RU2487419C1  System for complex processing of information of radio navigation and selfcontained navigation equipment for determining real values of aircraft navigation parameters  Google Patents
System for complex processing of information of radio navigation and selfcontained navigation equipment for determining real values of aircraft navigation parameters Download PDFInfo
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 RU2487419C1 RU2487419C1 RU2012103727/11A RU2012103727A RU2487419C1 RU 2487419 C1 RU2487419 C1 RU 2487419C1 RU 2012103727/11 A RU2012103727/11 A RU 2012103727/11A RU 2012103727 A RU2012103727 A RU 2012103727A RU 2487419 C1 RU2487419 C1 RU 2487419C1
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Abstract
Description
The invention relates to navigation of aircraft (LA), and in particular to the integration of navigation systems in navigation and aerobatic complexes to obtain highprecision parameters of aircraft navigation.
State of the art
The wellknown "Integrated inertialsatellite navigation system", patent RU No. 2277696 C2, dated April 21, 2004, including a radio receiver, a calculator for the location of navigation satellites, a user’s location, projection meters of the projection of angular velocity, apparent acceleration, the outputs of which are associated with a group of inputs of the navigation calculator parameters through the corrector. The system also includes an initial data calculator connected to the inputs of the information complexing unit, the second group of inputs is connected to the outputs of the angular velocity corrector and the apparent acceleration corrector. Correction of the information of the inertial part of the system from the projectors of the projection of the angular velocity and apparent acceleration occurs after the complex processing of information messages from the satellite navigation system (SNA) (when choosing the optimal constellation of satellites) and data from the initial data generation unit and the aircraft navigation parameters calculator.
However, when solving the complex processing during the correction of the output data does not sufficiently increase the reliability and accuracy of the navigation system when the SNA signals are turned off under conditions of deliberate counteraction and when the SNA signals are “obscured” or “broken”, as well as when flying at low altitude in hidden navigation mode, for example in foothill and mountainous areas.
In the works of I.N.Beloglazov, G.I. Dzhandzhgava, G.P. Chigin "Fundamentals of navigation on geodesic fields", Moscow, "Science", 1985, and N.V. Pavlov, N.D. Frolov " Determining the location of an aircraft with a reliefcorrelationextreme navigation system ”, Measuring Equipment and Metrology, 2007, shows the principles of building modern correlationextreme navigation systems (CENS), which build their work on previously known information about the sections of the aircraft route (reference information) . Obtaining information about the underlying surface field from sensors (current information), CENS using the correlationextreme methods determines the relative position of the current and reference fields. CENS determines the current error of the inertial navigation system (ANN). KENS are built on the basis of optoelectronic (ECO) and radar systems (radar). To improve the accuracy and reliability of CENS, the following pathways are distinguished: the development of CENS based on an OES operating on a stable relief field of the underlying surface, relief metric OES (ROES) and the development of CENS based on laser location stations (LLS).
However, the variability of the underlying surface field due to seasonal changes in the Earth’s optical field and adverse weather conditions reduce the accuracy and reliability of constructing the current underlying surface field for KENS based on OES and ROES, for KENS based on radar  adverse weather conditions, for KENS based on LLS  adverse weather conditions and the use of high technology.
In the system "Aiming and navigation complex of multifunctional aircraft equipment", patent No.RU 2392198 C1, dated June 15, 2009, containing an aiming and navigation complex of a multifunctional aircraft, which in addition to the ANN, SNA includes: radio altimeter (RV), opticallocation system (OLS), a system for determining the mutual coordinates of an aircraft in a group, a weapon control system, a control and information input system (UVI), an information display system (SDI), an interactive computing environment of the complex — additional navigation channels have been built, including on the basis of correlationextreme navigation. An additional navigation channel is constructed using the correlationextreme method for determining the residuals of the ANN according to coordinates and velocities. In the onboard graphic station (BGS), a color map of the area is formed to indicate to the crew.
