RU2713585C1 - Method of forming air-speed parameters of a manoeuvrable object - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: invention relates to measurement information systems and combat aircraft systems. Proposed method of forming air-speed parameters of manoeuvrable object consists in combined processing of information, including current values of air speed and angles of attack and sliding modules, which are measured by system of air signals and sensor of angles of attack and sliding, orientation of object relative to coordinate system, current design value of wind velocity module, as well as unknown to be evaluated functional parameters formed by results of inertial-Doppler correction of angles of true course, bank and pitch of object and module of track speed of object with determining its current spatial orientation relative to own coordinate system.

EFFECT: broader functional capabilities of modern aviation equipment and high accuracy and efficiency of its piloting and combat employment in all operating conditions.

1 cl, 11 dwg

Description

The invention relates to the field of integrated navigation systems, control systems and guidance of military targets.

Known methods for measuring and calibrating sensors of such air-speed parameters as airspeed, absolute barometric altitude, angles of attack and slip.

Some of them are given in I.M. Pashkovsky, V.A. Leonova, B.K. Poplavsky "Flight tests of aircraft and processing of test results", Moscow, "Engineering", 1985 [1] (p. 138-153).

In particular, in [1] two methods for calibrating an air pressure receiver (LDPE) are presented, namely:

- speed calibration method;

- barometric calibration method (p. 146-147),

as well as methods for pre-calibrating the sensor of angles of attack and slip (DUAS) and the subsequent formation of the true angles of attack and slip of the aircraft (p. 152-153).

The main drawback inherent in all of the above methods, based on the preliminary calibration of the LDPE, the air signal system (ATS) and the DUAS and the subsequent formation of the entire array of current airspeed information, is the use of a purely individual, non-systematic approach to its formation, which does not involve joint processing of the entire variety of available aboard current navigation, flight and primary airspeed information. The consequence of this approach is the unacceptable accuracy of the measurement of the considered parameters when they are dynamically changed in conditions of maneuverable flight, including the low-speed mode.

In the monograph of V.P. Selezneva “Navigation Devices”, Moscow, “Mashinostroenie”, 1974 [2] (pp. 266-278, 545-551) presents a method of forming air-speed parameters based on the joint processing of navigation and flight information and involving the implementation of elements of complex processing of measured SHS and DUAS of the airspeed module and the angles of its current orientation with respect to the Oxyz coordinate system (SSC) associated with the object, the analytically generated wind speed module and the unknown, to be estimated, its spatial angles orientation relative to the horizontal coordinate system (HSC) Oh _d y _z z _{g of the} object, as well as measured in the mode of inertial-Doppler correction of the current angles of the true course, roll and pitch of the object, its components and the module of its ground speed and its orientation angles relative to the HSC, according to the results conducting which form a complete list of airspeed information.

In its technical essence, this method of forming air-speed information can be adopted as the closest analogue of the proposed solution.

Its main disadvantages are:

1. The lack of a mathematical description of the geometry of the relative location on the LDPE object from the SHS and the inertial system and, as a result, the kinematic difference in the ground speed measured by the ANN at the place of its standard location and its current value at the LDPE location used as a mathematically correct description components and the airspeed module, and for the formation of adequate and physically justified equations for the connection of air-speed and inertial parameters for the general case of maneuverable flight and spatial model of the wind.

2. The lack of a systematic mathematical description of the entire list of air-speed parameters and the nature of the change in the errors of their measurement, necessary both for the effective evaluation and correction of the initially measured air-speed information, and for its recovery in the low-speed and hover mode.

3. The use in the proposed solution of the absent prototype of the formation of adequate and physically justified communication equations is a fairly effective tool in the synthesis of optimal estimation procedures, it is quite simple to obtain the appropriate expressions for the input signals of the optimal filter-identifier, determine the type of matrix for its observation and automate the accounting all components of errors included in the measurement signals.

The technical result of the invention is to expand the functionality of modern aircraft and increase the accuracy and efficiency of its combat use in all operating conditions.

и модуля

его путевой скорости с определяющими его текущую пространственную ориентацию относительно ГСК Ox_Гy_Гz_Г объекта расчетными значениями углов сноса α_СН и наклона траектории α_НТ, по результатам которой формируют полный массив воздушно-скоростной информации, дополнительно используемую модель ошибок воздушно-скоростных параметров расширяют за счет включения в нее математического описания координат Δn, Δh, Δе размещения (на объекте) приемника воздушного давления (ПВД) относительно инерциальной навигационной системы (ИНС), которое представляют в виде системы трех взаимосвязанных дифференциальных уравнений первого порядка в проекциях на оси географического сопровождающего трехгранника (ГСТ) ONHE, чем обеспечивают корректное формирование системы из трех физически обоснованных и математически строгих уравнений связи, на основе которых получают расчетные выражения для входных сигналов z₁, z₂, z₃ оптимального фильтра-идентификатора воздушно-скоростных параметров и элементов h_ij его матрицы наблюдения, реализуя замкнутую, встроенную в структуру оптимального оценивания процедуру автоматического учета кинематической разницы путевой скорости, измеряемой комплексной инерциально-доплеровской системой в месте размещения ИНС и ее значением, соответствующим месту установки ПВД, кардинально сужая круг возможных причин расходимости процедуры оптимального оценивания воздушно-скоростных параметров в штатных для СВС и ДУАС режимах маневренного полета, дополнительно, при формировании воздушно-скоростных уравнений связи используют прием замены идеальных значений x_j воздушно-скоростных параметров их физически адекватным представлением вида

и после переформатирования полученных уравнений связи приводят их к виду, удобному для формирования сигналов измерения z_i и элементов h_ij (i=1-3, у=1-13) матрицы наблюдения, для которых характерно построчное выполнение равенств вида

а при математическом описании ошибок измерения воздушно-скоростных параметров, типа ΔV, Δα, Δβ, используют легко реализуемые и подкрепленные опытными данными модели, которые, в совокупности с моделью, описывающей характер изменения пространственной ориентации скорости ветра, обеспечивают гарантированную наблюдаемость, быстродействие и точность оптимального оценивания всех воздушно-скоростных параметров в штатных для СВС и ДУАС режимах маневренного полета, при этом, измеряемую ИНС навигационную и пилотажную информацию формируют в процессе и по результатам инерциально-доплеровского оценивания, при реализации которого традиционную для ИНС модель ошибок расширяют за счет включения в нее дифференциальных уравнений, описывающих характер изменения координат Δξ, Δη, Δζ, размещения ИНС относительно доплеровского измерителя составляющих скорости (ДИСС) в проекциях на оси опорного трехгранника гироплатформы ИНС Оξηζ, чем обеспечивают математически строгое описание комплексной инерциально-доплеровской системы, и устраняя одну из основных причин расходимости ее фильтра в маневренном полете, достигают повышенные характеристики точности оценивания ошибок ИНС и коррекции ее выходной информации, при реализации которой, также, как и при синтезе самой процедуры оптимального инерциально-доплеровского оценивания, основанной на комплексной обработке счисленных ИНС горизонтальных составляющих V_x, V_y абсолютной линейной скорости объекта, географической широты

его текущего местоположения, угла

азимутальной ориентации опорного трехгранника Оξηζ ее гироплатформы, измеренных углов гироскопического курса

крена

и тангажа

объекта, и доплеровских составляющих

путевой скорости, вместо идеальных значений инерциальных параметров x_j используют их адекватное представление вида

и кинематические соотношения связи ошибок основной тройки навигационных

и пилотажных

параметров с малыми углами α_х, α_у, α_z рассогласования реального и опорного трехгранников гироплатформы ИНС, а сравнивая счисленные ИНС горизонтальные составляющие V_x, V_y абсолютной линейной скорости и аналогичные комплексные компоненты

абсолютной скорости, получают скоростные инерциально-доплеровские уравнения связи, из которых в функции измеренных навигационных и пилотажных параметров ИНС, формируют расчетные выражения для входных сигналов фильтра-идентификатора и элементов его матрицы наблюдения, чем обеспечивают синтез математически замкнутой, унифицированной процедуры автоматического, встроенного в структуру оптимального оценивания, учета ошибок счисления/измерения навигационной и пилотажной информации и ее эффективной коррекции как в процессе оптимального оценивания ошибок ИНС, так и по результатам прогноза, при этом восстановление полного массива воздушно-скоростной информации в режиме малых скоростей и висения осуществляют при справедливости гипотезы о стационарности скорости ветра и реализуют посредством решения обратной задачи пространственного треугольника скоростей.The specified technical result is achieved due to the fact that in the method of forming air-speed parameters of a maneuverable object, based on the joint processing of primary air-speed information, including the current values of the air module measured by the system of air signals (SHS) and the sensor of angles of attack and slip (DUAS) velocity V and angle of attack α and slip β of its orientation relative to the coordinate system (SSC) Oxyz associated with the object, the current calculated value of the module u of wind speed and unknown evaluation, the functional parameters cosΔψ _B , sinΔψ _B , α _{B of} its spatial orientation relative to the horizontal coordinate system (HSC) Ox _Г at _Г z _{Г of the} object, and formed by the results of inertial-Doppler correction of the angles of the true course ψ _and , roll γ and pitch υ facility constituting

and module

its ground speed with its current spatial orientation relative to the HSC Ox _G y _G z _{G of the} object with calculated values of the drift angles α _SN and the slope of the trajectory α _NT , the results of which form a complete array of air-speed information, the additionally used model of errors of air-speed parameters is expanded due to the inclusion in it of a mathematical description of the coordinates Δn, Δh, Δе of the location (on the object) of the air pressure receiver (LDPE) relative to the inertial navigation system (ANN), which is They are used as a system of three interconnected first-order differential equations in projections on the axis of the geographic accompanying trihedron (GTS) ONHE, which ensures the correct formation of a system of three physically sound and mathematically rigorous coupling equations, based on which the calculated expressions for input signals z ₁ , z are obtained _2, z _3, the optimum filter identifier air speed parameters and elements h _ij of the matrix of observations, realizing a closed, integrated in the structure of the optimal estimation proce uru of automatic accounting of the kinematic difference in ground speed measured by the integrated inertial-Doppler system at the location of the ANN and its value corresponding to the location of the LDPE, drastically narrowing the range of possible reasons for the divergence of the procedure for the optimal estimation of air-speed parameters in standard maneuverable flight modes for ASF and DUAS, additionally, the formation of air-speed communication using reception equations replace ideal values x _j airborne velocity parameters them physically hell cotton representation of the form

and after reformatting the obtained communication equations, they bring them to a form convenient for generating measurement signals z _i and elements h _ij (i = 1-3, y = 1-13) of the observation matrix, which are characterized by row-wise fulfillment of equalities of the form

and in the mathematical description of errors in measuring air-speed parameters, such as ΔV, Δα, Δβ, models that are easily implemented and supported by experimental data are used, which, together with a model describing the nature of the change in the spatial orientation of the wind speed, provide guaranteed observability, speed and accuracy of the optimal estimation of all air-speed parameters in standard maneuverable flight modes for the ASF and DUAS, while the navigation and flight information measured by the ANN is generated in process and according to the results of the inertial-Doppler estimation, during the implementation of which the error model traditional for the ANN is expanded by including differential equations describing the nature of the coordinate changes Δξ, Δη, Δζ, the location of the ANN relative to the Doppler meter of velocity components (DISS) in projections on the axis of the supporting trihedral of the ANN gyro platform Оξηζ, which provides a mathematically rigorous description of the complex inertial-Doppler system, and eliminating one of the main reasons for the divergence of its filter in anevrennom flight reach elevated characteristics estimation accuracy INS errors and correction of its output information, the implementation of which, as well as in the synthesis of the procedure the optimal inertial-Doppler estimation based on complex processing numeral ANN horizontal components V _x, V _y absolute linear velocity latitude

its current location, angle

azimuthal orientation of the supporting trihedral Оξηζ of its gyro platform, the measured angles of the gyroscopic course

roll

and pitch

object, and Doppler components

ground speed, instead of ideal values of inertial parameters x _j use their adequate representation of the form

and kinematic relations of the relation of errors of the main three navigation

and aerobatic

parameters with small angles α _x , α _y , α _{z the} mismatch between the real and the reference trihedra of the ANS gyro platform, and comparing the calculated ANS horizontal components V _x , V _{y of the} absolute linear velocity and similar complex components

absolute speed, speed inertial-Doppler communication equations are obtained, from which the functions of the measured navigation and flight parameters of the ANN are used to form the calculated expressions for the input signals of the filter-identifier and the elements of its observation matrix, thereby providing a synthesis of a mathematically closed, unified automatic procedure built into the structure optimal assessment, accounting for calculation / measurement errors of navigation and flight information and its effective correction as in the process of optimal on the estimation of ANN errors and according to the forecast results, while restoring the full array of air-speed information in the low-speed and hover mode, the hypotheses of the stationary wind speed are carried out with validity and implemented by solving the inverse problem of the spatial velocity triangle.

