RU2713582C1 - Method for optimal estimation of errors of an inertial navigation system and its correction on a fixed ground landmark with known geographical coordinates - Google Patents

Abstract

FIELD: navigation systems.

SUBSTANCE: invention relates to measurement information systems and combat aircraft and helicopter systems, in which method is developed for optimal estimation of complete list of inertial navigation system (INS) state parameters and effective correction of navigation and flight information measured by it. Method for optimal estimation of errors of inertial navigation system and its correction along fixed landmark with known geographical coordinates includes angular tracking of fixed landmark of correction (LC) and discrete measurement of the inclined distance to it in sparing mode for the laser range finder from the sighting system composition mode with frequency of emitting parcels of 0.5–1.0 Hz and is based on combined processing of measured current viewing angles of lC and inclined distance to it, current angles of true and gyroscopic courses, roll and pitch of object and counted INS of geographical coordinates of its location and current baro-inertial height. At that, in the mode of continuous angular tracking of the lC, one-two-second time intervals between adjacent measurements of the range to the lC are filled with its ten-Hz design values, which are formed in accordance with modified, invariable to the underlying surface of the elevation procedure for determining the inclined range, involving use of the current baro-inertial height of the object, the cosine of the angle between the geographical vertical and the direction of the lC, and formed by lC measurements of reference altitude of altitude above sea level, wherein components of the absolute linear speed of the object are estimated in accordance with the kinematic model of its motion relative to the fixed ground-based optical system in the projections on the axis of the inertial coordinate system. At that, two parallel operating procedures of optimal estimation are implemented – primary and auxiliary, first of which provides evaluation of extended vector of INS state parameters and subsequent correction of its navigation and piloting parameters, and second – formation of adequate with SNS position and speed signals used in main procedure of optimal estimation as signals of ideal meter.

EFFECT: broader functional capabilities of the sighting and navigation system of modern aircraft.

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Description

The invention relates to the field of measuring information systems and complexes of combat aircraft and helicopters, in which the development of a unified method for optimal assessment of the complete list of state parameters of an inertial navigation system (ANN) and effective correction of the navigation and flight information measured by it is described.

There is a method of determining current errors in calculating the geographical coordinates of the location of an aircraft (LA) and their correction according to the results of hardware angular tracking of a correction landmark (OK) with known geographical coordinates with the measurement of the current angles of its relative orientation and inclined range to it.

The specified method is presented in the monograph O.A. Babich "Information processing in navigation systems", M., "Engineering", 1991 [1] (subsection 3.4.1, pp. 225-229).

Consideration of its essence is advisable to start with the solution of the so-called direct problem and after presenting the parameters used in its solution, mathematical transformations and calculation relations, proceed to consider the inverse problem, in which the essence of the method that is proposed to be used as the closest analogue of the proposed algorithmic solution is revealed .

The essence of the direct task ([1], p. 226) is quite trivial and consists in determining the current values of the range, azimuth and elevation angle of the direction to the correction landmark with known geographical coordinates. It is assumed that the current, estimated ANN, geographical coordinates of the location of the object are known.

When solving it, the Greenwich coordinate procedure, known in the theory of navigation, guidance and control, is used, which consists in converting the geographical coordinates of the current location of the object and the correction landmark into linear rectangular coordinates in the projections on the axis of the Greenwich coordinate system.

будут иметь следующий вид:In the notation adopted below for the geographical coordinates of the current location of the object ϕ, λ, h and the correction landmark ϕ ₀ , λ ₀ , h ₀ , the expressions for calculating the Greenwich coordinates of the object X ', Y', Z 'and OK

will have the following form:

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

All necessary information about used in (1.1) and (1.2) and earth parameters, e ² is below.

The procedure for calculating the desired coordinates (range, azimuth, elevation angle) of the relative orientation of the correction landmark involves the preliminary reduction of the relative Greenwich coordinates of the OK location to the axes of the geographic accompanying trihedron (GTS) of the ONHE object (page 226 [1]).

Here is a complete summary of the expressions for calculating the mentioned ranges ΔD ₀ , azimuth A ₀ and elevation angle θ ₀ relative orientation OK:

- calculation of rectangular Greenwich coordinates relative orientation OK:

к осям географического сопровождающего трехгранника ГСТ ONHE объекта осуществляется в соответствии с векторно-матричным выражением (3), в котором используется матрица (5):- cast components

to the axes of the geographic accompanying GST trihedron, the ONHE object is carried out in accordance with the vector-matrix expression (3), in which the matrix (5) is used:

The above expressions are valid for the relative orientation of the GTS ONHE and the Greenwich coordinate system HSC OX'Y'Z 'shown in FIG. 12.

- calculation of the relative range ΔD ₀ , azimuth A ₀ and elevation θ ₀ OK:

до него, определяют текущие значения компонент D_x, D_y, D_z указанной дальности в проекциях на оси связанной с объектом системы координат (ССК) Oxyz. После чего, используя текущие значения истинного курса ψ_и, крена γ и тангажа υ объекта, указанные составляющие дальности приводят к осям ГСТ ONHE объекта и находят тем самым компоненты дальности D_N, D_H, D_E. Их аналог представлен 1-ой строкой системы (3.91) [1]. Используя указанные составляющие дальности D_N, D_H, D_E и относительные координаты текущего местоположения ОК

в проекциях на оси гринвичской системы координат (ГСК) (1.3), формируют некие уравнения, связывающие гринвичские координаты текущего местоположения объекта X', Y', Z' (ϕ, λ, h) и компоненты дальности D_N, D_H, D_E. Аналог указанных уравнений связи представлен на стр. 227 [1].In the inverse problem, according to the measured values of the angles ϕ _y , ϕ _{z of the} sighting OK and inclined range, measured by the survey-aiming system (OPS)

to it, determine the current values of the components D _x , D _y , D _{z of the} specified range in projections on the axis of the Oxyz coordinate system associated with the object (CCK). Then, using the current values of the true heading ψ _and , roll γ and pitch υ of the object, the specified range components lead to the axes of the GTS ONHE of the object and thereby find the range components D _N , D _H , D _E. Their analogue is represented by the first line of the system (3.91) [1]. Using the specified range components D _N , D _H , D _E and the relative coordinates of the current location OK

in the projections on the axis of the Greenwich coordinate system (HSC) (1.3), some equations are formed that connect the Greenwich coordinates of the current location of the object X ', Y', Z '(ϕ, λ, h) and range components D _N , D _H , D _E . An analogue of the indicated coupling equations is presented on page 227 [1].

Formalizing the above description of the procedure for solving the inverse problem, we present a complete list of mathematical operations and the expressions that implement them, in accordance with which the communication equations mentioned above are formed:

- the calculation of the components D _x , D _y , D _{z of the} range to the correction reference point according to the measurements of the SPS in projections on the axis of the SSC Oxyz is carried out in accordance with FIG. 5 and the vector-matrix expression (16), in which the matrix L ^{T of the} form (18) is used:

(29):The recalculation of the ranges obtained from measurements of the OPS components D _x , D _y , D _z (1.6) on the GTS axis of the ONHE facility is carried out in accordance with FIG. 6 and the vector-matrix expression (27) with the matrix used in it

(29):

до ОК и сформированным неким комбинированным устройством, совмещающим в себе оптический визир и курсовертикаль, текущим значениям углов азимута и угла места на ОК.In the closest analogue, the above mathematical procedures (1.6) and (1.7) for calculating the range components D _x , D _y , D _z and D _N , D _H , D _E are combined into one, which provides a direct calculation of the components D _N , D _H , D _E by measured oblique range

to OK and formed by some kind of combined device that combines an optical sight and a vertical line, the current values of the azimuth and elevation angles on the OK.

Operating experience with sighting systems indicates that such combined devices do not exist, especially with absolutely error-free measurements of azimuth and elevation.

Therefore, below this fact will be regarded as one of the disadvantages of the prototype.

(1.3) дальности, сформированными по результатам навигационных измерений (1.1), (1.2). Приведение составляющих D_N, D_H, D_E дальности до ОК (1.7) к осям ГСК OX'Y'Z' осуществляют в соответствии с векторно-матричным выражением (4).To form mathematically rigorous equations of coupling, it is necessary that the components D _N , D _H , D _{E of the} range (1.7), obtained from the measurements of the OPS, bring to the axes of the HSC OX'Y'Z 'and compare with similar components

(1.3) ranges formed by the results of navigation measurements (1.1), (1.2). Bringing the components D _N , D _H , D _{E of the} range to OK (1.7) to the axes of the HSC OX'Y'Z 'is carried out in accordance with the vector-matrix expression (4).

In the scalar form, the expressions for the range components (1.7) in the projections on the HSC axis OX'Y'Z ', in accordance with (4) and (6), will have the form:

Comparison of (1.3) with (1.8) leads to the following communication equations:

(1.2) известны абсолютно точно, а ошибочными являются счисленные ИНС значения географических координат

текущего местоположения объекта и адекватные им по точности линейные гринвичские координаты

(1.1) - полученные уравнения связи (1.9) правомочно трактовать, как уравнения, связывающие ошибки Δϕ, Δλ, Δh счисления географических координат

и соответствующие им ошибки ΔХ', ΔY', ΔZ' определения гринвичских координат

текущего местоположения объекта.Given that both the geographical coordinates ϕ ₀ , λ ₀ , h ₀ OK, and the Greenwich coordinates obtained on their basis

(1.2) are known exactly, and the calculated ANN values of geographical coordinates are erroneous

the current location of the object and adequate linear accuracy of Greenwich coordinates for them

(1.1) - the resulting communication equations (1.9) can be correctly interpreted as equations relating errors Δϕ, Δλ, Δh of the numbering of geographical coordinates

and the corresponding errors ΔX ', ΔY', ΔZ 'of determining the Greenwich coordinates

the current location of the object.

Indeed, if in the obtained communication equations (1.9) it is assumed that the ideal values of the coordinates ϕ, λ, h and X ', Y', Z 'of the current location of the object are determined by relations of the form:

- счисленные ИНС значения географических координат местоположения объекта;

- полученные на их основе гринвичские координаты; Δϕ, Δλ, Δh, ΔХ', ΔY', ΔZ' - соответствующие ошибки счисления, подлежащие определению, то полученные таким образом уравнения связи будут иметь представленную выше трактовку.Where

- calculated ANN values of the geographical coordinates of the location of the object;

- Greenwich coordinates obtained on their basis; Δϕ, Δλ, Δh, ΔX ', ΔY', ΔZ 'are the corresponding numbering errors to be determined, then the communication equations obtained in this way will have the interpretation presented above.

Δh в проекциях на оси ГСТ ONHE объекта.Indeed, in accordance with the figure of the terrestrial ellipsoid of revolution, it is quite simple to obtain expressions relating the variations of the linear Greenwich coordinates ΔX ', ΔY', ΔZ 'with linear variations

Δh in the projections on the axis of the GTS ONHE object.

We write them in the form of the following vector-matrix expression:

- представленная ниже ортогональная матрица (6), определяемая текущими значениями счисленных географических координат

местоположения объекта.Where

- the orthogonal matrix (6) presented below, determined by the current values of the calculated geographic coordinates

location of the object.

и Δh.Substituting (2) into (1.10) and further into the communication equations of the form (1.9), taking into account the last three relations of the system (1.10), we obtain a system of three algebraic equations with respect to

and Δh.

