The Theory Of Least Squares Estimation On Linear Model And It's Application

With the fast development of information industry, there exists the abroad problem of processing information in many fields of modern science and technology. According to different need, people study the optimal procession of these information under different optimal rules. As the produce and collection of information often gets all kinds of noise's bother, Datum are not certain and they are random datum with some statistic character. People have put forward some optimal rules, for example mean square error, linear least variance, least squares, and have gotten these estimations'resolve expression in some hypothesis under these optimal rules. It is difficult in practical problem to know the error variance. While least squares does not require any prior statistic information about the parameter. So this paper studies the theory of least squares estimation on linear model and it's development course. The clue is the different requires of designing matrix and error variance in linear model. We discuss the resolving expression and equivalence of BLUE and least squares. For a given linear model, what we are concerned about is not it's all parameters but some important parameters in practical application .So we think how to remove superabundant parameters and make them equivalence or least difference. Further it needs large storing space to estimate the partial parameters using least squares. We study reduced linear model to resolve above questions, and base on the past results to put forward to compare partitioned linear model and reduced linear model using relatively efficiency. Watermarking algorithm has been used widely and has had many embed algorithms. This paper makes use of the advantage of least squares which need not any prior information of parameters and brings forward a watermarking technology which uses linear least square (LS) with equality constraint to fuse from the perspective of information fusion. The fusion is based on the action of the attackers and uses the extracted reference watermarks to estimate the attack which the original watermarks got. It is independent of the idiographic algorithm. The results of experimentation show it is more robust.