
CONTENTS
S.G.Romanenko, B.E.Landau, S.L.Levin

On movement of electrostatic gyro rotors of the strapdown orientation system of an orbital space vehicle

3

The conventional requirements to autonomous systems of motion control of space vehicles (SV) on the
decreasing of mass and dimensions and power consumption , on reliability augmentation and
reduction (decreasing) of the cost have resulted in necessity of transition from the strapdown to gimballess
systems of attitude orientation, stabilisation and control. The increasing of accuracy of these systems require
precision electrostatic gyroscopes (ESG).
The case of the installation of two ESGs into the attitude orientation system of space vehicles is
considered. The vectors of moments of momentum H and H are arranged perpendicularly and parallel to
orbital plane or both are in orbital plane. The relations of direction cosines between rotation axis of rotor and
axes of the body and also expressions for projections of the drift rate are obtained as a result of the solution
of equations of precision motion in an analytical kind. Thus the analysis of influencing only of one of
significant in conditions of weightlessness of the revolting factors is in turn carried out: the withdrawing
moment from the bias (unbalance) and odd harmonics of rotor nonsphericity, the moment independent of
acceleration and a proportional to the fourth harmonic of the rotor shape, the moment from residual
magnetic fields. At the same time it is allowed, that the common solution can be sought by a method of a
superposition. The evaluation values of drift speed of ESG for the indicated orientations of gyros are
adduced, and also outcomes of simulation of relation of the angle between the vectors of moments of
momentum from time in a case, when the rotation axes of both ESGs are arranged in the orbital plane of the
space vehicle, or when one gyro is in the orbital plane, and the other is perpendicular to it.
The analogy between motions of vectors of moments of momentum of ESG, installed in space vehicles
according to the indicated orientations and motions of gyros installed on the Earth in "polar" and
"equatorial" orientations is considered. The problem of maintenance of a longlived cycle of continuous
construction of the base Inertial Reference (IR) with adequate accuracy taking into account convergences
(divergences) of vectors H and H is analysed. The contribution of different sources of errors of the
conservative and nonconservative nature to drift and parameters of motion of gyros of attitude orientation
system is estimated.

A.A.Galaktionov

Examination of temperature influence on electrostatic gyro drift

12

Temperature influence on the ESG drift is investigated. The reasons that may cause its temperature drift
are determined. The relations are derived for determination of ESG drift caused by different thermal
disturbing factors under different initial parameters of gyro's sensor. The calculation results are given for
temperature drift of the ESG with hollow rotor. It is shown that heterogeneity of temperature expansion
coefficient of rotor material is the main reason for ESG temperature drift. Drift velocity estimations are
obtained for the drift caused by the heterogeneity of rotor and chamber temperature fields and by the rotor
displacement inside the chamber along the main axis. The methods are suggested for elimination of the
temperature error by hardware or by algorithms.

L.N.Belsky, L.V.Vodicheva

Increase of gyrocompassing accuracy by choosing orientations of measuring instrument sensitivity axes

21

The technique of optimization of inertial sensor input axes orientations during gyrocompassing is
suggested. The criterion of optimization is the minimum of an azimuth determination error. Singleposition
and the most widely used twoposition schemes of gyrocompassing are studied in detail. Introduction of
singleposition schemes simplifies and makes physically obvious the procedure of optimization for twoposition
schemes. Complicated schemes are reduced to simple ones.
In a singleposition gyrocompassing scheme with a single sensor with measurement errors being
independent random variables a scale factor does not affect azimuth determination accuracy at all and a drift
influence is minimal if sensor input axis is orthogonal with respect to the measured vector. (2.2), (2.3), (2.4)
are expressions for an azimuth estimate, an azimuth estimation error variance and the minimal azimuth
estimation error variance.
In a twoposition scheme with a single sensor a constant component of a drift does not affect
gyrocompassing accuracy. The optimal rotation angle is obtained by minimizing a variance of an azimuth
determination error as a function of this angle. (3.3) is the expression for an azimuth estimate, (3.4) is the
expression for azimuth estimation error variance. Fig.2,3,4 depict variances of azimuth determination error
under rotation angles about p/2, p and the optimal one under various relations of error sources. They show
that under the same errors for some intervals of azimuth gyrocompassing error is essentially larger for
rotation angles about p or p/2 than for the optimal angle. Fig. 5 shows optimal angles as functions of azimuth
angle.
Singleposition scheme with two sensors with orthogonal input axes is reduced to the simplest singleposition scheme with a single hypothetical equivalent sensor. In this scheme accuracy improvement can be
achieved by optimal integrity of measurements.
Twoposition scheme with two sensors is reduced to the simpler twoposition scheme with single sensor
with optimization by rotation angle and azimuth angle. It is shown that if sensor drift instability is dominated
over rotation angle error the optimal value of a rotation angle is equal p. If rotation angle error is essentially
more than sensor errors the optimal value of a rotation angle is near p/2. In other cases the optimal angle
reduces azimuth determination error 1,52 times. Fig. 6 depicts azimuth determination error variance and
optimal angle as functions of error sources ratio. This scheme allows gyrocompassing under unknown
latitude with simultaneous eliminating of drifts as well. It is shown at the end of the paper. (6.1) and (6.2) are
expressions for azimuth estimate and azimuth estimation error variance. The optimal rotation angle in this
case is equal p.