Its solution allows us to determine the current calculation errors Δϕ, Δλ, Δh of the geographical coordinates of the location of the ANN and correct them in accordance with the last three relations (1.10).

If it is necessary to increase the accuracy of determining the coordinates numbering errors, after the corresponding reassignments are carried out, the second and subsequent iterations can be implemented.

The above method of correcting the calculated ANN of the geographical coordinates of the object’s location according to the type of correction, according to the information-measuring systems used and the basic methods and methods of mathematical transformation of the measured information, can be used as a prototype of the proposed method for correcting the inertial system based on a fixed reference point with known geographical coordinates.

Formalizing the above description of the prototype, stating it in terms used in solving similar problems of mathematical procedures and with emphasis on the physical essence of the operations performed in this case, we give it in the following form.

его ориентации, основанный на совместной обработке углов ϕ_y, ϕ_z визирования ОК и наклонной дальности

до него, формируемых ИНС текущих углов истинного курса ψ_и, крена γ и тангажа υ объекта и основной тройки ϕ, λ, h навигационных параметров, в процессе которой по измерениям ϕ_y, ϕ_z,

формируют текущие значения компонент D_x, D_y, D_z дальности до ОК в проекциях на оси связанной с объектом системы координат (ССК) Oxyz, которые, используя текущие значения углов ψ_и, υ, γ ориентации объекта и координат ϕ, λ его местоположения, последовательно приводят к осям географического сопровождающего трехгранника (ГСТ) ONHE и гринвичской системы координат (ГСК) OX'Y'Z', рассчитывая компоненты D_N, D_H, D_E дальности до ОК в проекциях на оси ГСТ ONHE и компоненты

дальности в проекциях на оси ГСК, дополнительно, используя приведенный срез рассчитывают текущие значения гринвичских координат

объекта и ОК

сравнением которых определяют текущие относительные координаты

местоположения ОК, а сопоставляя их с соответствующими составляющими D_X', D_Y', D_Z' дальности до ОК, формируют систему алгебраических уравнений связи идеальных гринвичских X', Y', Z' и географических ϕ, λ, h координат текущего местоположения объекта, на основе которых, используя прием замены идеальных x_j значений координат объекта их адекватным представлением вида

получают уравнения, связывающие ошибки Δϕ, Δλ, Δh счисления географических координат и соответствующие им ошибки ΔХ', ΔY', ΔZ' расчета гринвичских координат, которые известной в теории фигуры Земли подстановкой, связывающей вариации ΔХ', ΔY', ΔZ' гринвичских координат с линейными вариациями

Δh в проекциях на оси ГСТ объекта, приводят к системе алгебраических уравнений относительно Δϕ, Δλ, Δh, решая которую определяют ошибки Δϕ, Δλ, Δh счисления координат и корректируют их счисленные значения

A method for estimating the errors Δϕ, Δλ, Δh of the calculated inertial navigation system (INS) of the geographical coordinates ϕ, λ of the current location of the object and the complex baroinertial altitude h of its flight and their occasional correction according to the results of a short-term hardware reference to a fixed correction landmark (OK) with known geographical coordinates ϕ ₀ , λ ₀ , h ₀ with measurement of relative coordinates ϕ _y , ϕ _z ,

its orientation, based on the joint processing of angles ϕ _y , ϕ _{z of} sighting OK and inclined range

to it, formed by the ANN of the current angles of the true course ψ _and , roll γ and pitch υ of the object and the main triple ϕ, λ, h of navigation parameters, during which measurements ϕ _y , ϕ _z ,

form the current values of the components D _x , D _y , D _{z of the} range to OK in the projections on the axis of the coordinate system Oxyz associated with the object (SSC), which, using the current values of the angles ψ _and , υ, γ of the object’s orientation and the coordinates ϕ, λ of its location , sequentially lead to the axes of the geographic accompanying trihedron (GTS) ONHE and the Greenwich coordinate system (GSC) OX'Y'Z ', calculating the components D _N , D _H , D _{E of the} range to OK in the projections on the GTS axis ONHE and components

range in projections on the GSK axis, in addition, using the given slice, the current values of the Greenwich coordinates are calculated

object and ok

By comparing which determine the current relative coordinates

OK locations, and comparing them with the corresponding components of D _{X '} , D _Y' , D _{Z '} ranges to OK, form a system of algebraic equations for the connection of ideal Greenwich X', Y ', Z' and geographical ϕ, λ, h coordinates of the current location of the object on the basis of which, using the method of replacing the ideal x _j values of the coordinates of the object with their adequate representation of the form

get equations linking the errors Δϕ, Δλ, Δh of the calculation of geographic coordinates and the corresponding errors ΔX ', ΔY', ΔZ 'of calculating the Greenwich coordinates, which are known in the theory of the Earth's figure by substitution connecting the variations ΔX', ΔY ', ΔZ' of the Greenwich coordinates with linear variations

Δh in projections on the axis of the GTS of the object, lead to a system of algebraic equations for Δϕ, Δλ, Δh, solving which determine errors

дальности до ОК к осям ГСК OX'Y'Z' и ошибок ΔХ', ΔY', ΔZ' расчета счисленных значений гринвичских координат

текущего местоположения объекта.The advantage of this correction method is its invariance with respect to component reduction errors

range to OK to the axes of GSK OX'Y'Z 'and errors ΔX', ΔY ', ΔZ' of calculating the calculated values of the Greenwich coordinates

the current location of the object.

The disadvantages of this method of optimal error estimation of inertial information and its correction by a fixed landmark with known geographical coordinates are:

эволюции объекта.1. Lack of mathematical description and accounting for errors in recalculating the components D _x , D _y , D _{z of the} range to OK in the projections on the SSK axis Oxyz to the GTS ONHE axes, realized by expressions (1.7) and resulting from an erroneous measurement of current angles

evolution of an object.

2. The episodic, one-time nature of the correction with a limited list of estimated and correctable parameters of the ANN, which results in the impossibility of a full correction of the entire list of flight information, including the true course of the object, and the horizontal components of its absolute linear speed.

3. In the event of termination of the hardware, optical contact with the reference used for correction, it is not possible to implement not only long-term (up to 30-40 minutes), but any procedure for predicting the estimated ANN errors and performing subsequent correction based on its results.

The technical result of the invention is to expand the functionality of the aiming and navigation complex of modern aircraft by developing a mathematical procedure unified with inertial-satellite correction mode for optimal estimation of inertial information errors and its full correction according to the results of continuous angular tracking of a fixed landmark with known geographical coordinates to provide an effective solution navigation, combat and special tasks.

до него, текущих углов истинного

и гироскопического

курсов, крена

и тангажа

объекта, счисленных ИНС географических координат

его местоположения и текущей бароинерциальной высоты

дополнительно, в режиме непрерывного углового сопровождения ОК одно-двух секундные временные интервалы между соседними измерениями дальности до ОК заполняют ее десяти герцовыми расчетными значениями, которые формируют в соответствии с модифицированной, инвариантной к рельефу подстилающей поверхности угломестной процедурой определения наклонной дальности, предполагающей использование текущих бароинерциальной высоты объекта, косинуса угла между географической вертикалью и направлением на ОК, и сформированного по измерениям ОПС опорного значения высоты ОК над уровнем моря, при этом оценивание составляющих абсолютной линейной скорости объекта осуществляют в соответствии с кинематической моделью его движения относительно неподвижного наземного ОК в проекциях на оси инерциальной системы координат (ИСК), чем обеспечивают кардинальное упрощение описывающих ее дифференциальных уравнений за счет естественной поканальной декомпозиции модели относительного движения объекта, которую, из соображений повышения точности оценивания, дополнительно, модифицируют, переходя от уравнений для составляющих абсолютной линейной скорости и ускорения объекта в полных сигналах к их вариациям относительно измеренных ИНС текущих значений, при этом компоненты абсолютной линейной скорости движения объекта относительно ОК используют, как известное управление, а полученные в результате процедуры оптимальной фильтрации и идентификации оценки компонент дальности до ОК и составляющих абсолютной линейной скорости объекта используют для формирования позиционных и скоростных сигналов идеального измерителя, путем сравнения которых с соответствующими выходными сигналами ИНС формируют сигналы измерения оптимального фильтра-идентификатора ошибок ИНС и элементы его матрицы наблюдения, через которые осуществляют учет всех ошибок сигналов измерения, при этом процедуру их оптимальной фильтрации и идентификации реализуют в соответствии с традиционной для ИНС моделью ошибок, которую, из соображений корректности ее описания и точности оценивания, расширяют за счет включения в нее трех дифференциальных уравнений, описывающих характер изменения координат местоположения ИНС относительно ОПС в проекциях на оси опорного трехгранника гироплатформы (ОТГП) ИНС, по окончании оптимального оценивания ошибок ИНС, определяемого временем нахождения ОК в зоне оптического контакта с объектом, фильтр-идентификатор ошибок ИНС останавливают, его входные сигналы и коэффициенты усиления обнуляют, а сам фильтр переводят в режим долгосрочного прогноза полученных оценок, который реализуют в соответствии с рекуррентной процедурой формирования априорных ошибок ИНС, а полученные в результате прогноза значения ошибок ИНС используют для коррекции координат текущего местоположения объекта, горизонтальных составляющих его абсолютной линейной скорости, угла азимутальной ориентации ГП ИНС и углов текущей ориентации объекта.The specified technical result is achieved due to the fact that in the method for optimal estimation of errors of inertial information and its correction according to a fixed landmark with known geographical coordinates, including angular tracking of a fixed correction landmark (OK) and discrete measurement of the inclined range to it in a sparing laser rangefinder (LD) from the composition of the survey-aiming system (OPS), its operation mode with a frequency of emitting transmissions of 0.5-1.0 Hz, based on joint processing, is measured x with the current angles ϕ _y , ϕ _{z of the} OK sight and inclined range

to him, the current angles of true

and gyroscopic

courses, roll

and pitch

of an object calculated by the ANN of geographical coordinates

its location and current baroinertial height

additionally, in the continuous angular tracking mode, OK, one-two second time intervals between adjacent measurements of the range to OK fill it with ten hertz calculated values, which are formed in accordance with the modified invariant to the relief of the underlying surface elevation procedure for determining the inclined range, involving the use of current baroinertial heights object, the cosine of the angle between the geographic vertical and the direction to OK, and formed by the measurements of the OPS op the reference value of the altitude OK above sea level, while the components of the absolute linear velocity of the object are estimated in accordance with the kinematic model of its motion relative to the motionless ground OK in the projections on the axis of the inertial coordinate system (ISC), which provides a fundamental simplification of the differential equations describing it due to the natural channel-by-channel decomposition of the model of relative motion of an object, which, for reasons of increasing the accuracy of estimation, is additionally modified I go from the equations for the components of the absolute linear velocity and acceleration of the object in full signals to their variations relative to the measured ANN current values, while the components of the absolute linear velocity of the object relative to the OK are used as a known control, and the component estimates obtained as a result of the optimal filtering and identification procedure range to OK and components of the absolute linear speed of the object is used to form positional and speed signals of an ideal meter, by which, with the corresponding output signals of the ANN, generate measurement signals of the optimal filter-identifier of the ANN errors and the elements of its observation matrix through which all errors of the measurement signals are recorded, while the procedure for their optimal filtering and identification is implemented in accordance with the traditional error model for the ANN, which , for reasons of correctness of its description and accuracy of estimation, it is expanded by including three differential equations in it that describe the nature of the change in coordinates the location of the ANN relative to the OPS in the projections on the axis of the reference gyro-platform trihedral (GST) of the ANN, at the end of the optimal estimation of the ANN errors, determined by the time spent by the OK in the zone of optical contact with the object, the ANN error filter-identifier is stopped, its input signals and amplification factors are reset, and the filter itself is transferred to the long-term forecast mode of the obtained estimates, which is implemented in accordance with the recursive procedure for generating a priori errors of the ANN, and the values obtained as a result of the forecast are significant Error ANNs are used to correct the coordinates of the current location of the object, the horizontal components of its absolute linear velocity, the azimuthal orientation angle of the GP ANN and the angles of the current orientation of the object.