Here is a list and description of the figures that will be required in the implementation of the invention.

In FIG. Figure 1 shows the relative orientation of the geographic accompanying trihedron (GTS) ONHE and the horizontal coordinate system (HSC) Ox _Г y _Г z _{Г of the} object.

Their mismatch is determined by the angle of the true course ψ of the object.

The transition from the axes of the GTS ONHE to the axes of the HSC Ox _Г y _Г z _{Г is} carried out by rotation through the angle ψ with the angular velocity

является положительным.Referring to FIG. 1 reference direction of the angle ψ and angular velocity

is positive.

In FIG. 2 shows the relative orientation of the HSC Ox _Г y _Г z _Г and the coordinate system (SSC) Oxyz associated with the object.

Their mismatch is determined by the pitch angles υ and roll γ of the object.

и

соответственно.The transition from the HSC axes Ox _Г y _Г z _Г to the Oxyz axes is carried out by means of two successive rotations through the angles υ and γ with angular velocities

and

respectively.

и

является положительным.Referring to FIG. 2 reference direction of angles υ and γ and angular velocities

and

is positive.

In FIG. Figure 3 shows the relative orientation of the HSC Ox _Г y _Г z _Г and the trajectory of the coordinate system (TSC) Ox _T y _T z _T. Their mismatch is determined by the drift angles α _CH and the slope of the trajectory α _NT .

и

соответственно.Transition from GSK axes Ox _r y _r z _r to the axes Ox TSK _G y _r z _r is performed by two successive rotations through angles α and α _CH angular velocities with _HT

and

respectively.

и

является положительным.Referring to FIG. 3 direction of reference angles α _SN and α _NT and angular velocities

and

is positive.

путевой скорости объекта.In addition, it should be noted that a vector is associated with the axis Ox _T TSC

ground speed of the object.

In FIG. Figure 4 shows the relative orientation of the velocity coordinate system of the CSCS Ox _C y _C z _C and the CSC Oxyz.

The mismatch of these coordinate systems is determined by the slip angles β and attack α.

и

соответственно.The transition from the axes of the CCS of Ox _C y _C z _C to the axes of the CCS of Oxyz is carried out by means of two successive turns at angles β and α with angular velocities

and

respectively.

и

является положительным.Referring to FIG. 4 reference direction of angles β and α and angular velocities

and

is positive.

воздушной скорости объекта.On the x-axis vector _C is associated SkSK

airspeed object.

скорости ветра (ВСК) Ox_By_Bz_B.In FIG. 5 shows the relative orientation of the HSC Ox _Г y _Г z _Г and the coordinate system associated with the vector

wind speed (VSC) Ox _B y _B z _B.

The mismatch of these coordinate systems is determined by the directional angle of the wind velocity vector ψ _B and the vertical angle of its inclination α _B to the horizon plane Ox _Г z _Г.

и

соответственно.The transition from the axes of the HSC Ox _G y _G z _G to the axes of the HSC Ox _B y _B z _{B is} carried out by means of two successive turns at the angles ψ _B and α _B with angular velocities

and

respectively.

и

является положительным.Referring to FIG. 5 reference direction of angles ψ _B and α _B and angular velocities

and

is positive.

связан с осью Ox_B ВСК Ox_By_Bz_B.Wind speed vector

connected to the Ox _B axis of the BSC Ox _B y _B z _B.

воздушной скорости, вектор

путевой скорости объекта и вектор

скорости ветра. Для указанного треугольника скоростей справедливы векторные выражения вида:In FIG. Figure 6 shows the spatial velocity triangle whose sides are the vector

airspeed vector

ground speed object and vector

wind speed. For the indicated velocity triangle, vector expressions of the form are valid:

In FIG. 6, the following notation is used for angles between vectors

The first vector expression given above corresponds to the definition of airspeed; the second is a consequence of the first.

In FIG. 7 shows the relative orientation of the GTS ONHE and the OGPN ANN Oξηζ.

The transition from the axes of the GTS ONHE to the axes of the OTGP ANN Oξηζ is carried out by rotation through the angle χ of the azimuthal orientation of the OTGP ANN.

является положительным.Referring to FIG. 7 reference direction of the angle χ and angular velocity

is positive.

In FIG. Figure 8 shows the mutual orientation of the OTGP ANN Oξηζ SSK Oxyz.

Their mismatch is determined by the angles of the gyroscopic course ψ _g , pitch υ and roll γ of the object.

соответственно.The transition from the axes of the OGP Oξηζ to the axes of the SSK Oxyz is carried out by means of three successive rotations through the angles ψ _g , υ and γ with angular velocities

respectively.

является положительным.Referring to FIG. 8 reference direction of angles ψ _g , υ and γ and angular velocities

is positive.

In order to disclose the physical and mathematical essence of the proposed method for forming air-speed parameters, we present the direct and inverse vector-matrix transformations linking those shown in FIG. 1-5, 7, 8 coordinate systems, and the form of the matrices defining them.

In accordance with FIG. 1, the vector-matrix expressions relating the components of an arbitrary vector in the projections on the axis of the HSC Ox _Г y _Г z _Г and ГТС ONHE have the following form:

The transformation matrix G (1), in accordance with FIG. 1 is equal to:

Hereinafter, “s” means cosine, and “s” - sine of the corresponding angle.

Moreover, the matrix ^{T of the} inverse transformation (2), which is transposed with respect to the matrix T (3), will be equal to:

The direct and inverse transformations connecting the components of an arbitrary vector in the projections on the HSC axis Ox _Г y _Г z _Г and ССК Oxyz (Fig. 2) will have the following form:

where the matrix S and the matrix S ^T transposed to it, in accordance with FIG. 2 are equal to:

Similarly, the direct and inverse vector-matrix transformations for the components of an arbitrary vector in the projections on the HSC axis Ox _Г y _Г z _Г and ТСК Ox _T y _T z _T (Fig. 3) will have the following form:

where the matrices T and T ^T , in accordance with FIG. 3 will be equal to:

The direct and inverse vector-matrix transformations for the components of an arbitrary vector in the axes of the SSC Ox _C y _C z _C and the SSC Oxyz (Fig. 4) have the following form:

where matrices C and C ^T , in accordance with FIG. 4 will be equal to:

For the coordinate systems shown in FIG. 5, the direct and inverse vector-matrix transformations for the projections of an arbitrary vector will have the following form:

where matrix B and transposed matrix B ^T , in accordance with FIG. 5 are equal:

It seems appropriate to determine the course wind angle ψ _{B to} determine how:

where Δψ _B is the angle that determines the direction of the wind speed relative to the horizontal component of the ground speed of the object.

The vector-matrix expression for calculating the components of an arbitrary vector in the projections on the axis of the SSC Oxyz according to its known components in the axes of the OTGP ANN Oξηζ and its inverse expression are:

, в соответствии с фиг. 8, будут равны:where the matrix S ₀ and the matrix transposed to it

in accordance with FIG. 8 will be equal to:

The vector-matrix expression for calculating the components of an arbitrary vector in the projections on the axis of the OTGP ANN Oξηζ, according to its known components in the projections on the axis of the GTS ONHE and its inverse expression will look like:

where the matrix G and the matrix G ^T transposed to it, in accordance with FIG. 7 are equal to:

и путевой

скорости объекта, а также скорости ветра

, получим выражения для направляющих косинусов между рассматриваемыми векторами и тем самым определим косинусы углов δ₁, δ₂, δ₃, пространственного треугольника скоростей (фиг. 6). Это достаточно просто можно сделать, предварительно получив соответствующие векторно-матричные соотношения между векторами

After the above description of coordinate systems that determine the orientation of the vectors of air

and way

object speed as well as wind speed

, we obtain expressions for the directing cosines between the vectors under consideration and thereby determine the cosines of the angles δ ₁ , δ ₂ , δ ₃ , of the spatial velocity triangle (Fig. 6). This can be done quite simply by first obtaining the corresponding vector-matrix relations between the vectors

подставим его значение, определяемое выражением (5). В результате получим следующее полезное соотношение:To do this, in the vector-matrix expression (14) instead of the vector

we substitute its value defined by expression (5). As a result, we obtain the following useful ratio:

его значение, определяемое векторно-матричным выражением (10). Получим искомое соотношение вида:We substitute the vector into the specified expression

its value determined by the vector-matrix expression (10). We obtain the desired ratio of the form:

то есть сδ₁.The element of the first row and first column of the matrix C ^T ST ^T (23) determines the cosine of the angle between the vectors

i.e. cδ ₁ .

подставить его значение, определяемое выражением (18), получим 2-ое искомое соотношение:If in the vector-matrix expression (22) obtained above, instead of the vector

substitute its value defined by expression (18), we obtain the second desired ratio:

и скорости ветра

Косинус смежного с ним угла, который является внутренним углом пространственного треугольника скоростей, будет равен

The element of the first row and first column of the resulting matrix C ^T SB ^T determines the cosine of the angle between the airspeed vectors

and wind speed

The cosine of the angle adjacent to it, which is the internal angle of the spatial velocity triangle, will be equal to

его значение, определяемое выражением (18).To obtain the 3rd vector-matrix relation, we substitute the vector in the right side of expression (9)

its value defined by expression (18).

Оно имеет вид:As a result, we obtain a simple vector-matrix relation connecting two vectors

It has the form:

и вектор скорости ветра

ориентированы соответственно вдоль осей Ox_T и Ox_B, следовательно, косинус угла между векторами путевой скорости

и скорости ветра

будет определяться элементом первой строки и первого столбца матрицы ТВ^Т.Given that the ground velocity vector

and wind speed vector

are oriented along the axes Ox _T and Ox _B , respectively, therefore, the cosine of the angle between the path velocity vectors

and wind speed

will be determined by the element of the first row and the first column of the matrix TV ^T.

Opening the corresponding elements of the matrices of vector-matrix relations (23), (24), (25), we obtain the desired expressions for the direction cosines cδ ₁ . cδ ₂ , cδ ₃ . We give them:

An analysis of expressions (26) indicates that the only angle whose cosine in the normal flight mode can be calculated with accuracy determined by errors in measuring the attack and slip angles is the angle δ ₁ between the air and ground velocity vectors (Fig. 6).

Therefore, in the indicated flight mode, when the measured SHS and DUAS information is reliable and is issued with the corresponding sign, the expression for cδ ₁ (26) can be used for its intended purpose for a rough calculation of the wind speed module

и

- измеренные модули воздушной и приборной скорости.Where

and

- measured air and instrument speed modules.

It should be noted that this conclusion is valid for the case when the ANN operates in the inertial-Doppler correction mode.

Moreover, the expressions for cδ ₂ and cδ ₃ , after approximate calculation of their current values by solving the spatial velocity triangle, could be used as communication equations in the development of the procedure for optimal estimation and calculation of air-speed parameters.

However, taking into account that the list of parameters evaluated in this case is limited by errors in measuring the angles of attack and slip and the angles of the spatial orientation of the wind speed (26), it seems advisable to completely abandon their further use.

Moreover, in addition to the expressions obtained above (26), equations that can be obtained by reducing the air velocity components in the axes associated with the object to the axes have important theoretical and practical value in the development of unified mathematical procedures for optimal estimation of the entire list of errors of air-speed parameters speed coordinate system.

These equations, which, in contrast to expressions (26), are indeed the coupling equations in accordance with FIG. 4, have the form:

Exceptionally always, all physically justified constraint equations are valid for ideal values of the parameters included in them.

где под

в рассматриваемом случае следует понимать измеренные СВС и ДУАС значения параметров

But the ideal values of a series of parameters of interest, and, above all, air-speed ones, are usually either not known at all, or their current, erroneously measured values are known

where under

in this case, the measured values of the SHS and DUAS parameters should be understood

так и априори неизвестных параметров, определяющих ориентацию скорости ветра.In this case, the problem of optimal estimation is posed so that its solution is reduced to the determination of the error Δx _{j of} erroneously measured signals as current

and a priori unknown parameters that determine the orientation of the wind speed.

Formally, both of them are included in the list of parameters Δx _j subject to optimal estimation.

The mathematical technique that allows us to solve this problem involves replacing the ideal parameters x _j included in the coupling equation with their physically equivalent values of the form

а в левой - представленные в функции ошибок измерения Δx_j и априори неизвестных параметров.Then, the indicated communication equations are reformatted so that the terms depending on the measured signals are grouped in their right-hand side

and on the left, Δx _j and a priori unknown parameters presented in the error function.

