Research On Geodetic Observation Optimization Theory And Methods

The geodetic network geometry,observational error structure and the adjustment structure determine the precision and reliability of the geodetic parameters estimation.Relative to the traditional two-dimensional static geodetic network,GNSS(Global Navigation Satellite System)network composed of the satellite constellation and ground tracking stations is essential to be a three-dimensional dynamic continuously observing network.GNSS network optimization faces with more complicated network structure and multi-objectives,e.g.,the combinatorial optimization problem in GNSS satellite and station selection,observational structure optimization problem with regard to various model errors,model parameter estimator optimization from prior to posterior optimality.Besides this,modern geodetic services also need the optimization on the observational structure for precisely monitoring the Earth rotation,geocenter motion,and the Earth spatial environments.This paper discusses the optimization on GNSS geodetic network and the posterior estimation of model parameters.Analytical optimization on GNSS network,combinatorial optimization on GNSS satellite and station selection and the optimization on(nonlinear)adjustment system are studied.Adjustment system information measures are also discussed.Main contents and innovations are as follows:(1)There kinds of optimization problems are proposed.In this frame,the geodetic observation model optimization and optimal parameter estimation problem are unified.To solve complicated geodetic optimizations,uncertainty optimization model and algorithms are developed.Backward control algorithm for optimally readjusting prior probabilities of candidates is proposed to enhance the algorithm convergence.Optimization model in the infinite space to satisfy GNSS continuously geodetic observations is proposed.(2)Conception model and mathematical models are proposed to establish an adjustment system to satisfy and unify the modern adjustment theory and methods.In an adjustment system,mathematical analysis,state transition,state evaluation and optimal decision are discussed,while adjustment system decision tree is proposed to satisfy automation and intelligent data processing.(3)The analytical multi-layer method for solving the GNSS network optimization is developed.Analytical methodologies including the geometric method,algebraic method and asymptotic analysis method are developed to show whole knowledge and graphs of the optimal single-point positioning configuration.The conditional equations for optimal PNT satellite constellation,the optimal geodetic orbit,and the optimal configuration of the ground tracking stations are derived.Principle on the orthogonal design and uniform design are reveal both in frequency domain and spatial domain.Geometrical formulas for precision and reliability are given.(4)Random optimization model is proposed and the statistical foundation is established for solving the GNSS complicated combinatorial optimization.Three random algorithms are developed for GNSS satellite and station selection,including the algorithm with equally allocated probabilities,the algorithm with grid controlled probabilities and the algorithm with backward optimization on the initial allocated probabilities.Algebraic method and eigenvalue analysis method are also proposed to improve the traditional grid method for the satation slection.(5)Prior weight matrix design and posterior variance component optimization are discussed.Random sample method for gross detection is proposed,while the robust estimation in the parameter domain is also developped to solve the gross detection of small samples.The adjustment efficiency and robust efficiency are both proposed to develop an optimal robust estimation,and then a robust estimation algorithm is proposed by comprehensively utilizing the median estimation and the least squares estimation.(6)The Gaussian recursive elimination is proposed for the fast updating the system status when adding new parameters to an adjustment system.Meanwhile,the information criterion is used to evaluate the adjustment system to conduct the model selection.The proposed recursive algorithm dramatically enhances the model selection efficiency by the dynamic evaluation on the system.(7)Nonlinear M estimators and unbiased nonlinear parameter estimators are developed.Meanwhile,the best unbiased nonlinear parameter estimation is also discussed.Two unbiased parameter estimators are discussed where a direct bias estimation formula is derived.In the context of distance observations,nonlinearity analysis,nonlinearity diagnosing and nonlinearity measures are discussed.Barycenter method,Gauss-Jacobi combinatorial adjustment method and the closed-form of Newton method are developed.Besides,the proposed methods and algorithms have been applied to the GNSS orbit determination,real-time clock estimation,GNSS orbit fitting and positioning,GNSS/level fitting,acoustic positioning,laser positioning and GIS uncertainty evaluation.