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

To develop a unified procedure for correcting ANNs according to a fixed landmark with known geographical coordinates, it is advisable to introduce the following coordinate systems:

- inertial coordinate system (ISK) OXYZ;

- Greenwich coordinate system (HSC) OX'Y'Z '.

- geographic accompanying trihedron (GTS) ONHE;

- reference trihedral of the gyro platform (OGP) ANN Oξηζ;

- Oxyz coordinate system associated with the object (SSC);

- ray coordinate system (LSC) Ox _Л y _Л z _Л.

In FIG. Figure 1 shows the orientation of the OXYZ GCS, OX'Y'Z 'GCS, and ONHE GTS on the terrestrial rotation ellipsoid. GSK OX'Y'Z 'is the coordinate system associated with the Earth, the axis OX' of which is parallel to the axis of rotation of the Earth, the axis OZ '- lies in the plane of the Greenwich meridian, and the axis OY' complements them to the right orthogonal trihedron and is directed to the West.

OXYZ ISK is an absolutely motionless coordinate system associated with stars. The mismatch between the HSC OX'Y'Z 'and the HSC OXYZ is determined by the angle ut, where u is the angular velocity of the daily-annual rotation of the Earth, t is the current time (Fig. 1).

In FIG. 2 shows the relative orientation of HSC OX'Y'Z 'and GTS ONHE.

Their mismatch is determined by the angles of geographic longitude λ and latitude ϕ.

соответственно.The transition from the axes of the HSC OX'Y'Z 'to the axes of the GTS ONHE is carried out by two successive rotations through the angle λ and the angle ϕ with angular velocities

respectively.

является положительным.Referring to FIG. 2 reference direction of angles λ and ϕ and angular velocities

is positive.

In FIG. Figure 3 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. 3 reference direction of the angle χ and angular velocity

is positive.

In FIG. Figure 4 shows the mutual orientation of the OTGP ANN Oξηζ and 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. 4 reference direction of angles ψ _g , υ, γ and angular velocities

is positive.

In FIG. 5 shows the relative orientation of the SSC Oxyz and the BSC Ox _Л y _Л z _Л.

наклонной дальности до него (фиг. 5).Their mismatch is determined by the angles ϕ _y , ϕ _{z of the} sight OK. The axis ОX _Л ЛСК is directed to a landmark; the vector coincides with the indicated axis for angular tracking OK

slant range to it (Fig. 5).

соответственно.The transition from the axes of the SSK Oxyz to the axes of the LSK Ox _L y _L z _L. is carried out by means of two successive rotations through the angles ϕ _y and ϕ _z with angular velocities

respectively.

является положительным.Referring to FIG. 5 reference direction of angles ϕ _y , ϕ _z and angular velocities

is positive.

In FIG. Figure 6 shows the relative orientation of the ONHE GTS and Oxyz CCK.

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

соответственно.The transition from the axes of the GTS ONHE to the axes of the SSK Oxyz is carried out by means of three successive turns at the angles ψ _and , υ and γ with angular velocities

respectively.

является положительным.Referring to FIG. 6 reference direction of the angles ψ _and , υ and γ and angular velocities

is positive.

In FIG. 7 shows an approximate flight plan of the object relative to the landmark of correction OK with its angular accompaniment to ensure the correction of ANN.

Optical contact with OK and its angular tracking starts from the range D _K to the point of contact K with a circle of radius r _c along which the object is circulated.

For the helicopter shown in FIG. 7 parameters at its flight speed V = 144 km / h can be taken equal to D _K = 3-4 km, r _c = 1.2-1.5 km. With the specified parameter values, the time of optical contact with the OK and its angular tracking will be about 337-360 seconds, which will allow to implement a full-fledged procedure for evaluating and correcting ANNs.

For a combat aircraft, these parameters can be determined and refined based on the results of field work.

In order to reveal the physical and mathematical essence of the proposed correction method, we give a detailed description of the vector-matrix and scalar transformations used, the differential equations of the relative motion of the object and the parameters included in them, as well as the optimal mathematical procedures for linear discrete filtering and Kalman identification.

But before, a few clarifying and anticipating further research points of fundamental importance.

In the future, we will assume that the geographical coordinates of the correction landmark are absolutely accurate and equal to ϕ ₀ , λ ₀ , h ₀ , where h ₀ should be understood as the height of the OK above sea level.

The term “unified method of optimal estimation ...” used is understood to mean its algorithmic and software unification with the optimal filtering and identification procedure used in the optimal estimation of ANN errors in the inertial-satellite correction mode. At the same time, some differences of the considered procedures are allowed, determined by the variations of their observation matrices. The message matrices determined by the ANN error model should be adequate in the cases under consideration.

Considering that the procedure of optimal estimation in the mode of inertial-satellite correction of ANNs is quite worked out, the purpose of this study will be to consider only those specific issues of estimation and correction on the tracking-target system (OPS) accompanied by the television or thermal imaging channel, which allowed to adapt them to the engineering-developed algorithm of inertial-satellite correction as efficiently as possible.

It seems that for this it is necessary and sufficient in the process of angular support of OK on the measurements made by the TSO and the corrected navigation and flight information of the ANN (taking into account the errors of its measurement and calculation) to form the necessary values for the implementation of the correction mode under consideration for the geographical coordinates of the current location of the object and horizontal components its absolute linear velocity, which are used as measurement signals in the standard inertial-satellite correction procedure retitle.

до него будем считать абсолютно точными.We agree that the sighting and sighting system is an ideal sensor of primary information, therefore, the measurements of the viewing angles ϕ _y , ϕ _{z of the} sight OK and the reference values of the inclined range

before it we will consider it absolutely accurate.

Considering that the duration of the procedure for optimal estimation of inertial information errors should be 5-6 minutes, and there are time limitations on the operation of the laser range finder (LD) in the 10 Hz range measurement mode, it is proposed to use the LD in the low-frequency range measurement mode (f = 0, 5-1 Hz) with filling the intervals between the reference measurements of ranges with their calculated values obtained on the basis of a modified elevation method for their determination.

In order to disclose the physical essence and mathematical content of the proposed algorithmic solutions, we present all the necessary vector-matrix relations in accordance with which mutual transformations of the components of an arbitrary vector can be realized for the coordinate systems introduced into consideration.

Vector-matrix expressions for transforming the components of an arbitrary vector defined by projections on the HSC axis OX'Y'Z 'to the axes of the GTS ONHE and vice versa will have the following form:

The matrix G and the transposed matrix G ^T included in expressions (3), (4) have the form:

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 transposed matrix G ^T , in accordance with FIG. 3 are equal to:

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

в соответствии с фиг. 4, имеют вид:where the matrix S ₀ and the transposed matrix

in accordance with FIG. 4, have the form:

The vector-matrix expression for calculating the components of an arbitrary vector in the projections on the LSC axis Ox _L y _L z _L according to its known components in the projections on the LSC axis Oxyz and its inverse expression are:

The matrices L and L ^T included in (15), in accordance with FIG. 5 are equal:

To calculate the components of an arbitrary vector in the projections on the OXYZ ISK axis using its known components in the projections on the LSC axis Ox _Л y _Л z _Л it is necessary to know the matrix corresponding to this transformation.

To determine the type of said matrix find pre-matrix for the calculation of the random component vector in projections onto the axis of GSK OX'Y'Z 'of its components known in the axes Ox LCS _A y _A z _A.

According to (4), (8), (12) and (16), the transformation of an arbitrary vector specified in the axes of the LSC to the axes of the Greenwich coordinate system HSC OX'Y'Z 'can be carried out in accordance with the following matrix expression:

In accordance with the above expression, the matrix of the transformation under consideration is equal to

To transform an arbitrary vector defined by projections on the axis of the ray coordinate system, which should be understood as an oblique range array measured by a laser range finder, to the axes of the inertial reference frame, we use the matrix relation (19) obtained above, in which we mean the matrix G ^T (6) similar in structure, the matrix with the only difference being that instead of the geographic longitude λ counted from the plane of the green meridian, we will use the absolute longitude λ _a equal to:

a t_k - текущее время, которое рассчитывается в соответствии со следующим рекуррентным выражением:where u is the angular velocity of the daily-annual rotation of the Earth

at _k is the current time, which is calculated in accordance with the following recurrence expression:

where τ is the discrete count, which for the problem under consideration is 0.1 sec, t ₀ = 0.

The absolute longitude λ _a is measured relative to the OZ axis (Fig. 1), while the angle between the specified axis and the OZ 'axis is equal to the difference between the absolute λ _a and the geographical λ longitude.

When calculating the current time t _k (21), it must be counted relative to the beginning of a specific mode in which the considered vector-matrix transformation is used:

where G ^T (ϕ, λ _a ) is a matrix structurally similar to the matrix G ^T (6), but in the function ϕ and λ _a (20).

The vector-matrix expression, the inverse of the above (22), will look like:

where G (ϕ, λ _a ) is a matrix structurally similar to the matrix G (5), but in the absolute longitude function λ _a (20).

In accordance with the vector-matrix expressions (3) and (7), as well as taking into account (23), the expression for calculating the components of an arbitrary vector in the projections on the OGP axis Oξηζ using its known components presented in the OXYZ ICS axes and the inverse of it expression have the following form:

The vector-matrix expression for calculating the components of an arbitrary vector in the projections on the SSK axis Oxyz according to its known components in the projections on the GTS axis ONHE and its inverse expression are:

в соответствии с фиг. 6, равны:where the matrix S _g and the transposed (inverse) matrix

in accordance with FIG. 6 are equal to:

In accordance with (3), (26) and (4), (27), using expressions (3) and (4) instead of the matrices G and G ^T, their absolute analogues G (ϕ, λ _a ) and G ^T (ϕ , λ _a ), they obtain a vector-matrix expression for calculating the components of an arbitrary vector in the projections on the axis of the CCS Oxyz according to its known components in the axes of the CSI OXYZ, as well as its inverse expression. We give them:

The above vector-matrix transformations and the matrices included in them allow us to implement a discrete mathematical procedure for the optimal estimation of the components of the absolute linear velocity of the object based on the recursive linear filtering procedure and identification of the components of the range to OK in the projections on the OXYZ CSI axis, observed against the background of random uncorrelated measurement noise.

дальности до ОК по рассчитанным, в соответствии с (16), составляющим D_x, D_y, D_z дальности в проекциях на оси ССК Oxyz.In particular, the vector-matrix expression (31) will be used to calculate the components

range to OK according to the calculated, in accordance with (16), components of D _x , D _y , D _z ranges in the projections on the axis of the CCK Oxyz.

