Inequality Constrained Least Square Adjustment And Its Application In Kalman Filtering

Modern data processing theory in surveying has experienced a transformation from classical to generalized adjustment, but it was confined to the processing of preliminary observation data and it has not sufficiently utilize some useful prior information along the development. Meanwhile, with the development of science and technology, more observation methods arise, surveying information becomes more detailed and the acquaintance of physical or mechanical properties of any object gets more sufficient in geodetic surveying field, so the feasibility to establish constraints based on prior information becomes greater. A new estimation model and theory that can sufficiently express the prior information must be established urgently. The simplest expression of prior information is equality and inequality. The inequality constraints may relatively reliable to describe various prior information, if we can solve the problems in computing and accuracy assessment of inequality constrained adjustment, it would be widely used in geodetic data processing field. In the other hand, the geodetic data theory would be sufficiently developed and complemented as we extend equality constraints to linear inequality constrained adjustment(LICA).The author systematically studied many kinds of the algorithms of inequality constraints adjustment and compared it with the ones in optimization which relates to it in mathematics. The model and accuracy evaluation were also studied. An application to the dam deformation with inequality constraints adjustment shows a good effect. Then a initiative study on inequality constrained Kalman filtering has been done. The concrete method and content of this study is as follows:(1)By analyzing various algorithms proposed by scholars home and abroad and combining with the properties of surveying adjustment, this paper proposes a new classical algorithms based on Kuhn-Tucker condition.(2) This paper denotes the flaws of the generalized inverse method in rank deficient net with equality constraints and proposes a new method which displaces generalized inverse with Caly inverse. Then it is extended to inequality constrained situation and a new way to solve inequality constrained rank deficient net comes up.(3) This paper analyses the solution and statistical properties of equality constrained Kalman filtering and relates it to inequality constrained Kalman filtering. It proposes the active set method to solve the latter problem and lists the statistical properties.(4) This paper analyses the effect and accuracy of inequality constrained model.(5)This paper calculates a deformation net of the dam in Fengtan powerstation with classical adjustment, rank deficient net and inequalityconstrained adjustment. The result shows the superiority of inequalityconstrained model.