A.V.Chernodarov, V.V.Enyutin, A.P.Patrikeev

Diagnosing of integrated navigation systems on the basis of combined UD procedures of filtering and
smoothing

34

This paper is devoted to the problem of protecting the integrity of integrated navigation systems (NS's),
which relies on the serviceability of all the modules of a redundant structure. Here typical modules are the
following ones: a strapdown inertial NS, a satellite NS, and also the extended Kalman filter (EKF). This EKF
unites, into an integrated structure, measuring aids that are dissimilar in the principle of operation.
Moreover, with this EKF, it becomes possible to reveal a discordance among equivalent parameters formed
by different NS's. However, from such a discordance, one cannot locate a trouble and determine the cause of
it. In order for this diagnosis problem to be solved, we propose that estimates obtained during filtering in
forward and backward time should be used jointly. In this case, it appears that the formation of generalized
parameters characterizing the state of each module of an integrated navigation system (INS) to the depth of a
component of the state vector is quite possible. The diagnosis technology under discussion relies on unified
UD procedures intended for the filtering of observations (see Fig. 3) and for the smoothing of estimates (see
Fig. 4). Such procedures maintain the computational stability of solution of direct and adjoint Riccati
equations and they permit one to decompose residuals and to process them sequentially. The proposed
modification of the conventional smoothing RTS (RauchTungStriebel) algorithm is meant for the situation
where external data necessary for the updating of inertial NS's come in an irregular manner; such a situation
is characteristic of maneuverable aircraft. The effectiveness of the algorithms obtained was confirmed by the
results of halfscale modeling.

Materials of the 7th Saint Petersburg International Conference
on Integrated Navigation Systems
P a p e r s
V.Z.Gusinsky, V.M.Lesyuchevsky, Yu.A.Litmanovich, V.G.Peshekhonov

High Precision GroundBased North Finder

49

The present paper deals with some of the major problems of the high precision groundbased North
Finder (NF) development. A schematic of a NF with an electrostatically suspended gyro (ESG) is presented.
The principle of NF operation and the effect of instrumental errors on NF performance are considered. The
preliminary test results of the basic component parts and NF as a whole are presented.

A.M.Lestev, I.V.Popova, À.À.Semenov, S.À.Zagrebelny, S.À.Vinogradov

Portable System of Autonomous Positioning

59

The outcomes of research, development and application portable inertial systems of positioning are
reported. Micromechanical gyroscopes and accelerometers are used in those systems as inertial sensors with
specification presented in table 1. Thermostatic control and modulation increase an accuracy of
micromechanical sensors sufficiently. Researches and experiments of thermostatic control, auto
compensation and calibration are stated and demonstrated in figures 1 and 2. System operation algorithm
computes orientation and navigation of mobile object in realtime that is described with equations 18. Those
systems utilising in transport monitoring and manual scanning are shown in figures 48.

S.F.Konovalov, A.A.Konovchenko, A.V.Polynkov, A.A.Trunov, V.M.Prokofiev, O.S.Kwon, H.G.Moon, J.B.Seo, F.Luc

LowNoise Accelerometer Development Experience

68

To solve a number of tasks connected with acoustic prospecting of oilfields in marine shelf, it is required
lownoise geophonic sensors. The pendulous accelerometers of compensation type, having measurement
range within 2g, threshold of 10^{6} g, natural frequency of 250Hz
and noise level in an output signal less 40 n g/(Hz)^{1/2}, can be used as the similar sensor. There is a pendulum in the instrument mobile unit, made of
monocrystalline silicon wafer by a method of anisotropic etching. The servoloop of the instrument is formed
by the capacitive pickoff, lownoise amplifier and twin magnetoelectric forcer. A nontraditional mutually
perpendicular arrangement of pendulum flexures is used in the instrument. The special measures are
attempted to eliminate influence on bias stability of difference in value of coefficients of thermal expansion of
materials of a pendulous unit and case members contacting the pendulum. The results of experimental
examination of the instrument on test bases of Russia, Korea and France are presented in the paper.

A b s t r a c t s

78

Brief notes
N.S.Ivanova

Experimental research of electromagnetic field of a free gyro electric drive stator

94

Under the experimental study drive free gyroscope with electroconductor hollow spherical rotor and with
stator without magnetowire measured influence of screen and shell of rotor on the value and nature of
sharing an induction in the air clearance.
At presence of rotor an amplitude of main harmonica of magnetic field a windings stator decreases in 1,8
on the frequency 1400 Hz times.
Electromagnetic screen plays a role external magnetowire for stator and reduces a third spatial
harmonica level.
Reason of low efficiency drive at the dispersal of rotor is a high third spatial harmonica level (50%) in
crooked sharing the inductions in the air clearance.
One of the directions of raising efficiency drive is a configuration changing the windings stator, but other
 an optimization of frequency of power supply drive.

N.S.Ivanova

Peculiarities of determining parameters of the equivalent circuit of a free gyro electric drive

99

In the article considered particularities of determination of parameters of scheme of substituting drive
electrostatic gyroscope with hollow spherical electroconductor rotor. Offered method of determination of
parameters of scheme of substituting drive free gyroscope on frequency of the maximum moment. Brought
accounting and experimental mechanical features drive. The mechanical features tinned by the accounting
way on determined offered by the method to parameters a substituting scheme, are distinguished from tinned
experimental not more, than on 10%.

E.A.Artyukhov, V.V.Bernadsky, V.V.Gromov, V.G.Oleshkevich

A speedlimiting device for rotor revolvingaround

105

A saver for limiting the speed of the revolving rotor with a central aperture is considered. The device
consists of external and internal supports and makes it possible to specify admissible normal reactions of
these supports by choosing relationships of their stiffnesses and clearances. This ensures troublefree
stopping of the rotor when a noncontact support fails. Efficiency of the solution suggested is verified by the
results of rotor movement simulation in the program Pro/Mechanica.

Information
Russian and international conferences, symposiums, exhibitions

113

M.B.Rozengauz

4th IFAC symposium on fault detection, supervision and safety for technical processes

114

O.A.Stepanov

A review of the book by Yu.A.Soloviov "Satellite navigation systems"

115