As follows from expression (16), when calculating the components D _x , D _y , D _z , the measured SPS values of the angles ϕ _y , ϕ _{z of the} OK sight (18) and the current value of the inclined range to it are used.

компонент дальности до ОК в проекциях на оси ИСК, в соответствии с векторно-матричным выражением вида:Estimates obtained by the results of optimal filtering

the component of the range to OK in the projections on the axis of the ISK, in accordance with the vector-matrix expression of the form:

they lead to the axes of the ONHE GTS and are used to form the geographical coordinates of the current location of the object, which are used as positional signals of an ideal meter.

абсолютной линейной скорости объекта к осям ОТГП Oξηζ и последующее их использование в качестве скоростных сигналов идеального измерителя.Additionally, in accordance with the vector-matrix expression (24), the estimated components are reduced

absolute linear velocity of the object to the axes of the OTGP Oξηζ and their subsequent use as speed signals of an ideal meter.

In this case, according to the positional and speed signals of the ideal meter formed below and the current values of the geographical coordinates of the location and the horizontal components of the absolute linear velocity of the object calculated by the inertial system, the input signals of the optimal filter-identifier that implement the optimal ANN error estimation are generated.

In the future, we will treat everything related to the optimal estimation of ANN errors as the main procedure for optimal filtering and identification.

In this case, by the auxiliary procedure of optimal estimation, we mean the procedure carried out in accordance with the differential equations of motion of the object relative to a fixed correction landmark in projections on the OXYZ CSI axis.

дальности и оценивание составляющих

абсолютной линейной скорости объекта с их последующим использованием для формирования позиционных и скоростных сигналов измерителя в обеспечение реализации основной процедуры оценивания.Its main purpose is to optimally filter the measured / calculated components.

range and component evaluation

absolute linear velocity of the object with their subsequent use for the formation of positional and speed signals of the meter to ensure the implementation of the basic evaluation procedure.

And in this sense, this procedure is, indeed, auxiliary, performing the functions of information support for the optimal estimation of current errors of the inertial system.

The fact that the auxiliary optimal estimation procedure is carried out in accordance with the model of the relative motion of the object in the projections on the OXYZ ISK axis is not accidental, since only in this case the differential equations of the object’s motion relative to OK are simplified so much that they take the form of three channel-independent independent systems of differential equations of the first order . Get them.

In accordance with the well-known lemma on finding the absolute derivative of a certain vector given in the Course of Theoretical Mechanics, L.G. Loytsyanskogo A.I. Lurie, Volume 1, Moscow, Nauka, 1982 [2] (pp. 301-302), it can be shown that the vector differential equation of the relative motion of the target has the form:

- вектор дальности между объектом и целью;

- векторы абсолютной линейной скорости цели и объекта соответственно;

- вектор абсолютной угловой скорости вращения подвижной системы координат Oxyz;

- символ локальной производной.Where

- the distance vector between the object and the target;

- vectors of the absolute linear velocity of the target and object, respectively;

- the vector of the absolute angular velocity of rotation of the moving coordinate system Oxyz;

is the symbol of the local derivative.

абсолютной угловой скорости которой равны ω_x, ω_у, ω_z, то в этом случае система скалярных уравнений относительного движения цели будет иметь следующий вид:In the scalar representation of the vector equation (33), it must be remembered that it must be written in projections on the axis of the moving coordinate system Oxyz. If Oxyz CCK is selected as mobile, the components

the absolute angular velocity of which are equal to ω _x , ω _y , ω _z , then in this case the system of scalar equations of relative motion of the target will have the following form:

The given system of differential equations describes the relative motion of an object and a target in the most general case. The indicated structure will have differential equations in projections on the axis of the GTS ONHE, OGP Oξηζ.

Differential equations in the projections on the LSC axis Ox _Л y _Л z _Л and ГСК OX'Y'Z 'fall out of this series. A special place in this series is occupied by the case when the absolutely motionless coordinate system, namely, the OXYZ ISK, is taken as the moving one.

The fundamental difference between this option and those presented above is that the absolute angular velocity of the moving (inertial) coordinate system relative to the fixed (inertial) coordinate system will be zero, i.e. ω _X = ω _Y = ω _Z = 0, which leads to a regular simplification of the above system of differential equations (34), which in this case takes the form:

For the first time in the textbook R.V. Mubarakshina, V.M. Balueva, B.V. Voronova "Aiming systems of firing", part 1, VVIA them. NOT. Zhukovsky, 1973, [3] (p. 49, from 5th to 9th lines from the top).

To form a complete model of the relative motion of the target, it is necessary to supplement the differential equations (35) with equations describing the nature of the change in the speed of the target for the case of its movement with constant acceleration. In accordance with the above lemma [2], which establishes the procedure for determining the absolute derivative in a moving coordinate system, these equations will have the following form:

абсолютной линейной скорости движения цели - в рассматриваемом случае, ориентира коррекции, известными, поскольку известны его географические координаты, и ускорения - равными нулю, а составляющие

абсолютной скорости и ускорения а _Х, a _Y, a _Z движения объекта подлежащими оптимальному оцениванию, запишем их в следующем измененном виде:Assuming the components in the above equations

the absolute linear velocity of the target’s movement - in this case, the correction landmark, known since its geographical coordinates are known, and the accelerations are equal to zero, and the components

the absolute speed and acceleration a _X , a _Y , a _Z of the object’s movement subject to optimal evaluation, we write them in the following modified form:

Thus, a system of three channel-independent independent differential equations (36), (37), (38), which in the mode of reference to a moving target is used to optimally estimate its motion parameters, in its modified representation (39), (40), ( 41) is intended for optimal filtering and identification of the object’s motion parameters relative to a fixed landmark, carried out, as in the target snap mode, by measuring the distance to the correction landmark observed against random uncorrelated noise measurements V _X , V _Y , V _Z :

The components of the absolute linear velocity OK in (39), (40), (41) in the projections on the GH axis ONHE are due to the angular velocity of the daily-annual rotation of the Earth and are equal to:

в проекциях на оси ИСК, может быть осуществлен в соответствии с векторно-матричным выражением, обратным (32):Component calculation

in projections on the ISK axis, can be implemented in accordance with the inverse vector-matrix expression (32):

In expressions (43), (44), ϕ ₀ , λ ₀ , h ₀ are the geographical coordinates of OK, while its absolute longitude λ _a is equal to:

измеренных инерциальной системой составляющих

подчиняющимся соотношениям вида:Considering that in the correction mode under consideration, in the process of optimal ANN error estimation, the object, after approaching the correction reference point, enters the circulation mode with the subsequent exit to the course prescribed by the task (Fig. 7), for guaranteed accurate estimation of the components of the absolute linear velocity and acceleration of the object it seems appropriate from estimation option in full signals (39), (40), (41) go to error estimation variant

components measured by inertial system

subject to relationships of the form:

- измеренные/рассчитанные ИНС составляющие абсолютной линейной скорости объекта, приведенные к осям ИСК (25).Where

- measured / calculated ANN components of the absolute linear velocity of the object, reduced to the axes of the ISK (25).

Substituting (46) into differential equations (39), (40), (41) and passing in the equations for the components of velocity and acceleration to their variations, we obtain the following modified system of equations:

The presented technique for modifying the differential equations of the relative motion of the object will practically eliminate possible dynamic errors in estimating the absolute linear velocity of the object in circulation.

абсолютной линейной скорости объекта формируются посредством применения к измеренным инерциальной системой горизонтальным составляющим

абсолютной линейной скорости объекта матричного преобразования вида (25):The components of Eqs. (47), (48), (49)

absolute linear velocity of the object are formed by applying horizontal components to the measured inertial system

absolute linear velocity of the matrix transformation object of the form (25):

в процедуре оптимального оценивания используются, как известные управления.Speed components

In the procedure of optimal estimation, they are used as well-known controls.

абсолютной линейной скорости объекта рассчитываются в соответствии с выражениями вида (46):At the same time, current estimates of the components

absolute linear velocity of the object are calculated in accordance with expressions of the form (46):

оценки ошибок измеряемых ИНС составляющих абсолютной линейной скорости (46).Where

error estimates of the measured ANN components of the absolute linear velocity (46).

измерения счисленных инерциальной системой составляющих

абсолютной линейной скорости, поскольку разработанную на их основе математическую процедуру оптимального оценивания будет отличать высокая степень их поканальной унификации, простота алгоритмической и программной реализации, высокое быстродействие и точность.The above equations (47), (48), (49) are intended for the synthesis of an auxiliary procedure for optimal filtering and identification of measurement signals (42) and error estimation

measuring inertial components calculated by the inertial system

absolute linear speed, since the mathematical procedure for optimal estimation developed on their basis will be distinguished by a high degree of their channel-by-channel unification, simplicity of algorithmic and software implementation, high speed and accuracy.

Here is a summary of the relationships used in the optimal estimation presented in E. Sage, J. Mels, “The theory of evaluation and its application in communication and management”, “Communication”, Moscow, 1976, [4] (p. 269).

The optimal estimation procedure below will be used in the synthesis of the filter-identifier to ensure the estimation of ANN errors.

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 optimal amplification factors:

6. The calculation of the matrix of a priori estimation errors:

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

In the above ratios, 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 system (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.

Here are some considerations regarding the accuracy of estimating the components of the absolute linear velocity of an object.

The assumption that all measurements made by the survey-aiming system are absolutely accurate means the accuracy of calculating the components D _x , D _y , D _{z of the} range to OK in the projections on the Oxyz CCK axis.

With the erroneously measured angles ψ _and , υ, γ of the evolution of the object and the calculated geographical coordinates ϕ, λ of its current location, the components D _X , D _Y , D _{Z of the} range to OK in the projections on the axis of the ISS OXYZ will be calculated with errors due exclusively , by recalculating the distance components from the axes of the CCS Oxyz to the axes of the GTS ONHE and further to the axes of the CSI OXYZ.

абсолютной линейной скорости объекта. Для корректно организованной линейной процедуры оптимальной фильтрации и идентификации согласованность ошибок рассматриваемых параметров в проекциях на оси ИСК является следствием асимптотической сходимости их оптимальных оценок.Errors in calculating the components D _X , D _Y , D _Z range will lead to the corresponding and consistent errors in determining the components

absolute linear velocity of the object. For a correctly organized linear procedure of optimal filtration and identification, the consistency of the errors of the considered parameters in the projections on the ISK axis is a consequence of the asymptotic convergence of their optimal estimates.

дальности к осям ССК Oxyz приведет к ожидаемому устранению ошибок прямого преобразования.Countdown, but component estimates

the distance to the Oxyz SSK axes will lead to the expected elimination of direct conversion errors.

абсолютной линейной скорости объекта в инерциальных осях, так и безошибочность оценок компонент

дальности в связанных осях, учитывая их согласованность с соответствующими оценками составляющих

абсолютной линейной скорости, следует рассматривать как необходимое и достаточное условие безошибочного определения последних в осях ССК Oxyz.Thus, as the error of the discrete array of components of the range to OK in the projections on the axis of the ISK was the cause of the erroneous estimation of the components

absolute linear velocity of the object in the inertial axes, as well as the error-free estimation of the components

ranges in the associated axes, given their consistency with the corresponding estimates of the components

absolute linear velocity should be considered as a necessary and sufficient condition for the error-free determination of the latter in the axes of the CCS Oxyz.

