A new ridge estimation method on rank-deficient adjustment model

In this paper, we present a new ridge estimation method for solving rank-deficient least squares problems, in which a rank-deficient matrix is regarded as an almost rank-deficient. First, we give an algebraic derivation that the optimal solution can in fact be obtained by solving a related regularized problem on the optimal worst-case residual. Second, we give a new iterative algorithm to solve ridge parameter and prove its convergence. Finally, examples are given to demonstrate the efficiency of our new method. It is shown that the proposed algorithm can not only assess the stability of solution but also use additional prior information to guarantee the uniqueness of solutions to the problem of rank-deficient free-network adjustment.