However, the complex does not provide for complex processing of information from the ANN and the data of the correlationextreme navigation channel, which reduces the reliability and accuracy of determining the coordinates of the aircraft, for example, during lowaltitude flight or radio interference.
The closest analogue is given in the book of EG Kharin, “Integrated processing of information from navigation systems of aircraft”, Moscow, MAI Publishing House, 2002, [p. 64, ..., 143] and [p. 146, ..., 160], which is the configuration of flightnavigation and navigation systems (PNK and NK), including measuring sensors and systems: inertial navigation systems (ANNs), course verticals (KB), shortrange radio systems (RSBN), longrange radio systems ( RSDN), satellite navigation systems (SNA), Doppler from speed and drift meters (DISS), air (aerometric) sensors and systems (GVA), a complex of onboard trajectory measurements (KBTI). Aggregation is based on the correction of autonomous sensors and systems, for example, ANNs or the Doppler coordinate calculator of aircraft, according to the correctors: SNA, RSBN, RSDN and others. In order to improve the accuracy of PNK or NK on board the aircraft (or after flight), complex processing is carried out information (CFI) from autonomous systems and correctors when using the Kalman filter [p. 146, ..., 160].
The autonomy and noise dependence of the ANN radio correctors (RSBN, RSDN, SNA), the influence of the geometrical factor of the location of ground stations or the used constellation of the SNA satellites, as well as the removal of the SNA from the base correction station (BCS) reduces the accuracy of determining the location coordinates of the aircraft. The insufficiently high reliability and accuracy of the navigation system A, the possible shutdown of the SNS signals under conditions of intentional counteraction or during the “shadowing” or “disruption” of the SNS signals leads to insufficiently high reliability and accuracy of the navigation complex, for example, during lowaltitude flight.
Progress in creating accurate smallsized systems for autonomous error correction of ANNs operating in geophysical fields, and progress in the formation of CRIs for aerospace images and topographic maps with a significant increase in the processing power of onboard processors predetermine the task of increasing the degree of autonomy or creating fully autonomous integrated navigation systems.
The technical solution to achieve the claimed invention is to increase the degree of autonomy and noise immunity of the navigation system when using radio navigation and autonomous navigation aids (under conditions of possible deliberate radio interference or during natural "shadowing" and "disruption" of radio navigation signals) when determining the actual values of the parameters of navigation and increasing the reliability and the accuracy of trajectory measurements of aircraft (on routes, near aerodrome zones, during lowaltitude flights in foothill and mountainous areas) while maintaining the positive qualities of the prototypes by means of integrated processing of ANN data and information from two heterogeneous correctors: radio navigation and autonomous, or by complex processing of ANN data and information only from an autonomous corrector.
Salient features
For the implementation of the claimed technical solution in the integrated information processing system of radio navigation and autonomous navigation aids to determine the actual values of the parameters of navigation on the routes, in the aerodrome zones, during lowaltitude flights in the foothills and mountains, which includes an autonomous means of inertial navigation system (INS) in the side part and radio navigation corrector  satellite navigation system (SNA) (in standard and differential operation using control base station (BCS) or control corrective station (CCS), the outputs of which are in the computing environment of an onboard digital computer (BTsVM) or a specially installed modified complex of onboard path measurements (KBTIM), are separately connected to the inputs of the complex information processing unit (KOI ), namely, to the inputs of the formation of measurement information (AI), which is connected to seriesconnected blocks: the formation of measurement vectors (FVI) with measurement control to protect the Kalma filter a, error estimation of ANN (OP ANN) when using a modified Kalman filter, calculation of navigation parameters (GNP) with the output of the AI block simultaneously connected to it, the following are additionally introduced into the digital computer (or KBTIM): autonomous ANN data corrector  correlationcomputing unit extreme information processing (KEOI), connected separately with airborne meters: ANN, air (aerometric) sensor and system (GVA), radio altimeter (RV), and a unit of data of reference values of the elevation model of the terrain connected to KEOI the number and composition (MVR and OS) of the flight area located in the BCVM (or KBTIM) buffer, and the ground part of the system is executed on a personal electronic computer (PC). The personal computer includes: second blocks interconnected sequentially: MVR and OS, KEOI and KOI, a data bank (DB) of spatial reference models of terrain and object composition, containing a block of digital cartographic information (TsKI) and a module of mathematical methods of approximation by splines (MPS) ) associated with the outputs with the inputs of the shaper of the coordinate line system (FCL), an accompanying mathematical modeling (SMM) computing unit, including an aircraft motion simulation unit (ID) in the area of the planned flight, associated with it modeling the measurement signals (MIS) main board meters. The output of the FCL DB is connected to the second block of MVR and OS, and the MIS SMM output is connected to the second blocks of KEOI and II KOI for preflight processing and accounting for the influence of the error of the radioactive system, systematic and random errors of alignment on the routes, in the nearaerodrome zones, during lowaltitude flights in the foothill and highlands.
