
CONTENTS
N.Barbour, G. Schmidt

Inertial Sensor Technology Trends

3

This paper presents an overview of how inertial sensor technology is applied in
current applications, and how it is expected to be applied in near and far term
applications. The ongoing trends in inertial sensor technology development are
discussed, namely interferometric fiberoptic gyros, micromechanical gyros and
accelerometers, and microoptical sensors. Micromechanical sensors and improved
fiberoptic gyros are expected to replace many of the current systems using ring
laser gyroscopes or mechanical sensors. The successful introduction of the new
technologies is primarily driven by cost, and cost projections for systems using these
new technologies are presented. Externally aiding the inertial navigation system
(INS) with the global positioning system (GPS) has opened up the ability to navigate
a wide variety of new, largevolume applications, such as guided artillery shells.
These new applications are driving the need for extremely lowcost, batchproducible sensors.

V.Z.Gusinsky, V.M.Lesyuchevsky, A.A.Stolbov

Automatic Calibration of Transducers for Gimballed Inertial Navigation System on Uncontrolled Gyros

16

In the work a new approach to calibration of gimbaled Inertial Navigation
system (INS) based on two electrostatically suspended gyros (ESG) is considered.
The automatic calibration procedure of the inertial measuring unit (IMU) error
models parameters, namely, the gimbal pickoff errors, is examined. The
measurement errors for angle rotor position are described by equation (1). The
gimbal pickoff errors are described by equation (3). The relationship between the
gimbal pickoff errors and INS output errors is described by equation (14). The
Kalman filter observation equation is received. The IMU calibration procedure is
tested by the experimental study. The tests results are shown in Fig.1. It was shown,
that the calibration errors are equal to (5……..10) %. The calibration time is equal
to 5 hours.

S.P.Dmitriev, O.A.Stepanov

Noninvariante Algorithms for Information Processing of Inertial Navigation System

24

The classical approach to the development of the algorithms for various inertial
navigation systems (INS) is based on kinematic equations of mechanics for
navigation parameters (NP) (vehicle coordinates, velocity, and orientation angles).
These algorithms are reduced to the solution of differential equations whose right
parts contain measurements of INS sensors: accelerometers and gyros. NP
generated by these algorithms using errorfree (ideal) measurements will also be
errorfree. That is why these algorithms are often called the «ideal operation»
algorithms. When the external aids are available, the «ideal operation» algorithms
are complemented by the filtering algorithm.
The aim of this complement is to
estimate INS error on the background of errors of external navigation meters. The
measurements for this filtering problem are formed by comparing the readings of
the INS and those of the external meters. It is essential that navigation parameters
are not included in the statevector. Due to this approach the errors of the
parameters under estimation do not depend on realizations of the parameters in the
case of the linear character of differential equations for the "ideal operation"
algorithms. As a consequence, the algorithms obtained on the basis of this approach
are frequently called invariant algorithms. The advantages of invariant INS
algorithms are their comparative simplicity and little error dependence on the
character of NP changes. However, they have an essential drawback, as the NP
properties generated by the vehicle dynamics are not taken account of.
The aim of the paper is to optimize INS algorithms using this additional
information about the NP properties. In order to take into account this information,
the equations of the vehicle's dynamics are included into the equation for the state
vector. Thus, the navigation parameters are described as stochastic processes and
their estimates are calculated as a result of solving the filtering problem for the
navigation parameters themselves. The accelerometer and gyro readings are used
directly (along with possible external data) as measurements in the filtering
problem. It is essential that the obtained algorithms will lose the invariance
property that justifies their definition as noninvariant algorithms. At the same time
these algorithms are adaptive ones as they are adjusted to the dynamic properties of
the vehicle where the INS is mounted.
Optimization of the INS algorithm and the analysis of its accuracy are oriented
at strapdown inertial navigation systems (SINS). These systems are widely used due
to the simplicity of their construction and a comparatively low cost.
The efficiency of the approach suggested is illustrated when estimation problem
is solved for marine ship NPs using data from SINS and satellite system.

