Some Remarks on the Adjustment with Rank-Defects by Using Pseudo-observations

This paper is a study report after having attended the lectures by Prof.W.Welsch of West Germany,given at Wuhan in May 1980.The theory of the adjustment with rank-defects by using the generalized inverse is discribed.while the coefficient matrix of the pseudo-observations equation must satisfy AB^T=0 and BB^T=I as is required in the above mentioned lectures,it is shown here in this article that only AB^T=0 and rank =d is necessary.That is to say that,in order to realize the minimum biased adjustment in the case of rank defects,we need not use the pseudo-inverse(A^T A)⁺ but may use the generalized inverse(A^T A)^-,which meets the Penrose conditions(1) and(4) only.Thus the conditions needed for the pseudo-observations can be reduced.