Algorithms of a linear estimation of a poorly worded matrix and errors of observations--uncertain functions of time

BMLS1 and BMLS2--the variants of algorithms of the method of least squares--are stated. They are Baye's algorithms for the linear estimation of a vector of parameters. These algorithms are correct in the sense of the classical theory and keep an applied correctness at small singular numbers of a matrix of system of the linearized equations of a file of observations. Without the assumption of the normal laws of distribution of random vectors the BMLS1 recursion form, adequate to the modified form of the algorithm of the standard Kalman's filter, is deduced. In the present observations smooth and small in size of functions of time the parametrization is used on the basis of Bernstein's polynomials. We state and carryout the numerical analysis of the accuracy of the decision of a task of precision relative positioning of two orientations on the surface of the Earth, which is made on signals from one satellite.