дальности до ориентира коррекции и составляющих

абсолютной линейной скорости в проекциях на оси ССК Oxyz являются абсолютно точными.Based on the foregoing, further, when forming positional and high-speed measurement signals and determining the corresponding elements of the observation matrix, we assume that the component estimates

range to the correction landmark and components

the absolute linear velocity in projections on the Oxyz SSK axis are absolutely accurate.

дальности и составляющих

абсолютной линейной скорости предполагает приведение первых к осям ГСТ ONHE, а вторых -

- к осям ОТГП ИНС Oξηζ.Further use of the assessments in question

range and components

absolute linear speed involves bringing the first to the axes of the GTS ONHE, and the second -

- to the axes of the OTGP ANN Oξηζ.

эволюции объекта и счисления географической широты

а составляющих его абсолютной линейной скорости

- ошибками измерения углов

Given the nature of these transformations, it should be expected that the coordinate errors of the current location of the object will be determined by errors in measuring angles

object evolution and latitude reckoning

and its absolute linear velocity components

- angle measurement errors

We present all the necessary auxiliary operations for obtaining the velocity and positional equations of coupling and the formation on their basis of measurement signals for speed and coordinates, as well as the corresponding elements of the observation matrix of the main optimal estimation procedure.

The mathematical technique that will be used in this case has effectively proved itself in the development of algorithms for optimal estimation and correction of ANNs from measurements of the satellite navigation system (SSS) and the Doppler meter of velocity components (DISS).

With the same efficiency, it can be used in the considered procedure of optimal estimation and correction.

At the same time, expressions (1.10) are used for ideal navigation signals, and for aerobatic signals, relations of the form:

- измеренные значения соответствующих углов; Δψ_г, Δψ_и, Δυ, Δγ - ошибки их измерения.Where

- measured values of the corresponding angles; Δψ _g , Δψ _and , Δυ, Δγ are the errors of their measurement.

Efficiency of use of said reception due to the fact that introduced in consideration of the navigation Δφ errors, Δλ, Δχ and aerobatic Δψ _r, Δψ _and, Δυ, Δγ parameters can be represented as a function of small angles α _x, α _y, α _z mismatch of the real and the reference trihedrons GP INS, namely:

And the fact that the angles α _x , α _y , α _z are included in the list of estimated parameters of the ANN state makes it possible to automate the accounting of the above errors (60), (61) of the numbering of navigation and measurement of flight parameters as part of the standard procedure for optimal estimation by correctly forming positional and velocity elements of the observation matrix.

Here is a detailed description of the procedure for generating high-speed measurement signals and the corresponding elements of the observation matrix.

абсолютной линейной скорости объекта привести к осям ОТГП Oξηζ.Given that the ANN error estimation is carried out in accordance with the system of differential ANN error equations presented in projections on the OTPG axis Oξηζ, the components of the estimates obtained in accordance with the vector-matrix expression of the form (30) are necessary

the absolute linear velocity of the object lead to the axes of the OGP Oξηζ.

имеет вид (14).To do this, we use the vector-matrix transformation (12), in which the matrix used in its implementation

has the form (14).

Representing expression (12) in a scalar form, in accordance with (14), we obtain:

в функции измеренных углов

эволюции объекта и ошибок Δψ_г, Δυ, Δγ их измерения:Substituting in (62) the ideal values of the angles ψ _g , υ, γ (59), we obtain the following intermediate representation of the expressions for

in function of the measured angles

object evolution and errors Δψ _g , Δυ, Δγ of their measurement:

We rewrite the above expressions, revealing in them the sines and cosines of two angles, assuming that the angles Δψ _g , Δυ, Δγ are small:

Opening the above expressions, neglecting the values of the second and more orders of smallness with respect to Δψ _g , Δυ, Δγ, we obtain the following representation for the components of the absolute linear velocity under consideration:

абсолютной линейной скорости объекта целесообразно представить в следующем виде:Expressions (65) obtained above for horizontal components

the absolute linear velocity of the object, it is advisable to present in the following form:

абсолютной линейной скорости объекта и ошибки

их расчета, в соответствии с выражениями (65), будут равны:where are the calculated components

absolute linear velocity of the object and errors

their calculation, in accordance with expressions (65), will be equal to:

To generate speed measurement signals, we write down the expressions for the horizontal components V _x , V _{y of the} absolute linear velocity measured by the ANN.

As experience in the derivation of differential equations describing the nature of changes in ANN errors shows, the traditional and most common form of representing its output signals by speed is a representation of the form:

where: V _ξ , V _η , V _ζ are the components of the absolute linear velocity in the projections on the axis of the OTGP ANN Oξηζ; ΔV _x , ΔV _y - errors of their measurement / calculation; α _x , α _y , α _z - the small mismatch angles introduced above for the mismatch between the real and the reference trihedra of the INS GP.

The components V _ξ , V _η , V _ζ are the components of the absolute linear velocity of the object, measured by the ANN in case of its perfect functioning.

Taking into account the kinematic components ΔV _ξ , ΔV _η , ΔV _{ζ of the} velocity occurring at different constructive placement of the sighting and inertial systems on the object and performing its maneuver, such as "circulation" (Fig. 7), the above expressions (69) should be specified and presented as follows:

Writing the above expressions (66) in a slightly modified form:

and comparing them with the corresponding expressions describing the output signals of the ANN (70), we obtain the following communication equations:

The left-hand sides of the given coupling equations (72) are the result of comparing the corresponding components of the absolute linear velocity, measured by ANNs (70) and formed from OPS measurements (71).

We denote them by z ₃ and z ₄ and in the future we will treat them as signals for measuring the optimal filter identifier for ANN errors:

Expressions (73) are easily realizable, since the signals used in their formation are either measured (V _x , V _y ) or calculated

By the form of the right-hand side of equations (72), the velocity elements of the observation matrix used in the main estimation procedure to calculate the optimal gain (56), the posterior error estimation matrix (58), and also to calculate the optimal estimates of the ANN state parameters (55) are determined.

(68) скорости, характеризующих ошибки расчета составляющих (67), (71).But for this, it is necessary to know the composition of the vector of the ANN state parameters and the mathematical description of the kinematic components ΔV _ξ , ΔV _η , ΔV _{ζ of the} velocity (70) and the components

(68) velocities characterizing the errors in the calculation of components (67), (71).

(68) в функции входящих в перечень параметров состояния ИНС малых углов, характеризующих погрешности α_x, α_у выдерживания вертикали и азимутального ухода α_z гироплатформы ИНС, воспользуемся кинематическими соотношениями связи (61).To describe the latter

(68) as functions of small angles included in the list of parameters of the state of the ANN that characterize the errors α _x , α _for vertical and azimuthal departure α _{z of the} ANS gyro platform, we use the kinematic relations of coupling (61).

группируя их по ошибкам Δψ_г, Δυ, Δγ измерения углов эволюции объекта:But first, we transform the expressions (68) obtained above for

grouping them by errors Δψ _g , Δυ, Δγ measuring the angles of evolution of the object:

(67) и видом матрицы

(14), запишем в более компактном виде:Expressions (74), in accordance with the expressions for

(67) and the form of the matrix

(14), we write in a more compact form:

Substitution in expressions (75) instead of small angles Δψ _g , Δυ, Δγ of measurement errors of the current orientation angles of the object of their values, defined by relations (61), leads to expressions of the form:

After casting such terms, the resulting expressions will take the form:

Given the type designations:

(77) можно представить в следующем компактном виде:expressions for

(77) can be represented in the following compact form:

In order to formulate expressions for the kinematic components ΔV _ξ , ΔV _{η of} velocity included in (70), (72), it is advisable to give differential equations describing the nature of the change in the coordinates of the location of the ANN relative to the OPS in the projections on the OTPG axis Oξηζ

From simple physical considerations, it can be shown that these equations, and at the same time the expressions for ΔV _ξ , ΔV _η , ΔV _ζ , have the form:

- составляющие угловой скорости объекта относительно ОТГП ИНС Oξηζ.Where

- components of the angular velocity of the object relative to the OTGP ANN Oξηζ.

The parameters Δξ, Δη, Δζ, along with the parameters traditional for the ANN, are included in the list of estimated state parameters of the ANN.

We present the full vector X ^{T of} its state parameters:

where ε _x , ε _y , ε _z are uncompensated components of the systematic departure of the gyrostabilized ANN platform.

(79), дифференциальными уравнениями/выражениями (80) и видом вектора параметров состояния ИНС (81), скоростная часть матрицы наблюдения для рассматриваемой процедуры оптимального оценивания ошибок ИНС может быть представлена в виде:In accordance with the coupling equations (72), the expressions for

(79), differential equations / expressions (80) and the form of the vector of state parameters of the ANN (81), the velocity part of the observation matrix for the considered procedure for optimal estimation of ANN errors can be represented as:

with elements h _3j , h _4j (j = 1 ÷ 13) equal to:

скорости, используемые в качестве сигналов измерителя (67) сформированы с ошибками

характер которых известен и описан выражениями (68), (74), (75)-(77), (79), позволяет через матрицу наблюдения (82), (83) учесть все ошибки сформированных по измерениям ОПС составляющих

абсолютной линейной скорости объекта и тем самым обеспечить эффективное оценивание всех, зависящих от рассматриваемых измерений (73), параметров состояния ИНС, причем без ущерба для точности ее коррекции.It is shown above that the approach used in the present invention based on the use of kinematic relations of the error relation Δψ _g , Δυ, Δγ of measuring the evolution angles of an object with small angles α _x , α _y , α _{z of the} departure of a real GP ANN (61), with measurement signals (73), and this is indeed so, since the components

speeds used as meter signals (67) are formed with errors

the character of which is known and described by expressions (68), (74), (75) - (77), (79), allows, through the observation matrix (82), (83), to take into account all the errors formed by the measurements of the SPS components

absolute linear velocity of the object and thereby provide an effective assessment of all parameters of the ANN state that depend on the measurements considered (73), without compromising the accuracy of its correction.

дальности до ОК к осям ССК Oxyz (30) и далее к осям ГСТ ONHE (27) с последующим преобразованием полученных в общем случае, ошибочных линейных компонент дальности

в некоторые угловые составляющие

соответствующие широтно-долготной сетке в точке текущего местоположения объекта.As the main option for calculating the geographical coordinates of the current location of the object, a method is proposed based on the reduction of estimated components

range to OK to the axes of the CCS Oxyz (30) and further to the axes of the GTS ONHE (27) with the subsequent conversion of the generally obtained erroneous linear range components

into some corner components

corresponding to the latitude-longitude grid at the point of the current location of the object.

(29), запишем скалярные выражения для составляющих

дальности до ориентира коррекции в проекциях на оси ГСТ ONHE:In accordance with the vector-matrix expression (27) and the type of matrix used in it

(29), we write the scalar expressions for the components

range to the correction reference point in projections on the ONHE GTS axis:

измеряемых с ошибками Δψ_и, Δυ, Δγ.At real angles of evolution of the object

measured with errors Δψ _and , Δυ, Δγ.

expressions for their true values will be determined by relations (59).

