9. Авиация и космонавтика
Nickolay Zosimovich
National
aviation university, Kiev, Ukraine
Space vehicle identification
parameters on the basis of an optimum filtration
Introduction.
The
problem of control of Space Vehicle (SV) descent in planet atmosphere
represents enough challenge, which even more becomes complicated presence of
casual indignations, absence of the qualitative aprioristic information on
environmental parameters and about a condition vehicle during the initial
moment of time. It leads to increase of the requirements shown to various
systems of SV and, first of all, to systems of navigation and control.
At the decision of a
considered problem it is possible to use the algorithms of navigation founded
on statistical methods of the information processing [1-3]. Considering, that
information processing is carried out with use of the onboard computer,
algorithms of identification should have recurrent character. Such algorithms
can be as follows: 1) the algorithms based on Kalman filtration ratio and 2)
the algorithms based on definition of a maximum density of aposteoristic
probability concerning results of measurements with use of a method of
invariant immersing [4].
1. Statement of the problem of
parameters identification of the SV condition under the Kalman ratio basis. Generally
the equations of SV movement and measurements can be described by the formulas
[5]:
(1)
(2)
where 
th degree
condition of vector-function 
controls 
and time 
degree
vector-function of measurements; 
degree vector
of measurements; 
degree matrix
of indignations; 
degree vector
of indignations; 
degree vector
of noise of the measurements channel; 
and 
Gausses white
noise with diagonal matrixes of intensity 
and 
[6].
Components of
the vector of condition 
during the
initial moment of time are random variables, which submit to the normal law of
distribution with next parameters 
Using methods of
identification by means of Kalman ratio are demanding linearing initial systems
(1) and (2). It is recommended providing linearing by leading under relation of
estimation 
on the
previous step at the moment of time 
as at linearing concerning a nominal condition
convergence of estimations can be appear insufficiently high. Because of
complexity and considerable nonlinearity of expressions (1) and (2)
linearization was spent by use of numerical methods.
As a result of linearization on the interval 
the initial
system is leading as
(3)
(4)
where 
Let's consider two algorithms of identification based
on Kalman recurrent ratio, namely, the expanded Kalman filter and the iterative
consecutive Kalman filter. Taking into account it the algorithm of expanded
Kalman filter can be written down in a kind [7]:
Algorithms of identification on the basis of a method
of invariant immersing allows to avoid errors, arising at linearing the
equations (1) and (2). On the other hand, using the given algorithm puts forward
rigid requirements to formation of a SV condition vector that is caused by
increase in volume of the computing operations connected to calculation of a
dispersions matrix at identification in real time.
2. Construction of vector measurements of SV linear accelerations and
angular speeds at descent in atmosphere. Apriority we accept, that
sources of the information are gauges linear acceleration and the angular
speeds, established on connected axes of SV [8, 9]. Such form of gauges installation
is usually used in non-platform inertial systems of navigation which till now
have shown reliability in operation and are widely distributed [10-13]. In that
case the vector of measurements can be submitted as system of algebraic expressions.
where 
mistakes in indications
of gauges.
There are some sources
of mistakes of gyroscope and accelerometers [5]. In this article we shall
consider only most essential of them, namely, mistakes of scaling, casual
leaving of a gyroscope, nonortogonal axes and drift of zero. Mistakes are set
as stationary Gauss process with exponential correlation function. Simulating
mistakes of measurements is carried out by means of forming filter of the first
order with constant factors [14]:
(5)
where 
index of a source
of mistakes; 
dispersion of a
mistake; 
white noise. The
system of the equations describing indignant movement SV in an atmosphere,
added with ratio (5), gives the expanded system of the equations of movement SV
with error check of measurements.
The operational and information
analysis of algorithms expanded and iterative Kalman Filter Approach, carried
out with the purpose of an opportunity estimation their realization in
integrated system SV onboard control, has shown, that the given algorithm to
volume of operative memory of an onboard computer requirements does not didn’t.
In the assumption, that on each step of algorithm functioning will be made no
more than [15], required speed will make 800 000 ор/s at length of short operation about 1 мks. Thus, the
suggested algorithms of a vector estimating of condition SV on a site of
descent in atmosphere can be successfully realized by means of onboard
computers.
Conclusion. The problem of spacecraft
identification by means of basis Kalman filtration and a methode aposteoristic
was put to density of probability. As a result of the decision of this problem
algorithms of identification which are based on a method of invariant immersing
process of the equations are reseived. Hence, the considered algorithms of
identification can be applied to parameters of condition estimation of space
vehicle at descent in planet’s atmosphere.
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