Abstract
The authors of this paper demonstrate how, with the on-board multi-position information received from a satellite navigation system and the inertial information delivered from three dimension accelerometers with orthogonal axes of sensitivity, forming a movable coordinate trihedron, for the latter one the orientation and angular velocity of the rotation in projections on its own axis can be determined. The mathematical model of the inverse problem in the "state-measurement" form is presented as 1) a dynamic group of equations of functioning of the inertial navigation system (without gyroscopes), with the state vector, which includes the coordinates, specific impulses and angular velocities of the instrumental trihedron rotation, and 2) equations for measurement of the object's location coordinates, identified with the coordinates of trihedron tops in the projections on its axis. A dynamic pseudo inversion (solution) of the problem is realized by the neural network, the model of which is based on Kalman-type algorithm in its multi-model presentation, which allows a judgment about a fair competition between the models in the progress of the state vector evaluation. The concept of "nuclear" and "nuclear-free" setting mechanisms of the neural network synaptic coefficients is introduced. Hypothesizes about a possibility of broadcasting of the characteristics, used in the description of an artificial neural network, are introduced in presentations concerning organization and functioning of the populations of the biological ("live") neurons. The results of the computational experiments are presented.
Highlights
Математическая модель обpатной задачи вида "состояние— измеpение" пpедставлена: 1) динамической гpуппой уpавнений функциониpования безгиpоскопной инеpциалъной навигационной системы с вектоpом состояний, включающим кооpдинаты, удельные импульсы и угловые скоpости вpащения пpибоpного тpехгpанника и 2) уpавнениями измеpений кооpдинат места объекта, отождествляемых с кооpдинатами веpшины тpехгpанника в пpоекциях на его оси
The authors of this paper demonstrate how, with the on-board multi-position information received from a satellite navigation system and the inertial information delivered from three dimension accelerometers with orthogonal axes of sensitivity, forming a movable coordinate trihedron, for the latter one the orientation and angular velocity of the rotation in projections on its own axis can be determined
The mathematical model of the inverse problem in the "state-measurement" form is presented as 1) a dynamic group of equations of functioning of the inertial navigation system (without gyroscopes), with the state vector, which includes the coordinates, specific impulses and angular velocities of the instrumental trihedron rotation, and 2) equations for measurement of the object’s location coordinates, identified with the coordinates of trihedron tops in the projections on its axis
Summary
Поëаãая, ÷то оpиентаöия тpехãpанника ~oq опpеäеëена (это обсужäено выøе), из äвух ãpупп базовых уpавнений ìетоäа, äинаìи÷еской и кинеìати÷еской [2], составëяþщих сутü ìатеìати÷еской ìоäеëи ИНС, ìожет бытü оставëена тоëüко пеpвая из них — äиффеpенöиаëüные уpавнения äвижения ìатеpиаëüной то÷ки, с котоpой совìещена то÷ка ~o. Δzi = δqi + εi, i, j, k = 1, 3 , ãäе G = (Γij) = (∂Gi/∂qj) — ãессиан сиëовой функöии ãpавитаöионноãо поëя; f = ( fi), e = (εi) — вектоpы соответственно инстpуìентаëüных поãpеøностей нüþтоноìетpов и поãpеøностей оöенок кооpäинат ìеста ТП по äанныì НСС; кpоìе тоãо, зäесü пpеäпоëаãается, ÷то пpи pеаëизаöии ìоäеëи ãpавитаöионноãо поëя выпоëнено заìещение G(q) на G(z), c(t) = (χi(t)) — скоpостü изìенения вектоpа δw = (δωi). Заìетиì, ÷то äëя pазpеøиìости заäа÷ типа (3) (обpатных заäа÷ по сути) необхоäиìо, ÷тобы паpа ìатpиö (C, H) иëи (F, H) быëа набëþäаеìа [4] (зäесü F — пеpехоäная ìатpиöа состояния систеìы ëинейных уpавнений эвоëþöии вектоpа δx и, ÷то существенно, яäpо интеãpаëüноãо пpеобpазования в известной фоpìуëе Коøи äëя pеøения этой систеìы уpавнений)
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