Abstract: The perspective projection model of the theodolite is analyzed and the mathematical model of the three-dimensional coordinates measuring system with bino-theodolites(TCMSBT) is analyzed. A new method, involving a direct linear solution and an iterative nonlinear solution, to determine all the geometrical parameters of the TCMSBT is proposed. Firstly, essential matrix E can be determined from 8 or more point correspondences in two projective planes of bino-theodolites and on the basis of absolute distance constraint, the projective matrix of the right theodolite can be determined by the singular value decomposition of E with closed-form method. Secondly, taking the parameters obtained in the first step as an initial guess, all the accurate geometrical parameters of the TCMSBT are estimated by nonlinear minimization of the cost function relative to the distance error affected by the measurement errors for the three coordinates of the space point and the co-planarity errors which two projective points and two observed centers of the bino-theodolites should follow. The two-steps procedures to determine the geometrical parameters permit a rapid estimation considerably reducing the number of iterations, moreover, the convergence is nearly guaranteed due to the linear guess obtained in the first step. It shows that this method is practical by experiments.

Key words: Coordinate measuring, Epiopolar constrained, Essential matrix, Perspective projection, Theodolite