Fig. 12. Simplified scheme of inertial navigation system, oriented by axes of geographical trihedron
The
platform contains three gyros Г
and
three accelerometers
А.
Initial
data are measured values
,
,
,
by which, however, we can’t directly calculate velocities.
The fact is that these values contain components, caused by the
Coriolis
acceleration
and
centripetal
acceleration. These components, as well as anomalies
of gravity acceleration, should be taken into account and
compensated.
After
a
single
integration
projections of velocity
,
,
are obtained. Due to these projections velocity
in relation to the Earth can be calculated. Via the integration of
velocity
it
is possible to obtain altitude
.
The value of
mostly contains fast-time errors, so it is used only short-term.
Multiplying
on
,
we
can get derivative
of geographic latitude.
Due
to
the
need to consider
the
convergence
of
meridians
the value
should be multiplied on
in purpose to obtain
.
After integration
of
the values
and
we can get data about coordinates
and
.
In order for the platform was always properly oriented with respect to the Earth, the axes of the platform should rotate with following angular velocities:
These velocities can be generated in the way, explained by the fig.12, and used as initial data for the platform (data for gyro control).
As
initial data we should set starting values
and
,
that are initial contained in the current values of altitude
,
velocity
,
longitude
,
and latitude
.
For aircraft a simplified system is mostly used without specifying
altitude.
Alignment of the platform. Platform, oriented by axes of the Earth, should be arranged before the operation so that its axes will coincide with the axes of the chosen reference system. If east - north – zenith system is chosen, then one axis of the platform should be directed vertically, while the other two in the horizontal plane in the respective directions.
Vertical alignment, as a rule, is implemented automatically, and accelerometers of the platform are used as horizon sensors.
The platform is automatically aligned in azimuth with the help of its accelerometers and gyroscopes (gyrocompass method or analytic alignment).
Besides, azimuth can be input manually using external sensors (optical, radio, gyrocompass) if automatic alignment is not possible (huge drift of gyros, large oscillations of the airplane, flight in high latitudes and so on).
9. ERRORS OF INERTIAL SYSTEMS
The main errors of inertial systems can be divided into 5 groups:
Errors of construction. These errors are connected to installation of the system on an airplane (errors of assembly and adjustment of elements on the platform);
Errors of elements. These are errors because of real elements’ deviation from design condition;
Errors of system algorithm. These errors appear because of increments, which are taken to simplify the system during its algorithm creation;
Errors of the system preparation. These are errors, caused by imperfect means to the system alignment, and so on;
Errors, connected with maneuvers. Such errors are associated with acceleration change, and that is why they depend on quantity of maneuvers and their duration for airplanes, flying in cruising regime.
In spite of huge variety of error sources in inertial systems, the errors can be classified as instrumental errors, errors of the device trihedron’s initial orientation, errors of initial conditions input into on-board calculator, and errors, caused by simplifications of model equations (methodical errors).
Instrumental errors of inertial systems are caused by errors of their inertial elements (accelerometers and gyroscopes), errors of follow-up stabilization systems and integrators, errors of the calculator (not connected with calculating algorithm simplification).
The nature and proportion of ground and speed errors of inertial systems in dependence on gyro drifts are presented in the item 4. As “drift” of gyro we can consider integrator errors, and errors of platform stabilization systems.
Methodical errors of inertial systems are connected mainly with algorithm simplification of navigational equation calculation and simplified representation of the Earth form. Nowadays modern on-board calculators are created, which allow implementation of high-accuracy algorithms. Manufacturing of precision inertial elements (accelerometers and gyroscopes) still is the most expensive and difficult thing in creation of accurate inertial systems, capable to work for a long time.