Experimental design and data processing in a distance navigation problem for position of the object location

Abstract

A problem of optimizing the configuration of a navigation measuring system is considered in terms of the experimental design using a distance navigation problem for position of the object location. It is shown that the stated problem is equivalent to the problem of A-optimal experimental design for a regression function (nonlinear in parameters) and can be reduced to a trigonometric model. The response function, Fisher’s information and the sensitivity factor of the navigation system in case of two and three beacons and correlated measurements are presented in an explicit form. Using the equivalence theorem for A-criterion in the case of two-dimensional (plane) distance problem we confirm again the Barabanovs’s result that matrixes of A-optimal designs are the Kolmogorov – Maltsev matrixes. A similar result holds for the D-optimality criterion in the considered case. The effect of the measurement correlation in a distance navigation problem with two and three reference points is considered. The formulas for the sensitivity factors expressed in terms of bearings on the reference points and intersection angle of object are derived. In addition to a problem of optimizing the network configuration, the data processing problem in two-dimensional distance navigation problem with two reference points is also considered. The location of the object is determined in two ways, i.e., using the geometrical method and method of resultants. In the first method the solution of a distance navigation problem comes to the consideration of two independent quadratic equations for determination of the first and the second coordinates of the object. The equations are obtained in the explicit form. The second method also leads to two quadratic equations for determination of the object location. This is an option of the exclusion method which provides for an explicit form of conditions ensuring the solution of the considered problem for determination of the object location. Examples are considered that confirm the stated conclusions.