In addition, for visualization and subsequent posterior analysis of flight results in dynamics, especially in conditions of lowaltitude flight in foothill and mountainous areas, a block for estimating, analyzing, and visualizing (OAV) the aircraft trajectory in the environment of the reference MVR and OS in 3D format was introduced into it. The input OAV connected to the outputs of the blocks (MVR and OS) and GNP. To improve the accuracy and reliability of determining the actual values of the parameters of navigation on the routes under the conditions of possible deliberate radio counteractions and during natural “shadowing” and “disruption” of radio navigation signals, KOIs are used based on sufficient information only from autonomous means — ANN and KEOI.
At the same time, for constructing highprecision MVR and OS on the flight zone on the flight center, curvilinear coordinate lines were formed on the elevation profiles parallel to the axes of the geodetic coordinate system with the construction of interpolation or locally approximating splines, and to preserve the geometric characteristics of the relief height and object composition on the formed coordinate lines, isogeometric splines; reference height values at any point of the MVR and OS are defined as the tensor product of onedimensional isogeometric splines constructed on a grid of elevation profiles of the terrain parallel to the axes of the geodetic coordinate system; reference models are certified and archived in the databank of reference models (DB), taking into account acceptable restrictions on the aircraft trajectories for subsequent refinement and use with navigation data.
To increase the accuracy of determining the current profile of the relief, formed by the difference of the signals of the baroinertial and geometric altitude, the altitude values are approximated by local splines against the background of random components of measurement errors.
Thus, the technical result is achieved by the fact that in the operational part of the digital computer or in the KBTIM kit specially installed on board the aircraft, a computational unit for correlationextreme data processing is introduced, and in their longterm memory (or buffer) digital data of the reference MVR and OS on the track flight. The inputs to the KEOI block are recorded informational messages from the ANN, RV, GVA and data from the reference MVR and OS.
The formation of the reference MVR and OS is introduced according to CKI data using effective methods of spline approximations of functions: rational, local, and isogeometric splines that preserve the geometric properties of the approximate surface of the terrain. The creation of a bank of reference MVR and OS is introduced for subsequent clarification and operational use.
We introduce the use of accompanying mathematical modeling in the implementation of the KEOI algorithms for estimating the effect of airborne errors depending on the flight altitude and the components of the flight path reference errors when used over the flight area.
The present invention is illustrated in the block diagram of a complex information processing system and is presented in figure 12.
