Dependence of the Space-Intended Rocket Insertion into Orbit Parameters on the Inertial Platform System Initial Alignment


Аuthors

Naumchenko V. P.

JSC «TsENKI» – «NII PM», Moscow, Russia

e-mail: 8987nau@mail.ru

Abstract

Cutting time and structure simplification of the initial alignment algorithm for efficiency increasing of the inertial navigation systems (INS) in the instances requiring operative turn-on and execution of the carrier target task is an important problem. To this end, an optimization algorithm development for the initial alignment of the INS platform keeps on. As part of the previously obtained backlog, a refined functional diagram of the initial alignment and block diagram of the optimization problem solution algorithm were compiled.
Conceptual mathematical model of the three-axis platform alignment is being adduced for the first time jointly with the functional diagram clarifications. The form of the model record herewith allows its application for the equations of initial alignment description for leveling and gyro-compassing of both uniaxial and biaxial platforms. Logic elaboration of the initial alignment algorithm is possible with the two conceptual approaches with regard to readings anti-gradient d and method step λ. The first approach, widely adduced in the technical literature, is based on the classical interpretation consisting in employing objective function of the measurement model and its derivatives. The second one consists in direct application of the filtered primary readings of sensitive element for the anti-gradient computing. Scaling of the method steps λ for the algorithm speeding is feasible by adding the alignment speed regulation block.
To enhance modeling speed and computer resources assignment, modeling is being performed in multiprocessor mode and with the Python3 language libraries aid. A significant amount of parameters has to be varied while simulation, and Pareto optimal methods are being applied to search for the best results, namely the method of effective multi-criteria programming and the method of negative weighting according to the criteria of error of the alignment and overshoot. In the course of the simulation results filtering, a set of adjustment coefficients, which can be entered into the non-volatile memory of the INS, is being obtained.
To assess the impact of the errors in the initial alignment on the target problem solving accuracy, the task of a space rocket (SR) launching into a low Earth orbit is being modeled. The leading-out error is being regarded as a function of the initial platform alignment error without account for the atmospheric model errors, the errors of aerodynamic forces and thrust of the SR engine.

Keywords:

inertial navigation system, gyro platform, initial alignment optimization algorithm, gradient descent method, space rocket, accuracy of launching into the target orbit

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