The right-hand sides of these equations are taken as measurement signals z _i , and the left-hand sides are formally equal to the corresponding measurement signals used to determine the elements h _{ij of a} certain measurement matrix, by which the errors Δx _j are weighted by measuring the corresponding parameters

It is obvious that, for each z _{i, the} sum Σ _j h _ij Δx _{j of} weighted values should be equal to the corresponding measurement signal z _i .

If there is an adequate and physically justified description of the parameters Δx _{j to} be evaluated, an effective procedure for their optimal assessment is implemented.

In accordance with the above scheme, we transform the above communication equations (28) and, based on them, we obtain expressions for calculating the measurement signals z _i and elements h _ij (i = 1-3, j = 1-13) of the observation matrix.

But first, we present the expressions convenient for practical use for the components of the air velocity V _x , V _y , V _z in the projections on the Oxyz axis.

In their formation, we will proceed from the definition of airspeed, as the speed of movement of an object relative to the wind.

To do this, we obtain useful vector-matrix relations establishing a connection between the projections of an arbitrary vector in the axes of the SSC Ox _T y _T z _T and the SSC Ox _B y _B z _B with its components in the SSC axes Oxyz

подставить его значения, определяемые векторно-матричными соотношениями (10) и (18).The indicated relations can be quite easily obtained if, in the vector-matrix relation (5), instead of the vector

substitute its values determined by the vector-matrix relations (10) and (18).

As a result, we get:

путевой скорости и модуль u скорости ветра, приведенные выше соотношения применительно к составляющим

путевой скорости объекта и составляющим u_x, u_y, u_z скорости ветра могут быть представлены в виде следующих векторно-матричных выражений:Considering that the modulus is associated with the longitudinal axes Ox _T ТСК and Ox _B ВСК

ground speed and wind speed modulus u, the above ratios as applied to the components

the path speed of the object and the components u _x , u _y , u _z of the wind speed can be represented in the form of the following vector-matrix expressions:

путевой скорости объекта и составляющих u_x, u_y, u_z скорости ветра:Opening the matrices ST ^T and SB ^T , finding the values of the elements of their 1st column, we obtain the following expressions for the components

the path velocity of the object and the components of the wind speed u _x , u _y , u _z :

путевой скорости объекта далее будем рассматривать, как составляющие скорости, полученные по измерениям комплексной инерциально-доплеровской системы, которые соответствуют путевой скорости объекта в месте размещения ИНС. Используемый при этом модуль

путевой скорости рассчитывают в соответствии с одним из выражений вида:The given expressions (34) for the constituents

the ground speed of the object will be further considered as velocity components obtained from measurements of the complex inertial-Doppler system, which correspond to the ground speed of the object at the location of the ANN. The module used for this

ground speed is calculated in accordance with one of the expressions of the form:

и

- составляющие путевой скорости объекта в проекциях соответственно на оси ГСТ ONHE или связанной с объектом системы координат ССК Oxyz (34).Where

and

- components of the path velocity of the object in the projections, respectively, on the GTS axis ONHE or the coordinate system Oxyz associated with the object (34).

The calculation of the trajectory drift angles α _CH and the slope of the trajectory α _NT used in (34) are carried out in accordance with the following chain of relations (see Fig. 1, Fig. 3):

- составляющие путевой скорости объекта в проекциях на оси ГСК Ох_Г у_Г z_Г; ψ - истинный курс объекта.Where

- components of the ground speed of the object in projections on the axis of the GSK Oh _G y _G z _G ; ψ is the true course of the object.

Given that in order to describe the airspeed components measured by the SHS, it is necessary to know the components of the object’s ground speed at the installation site of the air pressure receiver (LDPE) from the SHS, we give a mathematical description of the kinematic components of the speed of movement of the LDPE relative to the ANN in the projections on the GTS axis ONHE taking place with angular evolutions of an object.

The indicated components of the velocity are uniquely determined by the nature of the change in the coordinates Δn, Δh, Δе of the relative placement of the LDPE and ANN.

From simple physical considerations, it can be shown that the differential equations describing the nature of the change in the coordinates Δn, Δh, Δе of the relative placement of the LDPE and ANN in the projections on the GTS axis ONHE have the form:

- составляющие угловой скорости объекта относительно ГСТ ONHE.Where

- components of the angular velocity of the object relative to the ONHE GTS.

кинематической скорости перемещения ПВД относительно ИНС, поскольку для них справедливы соотношения вида:The right-hand sides of these equations (34.4) simultaneously determine the desired components

kinematic velocity of the LDPE relative to the ANN, since for them the following relations are valid:

путевой скорости объекта в месте установки ПВД:Thus, expanding the model describing the nature of the change in the measurement / calculation of air-speed parameters, including differential equations (34.4), it becomes possible to estimate the coordinates Δn, Δh, Δе of the LDPE placement relative to the ANN and determine the current values of the kinematic velocity components (34.5) LDPE and after they are reduced to the axes of the coordinate system of the SSC Oxyz associated with the object to form the desired components

ground speed of the object at the place of the LDPE installation:

кинематической скорости относительного перемещения ПВД определяют в соответствии с векторно-матричным соотношением вида:where are the components

the kinematic velocity of the relative movement of the LDPE is determined in accordance with the vector-matrix relation of the form:

where the matrices G and S used in (34.7) are presented above (3) and (7).

Representing (34.7) in scalar form, we obtain the following expressions for

их значений, определяемых (34.5), (34.4), получим следующие развернутые выражения для

After substituting in (34.8) instead of

their values determined by (34.5), (34.4), we obtain the following expanded expressions for

,

,

в следующем виде:Reducing similar terms in (34.9), grouping them by Δn, Δh, Δе, we write the expressions for

,

,

in the following form:

We write the resulting expressions in a more compact form, namely:

The following notation is used in expressions (34.11):

By definition, airspeed is the speed at which an object moves relative to the wind.

Therefore, finding the difference between the corresponding components of the ground speed of the object at the installation location of the LDPE (34.6) and the wind speed (33), we obtain the desired expressions for the components of the air velocity in the projections on the axis of the SSK Oxyz:

(34) и

(34.11). В результате получим следующую запись для составляющих V_x, V_y, V_z воздушной скорости в месте установки ПВД:We substitute in (35) the expressions obtained above for the components of wind speed (33) and ground speed (34.6), taking into account the components that determine them

(34) and

(34.11). As a result, we obtain the following record for the components of V _x , V _y , V _z airspeed at the location of the LDPE:

For the case of a small value of the parameter α _{B of the} vertical wind and ψ _B = α _CH + Δψ _{In the} expression (36) can be written in the form:

The condition for a small value of the vertical wind angle should not be regarded as something obligatory and narrowing the scope of the proposed method for the formation of air-speed parameters, since it, in this sense, is not decisive and can also be easily canceled, since it only reduces by one synthesized system order.

And the fact that it supposedly allows for optimal filtering and identification in the framework of a linear procedure, this, as will be shown below, is absolutely not true, since nonlinearity, such as the product of the system state parameters when determining the elements of its observation matrix, is not excluded and, more Moreover, it does not cause any computational problems with the software implementation of the method in question.

Given that the description of the proposed method is carried out practically from a “clean slate”, in order to ensure the possibility of subsequent work with it, the conclusion and conversion of all, especially bulky expressions, is carried out in as much detail as possible, without any difficult to track transitions. This seems to facilitate his first reading.

The last expressions for V _x , V _y , V _z (37), after revealing in them with (α _CH + Δψ _B ) and s (α _CH + Δψ _B ) and resulting such terms, will take the following form:

Further, the obtained airspeed components (38) must be substituted into the above communication equations (28), while taking:

- измеренные/рассчитанные значения углов атаки, скольжения, воздушной скорости и скорости ветра; Δα, Δβ, ΔV, Δu - ошибки измерения/расчета представленных выше параметров.Where

- measured / calculated values of angles of attack, slip, airspeed and wind speed; Δα, Δβ, ΔV, Δu - measurement / calculation errors of the above parameters.

But first, we write the communication equations (28) in the following intermediate form:

Neglecting in the obtained equations of coupling the values of the second order of smallness with respect to Δα, Δβ, we present them in the following form:

Substituting expressions (38) for the airspeed components V _x , V _y , V _z into the obtained equations, taking into account the relations for and (39), we obtain the following detailed communication equations. The indicated equations are intermediate and have the form:

The given communication equations must be brought to a form convenient for their intended use, namely, for generating measurement signals or input signals of an optimal filter identifier for errors of air-speed parameters and determining elements of its observation matrix.

For this purpose, taking into account that the kinematic components of the velocity to be estimated and the error in calculating the wind velocity module do not exceed 1 m / s, and the errors in measuring the angle of attack and slip in the normal flight mode and the operation of the ASF and DUAS do not exceed 2.5 ÷ 3.0 degrees, it seems appropriate and justified to write down the given communication equations (42) up to second-order values of smallness with respect to such state parameters Δu, Δα, Δβ, sΔψ _B , сΔψ _B , α _B. For this purpose, we will change the form of their analytical presentation and write it in the following form:

where the components V _ix , V _iy , V _iz (i = 1 ÷ 3) included in (43), in accordance with (42) and the assumptions taken into account, have the form:

The above communication equations (43), taking into account the mathematical blocks defining them for V _ix , V _iy , V _iz (i = 1 ÷ 3) (44.1-44.3), in accordance with the traditional scheme of their further transformation, should be written so that in their right-hand sides, the terms that are independent of the parameters to be estimated were grouped, of the form ΔV, Δα, Δβ, Δu, sΔψ _B , cΔψ _B , α _B , and in the left - all the remaining members, that is, everything that is represented in the function above status parameters.

After that, the right-hand sides of these equations, which are determined solely from measurements of SHS and ANNs in the mode of its inertial-Doppler correction, are taken as input signals z ₁ , z ₂ , z _{3 for the} optimal filter identifier for errors of air-speed parameters, and according to their left parts — three rows of the observation matrix N. are formed corresponding to the indicated measurement signals.

Given the cumbersomeness of the transformations that precede the formation of the measurement signals and the observation matrix, we write the expressions for them without them, based solely on the above equations (43) and the mathematical blocks defining them (44.1) - (44.3), but with the necessary consideration of the above recommendations.

In accordance with the 1st equation of the system (43) and the system of mathematical blocks (44.1) that define the specified equation, we write the calculated expression for the measurement signal z ₁ :

In accordance with the 2nd equation of the system (43) and the system of mathematical blocks (44.2) defining the specified equation, the expressions for the measurement signal z ₂ will have the following form:

The expression for calculating the 3rd measurement signal z ₃ , in accordance with the 3rd equation of the system (43) and the mathematical blocks included in it (44.3), will have the following form:

From the above expressions for the input signals of the optimal identifier for errors in air-speed information, it follows that they are all formed by measurements of the SHS, DUAS and ANN in the mode of its inertial-Doppler correction.

, углы атаки

и скольжения

измеренным СВС и ДУАС, присущи ошибки ΔV, Δα, Δβ, которые подлежат их адекватному математическому описанию и оптимальному оцениванию. Указанные ошибки и, дополнительно, не входящие в явном виде в выражения (44.1), (44.2), (44.3) ошибка Δu расчетного значения скорости ветра

и неизвестные углы Δψ_В и α_B его пространственной ориентации в совокупности с кинематическими погрешностями (34.11) определения путевой скорости объекта в месте установки ПВД, входят в левые части тех уравнений связи, которые выше не были приведены по причине громоздкости их представления.For this reason, all parameters generated by inertial measurements are considered ideal, and all signals, such as airspeed

angles of attack

and slip

measured by SHS and DUAS, errors ΔV, Δα, Δβ are inherent, which are subject to their adequate mathematical description and optimal estimation. The indicated errors and, additionally, not explicitly included in expressions (44.1), (44.2), (44.3) error Δu of the calculated value of the wind speed

and unknown angles Δψ _B and α _{B of} its spatial orientation, together with kinematic errors (34.11) for determining the path velocity of the object at the LDPE installation site, are included in the left-hand sides of the communication equations that were not given above due to the cumbersomeness of their representation.

Having designated the right-hand sides of the indicated communication equations by z ₁ (45.1), z ₂ (45.2), z ₃ (45.3), it is obvious that their left-hand sides are the same z ₁ , z ₂ , z ₃ , but in the function of the subject estimation of system state parameters, the list of which includes such measurement / calculation errors of air-speed parameters as ΔV, Δα, Δβ, Δu, sΔψ _B , cΔψ _B , α _B , Δn, Δh, Δе.

The above list will be clarified after the development of a complete mathematical model that describes the nature of the change in these parameters.

The development of this model assumes an adequate mathematical description of the nature of the change in time of all the state parameters presented above. In this case, it is advisable to proceed from the experience of previous developments.