Figure 1 shows a block diagram of the onboard part of the proposed system of integrated information processing of radio navigation and autonomous navigation aids to determine the actual values of the parameters of navigation on the routes, in the aerodrome zones, during lowaltitude flights in the foothills and mountains, contains an autonomous means  inertial navigation system ( ANN) 1 and the radio navigation corrector  satellite navigation system (SNA) 2 (in standard and differential mode of operation using the base corrector projecting station (BCS) 3 or control correction station (CCS) 3), the outputs of which are in the computing environment of the onboard digital computer (BCVM) 4 or a specially installed modified complex of onboard path measurements (KBTIM) 4 are separately connected by outputs to the inputs of the complex unit information processing (KOI) 5, namely, to the input of the formation of measuring information (AI) 6, which is connected to seriesconnected blocks: the formation of measurement vectors (FVI) 7 with measurement control to protect the filter Almana, estimates of errors of the ANN (OP INS) 8 when using the modified Kalman filter, calculation of navigation parameters (GNP) 9 with the simultaneous connection of the output of the AI 6 block to it, in BCVM 4 (or KBTIM) additionally entered: autonomous data corrector ANN  CorrelationExtreme Information Processing (CEOI) 10 computing unit, separately connected with onboard meters: air (aerometric) sensor and system (GVA) 11, radio altimeter (RV) 12, ANN 1 and data block of model model reference values connected to CEOI 10 you terrain and object composition (MBP and OS) on the fly zone 13 located in the buffer board computer 4 (or KBTIM) 4.
Figure 2 shows a block diagram of the ground part of the system of the proposed system of integrated information processing of radio navigation and autonomous navigation aids to determine the actual values of the parameters of aircraft navigation on the routes, in the aerodrome zones, during lowaltitude flights in the foothills and mountains, including a personal electronic computer (PC) ) 14, which contains: second blocks interconnected sequentially: MVR and OS, KEOI and KOI 13, 10 and 5, a data bank (DB) of spatial reference models p terrain and object composition 15, containing a block of digital cartographic information (CCI) 16 and a module of mathematical methods of approximation by splines (MPS) 18, connected to the outputs of the inputs of the shaper of the coordinate line system (FCL) 17, the computing unit of the accompanying mathematical modeling (SMM) 19, including a block simulating the movement of aircraft (ID) 20 in the zone of the planned flight, the associated block simulation of measuring signals (MIS) of 21 main airborne meters. The output of FCL 17 DB 15 is connected to the MVR and OS 13 block, and the MIS 21 SMM 19 output is connected to the second blocks of KEOI 10 and AI 6 KOI 5 for preflight processing and taking into account the influence of radioactive errors, systematic and random binding errors on the routes, in the aerodrome zones , at low altitude flights in the foothills and mountains.
In addition, for visualization and subsequent posterior analysis of flight results in dynamics, especially in conditions of lowaltitude flight in foothill and mountainous areas, the unit for estimating, analyzing, and visualizing (OAV) the aircraft trajectory LA 22 in the environment of the reference MVR and OS in 3D format was introduced. The input OAV 22 is connected to the blocks (MVR and OS) 13 and KOI 5. To improve the accuracy and reliability of determining the actual values of the parameters of navigation on the routes in the conditions of possible deliberate radio interference and with the natural "shadowing" and "disruption" of radio navigation signals use KOI 5 at sufficient information only from autonomous means  ANN 1 and KEOI 10.
Moreover, to build highprecision MVR and OS 12 to the flight zone according to TsKI 15, curvilinear coordinate lines are formed on the grid of nodes with the construction of interpolation or locally approximating splines on the elevation profiles parallel to the axes of the geodetic coordinate system. To maintain the geometric characteristics of the height of the relief on the formed coordinate lines, isogeometric splines are used. Reference height values at any point of the MVR and OS are defined as the tensor product of onedimensional isogeometric splines built on a grid of elevation profiles of the terrain parallel to the axes of the geodetic coordinate system. Reference models are certified and archived in the Bank of Reference Models (DB) 15, taking into account acceptable restrictions on the aircraft trajectory for subsequent refinement and use with navigation data.
