capital, deficiency of technology and fast changing rates in local areas.