The article deals with the creation of integrated information and navigation system implementing the joint processing of inertial and satellite navigation information. It is assumed that the inertial navigation system, as a part of an integrated system, consists of three-block accelerometer module to measure the apparent acceleration vector. Thus, such system is distinguished from the classical inertial navigation system, which also includes three-sensor angular accelerations. Satellite navigation system is a distributed board receivers system of positional information that allows to find the orientation matrix of the movable connected coordinate system. As a result of this system configuration, the mathematical model of the inverse problem, aimed to evaluate the object's location vector and its linear and angular velocity vectors, consist of dynamic group of Newton's equations describing the particle motion in a rotating coordinate system under the influence of gravitational force and the resultant forces of non-gravitational origin (measured with accelerometers). Described statement of the problem represents original expectations associated with the ability to evaluate the angular velocity vector. This article substantiates the solvability of the problem in terms of finite calculations and changes precision. The algorithm for the problem solution is based on the novel concept of dynamic artificial neural network, appealing to the mathematical theory of Kalman filtering and some contemporary ideas about the structure of individual neurons and their functional communities. The results of numerical studies and computational experiments, showing the high efficiency of the proposed system, are presented. Interpretation of the integrated system as a system that extends functions of on-board navigation systems such as GPS / GLONASS is permissible.