дальности до ОК, как разности ошибочно рассчитанных компонент

дальности и соответствующих ошибок ΔD_N, ΔD_H, ΔD_E их расчета, обусловленных ошибками Δψ_и, Δυ, Δγ измерения углов эволюции объекта:Substituting (59) into (84) allows us to obtain expressions for ideal components

range to OK, as the difference of erroneously calculated components

range and corresponding errors ΔD _N , ΔD _H , ΔD _{E of} their calculation, due to errors Δψ _and , Δυ, Δγ of measuring the angles of evolution of the object:

и ΔD_N, ΔD_H, ΔD_E последовательно проведем описанные выше преобразования выражений (84).To get the desired expressions for

and ΔD _N , ΔD _H , ΔD _E sequentially carry out the above transformations of expressions (84).

дальности до ОК в функции измеренных углов

эволюции объекта и ошибок Δψ_и, Δυ, Δγ их измерения:Substituting (59) into (84), we obtain the following expressions for the components

range to OK as a function of measured angles

object evolution and errors Δψ _and , Δυ, Δγ of their measurement:

After revealing the sines and cosines of the corresponding angles and performing all the transformations necessary to obtain expressions of the form (86), neglecting the values of the second or more orders of smallness with respect to Δψ _and , Δυ, Δγ, we obtain the following intermediate expressions:

расчетные значения линейных компонент дальности до ОК, определяемые, исключительно, измеряемыми углами

эволюции объекта, а под ΔD_N, ΔD_H, ΔD_E - соответствующие погрешности их расчета, определяемые ошибками Δψ_и, Δυ, Δγ измерения углов эволюции объекта, в соответствии с (86) и на основании (88), запишем выражения для рассматриваемых компонент дальности:Understanding by

calculated values of the linear components of the range to OK, determined exclusively by measured angles

evolution of the object, and under ΔD _N , ΔD _H , ΔD _E - the corresponding errors in their calculation, determined by the errors Δψ _and , Δυ, Δγ of measuring the angles of evolution of the object, in accordance with (86) and based on (88), we write the expressions for the components under consideration range:

Considering that in the expressions for ΔD _N , ΔD _H , ΔD _E (90), the small parameters Δψ _and , Δυ, Δγ will be replaced by small angles α _x , α _y , α _{z of} departure of the real GP ANN, it is advisable to group all the terms of these expressions by errors in measuring the current angles of evolution of the object.

After the implementation of this operation, expressions (90) will take the form:

(89) и в соответствии с видом матрицы

(29), полученные выражения для ΔD_N, ΔD_H, ΔD_E (91) можно представить в следующем виде:Given the expressions for

(89) and in accordance with the type of matrix

(29), the obtained expressions for ΔD _N , ΔD _H , ΔD _E (91) can be represented in the following form:

следует понимать соответствующие элементы матрицы

(29), а под

- расчетное значение горизонтированной дальности, которая, в соответствии с фиг. 6, равна:In the above expressions (92) under

understand the relevant elements of the matrix

(29), but under

is the calculated value of the horizontal range, which, in accordance with FIG. 6 is equal to:

In the future, the expression for ΔD _H will not be used, since it is important for the synthesis of the vertical channel of the ANN, which is not the subject of the proposed solution.

(86), (88) до ОК. Гипотетическую потому, что, в действительности, нам известны только расчетные компоненты

дальности (89).Imagine such a hypothetical situation that we know the ideal values of the components

(86), (88) to OK. Hypothetical because, in reality, we only know the calculated components

range (89).

(86) горизонтированной дальности, в соответствии с известными выражениями могут быть рассчитаны соответствующие им идеальные приращения

географических координат текущего местоположения объекта относительно ОК. Приведем их:Using the indicated values of ideal components

(86) horizontal range, according to well-known expressions, their ideal increments can be calculated

geographical coordinates of the current location of the object relative to OK. We give them:

where R _N , R _E are the main radii of curvature of the earth's ellipsoid of revolution:

where a is the semimajor axis of the earth's ellipsoid of revolution; h is the height above sea level; e ² is the square of the first eccentricity:

b - minor axis of the Earth's ellipsoid of revolution.

и ошибок Δϕ и Δλ их счисления.When calculating R _N , R _E, it is advisable to use the baroinertial height, and as the geographical latitude ϕ and longitude λ, their ideal values represented by relations (1.10) as functions of the calculated ANNs

and errors Δϕ and Δλ of their number.

Before presenting expressions (94) in a form suitable for their further use, we transform the above expressions (95) to calculate the principal radii of curvature R _N , R _E.

Considering that the parameter e ² s ² ϕ is small and does not exceed F.N. accepted for the ellipsoid in the whole range of changes in geographical latitude The Krasovsky value equal to 0.0066934 (1946) seems appropriate with the accuracy of expression (95) sufficient for the synthesis of the considered method for optimal estimation and correction to calculate the principal radii R _N , R _{E of the} curvature of the earth's rotation ellipsoid to be written as:

и погрешности Δϕ ее счисления (1.10), с точностью до величины первого порядка малости относительно Δϕ получим следующие выражения для R_N, R_E:Substituting in (96) instead of geographical latitude its representation as a function of calculated latitude

and the error Δϕ of its number (1.10), up to a value of the first order of smallness with respect to Δϕ, we obtain the following expressions for R _N , R _E :

Obviously, expressions (97) can be represented in the form traditional for the current study:

ΔR_N, ΔR_E, в соответствии с (97), имеют вид:where are the expressions for

ΔR _N , ΔR _E , in accordance with (97), have the form:

получим следующие выражения для идеальных значений

отклонения объекта по широте и долготе относительно ориентира коррекции:By writing expressions (94) taking into account (98) and

we obtain the following expressions for ideal values

deviations of the object in latitude and longitude relative to the correction landmark:

обозначение вида:Introducing for a value of the 1st order of smallness with respect to Δϕ and ΔR _E included in the denominator of the expression for

type designation:

we get the following expression for

значения для ΔR_E и

(99), получим его следующее представление:Substituting in the expression for

values for ΔR _E and

(99), we obtain its following representation:

(100) и

(102) в ряд Тейлора в окрестности измеренных значений

ограничиваясь при этом линейными членами разложения, получим следующие выражения для

Expanding the above expressions for

(100) and

(102) in the Taylor series in the vicinity of the measured values

confining ourselves to the linear terms of the expansion, we obtain the following expressions for

(86) приводит, с точностью до величин первого порядка малости относительно ΔD_E, ΔD_N,

ΔR_N, к выражениям вида:Substitution in (104) expressions for

(86) leads, up to values of the first order of smallness with respect to ΔD _E , ΔD _N ,

ΔR _N , to expressions of the form:

Expressions (105) should be written in their traditional form, namely:

- расчетные значения угловых координат положения объекта относительно ОК; Δn, Δе - соответствующие ошибки их расчета, определяемые выражениями:Where

- calculated values of the angular coordinates of the position of the object relative to OK; Δn, Δе - the corresponding errors in their calculation, determined by the expressions:

Based on simple physical considerations, it can be shown that with absolutely accurate coordinates OK (ϕ ₀ , λ ₀ ), the coordinates of the current location of the object will be equal to:

- это расчетные значения координат местоположения объекта. Обозначая их через

запишем следующие выражения для их идеальных значений (108):Given expressions

- These are the calculated coordinates of the location of the object. Labeling them by

we write the following expressions for their ideal values (108):

Otherwise, the above expressions can be written as:

The coordinates of the current location of the object calculated by the inertial navigation system should be described by expressions of the form:

where Δϕ, Δλ are the errors of inertial reckoning, Δϕ _k , Δλ _k are the displacements of the coordinates of the ANN location relative to the OPS. Comparison of the corresponding coordinates of the current location of the object, calculated by ANN (111) and formed according to the results of OK sighting using OPS (110), leads to the following communication equations:

Taking the left-hand sides of the obtained communication equations as positional measurement signals:

according to their right-hand sides, in accordance with the above vector of state parameters of the ANN (81), the corresponding elements of the observation matrix are formed. But for this it is necessary that the components Δϕ _k , Δλ _k , Δn, Δе included in the right-hand side of the coupling equations (112) are represented as functions of the corresponding state parameters of the ANN, which are estimated during optimal filtering and identification. In the case of correction under consideration, this means their dependence on state parameters such as Δϕ, Δλ, Δξ, Δη, α _x , α _in (80), (81).

эволюции объекта.The expressions (92) obtained above, which determine the nature of the change in the components ΔD _N , ΔD _H , ΔD _{E, are} presented in the error function Δψ _and , Δυ, Δγ of the angle measurement

evolution of an object.

To represent the expressions for ΔD _N and ΔD _E , and, consequently, Δn and Δе, in the function of such state parameters as Δλ, α _x , α _y , it is necessary to substitute Δψ _and , Δυ, Δγ in expressions (92) for their values determined the kinematic relations of the relationship Δψ _and , Δυ, Δγ and Δχ, Δϕ, Δλ with small angles of mismatch between the real and the reference trihedra of the INS GP (61) and (60).

Given that by definition:

therefore, substituting in (114) the expressions for Δχ (60) and Δψ _g (61), we obtain the following expression for Δψ _and :

After substituting the kinematic relations defining Δυ, Δγ (61) and Δψ _and (115) into the expressions for ΔD _N and ΔD _E (92), we obtain their representation in the function α _x , α _у , Δλ:

Bringing similar terms into (116), grouping them according to the state parameters α _x , α _y , Δλ, we write them in the following form:

We introduce the following notation for the coefficients for α _x , α _y , Δλ:

Taking into account the introduced notation, the expressions for ΔD _N and ΔD _E (117) can be written in the following form:

положения объекта относительно ориентира коррекции могут быть представлены в следующем развернутом виде:In accordance with (107) and (119), the expressions for the errors Δn and Δе of calculating the values of the angular coordinates

the position of the object relative to the reference point of correction can be represented in the following expanded form:

ΔR_N, ΔR_E,

определяются выражениями (99), (101),

- выражениями (89), а

- полученными выше выражениями (118).Where

ΔR _N , ΔR _E ,

are determined by the expressions (99), (101),

- by expressions (89), and

- the expressions obtained above (118).

(99), (101), в виде:Introducing expressions for

(99), (101), in the form:

where A and B, in accordance with (99) and (101) are defined as:

expressions (120) are written as follows:

определены выше (107).Where

defined above (107).

The above differential equations (80) are also described that describe the nature of the change in the coordinates Δξ, Δη, Δζ of the location (location on the object) of the ANN relative to the OPS in the projections on the OTGP axis of the ANN Oξηζ.

указанных координат достаточно просто могут быть сформированы конструктивные компоненты Δϕ_k, Δλ_k, входящие в полученные выше уравнения связи (112) для позиционных сигналов:With known estimates

of the indicated coordinates, structural components Δϕ _k , Δλ _k that are included in the communication equations (112) obtained above for positional signals can be formed quite simply:

After determining all the parameters of the right-hand sides of the above communication equations (112), we present an analytical representation for the positional elements of the observation matrix H, namely, its first and second rows:

Elements h _1j , h _2j (j = 1 ÷ 13) of the observation matrix under consideration, in accordance with (81), (112), (123) and (124), will have the following form:

Thus, having erroneous coordinates of the current location of the object (110) and using them as signals from a meter of erroneously reckoned inertial coordinates (111), it is possible to realize an estimate of all parameters of the ANN state, guaranteed long-term forecast and correction of the signals being measured and measured by it with accuracy and speed .

A similar conclusion is made above with respect to high-speed measurement signals.