A.V.Sokolov, S.V.Usov, L.S.Elinson

Gravimetric Survey Experience When Carrying out Sea Seismic Work

39

The results of gravimetric survey carried out using the gravimetric complex
Chekan  A during the seismic work in one of the North Sea regions are analyzed in
the paper. The peculiarities of complex construction are considered. The
measurement accuracy dependence on sea states and parameters of digital
smoothing filter is studied. The measurement error evaluation on data of base
measurements and difference of anomaly values in the free air in the points of tack
crossing is given. The comparison of gravimetric data with seismic profile is
effected.

P.K.Plotnikov, V.Yu.Musatov, A.I.Sinev

Algorithms for Underground Pipeline Routes Positioning Using Inertial Magnetometric System

51

The stateoftheart of technological processes for manufacturing of lowcost
compound hemispherical resonators are presented in this paper. The compound
resonator consists of hemispherical shell (meniscus) and stem, which are made
separately with use of the well fulfilled technology of spherical and cylindrical
optics. Manufacturing technology of compound resonator elements is described in
the paper. Geometrical and dynamic characteristics of meniscus are given.
The use of highly effective technologies of optical production when
manufacturing resonators hemispherical resonator gyroscopes (HRG) allows us to
considerably reduce the production cost and to save, at the same time, their
dynamic characteristics at a level of resonators made of onepiece of glass.
With the purpose of increasing of adaptability to manufacture and cost reduction
we offer a construction of a compound resonator [13]. For checking the design
parameters of resonator's parts during their manufacturing well worked methods
and equipment are also applicable [4]. It is expected that the Qfactor of the
developed resonators will be rather high and mismatches in the Qfactor and in
frequency will be rather low (Table 1). This is because one of the main reasons of
energy dissipation in hemispherical quartz resonator are the losses in a surface
layer [3,5], and in the compound resonator a level of a surface roughness about
0.032 microns can be achieved (Fig.2).
Other major reason of HRG error is the technological defects of a resonator.
Due to application of accurate methods of checking of geometric parameters of
resonator's parts it is possible to considerably reduce a technological defects
during manufacturing, which influence on mismatches in Qfactor and in eigen
frequency (due to checking of such parameters as difference in thickness of a
resonator, eccentricity, tilt of a resonator stem axis etc.).
The dynamic model of a resonator, taking into account its stem and rigidity of
connection stem and hemisphere is considered in this work. The analysis of a loss
function and relative Qfactor is given, that will allow us to qualitatively evaluate
various designs of resonators, and also resonators made of various materials, to
define conditions for optimization of the stem parameters, to define the influence of
a rigidity of its fixing.
Experimental investigation results of dynamic characteristics of various
resonator's design and also made of various materials are analyzed.
The work was executed within the framework of the project 558 of Science and
Technology Center in Ukraine (STCU).

Papers from the VI Saint Petersburg International Conference
on Integrated Navigation Systems
J.Mark, D.Tazartes

Application of Coning Algorithms to Frequency Shaped Gyro Data

65

A key parameter of a strapdown inertial navigation system is its response to
coning motion. Substantial efforts have gone into the development of sophisticated
algorithms which reduce system drift errors in the presence of coning motion.
Presentday algorithms use incremental angle outputs from the gyros to form high
order correction terms which reduce net coning errors. These algorithms assume a
flat transfer function for the processing of the incremental angle outputs and are
structured to yield very high order responses. Techniques such as resolution
enhancement shape the frequency response of the gyro data and consequently
degrade the performance of the conventional coning algorithms. Likewise, many
gyros exhibit complex frequency responses and violate the assumptions used in
deriving the previously developed coning algorithms. The mismatch between the
assumed and actual frequency response of the gyro data leads to degradation of
performance in a coning environment as well as amplification of pseudoconing
errors. This paper discusses a method of deriving algorithms which are tailored to
the frequency response of the particular type of gyros used. These algorithms can be
designed to arbitrarily high order and can also supply an extremely sharp high
frequency cutoff to minimize pseudoconing errors. This work was motivated by the
desire to use resolution enhanced ZLG data to form the strapdown attitude solution
and was heavily influenced by the most recent work in Russia on coning algorithms
by Yury Litmanovich. However, the techniques developed equally apply to
mechanical, fiberoptic, and other types of gyros. Extensive simulation of the new
algorithms has been performed and we are now in a position to incorporate them in
the Litton ZLG product line.

