Theory And Method Of Adjustment Model With Linear Inequality Constrained Parameters

As the requirement of calculation capacity and surveying data processing's accuracy is improving, it is necessary to take advantage of some pretty useful prior information. Meanwhile, in modern geodetic surveying filed, more observation methods are arising, surveying information becomes more detailed and the awareness of physical or mechanical properties of any object is deepening, so there is much more possibilities for us to establish constraints (equality constraints or inequality constraints) according to prior information. Inequality constraints can relatively reliably describe a variety of prior information. Researchers have made some progress in algorithm of inequality constrained problem. On condition that we solved the calculation and precision problem of inequality constrained adjustment, this adjustment model can be widely used in surveying data processing filed. In particular, we should develop the adjustment theory from equality to inequality, so that the theory could have constant development and improvement.The paper makes a systemic research on the present inequality constraints adjustment algorithms and analyzes the characteristics of these algorithms. Besides, we propose a new method base on LCP, make a study on the rank defect free network with inequality constraints, and do some analysis of statistical properties of the model. Details are as follows:(1)The paper systematically analyzes the features of typical algorithm of inequality constrained adjustment; explains the difference with mathematical method, and denotes the deficiency of present methods still existing when evaluating the accuracy;(2)Under the concept of active constraints, the paper puts forwards a linear complementarity's method based on Kuhn-Tucker to solve the line inequality constraints adjustment model and prove the effectiveness of the algorithm that this method has the same answer to the other linear complementarity's methods. Also, this paper analyses differences and connections between equality constrain and inequality constrain; (3)The paper proposes a new method to solve rank defect free network adjustment with equality constraints, which has accordant results with other algorithm and can be generalized to inequality constrained adjustment. In addition, the paper gives a specific algorithm, and with an example it shows that it can be helpful to improve the adjustment results when properly using inequality prior information;(4)The paper analyzes the statistical properties of inequality constraints adjustment, compares with the properties of unconstrained and equality constrained adjustment model and throws light on some important conclusions.