может быть представлена выражением вида:And the experience in the development, testing and operation of optoelectronic sighting and navigation systems (OEPrNK) of modern military targets indicates that a mathematical model that describes the nature of the change in the error ΔV of air speed measurement

can be represented by an expression of the form:

- измеренное значение текущей воздушной скорости; Δk_V, ΔV₀ - некоторые параметры, описываемые, как постоянные случайные величины:Where:

- measured value of the current airspeed; Δk _V , ΔV ₀ are some parameters described as constant random variables:

параметры Δk_V и ΔV₀ должны быть включены в перечень параметров состояния системы.To determine the current error ΔV measurement of air speed

Δk _V and ΔV ₀ parameters should be included in the list of system status parameters.

и скольжения

следует отметить, что на одном из объектов указанные углы перед их использованием для решения специальных задач предварительно «взвешивались» некоторыми коэффициентами, равными 0,8-0,85 для угла атаки и 0,6-0,65 для угла скольжения, после чего их корректировали в соответствии с методом, основанным на справедливости гипотезы об отсутствии вертикального ветра.Regarding the practical use of measured angles of attack

and slip

it should be noted that on one of the objects the indicated angles were previously “weighted” by some coefficients equal to 0.8-0.85 for the angle of attack and 0.6-0.65 for the angle of glide before they were used to solve special problems, after which they corrected in accordance with the method based on the validity of the hypothesis of the absence of vertical wind.

The indicated approach to the formation of angles of attack and glide provided a rather effective application of the entire range of unguided aircraft weapons (ASA), but with some limitation on their use.

Considering the cited experience of the formation of the considered angles, it seems appropriate to characterize the errors Δα and Δβ of the measurement of the angle of attack and slip, by analogy with (46), in the form

- измеренные значения углов атаки и скольжения; Δk_α, Δk_β, Δα₀, Δβ₀ - некоторые параметры, описываемые, как постоянные случайные величины:Where

- measured values of the angle of attack and slip; Δk _α , Δk _β , Δα ₀ , Δβ ₀ are some parameters described as constant random variables:

In accordance with FIG. 1, 3, 5 and relation (21), the expression defining the course of the horizontal component of the wind speed relative to the direction to the North will have the following form:

where ψ _p - the path angle of the object: ψ _p = ψ + α _CH

For a stationary model of wind speed, its direction relative to the sides of the world at a given observation interval should be considered constant. This obviously means that

Having written expression (48) in the form:

and differentiating it, we obtain the following useful ratio:

The indicated relation makes it possible to quite simply obtain differential equations describing the nature of the change of such wind speed parameters as сΔψ _B and sΔψ _B. We give them:

The differential equation describing the nature of the change in the angle α _B , which determines the direction of the vertical wind, is presented in the form of an equation characteristic of color noise of the first order with nonzero mathematical expectation. It has the following form:

- параметры цветного шума 1-го порядка, характеризующие его изменчивость и интенсивность соответственно;

- белый шум 1-ой интенсивности.Where

- 1st-order color noise parameters characterizing its variability and intensity, respectively;

- white noise of the 1st intensity.

The differential equation describing the nature of the change in the error Δu of the calculation of wind speed can also be represented in the form of color noise of the first order with a non-zero mathematical expectation:

where μ _u , σ _u , w _u are the corresponding color noise parameters, are functionally similar to the parameters of equation (52).

Differential equations describing the nature of the change in the coordinates Δn, Δh, Δе of the relative location of the LDPE from the SHS and ANN in projections on the GTS axis ONHE are presented above and have the form (34.4).

Thus, we have the following vector x of air-speed state parameters that are subject to optimal estimation in standard maneuverable flight modes:

To conclude the description of the synthesized optimal filtering system, we present the form of its observation matrix H and the expression for calculating its elements h _ij (i = 1 ÷ 3, j = 1 ÷ 13).

The observation matrix H, in accordance with (45.1) - (45.3) and the form of the vector x of the state parameters of the system (54), has the dimension [3 × 13] and can be represented as follows:

When determining the linearized expressions for calculating the elements h _{ij of} the measurement matrix (55), the following expression was used:

presented in E. Sage, J. Mele "The theory of evaluation and its application in communication and management", "Communication", Moscow, 1976 [3] (pp. 446-448).

When finding them, we used the coupling equations (43) and the mathematical blocks (44.1), (44.2), (44.3) that enter into them, with terms depending on the state parameters of the system represented by vector (54) and the relations defining ΔV (46) and Δα, Δβ (47).

The expressions for calculating the elements h _{ij of} the observation matrix H presented in (55) are as follows:

After describing the nature of the change in the state parameters of the original system (46), (46.1), (47), (47.1), (48) - (51), (52), (53), (54), (34.4), obtaining the expressions for measurement signals (45.1), (45.2), (45.3), which are the input signals of the optimal filter identifier for measurement / calculation errors and, at the same time, the determination of unknown air-speed parameters and the implementation of rather labor-intensive mathematical transformations to ensure the formation of the measurement matrix H ( 55), elements of which (57.1), (57.2), (57.3), for reasons of increasing the accuracy of the optimal estimate calculations, taking into account nonlinear terms of the second order of smallness (57), we present in vector-matrix form the optimal procedure for a discrete Kalman filter.

Moreover, taking into account that the message model of the system under consideration is linear, and the elements of the measurement matrix are presented in an analytically developed, linearized form, we present it in the discrete form traditional for linear systems (p. 269 [3]):

1. The original message model:

2. Surveillance Model:

3. A priori data used in the synthesis:

4. The structure of the optimal filter:

Where

5. Calculation of the matrix of a priori estimation errors:

6. Calculation of optimal amplification factors:

7. The calculation of the matrix of posterior estimation errors:

The last operation represented by expression (64) should be considered as preparatory to the next step of calculations.

In the above relations (58 ÷ 64), the following conventions are used:

x _k is the vector of system state parameters;

- вектор оптимальных апостериорных оценок параметров состояния;

- vector of optimal posterior estimates of state parameters;

w _k is the vector of random perturbations of the message model;

V _k is the vector of random measurement noise;

Ф _{k + 1, k} is the fundamental matrix of the system (message model);

Г _{k + 1, k} is the matrix of transmission of random perturbations of the system;

H _k is the measurement matrix;

- вектор априорных оценок параметров состояния системы;

is the vector of a priori estimates of the system state parameters;

P _{k + 1, k} is the a priori correlation matrix of estimation errors;

P _{k + 1} - a posteriori correlation matrix of estimation errors;

Q _k - correlation matrix of random noise of the system;

R _k - correlation matrix of random noise measurements;

z _k is the vector of measurement signals;

K _{k + 1} is the matrix of optimal gain.

Let us summarize the above differential equations describing the nature of the change in measurement / calculation errors and determination of unknown air-speed parameters (46), (46.1), (47), (47.1), (51) - (53), (34.4) into a single system differential equations, representing it in a discrete form:

, w_u, w_n, w_h, w_e - некоррелированные шумы возмущения известной интенсивности.where τ is the discreteness of the solution of the problem in question (τ = 0.1 sec); w ₁ - w ₆ , w _s , w _c ,

, w _u , w _n , w _h , w _e are uncorrelated disturbance noises of known intensity.

It must be remembered that the first six state parameters of the reduced system of equations are related by relations (46), (47), which is important both in the formation of the observation matrix H and in the synthesis of the structure of the optimal filter identifier as a whole.

Based on the above system of discrete equations (65), the fundamental matrix Φ _{k + 1, k of} the system under consideration can be formed quite simply and the elements of the measurement matrix can be further defined.

как следует из выражения (56), должны быть представлены в функции их прогнозируемых значений, каждое из которых рассчитывается в соответствии с конкретным дискретным уравнением системы (65).Regarding the linearized measurement matrix H (55), it should be noted that its individual elements are presented in the function of a priori estimates of the state parameters of the system, such as

as follows from expression (56), they should be represented in the function of their predicted values, each of which is calculated in accordance with a specific discrete equation of system (65).

,

, α_B и координат Δn, Δh, Δе относительного размещения ПВД и ИНС, приведем математическое описание всех, используемых в процедуре (58)÷(64) матриц.In accordance with (58) ÷ (64), the above expressions for the signals z ₁ , z ₂ , z ₃ (45.1), (45.2), (45.3) and the measurement matrix H (55), (57.1) ÷ (57.3) as well as a message model (65) describing the nature of the time-varying measurement / calculation errors of the main triple ΔV, Δα, Δβ of air-speed parameters and, at the same time, determination of unknown parameters of the angular orientation of the wind speed

,

, α _B and coordinates Δn, Δh, Δе of the relative placement of the LDPE and ANN, we give a mathematical description of all the matrices used in the procedure (58) ÷ (64).

The expression for the fundamental matrix Φ _{k + 1, k of} dimension [13 × 13] is not given, since all its elements Φ _{ik k + 1, k} (i, j = 1 ÷ 13) can be obtained quite simply from the system of discrete equations (65 )

The perturbation transfer matrix of the system Γ _{k + 1, k} has the dimension [13 × 13] and is equal to the 13th order identity matrix times τ.

where [1] is the identity matrix of dimension [13 × 13].

The measurement matrix H is presented above (55) and has a dimension [3 × 13], its elements are determined by expressions (57.1) - (57.3). In this case, the vector z of measurement signals of dimension [3 × 1] is represented by the components z ₁ , z ₂ , z ₃ (45.1) - (45.3), observed against the background of additive uncorrelated measurement noise V ₁ , V ₂ , V ₃ with known intensities.

The noise matrix of the measurement R _k has a dimension [3 × 3] and is equal to:

- дисперсии соответствующих шумов измерения.Where

- variance of the corresponding measurement noise.

In accordance with the discrete system of equations (65), the matrix Q _{k of} noise of the perturbation of the system is of the 13th order, is diagonal with elements of the form:

- дисперсии шумов системы (65).Where

- noise variance of the system (65).

The a priori (62) and posterior (64) correlation matrices of estimation errors are positive definite symmetric matrices of dimension [13 × 13].

The matrix of optimal gains of the optimal filter identifier for errors of air-speed parameters has a dimension [13 × 3] and can be represented as follows:

In the algorithmic implementation of the considered method of forming air-speed parameters, we will use the discrete linearized optimal filtering and identification procedure (58) - (64).

However, in order to more clearly and meaningfully perceive the procedure under consideration, it seems advisable to additionally synthesize the structure of the optimal filter-identifier for the case of its continuous presentation.

In this case, the role and place of each measurement signal, message model (65), each optimal gain from the entire set of coefficients included in the matrix (69) and each element h _ij (i = 1 ÷ 3, j = 1 ÷ 13) will be determined observation matrices (55). The concept of each of the 3 residuals of the measurement ν ₁ , ν ₂ , ν ₃ will be sufficiently clearly revealed, and thereby the essence of all the errors that are present in them.

To synthesize the mentioned structure of the optimal filter identifier for errors of air-speed parameters, we use the matrix differential equation of the optimal filter identifier for the case of its continuous presentation / description:

- вектор оптимальных оценок параметров состояния системы; z - вектор сигналов измерения.where: F is the state matrix of the system; K is the matrix of optimal gain;

- the vector of optimal estimates of the system state parameters; z is the vector of measurement signals.

и матриц κ и Н соответствует представленному выше их описанию.The structure of vectors z,

and the matrices κ and H correspond to the above description.

и углов атаки

и скольжения

In this case, the state matrix of the system F will be determined by the system of the above differential equations (46.1), (47.1), (51), (52), (53), (34.4) with the obligatory allowance for relations (46) and (47), which determine the errors ΔV, Δα, Δβ airspeed measurements

and angles of attack

and slip

The structure of the optimal filter identifier for errors in air-speed parameters will be synthesized by the method of structuring the system of differential equations of the 13th order, formed in accordance with the matrix differential equation (70) and the form of the matrices F, K, H and vectors z,

, будет иметь следующий вид:We give the indicated system of differential equations, which, in accordance with the form of the matrices F, K, H and vectors z,

will have the following form:

In the given system of differential equations, ν ₁ , ν ₂ , ν ₃ should be understood as the corresponding measurement residuals formed in accordance with expressions of the form:

It should be noted that expressions (72) are a detailed line-by-line recording of the vector-matrix representation of the measurement residuals

The above system of differential equations (71) in conjunction with expressions (72) for the residuals of the measurement ν ₁ , ν ₂ , ν ₃ , as well as the measurement signals determining them z ₁ , z ₂ , z ₃ (45.1), (45.2), ( 45.3) and linearized elements (i = 1 ÷ 3, j = 1 ÷ 13) (57.1), (57.2), (57.3) the observation matrix H (55) uniquely determine the structure of the optimal filter identifier for measurement errors / calculation of air-speed parameters .

