A geodesic survey of an existing route requires one to determine the approximation curve by means of optimization using the total least squares method (TLSM). The objective function of the LSM was found to be a square of the Mahalanobis distance in the adjustment field ν . In approximation tasks, the Mahalanobis distance is the distance from a survey point to the desired curve. In the case of linear regression, this distance is codirectional with a coordinate axis; in orthogonal regression, it is codirectional with the normal line to the curve. Accepting the Mahalanobis distance from the survey point as a quasi-observation allows us to conduct adjustment using a numerically exact parametric procedure. Analysis of the potential application of splines under the NURBS (non-uniform rational B-spline) industrial standard with respect to route approximation has identified two issues: a lack of the value of the localizing parameter for a given survey point and the use of vector parameters that define the shape of the curve. The value of the localizing parameter was determined by projecting the survey point onto the curve. This projection, together with the aforementioned Mahalanobis distance, splits the position vector of the curve into two orthogonal constituents within the local coordinate system of the curve. A similar system corresponds to points that form the control polygonal chain and allows us to find their position with the help of a scalar variable that determines the shape of the curve by moving a knot toward the normal line.

A robust Kalman filter improved with IGG (Institute of Geodesy and Geophysics) scheme is proposed and used to resist the harmful effect of gross error from GPS observation in PPP/INS (precise point positioning/inertial navigation system) tightly coupled positioning. A new robust filter factor is constructed as a three-section function to increase the computational efficiency based on the IGG principle. The results of simulation analysis show that the robust Kalman filter with IGG scheme is able to reduce the filter iteration number and increase efficiency. The effectiveness of new robust filter is demonstrated by a real experiment. The results support our conclusion that the improved robust Kalman filter with IGG scheme used in PPP/INS tightly coupled positioning is able to remove the ill effect of gross error in GPS pseudorange observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all simulated gross errors added to GPS pseudorange observation are successfully detected and modified.

The use of quantitative methods, including stochastic and exploratory techniques in environmental studies does not seem to be sufficient in practical aspects. There is no comprehensive analytical system dedicated to this issue, as well as research regarding this subject. The aim of this study is to present the Eco Data Miner system, its idea, construction and implementation possibility to the existing environmental information systems. The methodological emphasis was placed on the one-dimensional data quality assessment issue in terms of using the proposed QAAH1 method - using harmonic model and robust estimators beside the classical tests of outlier values with their iterative expansions. The results received demonstrate both the complementarity of proposed classical methods solution as well as the fact that they allow for extending the range of applications significantly. The practical usefulness is also highly significant due to the high effectiveness and numerical efficiency as well as simplicity of using this new tool.