Space-time modelling as base of designing optical-electronic channels for aerospace information systems

V.V.Panov, A.V.Shevyakov

Russian academy of rocket and artillery sciences

Building 3, 1st Mjasnikovskaja, 3, Moscow, 107564, Russia

Abbreviations: ASIS - aerospace informational systemљљљљљљљљљљљљљљљљљљљ STM - spatially-temporal modeling OES - optical-electronic systemљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљ VR - virtual reality COI - channel of information obtainingљљљљљљљљљљљљљљљљљљљљљ VA - virtual abstraction SI - supply with informationљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљљ DSTM - discrete spatially-temporal modeling ASSTM - analytic-statistical spatially-temporal modelљ RR - receptor of radiation

 

 

 

 

 

 

 

Aerospace informational systems (ASIS) are intended for the solution of manifold problems of a remote sounding of the Earth and a surface of other planets, airspace and outer space probing. An ASIS can concern to classes , )>, and as function in various environments. Channels of obtaining of the information (COI) form on different physical principles in widespread optical - electronic systems (OES) an ASIS. The COI use various energy sources as information carriers about objects of supervision. Solar radiation (direct and Sun stray radiation), characteristic heat radiation objects, laser coherent radiation for illumination of object, etc. find application in COI.

At such variety an ASIS the problem of a supply with information of making COI the OES and an ASIS comes forward on the foreground. The supply with information (methods, mathematical models, algorithms, software) is a basis of making an ASIS and an OES and is intended for the solution of problems of an estimation, forecasting and optimization of these complex systems with use of private and integral indices and efficient control quality and risks on different stages of life cycle. The supply with information (SI) is necessary in life cycle an ASIS at formation of requirements of the technical project, the comparative analysis of alternative versions, an estimation and a substantiation of engineering solutions, carrying out of tests, tuning of technological parameters, control of quality and safety, organization and carrying out of certification. The comparative estimation of efficiency an ASIS of divers classes and designation, diverse an OES and them COI puts problems of the probabilistic analysis - problems of obtaining of comparable probabilistic estimations and estimations of accuracy of their functioning. Necessity maintenance of high quality of reception and processing of signals of a different physical nature in the conditions of effect of interferences - noise, background (spatial, spatially-temporal) fluctuations and quasi-determinate interfering signals puts forward problems of synthesis of systems of detection, recognition and an estimation of parameters of signals. It is necessary to notice, that at definite limitations and assumptions (for a linear problem with a quadratic functional and additive gaussian white noise) the principle of stochastic equivalence (the separability theorem) is fair. Separate statements and solutions of problems of optimum dimension (obtaining of estimations and a filtration on a method of the maximum credibility) parameters of signals in COI and optimum adjustment (control of objects and their elements) an ASIS) are possible.

Imitating modeling represents the most accessible and economic methodical apparatus for obtaining of authentic and comparable estimations of efficiency in the fixed operation conditions. Imitating modeling is based on making of analytic-statistical spatially-temporal models (ASSTM). Spatially-temporal modeling (STM) is a mathematical apparatus the SI and the tool of the solution of problems of the systemic and probabilistic analysis, deterministic and statistical synthesis of channels of obtaining of the information an OES (ASIS). Historical development a STM goes on a way of increase in dimension of space of modeling. Now modeling is connected with an exit in 3-dimensional space of items (space of objects and subjects of a model). It is caused by specificity of central projection an OES-mappings from space of items in space of images (focal plane OES). Central projection isn't affine mapping and thus not bijective (it is not surjective and isn't injective). Mapping doesn't possess property of mutual unambiguity (convertibility). It doesn't allow at the analysis and synthesis to limit a heuristic method of formation of an equation of supervision in a focal plane OES as the image can't be correlated with a particular 3-dimensional scene (an arrangement of objects, background formations and sources of interferences in 3-dimensional space of a model which is mapping of real physical space). Therefore essentially an important point the STM is formation of a prototype of a useful signal and signal - background (interference) situations (equation of supervision) in three-dimensional space of model with the subsequent transition in a plane projection an OES (space of images).