M.Yu.Shatalov, B.S.Lunin

Influence of Prestress on Dynamics of Hemispherical Resonator Gyroscope

78

Inner prestresses result from the mechanical treatment of a resonator or from
inertial motion of the gyroscope, for example, its rotation. The analysis is complex
from the theoretical viewpoint because it is necessary to consider the nonlinear
geometry of the shell. It is also difficult from the view point of numerical analysis by
means of finite element methods due to infinity of different possibilities for inner
prestress distributions. This problem of influence of the prestress on dynamics of a
hemispherical resonator gyroscope is investigated analytically. On the basis of
analysis of nonlinear geometry of a hemisphere the terms responsible for the
prestresses are introduced in the expression for the strain energy of the resonator
and the problem is solved in linear approximation. The example of an important
case of a particular distribution of local stresses is considered. The special case of
influence of centrifugal forces on the dynamics of a rotating gyroscope is
investigated.

S.F.Petrenko, Yu.A.Yatsenko, V.V.Vovk, V.V.Chikovani

Technological Aspects of Manufacturing of Compound Hemispherical Resonators for SmallSized Vibratory Gyroscopes

88

The stateoftheart of technological processes for manufacturing of lowcost
compound hemispherical resonators microns can be achieved (Fig.2).
Other major reason of HRG error is the technological defects of a resonator.
Due to application of accurate methods of checking of geometric parameters of
resonator's parts it is possible to considerably reduce a technological defects
during manufacturing, which influence on mismatches in Qfactor and in eigen
frequency (due to checking are presented in this paper. The compound resonator
consists of hemispherical shell (meniscus) and stem, which are made separately
with use of the well fulfilled technology of spherical and cylindrical optics.
Manufacturing technology of compound resonator elements is described in the
paper. Geometrical and dynamic characteristics of meniscus are given.
The use of highly effective technologies of optical production when
manufacturing resonators hemispherical resonator gyroscopes (HRG) allows us to
considerably reduce the production cost and to save, at the same time, their
dynamic characteristics at a level of resonators made of onepiece of glass.
With the purpose of increasing of adaptability to manufacture and cost reduction
we offer a construction of a compound resonator [13]. For checking the design
parameters of resonator's parts during their manufacturing well worked methods
and equipment are also applicable [4]. It is expected that the Qfactor of the
developed resonators will be rather high and mismatches in the Qfactor and in
frequency will be rather low (Table 1). This is because one of the main reasons of
energy dissipation in hemispherical quartz resonator are the losses in a surface
layer [3,5], and in the compound resonator a level of a surface roughness about
0.032 of such parameters as difference in thickness of a resonator, eccentricity, tilt
of a resonator stem axis etc.).
The dynamic model of a resonator, taking into account its stem and rigidity of
connection stem and hemisphere is considered in this work. The analysis of a loss
function and relative Qfactor is given, that will allow us to qualitatively evaluate
various designs of resonators, and also resonators made of various materials, to
define conditions for optimization of the stem parameters, to define the influence of
a rigidity of its fixing.
Experimental investigation results of dynamic characteristics of various
resonator's design and also made of various materials are analyzed.
The work was executed within the framework of the project 558 of Science and
Technology Center in Ukraine (STCU).

History Pages
S.A.Shestov, S.V.Mokryshev

Development of Ground Gyroscopes Based on Gyroscopic Tachometers

95

On materials of an open domestic and foreign seal [1, 58, 18, 19] the historico
analytical the review of development of gyrocompasses (GC'es), constructed on the
basis of gyrotachometeres (GT'es) is made. Volume of knowledge on such GC'es is
systematized. The analysis of the various circuits of construction (Fig. 3, 4, 5, 6)
GC'es and their comparison by criteria is carried out: accuracy (7), (16), (21), (24),
(29), (30), speed, protection against external influences and complexity of
realization. The technical characteristics of some samples GC'es, constructed on the
basis of GT'es are given.

Information
Russian and International Conferences, Symposiums, Exhibitions

113

Review on Monograph "Optical Gyros and Their Application"

114

Review on M.S.Finkelstein's Monograph "Stochastic Point Process Models in Reliability and Safety Problems"

116