The system works as follows
To obtain estimates of the errors of ANN 1 and determining the actual values of the parameters of navigation, complex processing of measurement information is used in two versions: in the first  when using data from ANN 1, SNA 2 and KEOI 10, in the second  when using information only from ANN 1 and KEOI 10 using a modified Kalman filter.
Comprehensive processing is carried out both during the flight and in the afterflight processing.
The groundbased statistical processing of flight results and the results of SMM 19 is introduced, combined according to the criteria of homogeneity and membership of the same population.
Visualization of the flight path in the environment of the spatial model of the terrain in the flight zone in 3D format is introduced.
The onboard part of the system (figure 1) operates as follows.
The BCVM 4 (or KBTIM) receives a combination of the spatial and angular parameters of the aircraft from the ANN (1), SNA (2), RV (12), GVA (11), BCS (KKS) (3) (if using differential mode SNA):
{φinsi, λinsi, VNinsi, VEinsi, ψinsi, γinsi, υinsi, Vy insi, U si};
{φсссi, λсссi, VNсссi, VЕснсi}; {Ng PBi, H Bi};
{ΔD1i, ..., ΔDni},
Where
φinsi, λinsi, VNinsi, VEinsi, ψinsi, γinsi, υinsi, Vy insi, U ci  values of coordinates, speeds, course angle, roll, pitch, vertical speed and drift angle of aircraft, as measured by ANN 1;
φснсi, λснсi, VNснсi, VЕснсi  values of the coordinates and speeds of the aircraft, respectively, measured by SNA 2;
Ng PBi, N Bi  values, respectively, of the geometric and barometric (absolute) aircraft altitude;
ΔD1i, ..., ΔDni  corrections in pseudorange from n satellites of SNA 2 from BCS (CCS) 3.
Digital information data of the reference spatial MVR and OS 13 are written to the BCVM (KBTIM) buffer (4) in advance on the flight path, retrieved from the bank of spatial models DB 15, formed before flight in the ground part of the inventive PC system 14, namely the following:
Where
Δij is the grid of nodes of a rectangular DEM on the flight path;
Xij, Yij are the values of the geodetic coordinates at the nodes of the grid Δij in the GaussKruger system;
Hij are the elevation values at the grid nodes Δij;
In the computing unit of KEOI 10, included in the software of the BCVM (or KBTIM) (4), correlationextreme processing of input information of the measured elevation of the relief of the underlying terrain Hpi and reference data from the MVR and OS 13 are carried out:
Hpi = f (Hг PBi, Н Bi, Vy insi, ψinsi, γinsi, υinsi).
They search for the trajectory and location of the aircraft that best matches the measurements of the elevation of the terrain in the flight zone, obtained from measurements of PB 12, baroinertial altitude and reference data from MVR and OS 13. In order to compensate for the inertia of barometric data from GVS 11, the measurements of Н Bi with Vy insi vertical velocity measurements from ANN 1.
In block KEOI 10 use a combined (search and refinement) binding algorithm based on the calculation of quadratic functionals of the difference between the reference and the measured elevation of the terrain of their gradients. To increase the accuracy of determining the current profile of the relief, formed by the difference of the signals of the baroinertial and geometric altitude, the altitude values are approximated by local splines against the background of random components of measurement errors. The size of the confidence square for the search algorithm is associated with the error in determining the coordinates of the location using ANN 1 in the autonomous inertial reckoning for an hour of flight or in the offline mode of reckoning for 30 minutes of flight after continuous correction according to information from the SNA 2. For reliable operation of the search algorithm, the length of the side of the trust square must exceed these values. The relief height at any point Hp (X, Y) of the reference spatial model of heights is calculated from the selected local data of heights and their derivatives of the nearest grid nodes Δij:
Hp (X, Y) = S _{izg} (Y, X) = ψ (X) F _{4.4} ψ ^{T} (Y),
Where
S _{izg} (Y, X)  twodimensional isogeometric spline;
F _{4.4}  matrix of heights, first and mixed derivatives at four nodes of the nearest neighborhood of the measured point, automatically selected from a combination of values:
where ψ (X), ψ ^{T} (Y) are vectors whose elements depend on the values of the arguments X, Y and the intervals of grid nodes Δij along the coordinate lines Xi and Yj.
