Abstract: With the alternating iterative algorithm, solved parameters estimation question of mathmatic model in the case of unknown error variances, which contains two linear models with the same parameters under linearinequality constraints, was investigated and two least square estimation sequences and the approximate solutions that refer to the parameters in the model were obtained, on the basis of which via fixedpoint theorem and numbers theorem of solutions of multivariate polynomial equation group it was proved that the estimation sequences are convergent in probability 1.

Key words: constrained model, least square estimation sequence, convergence