At present, the principal data processing methods involving complex observations are based on two strategies according to characteristics of the observation process, i.e., step-by-step and direct resolution. However, these strategies have some limitations, e.g. they cannot consider statistical observation error information, redundant observations and so on. This paper applies least squares methods to complex data processing to extend surveying adjustment theory from real to complex number space. We compared the two adjustment criteria for a complex domain in a quantitative way. In order to understand the effectiveness of complex least squares, tree height inversion from PolInSAR data is taken as an example. We firstly established both a complex adjustment function model and a stochastic model for PolInSAR tree height inversion, and then applied the complex least squares method to estimate tree height. Results show that the complex least squares approach is reliable and outperforms other classic tree height retrieval methods; the method is simple and easy to implement.

In order to achieve high short-term prediction accuracy of ionospheric TEC, first, we transform a seasonal time series for ionospheric Total Electron Content (TEC) into a stationary time series by seasonal differences and regular differences with a full consideration of the Multiplicative Seasonal model. Next, we use the Autoregressive Integrated Moving Average (ARIMA) model taken from time series analysis theory for modeling the stationary TEC values to predict the TEC series. Using TEC data from 2008 to 2012 provided by the Center for Orbit Determination in Europe (CODE) as sample data, we analyzed the precision of this method for prediction of ionospheric TEC values which vary from high to low latitudes during both quiet and active ionospheric periods. The effect of the TEC sample’s length on the predicted accuracy is analyzed, too. Results from numerical experiments show that during the ionospheric quiet period the average relative prediction accuracy for a six day time span reaches up to 83.3% with average prediction residual errors of about 0.18±1.9TECu. During ionospheric active periods it changes to 86.6% with an average prediction residual error of about 0.69±2.6TECu. For the quiet periods, above 90% of predicted residual is less than ±3TECu while during active periods, it is only about 81%. The two periods show that that the higher the latitude, the higher the absolute precision, and the lower the predicted relative accuracy. In addition, the results show that prediction accuracy will improve with an increase of the TEC sample sequences length, but it will gradually reduce if the length exceeds the optimal length, about 30 days. On the other hand, with the same TEC sample, as the predicted days increase, the predictive accuracy decreases. Athough the predictive accuracy is not apparent at the beginning, it will be significantly reduced after 30 days.

After implementing CGCS2000, establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications. Consequently, a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed. Specifically, we firstly analyze a minimum curvature equation of coordinate transformation, which possesses the characteristics of both the global and local smoothness, achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature. Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed. Meanwhile, a data structure of grid model is constructed. Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model. Using 48433 points of 2000 National Geodetic Control Network of China, we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000, and the external positional accuracies for both models are 0.26m and 0.03m respectively.

A novel tie point matching algorithm of aerial images with the assistance of airborne LiDAR point clouds and POS data is proposed Firstly, the conjugate point searching strategy used in traditional correlation coefficient matching is improved and a fast algorithm is presented. Secondly, an automatic camera boresight misalignment calibration method based on virtual ground control points is proposed, and then the searching range of image matching is adaptively determined and applied to the image matching of the entire surveying area. Test results verified that the fast correlation coefficient matching algorithm proposed in this paper can reduce approximately 25% of the matching time without the loss of matching accuracy. The camera boresight misalignment calibration method can effectively increase the accuracy of exterior orientation elements of images calculated from POS data, and thus can significantly improve the predicted position of conjugate point for tie point matching. Our proposed image matching algorithm can achieve superior matching accuracy with multi-scale, multi-view, and cross-flight aerial images.

The construction of thematic map symbols is a very complex and intellectually demanding process, but thematic symbols can be automatically generated and easily shared on the web using the syntactic structure of semantic symbols. In this paper, the symbol types, inner structure, and design pattern are discussed. A syntactic construction theory based on letter (thematic maps primitive)-word (single thematic symbol)-sentence (combined symbols or complex symbols) structure model is proposed to automate the construction of thematic map symbols. As a result of this research, symbols can be defined using cartographic primitives which are arranged according to syntactic principles. A semiotic model and word-centered construction theory can be integrated into interactive cartography as represented by the technology of Internet. Finally, the concepts and schema of this theory are discussed, and some examples are presented based a web thematic cartographic system to verify its utility.

According to the “theoretical admittance " and the "observation admittance" of the actual data, the theoretical value of effective elastic thickness in the study area was 10km. Combining the gravity anomalies and vertical gravity gradient anomalies, the admittance function is used to construct the 1'×1' bathymetry model over the Philippine Sea by using the adaptive weighting technique. It is found that the accuracy of the bathymetry model constructed is the highest when the ratio of inversion result of vertical gravity gradient anomalies and inversion result of gravity anomalies is 2∶3. At the same time, using multi-source gravity data to predict bathymetry could synthesize the superiority of gravity anomalies and vertical gravity gradient anomalies on the different seafloor topography, and the accuracy is better than bathymetry model that only used gravity anomalies or vertical gravity gradient anomalies. Taking the ship test data as the checking condition, the accuracy of predicting model is slightly lower than that of V18.1 model and improved by 27.17% and 39.02% respectively compared with the ETOPO1 model and the DTU10 model. Check points which the absolute value of the relative error of the predicting model is in the range of 5% accounted for 94.25% of the total.

In geodesy and geophysics, many large-scale over-determined linear equations need to be solved which are often ill-conditioned. When the conjugate gradient method is used, their ill-conditioning effects to the solutions must be overcome, which is studied in this paper. Through the regularization ideas, the conjugate gradient method is improved, and the regularization iterative solution based on controlling condition number is put forward. Firstly by constructing the interference source vector, a new equation is derived with ill-condition diminished greatly, which has the same solution to the original normal equation. Then the new equation is solved by conjugate gradient method. Finally the effectiveness of the new method is verified by some numerical experiments of airborne gravity downward to the earth surface. In the numerical experiments the new method is compared with LS, CG and Tikhonov methods, and its accuracy is the highest.

The 3-dimension coordinate datum transformation is very important in geomatics. Generally, there are small angle coordinate transformation model (i.e., Bursa model, et al) and large angle coordinate transformation model (i.e., Rodrigo matrix model, et al). However, these papers only focus on the fixed and static situation regardless of the small or large angle. This paper proposes the conception of coordinate transformation gradient field,which can realize the space coordinate transformation from small angle to arbitrary angle, and from static to dynamical. Based on the equivalent characteristics of the unit quaternion rotation matrix and the Rodrigo matrix, through studying the mathematical relationship between the spatial coordinate transformation and the functional gradient, we derive a functional gradient expression of the arbitrary transformation formula in space. The study shows that the essence of spatial coordinate transformation is a kind of potential field mathematically. This potential field conception can unify all the space coordinate transformations. It is the theoretical foundation for the further study of time continuous space coordinate transformation,and this study gives a new solution for the attitude determination of motion carriers.