The refinement algorithm is implemented on the basis of an estimate of the global minimum of the quadratic functional (against the background of possible parasitic local minima) of the differences in the derivative heights of the reference and measured profiles of the terrain. The derivatives at the points of the reference profile are determined from the local data of the derivatives and their mixed derivatives of the twodimensional isogeometric spline at the grid nodes of the nearest neighborhood.
AI 6 of the computing unit KOI 5 receives a set of information messages from ANN 1, SNA 2 and the values of correcting corrections calculated to KEOI 10 for ANN 1 coordinates, aircraft speeds (with reliability estimates) and errors of their determination:
{Δφkeoii, Δλkeyoi, V Nkeoii, VEkeoii},
Where
Δφkeoii, Δλkeyoi, VNkeoii, VEkeoii are the values of the corresponding corrections to the ANN coordinates and the values of the aircraft speeds, which are determined in the block of KEOI 10.
Corrections are introduced to the coordinates of the aircraft obtained from the accompanying mathematical modeling of SMM 19 for the flight zone. These corrections can be introduced during ground processing of flight information.
From the totality of information received in AI 6 from ANN 1, SNS 2 and KEOI 10 in FVI 7, measurement vectors with control for protecting the Kalman filter are formed, consisting of corrections to the coordinates and speeds of the aircraft along the axes of the ANN 1 platform when using information in two ways: when using data from the autonomous corrector KEOI 10 or when using information from two heterogeneous correctors SNA 2 and KEOI 10:
 in the first case, the measurement vector takes the form:
Zk = [ΔSx keoii, ΔSy keoii, ΔVx keoii, ΔVy keoii].
 in the second:
Zk = [ΔSx ssi, ΔSy ssi, ΔSx keoii, ΔSy keoii, ΔVx ssi, ΔVy ssi, ΔVx keoii, ΔVy keoii],
where ΔSx scci, ΔSy ccci, ΔVx cci, ΔVy scci are the corrections, respectively, in coordinates and speeds in the axes of the platform ANN 1 according to SNA 2;
ΔSx keoii, ΔSy keoii, ΔVx keoii, ΔVy keoii  corrections, respectively, in coordinates and speeds in the axes of the platform ANN 1 according to the data of KEOI 10.
In the OP INS 8 unit, when using the generated measurement vectors and complex information processing using the modified Kalman filter, the errors of ANN 1 are estimated, namely, the set of parameters:
{ΔSx, ΔSy, ΔVx, ΔVy, θx, θy, θz, ωxx, ωxy, ωyz, ωyy, ωxn, ωyn, ωzn, Δm _{1} , Δm _{2} };
Where
ΔSx, ΔSy are the components of the ANN 1 error in determining the coordinates (in the horizontal axes of the platform);
ΔVx, ΔVy  components of the error of ANN 1 in the determination of speeds;
θx, θy, θz  angular errors in determining the vertical and heading;
ωxx, ωxy, ωyz, ωуу  proportionality coefficients in the components of the drift velocity of gyroscopes, depending on acceleration;
ωxn, ωyn, ωzn are the constant components of the drift of the gyroscopes in the axes of the instrument trihedron;
Δm _{1} , Δm _{2}  scale factors in the errors, depending on the acceleration.
In GNP 9, according to the estimates of the errors of ANN 1 obtained in the OP ANS 8 and the initial information of AI 6, the set of actual values of the navigation parameters of the aircraft is calculated, both when using sufficient information from the autonomous corrector KEOI 10, and when using redundant information from the correctors KEOI 10 and SNA 2.