Modeling COI (OES), created on different physical principles, should be carried out on an ASSTM, developed on the basis of the unified methodology understood as combination of methods of research of processes of getting, processing and information use, and also as a scientific method of knowledge - a method of the analysis and synthesis of complex systems. The mathematical model covers a class of abstract (symbolical) mathematical objects (such as numbers, points, vectors, sets, matrixes) and relations between these objects. The basis a STM is made by algebraic structures - sets with the operations (mappings) determined in them. Relations can be described by means of the mathematical operations connecting one or several objects (an operand, operands) with other object or set of objects (result of operation). Constructive definition enters a new mathematical model, using already known mathematical concepts. Information and logical discrete processes are determining in modeling, the analysis and synthesis an ASIS. The STM leans on computer geometry, geometric modeling and uses methods of a computer-generated image. It gives the chance to work with the plane electronic (virtual) image and to control it in real time mode. The virtual image (geoimage) is considered as an spatially-temporal model of real or abstract objects and the situations, formed and existing in program-controlled environment and a creating capability for interaction with the observer. The geoiconics as a scientific direction distinguishes (geo) images of a virtual reality (VR) and virtual abstraction (VA). Modeling a VR highlights a problem of making of the image as much as possible close to a reality. Process VA consists in getting of natural and expressive models abstract (imagined, computational) objects with transfer of their spatial communications and exact fixation to territory (space). In this connection it is possible to notice, that the STM allows to realize a technique of modeling of visual illusions of flight (the recurring inadequate, deformed reflections of external and internal conditions of activity of a flight membership) which can be the reasons of aviation incidents. Modeling of atmospheric lights, aerosol and smoke formations of a natural and artificial origin is possible. Virtual images can include the animation sequences simulating aerospace start and an exit in an outer space and process of landing to a surface of a planet. At the solution of problems a STM methods, languages and program tools of visual modeling can be used. It is necessary for visualization of structure of a subject domain of a database, graphs geometric and energetic ratios in the course of modeling, structure of mappings of final sets of geometric and energetic elements an ASSTM.

Geometric models of objects and ambient ground (environment) are under construction in 3-dimensional euclidean affine space. In geometric modeling body (the connected set of the points placing from the interior of one external and some internal envelopes) most full describes geometry of object. Unclosed envelopes also are applied for the description of properties of objects and ground (environment) along with the bodies in most cases set by one external envelope. The set of points over which geometric transformations are made, is compared to a body or an unclosed envelope. Discrete spatially-temporal modeling (DSTM) operates with final sets of points. In this case the envelope of a multielement (faceted) model of object (ground) is described by a final number of sides. This description includes: final number of connected parts of a surface by which directions of the external normals coinciding with normals of a surface are attributed. Points (radius-vectors) of their position on a surface of object and an area of elements are set. Electronic and digital a district map (relief), electronic circuits, photoplans, aerospace images are used in preparation of initial data.

 

The worked out methodology of spatially-temporal modeling COI (OES), created on different physical principles, allows to solve problems of the systemic (deterministic) and probabilistic (statistical) analysis and to receive authentic and comparable estimations of efficiency - accuracy and probability characteristics of functioning an OES and an ASIS of divers classes and designation.

Optimization, first of all structural synthesis, channels of getting and processing of the information an OES consists in the solution of direct and inverse problems of synthesis. The solution of a direct problem of synthesis consists in getting of the mathematical spatially - energetic relations describing supervision received from object signals (scalar fields) of a different physical nature in a focal plane an OES and on an exit of a RR, depending from a vector of measured (concomitant) parameters and temporal argument. Formation in an ASSTM of an equation of supervision considers specific for an OES of interaction of a received useful signal with signals from elements of ground (ambient space) and other spatial (spatially-temporal) hindering effects. The STM considers signal in a background, shades from object and background formations and other effects. Systems of purpose functions and criteria, in which number scalar product of vectors, a credibility function, posteriori probability, average risk of decision-making etc. concern at statistical and deterministic approaches to synthesis. Synthesis puts and solves problems of optimization of block diagrams of a processing of signals in systems of detection, recognition, an estimation of parameters and a non-linear filtration in COI an OES. The inverse problem of synthesis consists in calculation of optimum estimations of detection and recognition of signals (objects) and estimations of values of their parameters at reception of real signal (in a considered case - scalar field realizations).

In conclusion we note:

1. Definition of prospects of development and working out the COI an OES an ASIS of divers classes, hierarchical levels, an organizationally-regular membership, workings in various environments having manifold functional purpose and created on different physical principles should lean against on a supply with information of activities on their making.

2. Spatially-temporal modeling is the effective and economic method the SI ensuring getting of estimations accuracy and probability characteristics of functioning of so diverse systems in comparable normalized operation conditions on stages of life cycle an ASIS. The STM leans against on the generalized description of spatially - energetic signal conditionings of different physical nature and formation of a prototype of the useful signal depending from a vector of measured and concomitant parameters, and a signal-background situation (equation of supervision) in 3-dimensional Euclidean affine space of a model with the subsequent central projection in space of images an OES. Thus the methodology a STM is understood and as combination of methods of research of processes of getting, processing and use of the information, the analysis and synthesis the COI an OES.

3. The worked out methodology and the families created on its basis an ASSTM are really working tool for the solution of problems of systemic and probabilistic analysis the COI an OES an ASIS and synthesis (statistical and deterministic) optimum systems of reception and a processing of signals ― systems of detection, recognition, an estimation of parameters and a non-linear filtration of signals and different physical nature fields.