To develop it, we use the method of structuring the system of differential equations (71).

A diagram defining the structure of the filter identifier in question is shown in FIG. 9, immediately after the above described FIG. 1-8. But at the same time, its description, as well as the two flowcharts of the algorithms shown in FIG. 10 and FIG. 11, which determine the general procedure for the formation, correction and restoration of the entire list of air-speed parameters, including the cyclogram of its organization, it is advisable to carry out at the end of their development, which will contribute to their more meaningful perception.

Therefore, everything shown in FIG. 9, 10 and 11 should be considered as one of the possible examples of the implementation of the proposed method for the formation of air-speed parameters (VSP).

In the structural diagram (Fig. 9), designations traditional for control theory are adopted for amplifying, integrating, and summing blocks.

The designations for the optimal amplification factors k _ij (i = 1 ÷ 13, j = 1 ÷ 3) and transmission units that implement the function of "weighing" the signals passing through them are absolutely similar.

проведена в соответствующей модели формирования оценок

(см. фиг. 7).The only feature that makes the structural diagram under consideration different from its mathematical description is the fact that instead of the matrix elements h ₁₁ , h ₁₃ and h _{15, it} uses the elements h ₁₂ , h ₁₄ and h ₁₆ , since it is used in h ₁₁ , h ₁₃ and h ₁₅ weighing operation with the current measured signal values

carried out in the corresponding model for the formation of assessments

(see Fig. 7).

It should also be noted one fact that is quite important for the software implementation of the optimal estimation procedure under consideration, that it can be significantly simplified by using the well-known technique of filter decomposition.

воздушной скорости (46), (46.1)).Its essence is that instead of the software implementation of the 13th-order filter with three measurement signals, it is proposed to develop three independent identifier filters, each of which operates on its own measurement signal. In this case, the first of them will have the 13th order, and the dimension of the other two will be two orders of magnitude smaller (due to the lack of a description of the parameters ΔK _V , ΔV ₀ that determine the error ΔV of the module measurement

airspeed (46), (46.1)).

The indicated trick will significantly reduce the amount of computation performed and, as a result, increase the speed of the optimal estimation procedure with virtually no damage to its accuracy.

The crown of the optimal estimation procedure is the correction of the measured air-speed parameters and the formation of their complete list in the normal flight mode. By regular, we will further understand such a flight in which the measured SHS and DUAS parameters are formally reliable. We bring her.

ошибок измерения воздушной скорости

и углов атаки

и скольжения

используют для их коррекции и формирования истинных значений указанных параметров:Received as a result of optimal assessment current values of estimates

airspeed errors

and angles of attack

and slip

used for their correction and the formation of the true values of these parameters:

(73), рассчитывают истинные составляющие воздушной скорости в проекциях на оси ССК Oxyz объекта. Указанные составляющие, в соответствии с векторно-матричным выражением (13) и видом матрицы С (15), имеют вид:Using the obtained values

(73), calculate the true components of the airspeed in the projections on the axis of the SSC Oxyz object. These components, in accordance with the vector-matrix expression (13) and the form of the matrix C (15), have the form:

ошибки расчета модуля скорости ветра

рассчитывают его откорректированное значение

:Additionally, knowing the current rating value

errors in calculating the wind speed module

calculate its adjusted value

:

текущей пространственной ориентации скорости ветра

один из которых рассчитывают по известным оценкам

At known angles

current spatial orientation of wind speed

one of which is calculated according to known estimates

:and the drift angle α _CH formed by inertial measurements, in accordance with (21), the directional angle of the wind is calculated

:

определяющих пространственную ориентацию скорости ветра относительно ГСК Ox_Гy_Гz_Г и ГСТ ONHE (фиг. 5, фиг. 1), рассчитывают составляющие скорости ветра в проекциях на оси ГСК Ox_Гy_Гz_Г и ГСТ ONHE:Then, using the current values of the angles

determining the spatial orientation of the wind speed relative to the HSC Ox _G y _G z _G and GTS ONHE (Fig. 5, Fig. 1), calculate the components of the wind speed in the projections on the axis of the HSC Ox _G y _G z _G and GTS ONHE:

In accordance with the vector-matrix expression (5) and the form of the matrix S (7), the components of the wind speed are calculated in the projections on the Oxyz CCK axis:

The given components (79), together with the corrected airspeed components (74), in the normal flight mode can be used to calculate firing corrections when using the entire range of unguided aircraft weapons (ASA), as well as in solving special problems.

For a super-maneuverable fighter with a controlled thrust vector, standard flight modes today are all modes in which it is assumed to perform highly dynamic aerobatics such as “barrels”, “Nesterov loops”, combat turn, ... which do not lead to the reliability of the main air-speed parameters being removed, such as measured by the SHS module of air (instrument and true) speed and DUAS - angles of attack and glide, the exact knowledge of which is important not only for solving combat and special tasks, but above all for pi otirovaniya that beyond the scope of some other order-related safety, and requires more careful attention to both the control and the formation of the above parameters.

And in this sense, the most informationally unprotected modes are low-speed modes, which are characteristic not only for helicopters - the hover mode, but also for modern highly maneuverable fighters, such as SU-30SM, MiG-29SMT, MiG-35, when they, performing figures of higher aerobatics, stop briefly, hovering in the air. This takes place when performing such figures as the “Pugachev cobra”, “Kvochur's bell”, etc.

And this insecurity is caused solely by the fact that in low speed modes, with:

снимается ее достоверность;- airspeed

its reliability is removed;

выдаются ошибочно измеренные углы атаки

и скольжения

со снятыми признаками их достоверности;- airspeed

erroneously measured angle of attack

and slip

with signs of their reliability removed;

снимается достоверность углов атаки и скольжения, а измеряемые значения углов обнуляются.-

the accuracy of the angle of attack and slip is removed, and the measured values of the angles are reset.

полет из разряда штатного переводить в разряд малых скоростей и, как следствие, описанную выше процедуру оптимального оценивания ошибок измерения/расчета воздушно-скоростных параметров приостанавливать, весь срез полученных оценок, и прежде всего, определяющих параметры пространственной модели скорости ветра, запоминать, и после расчета составляющих скорости ветра в проекциях на оси ГСТ ONHE (78), переходить к решению обратной задачи пространственного треугольника скоростей.Based on the data presented it seems appropriate when

to transfer the flight from the regular discharge to the low-speed discharge and, as a consequence, to suspend the entire procedure for the optimal estimation of measurement / calculation errors of air-speed parameters, remember the whole section of the obtained estimates, and, first of all, determining the parameters of the spatial model of wind speed, and after calculating components of wind speed in projections on the GTS axis ONHE (78), proceed to solving the inverse problem of the spatial velocity triangle.

Its essence is to restore the entire list of air-speed parameters based on the use of components (78) and the current components of the ground speed measured by the ANN in the mode of its inertial-Doppler correction.

The first operation to solve this problem is to calculate the airspeed components in the projections on the ONHE GTS axis. It is performed in full accordance with the definition of airspeed, as the speed of movement of an object relative to the wind:

- запомненные компоненты скорости ветра (78);

- составляющие текущей путевой скорости объекта.Where

- memorized components of wind speed (78);

- components of the current ground speed of the object.

The next operation is the calculation of the air velocity components in the projections on the Oxyz CCK axis. It is carried out in accordance with a vector-matrix expression of the form:

which can be obtained quite simply by substituting (1) in (5).

Representing (81) in a scalar form, we obtain the following expressions for calculating the components

Air speed components (82), in combination with wind speed components (79), can be used to calculate current firing corrections.

и скольжения

по известным составляющим (82).And the last operation is the calculation of the restored angles of attack

and slip

according to known components (82).

Expressions for calculating the indicated angles can be obtained based on the use of relations of the form:

на оси ССК Oxyz (фиг. 4). В соответствии с (83), искомые выражения для расчета углов атаки

и скольжения

будут иметь следующий вид:for projections of the airspeed vector

on the axis of CCK Oxyz (Fig. 4). In accordance with (83), the sought expressions for calculating the angle of attack

and slip

will have the following form:

Above are two mathematical procedures that are close in physical essence to the formation of air-speed parameters.

The first of them is represented by expressions (73) - (79) and is used in normal flight mode to correct and form a complete list of airspeed parameters based on the results of optimal estimation of both the current angles of the spatial orientation of the wind speed with Δψ _B , sΔψ _B , α _B , and measurement or calculation errors of the main ones, such as ΔV, Δα, Δβ, Δu.

The second procedure is represented by expressions (80) - (84) and is intended to form a complete list of airspeed information and, first of all, to restore that part of it that loses its reliability in flight modes critical for SHS and DUAS, characterized by a low speed head. The indicated procedure is used in the mode of low speeds and for its implementation involves the stationary nature of the change in wind speed.

Moreover, given that the flight mode under consideration is short-term and does not exceed units of seconds for an airplane, and units of minutes for a helicopter, the above condition should not be considered as something that limits the scope of the method under consideration.

It is also important to note that both of the above algorithms for the formation of air-speed parameters are based on the implementation of the key procedure for optimal filtering and identification of all state parameters necessary for this, including:

- the formation of physically and mathematically correct communication equations;

- the formation of the input signals of the optimal filter identifier;

- obtaining linearized expressions for calculating the elements of the matrix of the measurement system;

- a mathematical description of the nature of the change in all state parameters of the system in question and the formation of an engineering-based model for changing its state parameters;

- description and synthesis of the structure of the optimal filter identifier of measurement errors / calculation of air-speed parameters and estimation of the current angles of spatial orientation of the wind speed.

The place, interaction and the sequence diagram of the inclusion in the work of each of the above procedures, namely:

- optimal filtering and identification of air-speed parameters (OFIVSP);

- correction of their current, erroneously measured values (CVSP);

- the formation of the entire nomenclature of air-speed information in the low-speed mode (FVSI), is quite clearly shown in the block diagram of the algorithm (Fig. 10) of the information interaction of the OFIVSP subroutines (block 2), KVSP (block 10), FVSI (block 17).

In FIG. 10, the tracing of logical blocks (blocks 1, 6, 7, 11, 12, 15, 16, 22), routines (blocks 2, 10, 17), time counters (blocks 4, 18), and assignment blocks / reassignment (blocks 3, 5, 8, 9, 13, 14, 19, 20, 21, 23, 24).

The given block diagram is characteristic for all flight modes, starting from take-off, the maneuverable flight mode and the low-speed mode, which is standard for a combat object.

OFIVSP subroutine (block 2), the block diagram of which in its continuous execution is shown in FIG. 9, precedes both the regular correction mode implemented by the KVSP subroutine (block 10) and the low-speed mode implemented by the FVSI subroutine (block 17).

In this case, the VSP correction procedure in the normal mode of maneuverable flight is implemented at flight speeds V> 100 km / h (block 1) and begins 180 seconds later (block 6) after the start of the optimal VSP error identifier filter.

The indicated time shift is selected for reasons of use for the correction of the guaranteed accurate values of the error estimates of the VSP.

(блок 16). Для гарантированного выполнения полета в режиме малых скоростей необходимо, чтобы пр. ОФИ (блок 9, где он устанавливается, и блок 15, где он контролируется) был равен 1.Next, the optimal assessment procedure (OFIVSP) and VSP correction (KVSP) are performed in parallel. Moreover, until the object switches to the low-speed mode, at which the averaged airspeed is taken equal to

(block 16). For guaranteed flight performance in low-speed mode, it is necessary that the AOF (block 9, where it is installed, and block 15, where it is controlled) be equal to 1.

It should be noted that in the low-speed mode, the optimal filtering and identification procedure is suspended. And for the formation of a complete list of air-speed information, the wind speed values and current ground speed values measured in the inertial-Doppler correction mode generated at the time of the suspension of the operation of the HFSPSP are used.

воздушной скорости формируют в соответствии с алгоритмом, приведенным на блок-схеме фиг. 11.After the end of the low-speed mode and a steady transition to the normal flight mode, the above operation procedure is repeated. The values used in the above block diagram (Fig. 10) averaged over a 3-second time interval t _ocp (block 11)

airspeed is formed in accordance with the algorithm shown in the block diagram of FIG. eleven.

The procedure for finding the average is carried out in accordance with the recurrence expression of block 6 (Fig. 11).

In this case, the current values of the airspeed module V measured by the SHS are used (see the expression of block 6).

хранится в памяти (блок 13) и используется на следующем интервале осреднения до получения его обновленного значения.The obtained average value of airspeed

stored in memory (block 13) and is used in the next averaging interval until its updated value is received.

The above averaging procedure is cyclic and is carried out over the entire flight interval.