(46) измерения инерциальной системой составляющих

абсолютной линейной скорости объекта расписать более подробно.Considering that the above differential equations (47), (48), (49) describing the nature of the object’s movement relative to the correction reference point, are modified and differ from their original counterpart (39), (40), (41), the optimal estimation procedure seems appropriate component D _X , D _Y , D _Z range and error

(46) inertial component measurement

absolute linear velocity of the object to paint in more detail.

In accordance with the system of differential equations (47), (48), (49) presented per channel, the discrete message model of the considered system in terms of optimal filtering (52) - (58) has the form:

1. Channel X

2. Channel Y

3. Channel Z

where w _Xik , w _Yik , w _Zik (i = 1-3) are the white noise of the disturbances acting in each channel; τ - discreteness of calculations.

In accordance with (127) - (129), the fundamental matrices for channels X, Y, and Z will have the form:

The matrices Г _{Xk + 1, k} , Г _{Yk + 1, k} , Г _{Zk + 1, k of the} transmission of random perturbations w _Xik , w _Yik , w _Zik will obviously be equal to:

The correlation matrices Q _X , Q _Y , Q _{Z of} disturbing noises of the message model can be represented as follows:

- дисперсии возмущающих шумов по дальности, скорости и ускорению соответственно.Where

- variance of disturbing noise in range, speed and acceleration, respectively.

The measurement matrix H _X , H _Y , H _Z , given that the state parameter vectors for each of the channels are:

will be equal to:

The correlation matrices R _X , R _Y , R _Z of the measurement noise are:

where σ ² is the dispersion of the measuring noise in each path for measuring the range components.

Matrices of optimal gain for each of the channels under consideration will have the form:

The calculation procedure for these matrices is traditional and is carried out in accordance with the matrix expression (56).

In accordance with (55), the expressions for calculating posterior estimates will have the form:

In the above equations, components with indices k + 1, k are a priori estimates of the corresponding state parameters of the system. The expressions for their calculation, in accordance with (127) - (128), will be equal to:

компонент дальности до ОК используют в соответствии с представленным выше описанием, а расчет идеальных составляющих абсолютной линейной скорости объекта осуществляют в соответствии с выражениями (46), используя при этом вместо

их оценки

Estimates obtained in the process of optimal assessment

the component of the range to OK is used in accordance with the above description, and the calculation of the ideal components of the absolute linear speed of the object is carried out in accordance with expressions (46), using instead

their ratings

The modified procedure for the formation of the range to the correction reference point is used to filter the components of the range to OK and to optimally estimate the speed errors of the inertial system and is intended to fill one or two second time intervals between adjacent range measurements (LD spacing intervals) with its ten hertz calculated values.

The indicated option is advisable if it is necessary to measure the range at sufficiently long time intervals of units of minutes, when the LD, as a rule, operates in a mode sparing for it with a frequency of emitting transmissions not higher than 0.5-1.0 Hz.

When solving high-tech problems involving the use of optimal filtering and identification procedures, an acceptable information processing frequency is 10 Hz.

The correction task under consideration involves the implementation of two optimal estimation procedures at the same time, namely, filtering the components of the range to OK and estimating the components of the absolute linear velocity of the object, which is an auxiliary procedure, and the main one, related to the estimation of particular errors of the inertial system and the correction of its output signals.

The essence of the proposed modified procedure for forming an inclined range is as follows.

Each measured value of the inclined range to OK, in addition to its use in accordance with the above description, is additionally used to calculate the current reference - until the next range measurement, the target altitude Δh ₀ or otherwise the inertial altitude OK.

и соответствующего указанному моменту времени значению косинуса с θ₀ угла между векторами географической вертикали и направлением на ОК определяют геометрическую высоту h₀ объекта относительно цели:For this, from the measured - reference value of the range

and the cosine value corresponding to the specified time moment with θ _{0 of the} angle between the vectors of the geographic vertical and the direction to OK determines the geometric height h _{0 of the} object relative to the target:

объекта, получают искомое - опорное значение высоты Δh₀ ОК над уровнем моря:Comparing the indicated height value with the current baroinertial height

object, get the desired - reference value of the height Δh ₀ OK above sea level:

Next, the obtained height value (144) is used on one or two second intervals of the rosacea LD for the formation of 10 hertz calculated range values.

объекта и известной опорной высоте ОК над уровнем моря Δh₀ (144) определяют текущее значение геометрической высоты объекта относительно ОК:Why, in each subsequent step, after measuring the reference range, the tact of solving the problem in question at the current value of the baroinertial height

object and the known reference altitude OK above sea level Δh ₀ (144) determine the current value of the geometric height of the object relative to OK:

The desired value of the current slant range is determined in accordance with an expression of the form:

where the current value with θ _i (i = 0, 1, ..., 9/19) (143), (146) is determined in accordance with the expression:

which is calculated with a frequency of 10 Hz.

At the end of the active phase of the optimal error estimation of autonomous inertial calculus, based on a recursive procedure for processing, filtering, and identifying a constantly updated input sequence of signals generated by ANN measurements and the auxiliary optimal estimation procedure, the ANN filter-identifier for errors is transferred to the long-term mode until the next evaluation session prediction of the received estimates. Moreover, the correction of the measured ANN of navigation and flight information is carried out both in the process of optimal estimation and forecast.

A feature of the operation of the ANN error identifier filter in the prediction mode is the zeroing of the filter input signals and the suspension of the mathematical procedure for calculating the optimal amplification factors, which are assumed to be zero for the entire forecast time.

As the initial values of the estimates in the forecast procedure, their values obtained at the end of the optimal estimation are used, and all the values of the transfer coefficients weighing the considered estimates are calculated in accordance with their analytical representation in the extended ANN error model.

…, а счисленные значения инерциальных параметров, как

V_x, V_y, …Further, when describing the inertial information correction procedure, the values of estimates obtained as a result of the forecast will be denoted by analogy with the optimal estimates, namely,

... and the calculated values of inertial parameters, as

V _x , V _y , ...

Here is the procedure for correcting the basic navigation and flight parameters.

The correction of the horizontal components V _x , V _{y the} absolute linear velocity of the object, presented in the form (69), is carried out in accordance with the expressions:

а также бароинерциальную составляющую V_ζ вертикальной скорости, в соответствии с выражениями (148), с точностью до величин первого порядка малости относительно

могут быть рассчитаны откорректированные составляющие

абсолютной скорости.Obviously, knowing the calculated values of the components V _x , V _{y of the} absolute linear velocity of the object and the current estimated or predicted values of the estimates

as well as the baroinertial component V _{ζ of the} vertical velocity, in accordance with expressions (148), up to first-order values of smallness with respect to

corrected components can be calculated

absolute speed.

и угла

азимутальной ориентации опорного трехгранника гироплатформы ИНС определяются выражениями вида (1.10), а именно:When correcting the geographical coordinates of the location of the object and its true course, we assume that the calculated coordinates

and angle

the azimuthal orientation of the supporting trihedron of the ANS gyro platform are determined by expressions of the form (1.10), namely:

where ϕ, λ, Δχ are the ideal values of the considered parameters, Δϕ, Δλ, Δχ are the errors of their calculation.

ошибок счисления указанных параметров, достаточно просто могут быть рассчитаны их откорректированные значения

:Therefore, having the current valuation values

errors in calculating the indicated parameters, their corrected values can be calculated quite simply

:

рассчитывается в соответствии с кинематическим соотношением вида (61):Moreover, the assessment

calculated in accordance with the kinematic relation of the form (61):

- оценка курсового ухода гироплатформы ИНС.Where

- assessment of the course care of the ANN gyro platform.

When correcting the true course of the object, we use the expression in accordance with which it is calculated:

Obviously, in variations this expression will look like:

from which it follows that the error Δψ _and forming true heading ψ _and determined by the error χ corner Δχ numeral azimuthal orientation reference trihedron SE INS and measurement error Δψ _r gyroscopic rate ψ _g.

Using the corresponding kinematic relations for Δχ (60) and Δψ _g (61), we write the expressions for Δψ _and (153) in the following form:

Given the relation for Δγ (61), it can be represented in the following algorithmically appropriate form:

From this expression that the error Δψ _and forming true heading ψ is independent _of the azimuth angle α _z care GP ANN.

счисленным значением географической широты

и измренными значениями тангажа

и гироскопического курса

объекта, может быть определена оценка

погрешности формирования истинного курса:Thus, having estimated or predicted valuation values

latitude

and measured pitch values

and gyroscopic course

object, can be determined

errors in the formation of the true course:

может быть определено в соответствии с выражением вида:In this case, the adjusted value of the course itself

can be determined in accordance with an expression of the form:

The procedure for correcting all aerobatic parameters, namely, the angles of the gyroscopic course ψ _g , roll γ and pitch υ of the object, involves the use of kinematic relations (61).

ухода реальной ГП ИНС, в соответствии с первым выражением системы (61), определяют оценку

ошибки измерения угла тангажа объекта:Indeed, knowing the current values of the estimates of small angles

the departure of a real GP ANN, in accordance with the first expression of the system (61), determine the estimate

errors of measuring the pitch angle of the object:

knowing which on the considered step the calculations calculate the corrected pitch value

в соответствии со 2-ым соотношением системы (61) определяют оценку

ошибки измерения крена

объекта:At the same measure, knowing the already adjusted pitch value

in accordance with the 2nd relation of system (61), an estimate

roll measurement errors

object:

then on the same measure determine its adjusted value:

And the last operations of the considered measure are associated with the correction of the gyroscopic course

ошибки измерения

In accordance with the 3rd ratio of the system (61) form an estimate

measurement errors

объекта:after which, the adjusted value of the gyroscopic course is determined

object:

The method for optimal estimation of errors of the inertial navigation system and its correction according to a fixed reference point with known geographical coordinates is implemented as follows:

1. When flying relative to a fixed landmark, correction along a pre-agreed path with continuous, for five to six minutes, its angular tracking and discrete measurement of the slant range to it in the operating mode sparing for the laser rangefinder from the sighting system with frequency parcels, not exceeding 0.5-1.0 Hz, while all arrays of current information measured by the OPS, ANN and a complex baroinertial channel for generating absolute height and vertical speed are processed Thus, in order to provide both effective optimal error estimation of calculated geographic coordinates of the current location of the object and measured ANNs, components of its absolute linear velocity, and the formation of error estimates of the angles of the current orientation of the object with the implementation of their long-term forecast, not exceeding 40 minutes, and parallel correction the entire array of its output parameters.

In this case, to achieve the technical result of the invention carry out:

абсолютной линейной скорости объекта, используемых в качестве сигналов скоростного измерителя в основной процедуре оптимального оценивания ошибок ИНС, одно-двух секундные временные интервалы между соседними измерениями дальности (интервалы роздыха ЛД) заполняют 10-ти герцовыми расчетными значениями, которые формируют в соответствии с модифицированной, инвариантной к рельефу подстилающей поверхности, угломестной процедурой расчета наклонной дальности до ОК, реализуемой на основе использования текущей бароинерциальной высоты

косинуса с θ_i угла между географической вертикалью и направлением на ОК и опорным 1-2-х герцовым значением высоты ОК над уровнем моря Δh₀. Указанная процедура приведена в описании изобретения и представлена выражениями (143)-(147).2. In support of the development of an accurate and efficient procedure for the optimal assessment of horizontal components

the absolute linear speed of the object used as signals of a speed meter in the main procedure for the optimal estimation of ANN errors, one-two second time intervals between adjacent range measurements (intervals of the LD output) are filled with 10 Hz calculation values, which are formed in accordance with the modified, invariant to the relief of the underlying surface, elevation procedure for calculating the slant range to OK, implemented using the current baroinertial height

cosine with θ _{i of the} angle between the geographic vertical and the direction to the OK and the reference 1-2 Hz value of the height of the OK above sea level Δh ₀ . The specified procedure is described in the description of the invention and is represented by the expressions (143) - (147).

