Consistency Of Mixed Integer Linear Model With Unknown Parameters, Bayes Estimates

The mixed-integer linear model rises from the data processing of GPS technology,and the solution of the integer ambiguity is one of the key issues in precise positioning. The model can usually be expressed as Y = AX + Bθ+ e,e-N(0,Q_y)where Y is the vector of observation, X is the vector of unknow baseline with real value,θis integer ambiguity with integer value ,A and B is design matrix .The very restriction thatθis integer not only cause trouble in the estimation of the parameters but more importantly makes the study of the estimators' stastistical properties very difficult.Although many ways of estimating the parameters have been developed, but no study about the consistency of these estimators is done yet.With a thorough study about soluting of these estimators, the author proved the consistency of these estimators and further verifid it by coumputer simulation.The above mentioned estimation of parameter X andθall was carried with assuption that variance componentσ~2 is know. However, when the value ofσ~2 is unknow, the estimation of parameter can not be derived.So it is very important to estimate the variance component.Based on Bayes principle, the author derived the maximum likelihood estimation respectively for the condition thatσ~2 has non informative prior andσ~2 has inverted gamma prior.In addition to that, author improved the Bayes estimation of integer ambiguityθ. The now existed Bayes estimation ofθconsider it with non informative prior and then derived the posterior distribution. The author used this posterior distribution as a prior information ofθ, proposed a new estimation ofθand further perfected the Bayes estimation ofθ.