The averaging time t _ocp (block 11) can be clarified by the results of field work and presumably brought from the accepted 3 seconds to 2 seconds.

Used in the block diagram under consideration, pr. P1 is a sign of the 1st pass.

The inventive method of forming air-speed parameters of a maneuverable object is implemented as follows:

и углов атаки

и скольжения

его текущей ориентации относительно связанной с объектом системы координат с ДУАС, расчетного значения модуля

скорости ветра и неизвестных, подлежащих оцениванию углов его пространственной ориентации относительно горизонтированной системы координат объекта, а также измеряемых в режиме инерциально-доплеровской коррекции текущих углов истинного курса ψ, крена γ и тангажа υ объекта, составляющих

и модуля

его путевой скорости, а также текущих значений углов сноса α_CH и наклона траектории α_HT его ориентации относительно ГСК объекта, по результатам проведения которой формируют полный перечень воздушно-скоростных параметров.1. Based on the processing of current air-speed, navigation and flight information, joint processing of the measured SHS of the airspeed module is implemented

and angles of attack

and slip

its current orientation relative to the coordinate system associated with the object with DUAS, the calculated value of the module

wind speed and unknowns, subject to estimation of the angles of its spatial orientation relative to the horizontal coordinate system of the object, as well as measured in the mode of inertial-Doppler correction of the current angles of the true heading ψ, roll γ and pitch υ of the object, constituting

and module

its ground speed, as well as the current values of the drift angles α _CH and the slope of the trajectory α _{HT of} its orientation relative to the HSC of the object, the results of which form a complete list of air-speed parameters.

Additionally, to achieve the claimed technical result is carried out:

его путевой скорости в месте установки ПВД (34.6) и компоненты u_x, u_y, u_z скорости ветра (33).2. In accordance with the definition of an object’s air speed as its speed relative to wind speed, air velocity components V _x , V _y , V _z are formed in the projections on the SSK axis Oxyz (35), (36), (37). To do this, use the appropriate components

its ground speed at the installation site of the LDPE (34.6) and the components u _x , u _y , u _z of the wind speed (33).

The use of components of ground speed (34.6) is dictated by the need to ensure the adequacy of the formed components of air speed (35) to their actual values obtained from measurements of SHS and DUAS.

кинематической скорости относительного перемещения ПВД (34.6), (34.7)÷(34.11), в перечень оцениваемых параметров состояния системы, наряду с воздушно-скоростными параметрами, включают координаты Δn, Δh, Δе местоположения ПВД относительно ИНС в проекциях на оси ГСТ ONHE.3. In order to implement a closed procedure for the formation of airspeed components (35) based on expressions (34.6) for the components of the object’s ground speed at the installation site of the LDPE and the inertial components (34) and their corresponding components that determine them

the kinematic velocity of the relative movement of the LDPE (34.6), (34.7) ÷ (34.11), along with the airspeed parameters, the coordinates Δn, Δh, Δе of the location of the LDPE relative to the ANN in the projections on the GTS axis ONHE are included in the list of estimated parameters of the state of the system

угловой скорости вращения объекта относительно ГСТ ONHE и описывается системой линейных дифференциальных уравнений вида (34.4), а сами составляющие

кинематической скорости движения ПВД относительно ИНС определяются выражениями (34.5) (см. фиг. 7).The nature of the change in these coordinates is determined by the components

the angular velocity of rotation of the object relative to the GTS ONHE and is described by a system of linear differential equations of the form (34.4), and the components themselves

the kinematic velocity of the LDPE relative to the ANN is determined by the expressions (34.5) (see Fig. 7).

The extension of the error model, traditional for air-speed parameters, and the inclusion in it of differential equations (34.4), describing the nature of the change in the coordinates of the relative location of the LDPE and ANN, allows:

- provide a mathematically correct and physically sound description of the system in question;

- implement a unified, closed procedure for solving the problem under consideration for the entire variety of military targets;

- and, as a result, to achieve maximum accuracy and speed of optimal estimation of the entire list of air-speed parameters (54) by eliminating the root cause of their possible divergence in maneuverable flight.

4. In order to obtain the calculated expressions for the input signals of the optimal filter identifier of the air-speed parameters of the state of the system (54) and the expressions for calculating the current elements of its observation matrix, an algebraic system of equations is formed that connect the ideal values of the air-speed, navigation, flight and other physically appropriate parameters, such as coordinates of the relative location of the LDPE and ANN.

In the proposed solution, these equations are formed by bringing the components V _x , V _y , V _{z of the} air speed V of the object to the axes of the velocity coordinate system Ox _C y _C z _C (Fig. 4). The indicated equations are represented by a system of algebraic equations (28).

и их идеальные значения V, α, β, u, получают искомую систему уравнений связи (43) с определяющими их математическими блоками для V_1x, V_1y, V_1z (44.1), V_2x, V_2y, V_2z (44.2), V_3x, V_3y, V_3z (44.3).After substituting into equations (28) the expressions for the components V _x , V _y , V _z (38) taking into account relations of the form (39) relating the measured / calculated values of the air-speed parameters

and their ideal values V, α, β, u, get the desired system of coupling equations (43) with the mathematical blocks defining them for V _1x , V _1y , V _1z (44.1), V _2x , V _2y , V _2z (44.2), V _3x , V _3y , V _3z (44.3).

5. In accordance with the traditional transformation scheme of the obtained equations (43), (44.1) - (44.3), they are presented in such a way that the terms independent of the parameters to be estimated are grouped in their right-hand sides, of the form ΔV, Δα, Δβ, Δu, sΔψ _B , сΔψ _B , α _B , Δn, Δh, Δе, and in the left - all the remaining terms represented in the function of the parameters listed above.

6. The right-hand sides of the indicated equations (43), which are determined by the SHS, DUAS, and ANN measurements, are taken for the measurement signals z ₁ , z ₂ , z ₃ (45.1), (45.2), (45.3), and on the left-hand sides, in accordance c (56), form linearized expressions for calculating the elements of the measurement matrix H (55).

The calculation of their current values is carried out in accordance with the expressions (57.1), (57.2), (57.3).

7. Based on experimental data based on many years of experience in operating and testing military targets, practical and engineering-based models are proposed that describe the nature of changes in measurement / calculation of the main air-speed parameters.

In particular, in accordance with the model represented by expression (46) and its type parameters (46.1), the aerodynamic errors of measuring the air speed of domestic SHS are changed.

Similarly, the model describing the nature of the change in the error in measuring the angle of attack and slip (47), (47.1) is based on experimental data obtained during flight operation and combat use of a number of modern military targets.

When developing differential equations describing the nature of the change in time sΔψ _B and cΔψ _B , it is shown that the angular velocity of the angle Δψ _B when the wind model is stationary relative to the sides of the world will be determined by the angular rate of change of the path angle, taken with the opposite sign (50).

In accordance with this, the equations describing the dynamics of changes of such wind speed parameters as sΔψ _B and cΔψ _B for the general case of maneuverable flight will have the form represented by differential equations (51).

These differential equations make it possible to efficiently evaluate the parameters described by them, both in the case of maneuverable flight, accompanied by a change in the path angle of the object, and without it.

Differential equations describing the nature of the change in the angle α _{B of the} vertical wind, as well as the errors Δu of the calculation of the wind speed, taking into account the variability of these parameters, are presented in the form of colored noise of the first order with nonzero mathematical expectations and known parameters characterizing their intensity and variability (52), ( 53).

поэтому при синтезе процедуры оптимальной фильтрации и идентификации представляется целесообразным использовать линейный вариант ее дискретной реализации (58)-(64).8. Considering that all the parameters presented above that determine the state vector of the considered system (54) are described by linear differential equations, and the nonlinear measurement matrix H (55), after applying the procedure (56) to its elements, acquire the character of a linearized matrix with elements h _ij ( i = 1-3, j = 1-13) (57.1), (57.2), (57.3) as a function of a priori estimates of air-speed parameters, of the form

therefore, when synthesizing the optimal filtering and identification procedure, it seems appropriate to use the linear version of its discrete implementation (58) - (64).

In relation to the proposed optimal estimation procedure, the form of the matrices and vector-matrix equations used in its implementation is represented by expressions (66) - (72).

9. The proposed method of forming air-speed parameters is used both in the normal flight mode and in the low-speed mode, which, unlike the standard one, is problematic for the ASF and the DUAS, since the information they measure at flight speeds less than 100 km / h loses its credibility.

In the normal flight mode, when the measured SHS and DUAS information is reliable, a recurrent procedure is implemented to optimally evaluate the errors of the measured and calculated airspeed signals and identify a priori unknown parameters that determine the values of the angles of the current orientation of the wind speed Δψ _B , α _B and coordinates Δn, Δh, Δе of the relative location of the LDPE and ANN in the projections on the GTS axis ONHE.

так и аналитического значения модуля

скорости ветра и формируют таким образом полный перечень откорректированной воздушно-скоростной информации, необходимой как для решения боевых и специальных задач, так и для пилотирования объекта.In parallel with it, using the estimates of air-speed parameters obtained in the process of optimal filtering and identification, correction of both the measured SHS and DUAS signals is carried out

and analytical value of the module

wind speeds and thus form a complete list of adjusted airspeed information necessary for both combat and special missions, and for piloting an object.

The operations in accordance with which the aforementioned correction and the formation of air-speed information are carried out are represented by expressions (73) - (79).

(75) и запомненные значения углов

его пространственной ориентации используют для формирования его составляющих в проекциях на оси ГСТ ONHE (78), на основе которых формируют полный срез воздушно-скоростных параметров (80)-(84), используя при этом текущие значения соответствующей навигационной и пилотажной информации, измеренной ИНС в режиме инерциально-доплеровской коррекции.10. In the low-speed mode, when the reliability of the measured SHS and DUAS information is lost, the optimal estimation procedure is stopped, the values of estimates of the air-speed parameters obtained before the emergency situation for the SHS and DUAS are remembered and used as initial conditions in the next assessment session, while last adjusted wind speed

(75) and stored angles

its spatial orientation is used to form its components in the projections on the ONHE GTS axis (78), on the basis of which a complete cut of the air-speed parameters (80) - (84) is formed, using the current values of the corresponding navigation and flight information measured by the ANN in inertial-Doppler correction mode.

The next session of the optimal assessment is implemented in the standard operating mode for the SHS and DUAS.

11. The fact that when developing the proposed method for forming air-speed parameters, the communication equations (28) are used is not accidental, since it seems that only in this case the description of the air-speed parameters is carried out from system-wide positions.

Indeed, in addition to the technique that is directly used in the formation of equations (28), this approach presupposes the obligatory preliminary formation of the airspeed components in the projections on the Oxyz SSK axis (35), in accordance with its definition as the speed of the object relative to the wind.

The bulkiness of the working expressions obtained in this case is a logical consequence of the approach used to form the selected communication equations.

It seems that in the case of using a scalar notation of a vector expression of the form:

in projections on the SSK axis Oxyz, the communication equations and, as a consequence, the entire subsequent synthesis procedure, will be somewhat simplified.

But even in this case, those fundamental methods of synthesis should be used that make up the physical and mathematical essence of the proposed solution.

The main ones are the following:

- a mathematical model that describes the nature of the change in the air-speed parameters of the state of the system, such as errors in measuring the angles of attack Δα and slip Δβ and the airspeed module ΔV, as well as the current values of the parameters sΔψ _B , сΔψ _B , α _B that determine the spatial orientation of the wind speed , including the error Δu of its calculation, must have the form presented during the implementation of the invention;

- for the purpose of a correct mathematical description of the communication equations, of the form (85), and, as a result, increase of observability, speed and accuracy of the optimal estimation of the entire list of air-speed state parameters, the model of their changes presented above is expanded to include differential equations of the form (34.4 ), describing the nature of the change in the coordinates Δn, Δh, Δе of the relative location of the LDPE and ANN in the projections on the GTS axis ONHE;

для решения поставленной задачи представляется целесообразным использовать известный прием замены идеальных значений x_j рассматриваемых параметров их физически равноценными значениями, равными

(39), где Δx_j - неизвестная, подлежащая оцениванию погрешность измерения или расчета сигнала

- taking into account the fact that the constraint equations (28), (85) are valid exclusively for the ideal values x _{j of the} parameters included in them, but, as a rule, some of them are either not known at all (sΔψ _B , сΔψ _B , α _B , Δn, Δh, Δе), or their current erroneously measured values are known

To solve this problem, it seems appropriate to use the well-known method of replacing the ideal values x _{j of the} considered parameters with their physically equivalent values equal to

(39), where Δx _j is the unknown measurement error or signal calculation error to be estimated

Obtained after the indicated replacement of the communication equations lead to a form convenient for determining the measurement signals z _j and the elements h _ij (i = 1-3, y = 1-13) of the observation matrix;

- in order to concretize the problem under consideration and reduce it to the framework of estimation and correction, exclusively of air-speed parameters, it seems appropriate to carry out its decision taking into account the fact that the inertial information used in this case is measured by ANN functioning in the mode of inertial-Doppler estimation of its errors and with correction carried out according to an open circuit, in this case, when the reliability of the measured DISS information is lost, the evaluation procedure is stopped and, without interrupting the correction, they are implemented about the results of the forecast of the received estimates.