The parameters of aircraft calculated in the block KOI 5, namely the set of real values:
{φdi, λdi, VNdi, VEdi, ψdi, Usdi},
Where
φдi, λдi, VNдi, VEдi  values of the coordinates and speeds of the aircraft;
φdi, Us di  values of the course and drift angle of the aircraft;
after the flight, they enter the OAB 22 assessment and analysis unit of the ground system.
The ground part of the system (figure 2) operates as follows.
Form the reference MVR and OS 13, allowing:
 reduce by an order of magnitude the number of useful nodes about the height of the relief in comparison with the initial information taken from the TsKI 16;
 build a relief field with the accuracy of topographic maps or plans on plain, hilly, foothill and mountainous terrain.
In this case, the initial digital cartographic information of TsKI 16, obtained from topographic maps, plans, or satellite images of different scales, is used to construct elevation profiles of the terrain on the flight zone with the following conditions and assumptions.
1. The function of the height of the relief in any direction is characterized by a different degree of smoothness, convexity, concavity, break points, as well as possible large gradients.
2. The domain of existence of the elevation height function is a rectangular region oriented along the X and Y axes of the GaussKrueger geodetic coordinate system. The elevation profiles of the relief are parallel to the geodetic axes X and Y. The interval for partitioning the profiles and the distance between the profiles are selected depending on the characteristic and special relief points: extreme places in height, inflection points, kinks, etc. The value of the variable step of the partition is related to the correlation interval and the change in the gradient on the profiles;
3. In order to reduce the number of nodes of initial information about the height of the relief on the site profiles constructed along the X and Y axes, analytical concentration of the height values can be carried out, carried out by interpolation or approximation mathematical methods, which should simultaneously satisfy the requirements of a quantitative and qualitative nature when approaching the height of a flat and mountainous terrain. The values of the elevation of the relief at the nodes of the condensed mesh are estimated as the average value of the heights of the nodes of the profiles constructed along the X and Y axes;
4. In order to comply with the conditions of simplicity and costeffectiveness of the computing process, the elevation at any point should be determined from local data of the closest neighborhood of the grid nodes including this point.
In MPS 18, in order to compress useful information, interpolate and approximate elevations of a relief while maintaining its geometric characteristics on profiles, such as positivity, monotonicity, convexity, the presence of linear sections, break points, large gradients in the elevation difference, rational, local, and isogeometric splines (see Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. Methods of spline functions. M: Nauka, 1980, p. 187, ..., 193; see B.I. Kvasov, Methods of isogeometric approximation by splines. 2006, p. 195, ..., 218).
In FKL 17, using rational or locally approximating splines along the X and Y axes, a system of curvilinear coordinate lines is constructed on the elevation profiles of CKI 16. In order to maintain the geometric characteristics of the relief height, isogeometric splines are constructed on the formed coordinate lines, for which the values of the first and second derivatives are adjusted in height, based on the requirements of isogeometry: to preserve the positivity, monotony and convexity of the relief, and make the choice of expanding the grid nodes of additional inflection points. Possible types of constraints of the first and second derivatives in the node xi are formalized and classified using the integer index, which is calculated in xi (1≤i≤N1).
Check the conditions of monotony and convexity on the subsegments, where the values of the derivatives did not change. If these conditions are not fulfilled, rational splines are built on these subsegments, and adapting to linear sections, break points and large elevation gradients. As a result, a system of curved coordinate lines (isogeometric splines S _{izg} ) is generated on a rectangular section, generating a regular grid of Δij nodes:
S _{izg} = f (Hpi, xi, mi, N, Xi, k);
Where
Hpi  values of the elevation height function;
xi are the argument values in nodes;
mi  values of the 1st derivative of the spline;
N is the number of points on the grid;
Xi  argument values in which spline values are calculated,
k is the order of the calculated derivative of the spline.
The elevation surface of the terrain MVR and OS 13 is constructed as a twodimensional spline, defined as the tensor product of onedimensional isogeometric splines S _{izg} .