3. The kinematic differential equations of the object’s motion relative to the OK are represented in the projections on the ISK axis, which provides a fundamental simplification of the equations describing it by implementing a natural channel-by-channel decomposition of the model of their relative motion, as a result of which, instead of an interconnected 9th-order kinematic model, three structurally identical and unrelated channels (36), (37), (38), on the basis of which three independent, structurally and algorithmically identical filter-identifiers are synthesized .

абсолютной линейной скорости объекта. После подстановки в них вместо составляющих

их значений, определяемых адекватными для них выражениями (46), переходят от уравнений для скорости и ускорения объекта в полных сигналах к уравнениям в вариациях, представленным в виде модифицированной системы дифференциальных уравнений (47)-(49), которую используют в процедуре оптимального оценивания ошибок

счисления составляющих

абсолютной линейной скорости. По известным счисленным значениям компонент

абсолютной линейной скорости объекта и оцененным ошибкам

определения ее текущих составляющих, в соответствии с (51), формируют искомые значения оценок

составляющих абсолютной линейной скорости.4. Given that in the problem under consideration the absolute linear velocity of OK can be determined accurately (43), (44), the differential equations of relative motion of the object (36) - (38) are modified and presented in the form (39) - (41), convenient for optimal component evaluation

absolute linear velocity of the object. After substitution in them instead of components

their values determined by expressions adequate for them (46) pass from the equations for the speed and acceleration of the object in full signals to the equations in variations represented in the form of a modified system of differential equations (47) - (49), which is used in the optimal error estimation procedure

numbering of components

absolute linear speed. According to the known calculated values of the components

absolute linear velocity of the object and estimated errors

determining its current components, in accordance with (51), form the desired values of the estimates

components of the absolute linear velocity.

дальности и ошибок

счисления абсолютной скорости и ускорения

объекта представлена уравнениями/выражениями (127)-(142).Procedure for the optimal assessment of current components

range and error

calculation of absolute speed and acceleration

the object is represented by equations / expressions (127) - (142).

дальности до ОК к осям ГСТ ONHE реализуют в соответствии с выражением вида (32).Recalculation of the components (51) of the absolute linear velocity of the object to the axes of the OTGP ANN Oξηζ is carried out in accordance with the vector-matrix expression inverse (50). At the same time, casting the filtered component estimates

the ranges to OK to the axes of the GTS ONHE are implemented in accordance with the expression of the form (32).

дальности до ОК к осям ГСТ ONHE определяются ошибками Δψ_и, Δυ, Δγ измерения углов

эволюции объекта (87)-(92), (116)-(119), а погрешности

(68) формирования составляющих

абсолютной линейной скорости объекта в проекциях на оси ОТГП ИНС Oξηζ (67) - ошибками

измерения углов гироскопического курса

тангажа

и крена

(74)-(79).5. In the corresponding section of the invention, on the basis of simple physical considerations, it is shown that the errors in bringing estimates of the components

the ranges to OK to the axes of the GTS ONHE are determined by the errors Δψ _and , Δυ, Δγ of the measurement of angles

the evolution of the object (87) - (92), (116) - (119), and the errors

(68) forming components

absolute linear velocity of the object in projections on the axis of the OTGP ANN Oξηζ (67) - errors

gyro angle measurement

pitch

and roll

(74) - (79).

(99), (101) расчета главных радиусов кривизны земного эллипсоида вращения, определяют, также, как и погрешности

(79) формирования горизонтальных составляющих абсолютной линейной скорости объекта (67), (71), в функции параметров состояния ИНС таких, как α_x, α_y, α_z, Δϕ, Δλ (79), (123).6. The total errors Δn, Δе of the formation of ideal values of the geographical coordinates ϕ, λ (109) of the current location of the object, taking into account the errors ΔR _N , ΔR _E ,

(99), (101) of calculating the principal radii of curvature of the earth's ellipsoid of revolution, determine, as well as the errors

(79) the formation of horizontal components of the absolute linear speed of the object (67), (71), as a function of the state parameters of the ANN such as α _x , α _y , α _z , Δϕ, Δλ (79), (123).

параметров ИНС кинематические соотношения их связи с малыми углами α_x, α_у, α_z ухода ее реальной гироплатформы (60)-(61).For this, characteristic for navigation Δϕ, Δλ, Δχ and aerobatic

ANS parameters, the kinematic relations of their connection with small angles α _x , α _y , α _{z of the} departure of its real gyro platform (60) - (61).

7. For the correct mathematical description of positional and high-speed signals, the measurements of the optimal filter-identifier of the ANN errors generate the corresponding communication equations (72), (112).

эволюции объекта с малыми углами α_x, α_у, α_z ухода реальной ГП ИНС.The left-hand sides of these equations are taken for the corresponding measurement signals (73), (113), and their right-hand sides determine the corresponding elements of the observation matrix (82), (83), (125), (126), which represent the ANN state parameter functions (81), for which they use the kinematic relations of the correlation errors of the calculus of the main three Δϕ, Δλ, Δχ of navigation parameters and angles

the evolution of an object with small angles α _x , α _y , α _{z the} departure of a real GP ANN.

8. The procedure for optimal filtering and identification of positional and high-speed measurement signals is implemented in accordance with the discrete version of its implementation, represented by vector-matrix equations / expressions of the form (52) - (58). In this case, the error model, traditional for the ANN, is used, which is represented by a system of differential equations of the 10th order, which is expanded by including a system of three interconnected differential equations of the first order (80) that describe the nature of the change in the coordinates of the Δξ, Δη, Δζ location (placement on object) ANN relative to the OPS in the projections on the axis of the OTGP ANN Oξηζ.

9. After the time of optimal estimation, determined by the time spent by the OK in the zone of optical contact with the object and amounting to 5.5-6 minutes, the filter-identifier of inertial information errors is stopped, its input signals and amplification factors are reset, and the filter is put into long-term mode prediction of his estimates, using for this a recurrent procedure for the formation of its a priori estimates (55).

текущего местоположения объекта, горизонтальных составляющих V_x, V_y его абсолютной линейной скорости, угла

азимутальной ориентации ее гироплатформы, углов

текущей ориентации объекта и его истинного курса

При этом коррекцию углов

и

осуществляют после предварительного формирования оценок ошибок счисления/измерения углов

в соответствии с кинематическими соотношениями их связи с оценками малых углов

ухода реальной ГП ИНС (60), (61). Использование указанных соотношений позволяет достаточно просто реализовать коррекцию практически всех счисляемых и измеряемых инерциальной системой сигналов, которую осуществляют в «разомкнутом контуре». Описанная выше процедура коррекции навигационных и пилотажных параметров приведена в описании изобретения и представлена выражениями (148)-(163). При этом маневр, который предполагается использовать в рассматриваемом режиме коррекции, типа круговой циркуляции вокруг ОК (фиг. 7), следует рассматривать, как методический прием, обеспечивающий оценивание всех параметров состояния ИНС, включая и слабонаблюдаемые, такие, как азимутальный уход ГП α_z и некомпенсированный дрейф ε_z курсового гироскопа.The estimated values obtained as a result of the forecast are used to correct the calculated geographic coordinates

the current location of the object, the horizontal components V _x , V _y its absolute linear speed, angle

azimuthal orientation of its gyro platform, angles

the current orientation of the object and its true course

In this case, the correction of angles

and

carried out after the preliminary formation of estimates of errors of reckoning / measuring angles

in accordance with the kinematic relations of their relationship with the estimates of small angles

care of real GP ANN (60), (61). The use of these ratios makes it quite simple to implement the correction of almost all signals counted and measured by the inertial system, which are carried out in an “open loop”. The above procedure for the correction of navigation and flight parameters is given in the description of the invention and is represented by expressions (148) - (163). At the same time, the maneuver that is supposed to be used in the correction mode under consideration, such as circular circulation around the OC (Fig. 7), should be considered as a methodological technique for assessing all parameters of the ANN state, including the weakly observed ones, such as azimuthal departure of the GP α _z and uncompensated drift ε _{z of the directional} gyroscope.

From the above description of a unified method for optimal estimation of inertial information errors and its correction by a fixed landmark with known geographical coordinates, it follows that the essence of the proposed solution is disclosed and the technical result is achieved.

Claims (1)

A method for optimal error estimation of an inertial navigation system and its correction using a fixed landmark with known geographical coordinates, including angular tracking of a fixed correction landmark (OK) and discrete measurement of the slant range to it in a sparing laser rangefinder (LD) from the sighting system (TSO) modes of operation with a frequency of 0.5-1.0 Hz emitting chip and based on joint processing of the measured current with the angles φ _y, φ _z and the hooded sight OK constant range

to him, the current angles of true

and gyroscopic

courses, roll

and pitch

object and estimated ANN of geographical coordinates

its location and current baroinertial height

characterized in that in the continuous angular tracking mode OK one-two-second time intervals between adjacent measurements of the range to OK fill it with ten-hertz calculated values, which form in accordance with the modified, invariant to the relief of the underlying surface elevation procedure for determining the inclined range, involving the use of current baroinertial height object, the cosine of the angle between the geographic vertical and the direction to OK, and formed by measurements PS of the reference value of the altitude OK above sea level, while the components of the absolute linear velocity of the object are estimated in accordance with the kinematic model of its motion relative to the motionless ground OK in the projections on the axis of the inertial coordinate system (ISC), which provides a fundamental simplification of the differential equations describing it due to natural channel-by-channel decomposition of the model of relative motion of an object, which, for reasons of increasing the accuracy of estimation, is additionally modified, passing from the equations for the components of the absolute linear velocity and acceleration of the object in full signals to their variations relative to the measured ANN current values, the components of the absolute linear velocity of the object relative to the OK are used as a known control, and the range components obtained as a result of the optimal filtering and identification procedure to OK and the components of the absolute linear velocity of the object are used to form positional and speed signals of an ideal meter, comparing them with the corresponding output signals of the ANN generate the measurement signals of the optimal filter identifier of the ANN errors and the elements of its observation matrix, through which all errors of the measurement signals are recorded, the procedure for their optimal filtering and identification is implemented in accordance with the traditional error model for the ANN, which , for reasons of the correctness of its description and the accuracy of estimation, it is expanded by the inclusion of three differential equations that describe the nature of the change in the coordinate inat of the location of the ANN relative to the OPS in the projections on the axis of the supporting trihedral of the gyro platform (OTGP) of the ANN, at the end of the optimal estimation of the errors of the ANN, determined by the time spent by the OK in the zone of optical contact with the object, the filter-identifier of errors of the ANN is stopped, its input signals and amplification coefficients are reset, and the filter itself is transferred to the long-term forecast mode of the obtained estimates, which are implemented in accordance with the recursive procedure for generating a priori errors of the ANN, and the results obtained from the forecast Achen INS error is used to correct the coordinates of the current location of the object, its absolute horizontal components of the linear velocity, azimuthal angle orientation angles SE ANN and the current orientation of the object.

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