In this case, in the synthesis of a complex inertial-Doppler system, it is necessary to use the following new engineering-practical and reasonably effective techniques and mathematical procedures.

One of the main methods of synthesis of the optimal procedure of inertial-Doppler estimation and correction effective in accuracy and speed is dictated by the need for algorithmic accounting for the relative placement of the ANN and DISS information systems involved in this mode.

Disregard of the coordinates of the ANN placement relative to the DISS when the object performs highly dynamic maneuvers, such as a “snake”, of coordinated or combat turns leads to the appearance of mathematically indescribable kinematic velocity components in the measurement signals, which, being algorithmically unaccounted for, instead of the methodically justified and expected estimation of all state parameters, including and slightly observable, leads to a completely opposite result, namely, to the divergence of the estimation procedure.

To implement algorithmic accounting for the relative location of the ANN and DISS, it is sufficient to expand the error model traditional for the ANN by including a system of three first-order differential equations describing the nature of the change in the relative coordinates Δξ, Δη, Δζ, and location of the indicated information systems on the object in projections on the reference axis trihedron of the ANS gyro platform.

From simple physical considerations, it can be shown that these equations will have the following form:

- составляющие угловой скорости вращения объекта относительно опорного трехгранника гироплатформы ИНС Oξηζ;

- кинематические составляющие скорости перемещения ИНС относительно ДИСС.Where

- components of the angular velocity of rotation of the object relative to the reference trihedral of the gyro platform ANN Oξηζ;

- kinematic components of the speed of the ANN relative to the DISS.

The inclusion of the above differential equations (85.1) in the projections on the OTGP axis of the ANN Оξηζ into the structure of the ANN error model correction traditional for the inertial-Doppler mode allows to obtain its extended model, which describes not only the ANN parameters and their relationships, but also those kinematic components measurement signals that were not previously taken into account.

The extension of the ANN error model allows eliminating the main cause of the algorithmic inconsistency of the known correction algorithms, which consists in an incorrect mathematical description of the original system, and thereby ensure guaranteed observability and stable convergence of all and, first of all, weakly observed parameters of the ANN state, such as the azimuthal angle α _z gyro platform departure and ε drift _at the ANN longitudinal channel.

Moreover, only in this case, algorithmic accounting and elimination of all undesirable consequences that result in mathematically undescribed kinematic velocity components occurring during the maneuver of the object and due to the geometry of the relative placement of the information systems involved in the considered mode can be provided algorithmically and simply enough.

Of great practical importance is the mathematically rigorous, structurally closed, unified procedure for algorithmic accounting of current errors in calculating / measuring navigation information and its effective correction according to the results of an optimal assessment or forecast.

The use of this procedure in the mode of inertial-Doppler estimation and correction is carried out each time, when the measurement signals of the optimal filter-identifier are generated.

When forming them, it is necessary to know the mathematical description of both the ANN output signals and similar signals generated from the DISS measurements using additional measurements of a number of navigation and flight parameters with the ANN.

It should be noted that during the development (derivation) of the ANN error model, the form of the analytical representation of its output signals by speed is important, which not only determines the type of the observation (measurement) matrix, but the ANN error model itself also depends on it.

Without citing or analyzing the possible forms of this representation, we note that the most common, developed and acceptable for solving the problem under consideration is a representation of the form:

where V _ξ , V _η , V _ζ are the components of the absolute linear velocity of the object in the projections on the axis of the OTGP ANN; α _x , α _y , α _z - the mismatch angles of the real and reference trihedrals of the GP; ΔV _x , ΔV _y are the measurement / calculation errors of the horizontal components of the absolute velocity, which, along with the small angles α _x , α _y , α _{z of the} mismatch, are included in the list of parameters of the ANN state.

The components (85.2) are purely inertial in their physical essence and do not explicitly include kinematic velocity components (85.1).

The kinematic components of the velocity will be presented when comparing the velocity components (85.2) and similar components formed from the current measurements of the DISS.

Before proceeding to the consideration of these issues, it is advisable to note that in this case, for the first time in the practice of developing such algorithms, the known kinematic relations connecting the errors Δϕ, Δλ, Δχ of the autonomous inertial calculus of the main navigation parameters, namely, the geographical latitude ϕ, will be used longitude λ and χ angle of azimuthal orientation of the reference trihedron gyroplatform ANN and error Δυ, Δγ, Δψ _r main measurement triple flight pitch angles υ, γ, and roll rate gyro ψ _r small errors α _x, α _y keeping the vertical angle α _z ANN azimuthal care its gyroplatform GP.

The indicated ratios have the following form:

When forming the horizontal components of the absolute linear speed of the object according to the DISS measurements using the calculated ANNs of the current values of the geographical latitude and the azimuthal orientation angle of the reference trihedron of its gyro platform, the following mathematical operations should be performed:

путевой скорости в проекциях на оси связанной с объектом системы координат к осям опорного трехгранника гироплатформы ИНС;- reduction of the measured DISS components

ground speed in projections on the axis of the coordinate system associated with the object to the axes of the supporting trihedron of the ANS gyro platform;

абсолютной линейной скорости, обусловленной суточно-годовым вращением Земли.- calculation of horizontal components

absolute linear speed due to the daily-annual rotation of the Earth.

The first operation can be quite simply implemented in accordance with the vector-matrix expression (21.2).

(21.3), выражения для расчета составляющих

будут иметь следующий вид:So, in accordance with (21.2) and the form of the matrix

(21.3), expressions for calculating the components

will have the following form:

путевой скорости объекта по измерениям ее компонент

в проекциях на оси ССК Oxyz предполагают использование точных углов ψ_г, υ, γ эволюции объекта.The above expressions for calculating the components

the path velocity of the object by measuring its components

in projections on the axis of the SSC Oxyz suggest the use of exact angles ψ _g , υ, γ of the evolution of the object.

Not having the indicated angles, we substitute in the expressions (85.5) instead of ψ _g , υ, γ their values determined by the relations:

- измеренные значения углов эволюции объекта; Δγ, Δυ, Δψ_г - погрешности их измерения.in which

- measured values of the angles of evolution of the object; Δγ, Δυ, Δψ _g - errors of their measurement.

(85.5), приведет к их следующему представлению:It can be shown that the substitution (85.6) in the expressions for

(85.5), will lead to their following representation:

путевой скорости и ошибок

их расчета:where the following notation is used for erroneously calculated components

ground speed and errors

their calculation:

Substituting in (85.9) instead of Δψ _g , Δυ, Δγ their values in the function of small angles α _x , α _y , α _{z of the} mismatch between the real and the reference trihedra of the INS GP (85.4), we obtain their following representation:

in which the following notation is accepted:

следует понимать соответствующие элементы матрицы

(21.3), но в функции измеренных углов эволюции объекта

In the above expressions (85.9), (85.11) under

understand the relevant elements of the matrix

(21.3), but as a function of the measured angles of evolution of the object

All subsequent operations will be performed based on the use of inertial information and kinematic relations (85.3), connecting the calculation errors of the main navigation parameters Δϕ, Δλ, Δχ with small angles α _x , α _y , α _{z of the} mismatch between the real and the reference trihedra of the INS GP.

Given that these operations are presented for the first time, we present them without abbreviations.

линейной скорости, обусловленной суточным вращением Земли:We write the expression for the ideal eastern component

linear velocity due to the daily rotation of the Earth:

where ϕ is the ideal value of geographical latitude.

Given that the ideal latitude, in the general case, is not known, we represent it in the form:

- счисленное значение широты, а Δϕ - погрешность ее счисления.Where:

is the calculated value of latitude, and Δϕ is the error of its calculation.

:Substituting (85.14) into (85.13), taking into account the relation for Δϕ (85.3), we obtain the following expression for

:

Included in (85.15) is the main radius R _{E of the} terrestrial ellipsoid of revolution, defined by an expression of the form:

we write in the following form, more suitable for further consideration:

In expressions (85.16) and (85.17), e ² should be understood as the square of the first eccentricity of the Earth's ellipsoid of revolution, which, for the measurements made by F.N. Krasovsky, is equal to e ² = 0,0066934; h is the baroinertial height of the object.

We substitute the relation (85.14) in (85.17). As a result, up to values of the first order of smallness with respect to Δϕ, we obtain:

Where

(85.15) получим следующее выражение для восточной составляющей линейной скорости, обусловленной суточно-годовым вращением Земли:Substituting (85.18) into the expression for

(85.15) we obtain the following expression for the eastern component of the linear velocity due to the daily-annual rotation of the Earth:

и ΔR_E (85.18), выражение (85.19) примет вид:Subject to the designations adopted for

and ΔR _E (85.18), expression (85.19) takes the form:

We write the last expression in a more acceptable form for further consideration:

на оси опорного трехгранника гироплатформы ИНС будут равны:Projection Expression

on the axis of the reference trihedron of the gyro platform, ANNs will be equal to:

Given that the ideal value of the azimuthal orientation angle of the supporting trihedron of the ANS gyro platform is:

(85.22) примут вид:expressions for horizontal components

(85.22) will take the form:

(85.21). В результате, с точностью до величин первого порядка малости относительно Δϕ и Δχ, получим следующие выражения для составляющих

и

We substitute in (85.24) the expression for

(85.21). As a result, up to values of the first order of smallness with respect to Δϕ and Δχ, we obtain the following expressions for the components

and

If the corresponding components of the ground speed (85.7) are added to the components (85.25), then, with accuracy determined by the first-order smallness values with respect to small quantities of the form Δϕ and Δχ, horizontal components of the absolute linear velocity of the object will be obtained. We give them:

In the future, despite the fact that during the formation (85.26) not only the information measured by the DISS was used, these components of the absolute linear velocity will be interpreted as the velocities formed from the measurements of the DISS.

описываются представленными выше выражениями (85.8) и (85.10).Speed components included in (85.26)

are described by expressions (85.8) and (85.10) presented above.

(85.25) абсолютной линейной скорости, обусловленные вращением Земли, целесообразно представить в следующем виде:Ideal Components Obtained Above

(85.25) of the absolute linear velocity due to the rotation of the Earth, it is advisable to present in the following form:

In the above expressions, in accordance with (85.25), the following notation is used:

Taking into account (85.27), expressions (85.26) will take the form:

It seems appropriate to express (85.29) as follows:

скорости (85.1), имеющие место при маневреном полете объекта и обусловленные координатами относительного размещения рассматриваемых информационных систем (ИНС, ДИСС), получим следующие уравнения связи:Comparing the corresponding expressions (85.2) and (85.30), subtracting the left parts of the expressions (85.30) from the left parts of the expressions (85.2) and similarly, for the right parts of the indicated expressions, taking into account the kinematic components

speeds (85.1) that occur during maneuverable flight of the object and due to the coordinates of the relative placement of the information systems under consideration (ANN, DISS), we obtain the following communication equations:

We denote the left-hand sides of the given coupling equations by z ₁ and z ₂ , meaning the measurement signals observed against the background of uncorrelated measurement noise V ₁ and V ₂ with known intensities:

и (85.8) для

получим развернутое представление для сигналов измерения z₁ и z₂:Substituting in (85.32) the expressions (85.28) for

and (85.8) for

we obtain a detailed representation for the measurement signals z ₁ and z ₂ :

We will consider the above expressions as expressions for calculating the measurement signals of the optimal filter identifier for the parameters of the complex inertial-Doppler system.

подставим соответствующие выражения (85.28) и (85.10). В результате получим следующее развернутое представление матричного выражения вида:On the right-hand sides of the obtained coupling equations (85.31) instead of

we substitute the corresponding expressions (85.28) and (85.10). As a result, we obtain the following detailed representation of a matrix expression of the form:

z = Hx + W,

where x is the vector of the state parameters of the system in question, H is the observation matrix.

и

(85.28) представить в функции инерциально-доплеровской системы параметров состояния. Для этого вместо Δϕ и Δχ необходимо подставить в них соответствующие соотношения системы (85.3).But before performing the substitutions mentioned above, expressions for

and

(85.28) represent in the functions of the inertial-Doppler system of state parameters. For this, instead of Δϕ and Δχ, it is necessary to substitute the corresponding relations of the system (85.3) into them.

