Correlated Self-born Weighted Construction And Robustness In Parameter Estimation Of Coordinate System Transformation

Mutual transformation between two coordinate systems is acommon issue in production practice and scientific experiment. The key issue ofcoordinate conversion is how to solve the coordinate transformation parameters.The4parameter and7parameter coordinate system transformation models aretwo of the most comcomly used models. Parameters of coordinate systemtransformation can be easily got access to by least squares. When theobservations are interfered by gross errors (about1%-10%of the total numberof observations), gross errors may lead to the distortion of parameters solution.Robust estimation methods are often used to extinct or weaken the impacts ofgross errors on transformation parameters.The domestic and international scholars have proposed many robustestimation methods. M estimation is one of the most common robust estimationmethods, which use the true error estimate of the least squares method toconstruct the equivalent weight. Self-born weighted least squares method(SBWLS) is put forward by the yong-hui ge and it get the utmost out of theeffective information about the criterias of equation, that the true error estimate of independent observations shall meet, to construct the equivalent weight ofobserved value, namely using multiple true error estimate to construct theequivalent weight. Yong-hui ge and others through the simulation experimentindicates that in the parameter estimation of the4parameter and7-parametercoordinate system transformation models, self-born weighted least squaresmethod has much better robustness and effectiveness than common robustestimation methods.Based on self-born weighted least squares method, it is studied that how tostructure the correlated self-born weight and select main parameters in theparameter estimation of the4parameter and7parameter coordinate systemtransformation models. Calculations found main diagonal element of thecorrelated self-born weight may be present negative numbers that lead to thenon-convergence of iterative calculation when observations contain greatergross error. In that case, a parameter (the filter factor) is introduced into theconstruction of the correlated self-born weight. After the filter factor sifting,the case of presenting negative numbers can be weaken or extincted.This paper discusses robustness of correlated self-born weighted leastsquares in the parameter estimation of the4parameter and7parametercoordinate system transformation models. The simulation experiments showthat CSBWLS and other robust estimation methods have a certain degree ofaccuracy loss relative to LS when observations have no gross error, but the lossdoes not cause a significant impact. Both CSBWLS and SBWLS have significant gains relative to LS and13often used robust estimation methodswhen the numbers of coordinate coincident points are5-8and observationscontain the numbers of gross errors between1and2. CSBWLS is more efficientrobust estimation methods on the4parameter and7parameter coordinatesystem transformation models.It is developed that the MATLAB program is used for the correlatedself-born weighted least squares method in the parameter estimation of the four-and seven-parameter coordinate system transformation models. It can bothbalance the4parameter and7parameter coordinate system transformationmodels and simulate its the simulation experiments.