The algorithm for the formation of the MVR and OS 13 of the ground part of the system includes the following main steps:
 the initial information on the height of the relief Hij at the nodes of the rectangular grid Δij is arranged in the form of a matrix, where the bordering rows and columns are boundary conditions  the first and mixed derivatives. Each row and column of this matrix contains the necessary and sufficient information for constructing an isogeometric spline along one of the lines Xi (i = 0, ..., M) or Yj (j = 0, ..., N);
 construct isogeometric splines from the variable Y of the geodetic coordinate system, S _{izg} (Y, Xj), j = 0, ..., M, according to the rows of the matrix Hij with boundary conditions from the boundary columns. Find the values of the first derivatives of the spline in height
values
 by matrix columns
 according to the data of the original matrix Hij, isogeometric splines S _{izg} (Yi, X), i = 0, ... N from the variable X are built, resulting in the values
As a result, in the nodes of the grid Δij form a set of values:
which completely determines the isogeometric spline of two variables, satisfying the interpolation and boundary conditions.
The accuracy of constructing spatial MVR and OS 13 over the entire surface is assessed using the original CKI 16.
The formed MVR and OS 13 are archived in the database of spatial reference models DB 15 for subsequent detailing and use with navigation data.
The accompanying mathematical modeling of SMM 19 is used to reduce the degree of influence on the accuracy of determining the coordinates of aircraft by the correlationextreme method: the errors of the PB 12 depending on the distance to the earth's surface, the orientation of the antenna pattern of the PB 12 due to the integration of the reflected signal over the entire spot of illumination from the PB 12 , taking into account the influence of systematic and random errors over the flight zone on the binding process to the underlying surface, and taking into account disturbing factors: errors are constructed I model the terrain, radio disturbance or failure.
In block ID 20 simulate the movement of the aircraft in the desired flight mode over a given path. The movement of the aircraft is carried out by the method of dead reckoning with the given values of ground speed, altitude, course, roll, pitch and numbering interval with permissible restrictions on the flight path.
In MIS 21, using the reference aircraft trajectory and known models of measurement errors, the values of the main parameters are determined by the onboard meters ANN 1, SNS 2, GVS 11 and RV 12, consisting of an additive mixture of the useful part of the signals, systematic and random components of the measurement errors. It is allowed that systematic and random components of measurement errors belong to the class of stationary random processes located in disjoint frequency ranges and distributed according to the normal law.
In the second computing unit KEOI 10 carry out the correlationextreme processing of the output information from the MIS 21 and the data from the second block of the MVR and OS 13. Form the reference trajectory of the aircraft and the corresponding reference profile of the height of the relief. They search for the trajectory and location of the aircraft according to the obtained terrain measurements that best match the reference profile of the height of the terrain in the flight zone.
To determine the actual values of the navigation parameters of the aircraft in the second block of KOI 5, complex processing of the measuring information received from the MIS 21 and the second block of KEOI 10 is used. The sequence and variants of the complex processing of the measuring information to determine the actual values of the parameters of aircraft navigation in the second block of KOI 5 during ground processing similar to handling in flight.
In OAV 22, when using the aircraft reference flight path, the corrections of the second KEOI 10 block are evaluated according to the coordinates and the accuracy of determining the parameters of aircraft navigation using the second KOI 5 block is assessed and the joint image of the lowaltitude flight path of the aircraft is visualized in the environment of the second spatial reference unit MVR and OS 13 in 3D format. In block OAV 22 also evaluate, analyze and visualize the trajectory of the aircraft obtained in flight. During ground processing, the coordinates of the aircraft obtained from flight data and as a result of the accompanying mathematical modeling are combined according to the criteria of uniformity of conditions and checked for belonging to the same general population. Based on the totality of flights and simulation implementations, statistical characteristics of the values of the parameters of aircraft navigation are estimated.
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