As a result, we get:

Grouping the terms in the above expressions according to the state parameters α _x , α _y , α _z , we obtain their following representation:

We give a compact representation of the obtained expressions:

where the following notation is accepted:

(85.28) к алгоритмически целесообразному виду (85.36) могут быть реализованы упомянутые выше операции по приведению правой части уравнений связи (85.31) к виду, удобному для формирования элементов матрицы наблюдения.After casting the expressions for

(85.28) to an algorithmically appropriate form (85.36), the above operations can be implemented to bring the right-hand side of the communication equations (85.31) to a form convenient for generating elements of the observation matrix.

For this, we substitute (85.36) and (85.10) into (85.31). As a result, we obtain the following representation for the measurement signals:

After reducing such terms in the expressions for z ₁ and z ₂ (85.38), they will take the following form:

To form the observation matrix, it is necessary to know the order of the state parameters of the system in question in the vector of estimated parameters. We give it:

In accordance with (85.39) and (85.40), the observation matrix will have the following form:

From the obtained observation matrix, it follows that in the considered inertial-Doppler correction mode, practically all state parameters, except for uncompensated drifts ε _х , ε _y , ε _z , have a direct direct connection and, as a result, the output signals are measured by ANN signals, which indicates about the potential observability of these parameters.

The ability of the state parameters of the system under consideration to directly affect the nature of the change in the ANN output signals should be regarded as a necessary condition for their observability.

And the main thing at the same time is to activate these potentially existing relationships between specific parameters and measured output signals. The main tool for managing these relationships is the movement of an object, and specifically, various types of maneuvers performed by it. And this is important, first of all, for controlling the procedure of stable assessment of all state parameters of the system in question and, above all, of the weakly observed ones.

A distinctive feature of the proposed method for the correction of ANN by measuring DISS, which distinguishes it from the whole variety of existing algorithms, is that for the implementation of an effective procedure for optimal estimation and correction, including the correction of autonomously calculated coordinates of the object’s location, for the first time in the practice of developing such algorithms, in addition to algorithmic accounting the geometry of the relative spatial distribution of complimented systems, when generating signals and a measurement matrix, kines are used mathematical relations between the errors in the calculation of the main three navigation parameters Δϕ, Δλ, Δχ and the errors in measuring the evolution angles of the object Δυ, Δγ, Δψ _g with small angles α _x , α _y , α _{z the} mismatch between the real and the reference trihedra of the ANN gyro platform.

And in this case, the aim is primarily to ensure the most correct and mathematically rigorous description of the original system, which works exclusively to achieve the stated above main goal of the proposed correction method, namely, to increase its accuracy and speed.

It is this approach, in the absence of accurate navigation and flight parameters, that allows, up to first-order values of smallness with respect to such parameters as small angles α _x , α _y , α _{z the} mismatch between the real and the reference trihedra of the ANS gyro platform, to obtain the mathematically rigorous and information-rich expressions for determining measurement signals of the optimal error identifier of the ANN and elements of its observation matrix.

погрешностей выдерживания вертикали и оценки

угла азимутального ухода гироплатформы позволяет не только откорректировать составляющие абсолютной линейной скорости V_x, V_y, но и сформировать оценки ошибок

а также

и откорректировать счисленные ИНС навигационные парметры и измеренные углы эволюции объекта.Availability of accurate estimates

vertical retention errors and estimates

angle of azimuthal departure of the gyro platform allows not only to correct the components of the absolute linear velocity V _x , V _y , but also to form error estimates

and

and correct the calculated ANN navigation parameters and the measured angles of the evolution of the object.

To evaluate all ANN errors, the mathematical description of which is presented in the form of an expanded system of interconnected differential equations of the first order with a vector of state parameters of the form (85.40), it is necessary to provide two sections of flight.

In the first horizontal section of a straight flight without accelerations, the so-called “horizontalization” of the gyro platform is carried out with the assessment of the well-observed parameters of the ANN horizontal channels, such as ΔV _x , ΔV _y , α _x , α _y , ε _x and a coordinated (not separate) estimation of weakly observed parameters, of type α _z , ε _y . The duration of this correction section is no more than 4.5-5 minutes, at the end of which, in order to accurately assess the weakly observed parameters, a maneuver is performed, such as a “snake”, coordinated or combat turns.

The duration of the maneuver, as a rule, does not exceed 30-40 seconds.

As a result of its implementation, an accurate assessment of state parameters such as α _z , ε _y , Δξ, Δη, Δζ, as well as the refinement of the estimate of the drift ε _{z of the} azimuthal gyroscope is carried out.

An accurate estimation of the coordinates Δξ, Δη, Δζ of the location of the ANN relative to the DISS is an indicator of the quality of the optimal estimation as a whole.

At the end of the maneuver, the active phase of the optimal error estimation of autonomous inertial numbering is completed, based on a recurrent procedure for processing, filtering, and identifying a constantly updated input sequence of signals generated by ANN and DISS measurements.

After that, the filter-identifier is transferred to the long-term mode - until the next correction session, the forecast of the obtained estimates, according to the results of which, as well as in the process of optimal estimation, all calculated and measured ANN parameters are corrected.

и пилотажных

параметров, включая и истинный курс

объекта, осуществляют в соответствии с кинематическими соотношениями (85.3) и (85.4) и с учетом таких удивительных свойств инерциальных систем, построенных на основе принципа невозмущенного измерения ускорений, которые заключаются в их способности опосредованно «запоминать» и «хранить» информацию о текущих значениях ошибок автономного инерциального счисления.The navigation correction procedure itself

and aerobatic

parameters, including the true course

object, carried out in accordance with the kinematic relations (85.3) and (85.4) and taking into account such amazing properties of inertial systems built on the basis of the principle of unperturbed measurement of accelerations, which consist in their ability to indirectly "remember" and "store" information about current error values autonomous inertial reckoning.

Formally, these properties are precisely represented by the above relationships.

And their physical meaning lies in the fact that the current values of the errors Δχ, Δλ, Δϕ (85.3) of the calculation of the main three navigation parameters χ, λ, ϕ and errors Δψ _g , Δγ, Δυ (85.4) measure the current angles ψ _g , γ, υ the evolution of an object can be determined by the optimal estimation of such parameters of the ANN state as the small angles α _x , α _y , α _{z of the} departure of the real GP of the ANN (virtual GP for SINS) relative to its reference trihedron, included in (85.3) and (85.4).

малых углов α_х, α_у, α_z ухода реальной/виртуальной ГП ИНС/БИНС относительно ее опорного трехгранника, полученными в процессе инерциально-доплеровского оценивания, и счисленными/измеренными значениями навигационных ϕ, λ, χ и пилотажных параметров ψ_г, γ, υ достаточно просто могут быть сформированы оценки

ошибок счисления навигационных параметров и оценки

ошибок измерения углов эволюции объекта, и откорректированы все ошибочно счисленные/измеренные параметры ИНС, включая и истинный курс.Thus, having the current valuation values

small angles α _x , α _y , α _{z of the} departure of the real / virtual GP INS / SINS relative to its reference trihedron, obtained in the process of inertial-Doppler estimation, and the calculated / measured values of the navigation ϕ, λ, χ and flight parameters ψ _g , γ, υ simple enough estimates can be formed

number errors of navigation parameters and estimates

errors in measuring the angles of evolution of the object, and all incorrectly calculated / measured ANN parameters, including the true course, are corrected.

In this case, the correction of the true course ψ _{and the} object is carried out according to the same scheme as the navigation and flight parameters presented above.

ошибки определения истинного курса объекта будет равно:In accordance with (85.3) and (85.4), it can be shown that the current value of the estimate

errors determining the true course of the object will be equal to:

может быть определено в соответствии с выражением:Therefore, the corrected true rate value

can be determined in accordance with the expression:

определения истинного курса объекта не зависит от угла α_z азимутального ухода ГП ИНС, являющегося следствием нескомпенисрованного ухода ε_z ее ГП.It follows from the presented correction procedure that the error estimate

determining the true course of the object does not depend on the angle α _{z of the} azimuthal departure of the GP ANN, which is the result of uncompensated departure ε _{z of} its GP.

From the above description of the proposed method for the formation of air-speed parameters of a maneuverable object, it follows that the essence of the proposed method is disclosed and the technical result of the invention is achieved.

Claims (1)

A method for generating air-speed parameters of a maneuverable object, based on the joint processing of primary air-speed information, including the measured values of the airspeed module V and attack angles α and slip β, measured by the air signal system (SAS) and the sensor of angles of attack and slip (DACS), its orientation relative to the coordinate system (SSC) Oxyz associated with the object, the current calculated value of the module u of the wind speed and the unknown, subject to evaluation, functional parameters cosΔψ_B, sinΔψ_B, α_B its spatial orientation relative to the horizontal coordinate system (HSC) Ox_Gy_Gz_G object, and formed by the results of inertial-Doppler correction of angles of the true course ψ_and, roll γ and pitch υ of the object, constituting

 and module

 its ground speed with its current spatial orientation relative to HSC Ox_Gy_Gz_G object calculated values of drift angles α_CH and inclination of the trajectory α_NT, the results of which form a complete array of air-speed information, characterized in that the model of errors used in air-speed parameters is expanded by including a mathematical description of the coordinates Δn, Δh, Δе of the location (on the object) of the air pressure receiver (LDP) relative to the inertial navigation system (ANN), which is represented as a system of three interconnected differential equations of the first order in the projections on the axis of the geographic accompanying trihedron (GTS) ONHE, which ensures vayut correct formation of a system of three physically reasonable and mathematically rigorous constraint equations, which are obtained based on the calculated expression for the input signals z₁z₂z₃ the optimal filter identifier of the air-speed parameters and elements of its observation matrix, implementing a closed, built-in optimal estimation structure, procedure for automatically taking into account the kinematic difference in ground speed measured by the integrated inertial-Doppler system at the ANN location and its value corresponding to the LDPE installation location, drastically narrowing the range of possible reasons for the divergence of the procedure for the optimal estimation of air-speed parameters in standard maneuver for SHS and DUAS flight, in addition, in the formation of air-speed communication equations using the method of replacing the ideal values of x_j air-speed parameters by their physically adequate representation of the form

 and after reformatting the obtained communication equations, they bring them to a form convenient for generating measurement signals z_i and elements h_ij (i = 1-3, j = 1-13) observation matrices, which are characterized by row-wise fulfillment of equalities of the form

 and in the mathematical description of errors in measuring air-speed parameters, such as ΔV, Δα, Δβ, models that are easily implemented and supported by experimental data are used, which, together with a model describing the nature of the change in the spatial orientation of the wind speed, ensure guaranteed observability, speed and accuracy of the optimal estimation of all air-speed parameters in standard maneuverable flight modes for the ASF and DUAS, while the navigation and flight information measured by the ANN is generated in essay and according to the results of inertial-Doppler estimation, during the implementation of which the error model traditional for the ANN is expanded by including differential equations describing the nature of the coordinate changes Δξ, Δη, Δζ, the location of the ANN relative to the Doppler meter of velocity components (DISS) in projections on the axis of the supporting trihedral of the gyro platform ANN Оξηζ, which provides a mathematically rigorous description of the complex inertial-Doppler system and eliminating one of the main reasons for the divergence of its filter in m nevrennom flight characteristics achieved by increasing the accuracy of estimating the INS errors and correcting its output information, the implementation of which, as well as in the synthesis of the procedure optimal inertial-Doppler evaluation, based on a complex processing of notation INS horizontal components V_x, V_y absolute linear velocity of the object, geographical latitude

 its current location, angle

 azimuthal orientation of the supporting trihedron Oξηζ, its gyro platform, measured angles of the gyroscopic course

 roll

 and pitch

 object, and Doppler components

 ground speed, instead of ideal values of inertial parameters x_j use their adequate representation of the form

 and kinematic relations of the relation of errors of the main three navigation

 and aerobatic

 parameters with small angles α_x, α_at, α_z the mismatch between the real and the reference trihedra of the ANN gyro platform, and comparing the calculated ANN horizontal components V_x, V_y absolute linear velocity and similar complex components

 absolute speed, they obtain high-speed inertial-Doppler communication equations, from which the functions of the measured navigation and flight parameters of the ANN form calculation expressions for the input signals of the filter-identifier and elements of its observation matrix, which ensures the synthesis of a mathematically closed unified automatic procedure built into the optimal estimation structure , accounting errors of calculation / measurement of navigation and flight information and its effective correction as in the process of optimal estimation of ANN errors, as well as according to the forecast results, while restoring the full array of air-speed information in the low-speed and hover mode, the hypotheses of the stationary wind speed are carried out with validity and are realized by solving the inverse problem of the spatial velocity triangle.

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