RU2617565C1 - Method of inertial data estimation and its correction according to measurement of satellite navigation system - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: method of inertial data estimation and its correction according to measurement of satellite navigation system consists in using the traditional Kalman optimum filtering and identification procedure, for which the optimal identifier filter measurement signals generate by comparing the same geographic location coordinates and horizontal components of the absolute linear velocity in the projections on the axis of the gyroplatform (GP) reference triad of the INS formed according to the measurements of the satellite navigation system (SNS), and its structure is synthesized in accordance with the traditional INS error model, the flying mode is systematically organized in such a way that after 270 seconds of rectilinear horizontal flight, which the exact "horizon" of the gyroplatform is realized and the well-observed parameters of the INS horizontal channels are evaluated, bank-to-bank reversal, coordinated or combat turns are performed, after that the active phase of the optimum filtering and identification procedure is suspended and the identifier filter is put into the long-term forecast - until the next correction session, for its implementation the measurement signals are reset, and the values of the estimates at the end of the estimation procedure active phase are used as initial conditions in the forecast procedure, while the forecast itself is performed in accordance with the calculating discrete equations of the a priori error estimates of the INS, and the correction of the INS output parameters - the geographical location coordinates and the components of the absolute linear velocity, is realized in the open INS scheme, using the current predicted values of the INS state parameter estimates. At the same time the INS error model is expanded by including the mathematical description of its location coordinates relative to the SNS antenna unit (AU) and present them in the form of a system of three interrelated first order differential equations in the projections on the INS GP reference triad axle that simultaneously describe the additively included in the measuring speed signals kinematic components of the INS relative velocity, and during the formation of the measurement signals and the observation matrix kinematic relations between the error Δϕ, Δλ, Δχ numeral geographical coordinates of the location and angle of the azimuthal orientation of a INS GP reference triad errors are used to a vertical holding tolerance α_x, α_y and the angle α_z of an INS GP azimuthal departure correct to the second order infinitesimal relative to such parameters as Δϕ, Δλ, α_x, α_y, α_z, provide a definition of the current values of the message matrix elements and observation.

EFFECT: improved accuracy and speed of the optimal evaluation and correction of the measured by inertial navigation system navigation and flight parameters to the provision of the effective solution of navigation, combat and special missions.

2 cl, 4 dwg

Description

The invention relates to the field of integrated navigation systems, control systems and guidance of aircraft (LA).

There is a method of optimal estimation and correction of inertial information on measurements of satellite navigation system (SNA), presented in the training manual VV Meleshko, O.I. Nesterenko “Platform-based inertial navigation systems”, K., “Polymed service”, 2011 [1].

The specified method is based on the use of the optimal Kalman filtering procedure. The input signals of the inertial navigation system (ANN) error identifier filter are the differences of the geographical coordinates of the location and the absolute linear velocity components measured by the ANN and generated from the SNS measurements.

These signals, after their optimal processing, including both filtering and identification, in accordance with the mathematical description of the original system, firstly, are practically “cleared of high-frequency SNA errors”, and secondly, they are divided into the known, mathematically described components of ANN errors .

At the same time, the errors of the ANN channel are not evaluated and the parameters measured by it are not corrected (see [1], pp. 97-107).

,

, составляющие V_x, V_y абсолютной линейной скорости и углы крена

и тангажа

объекта, причем последние - в случае, когда диапазон их изменения не превышает 5-10-ти градусов.In accordance with the description of the method under consideration, only the current values of the geographical coordinates of the location are adjusted

,

constituting V _x , V _y absolute linear velocity and roll angles

and pitch

object, and the latter - in the case when the range of their change does not exceed 5-10 degrees.

Two variants of the algorithmic implementation of the indicated correction method are presented, namely, an option with an open integration scheme and an option with a closed correction scheme.

Based on the materials given in [1] and the conclusions made there, the following disadvantages of the considered correction method should be noted:

, расчетного значения угла

азимутальной ориентации опорного трехгранника гироплатформы (ГП) ИНС и истинного курса

объекта (см. [1], стр. 98);- the lack of the ability to evaluate the parameters of the course channel ANN and correction of the gyroscopic course

calculated angle

azimuthal orientation of the supporting trihedral of the gyro platform (GP) of the ANN and the true course

object (see [1], p. 98);

- the lack of implementation of the algorithmic procedure for the correction of the measured ANN angles of evolution of the object in the entire range of their changes.

These disadvantages should not be considered as disadvantages objectively inherent in the above correction method.

It will be absolutely correct to regard them as a result of its unexplored possibilities.

And this is indeed so, since for a number of decades, both in Russia and abroad, such a methodically accessible and effective technique as a highly dynamic maneuver, such as a highly dynamic maneuver, has been used to estimate the angle α _{z of the} azimuthal drift of the INS / SINS GP and the drift ε of _the longitudinal channel gyroscope "Snakes", coordinated or combat turns.

To justify the physical feasibility and the need to use this technique from well-known open sources, we can refer to “Addition to the task of the exhibition on a moving basis” L.G. Klibanova and V.L. Leonidova (see [2], pp. 155-162) in the monograph by A. Lipton “Exhibition of inertial systems on a moving base”, “Science”, M., 1971 [2], in which for the first time in practice the solution of such problems is considered reduced optimal estimation procedure in the problem of matching the GP of two inertial systems - the base and the exposed.

The review is being carried out in relation to solving the problem of the initial exhibition of an INS rocket using high-speed information measured by an INS of a carrier, in which its authors cite the main thing that prompted to turn to the indicated source, namely: “... to ensure the best assessment, the influence of the system state matrix is essential (read, models of ANN errors), depending on the trajectory (parameters) of the object’s movement. ” And further, the authors of this appendix cite Sutherland A.'s famous article in engineering circles, “The Kalman Filter in Transfer Alignment of Inertial Guidance Sistems”, journal Spacecraft and Rockets, vol. 5. No 10. 1968. - Sutherland A. “Kalman filter in the task of the initial INS exhibition in flight”, which selects the optimal, from the point of view of the best estimate, maneuvers of the object during the exhibition of inertial systems in flight (see [2], the last paragraph p. 162).

Given this, it will be fair to assume that in the above method of optimal estimation and correction of ANNs [1], all the parameters of its heading channel are not observable, but poorly observed, effective and separate assessment of which requires appropriate maneuver.

Therefore, the specified method for the correction of ANN can be considered the prototype of the proposed method for the optimal estimation of errors of inertial information and its correction by measuring the SNA.

Formalizing the description given above [1], [2], expounding it in terms of mathematical procedures used in solving similar problems with an emphasis on the physical operations performed in this case, we present it in the following form.

A method for optimal estimation and correction of inertial information on SNA measurements, based on the procedure of optimal filtering and identification of measurement signals, which are formed by comparing the geographical coordinates ϕ, λ of the current location, calculated ANNs and measured SNA, as well as the horizontal components V _x , V _y absolute linear velocity, measured ANN and similar components formed by measurements of the SNA, and the evaluation itself is carried out in full accordance with the mathematical description the bottom of the system, while the flight is organized in such a way that after 270 seconds of a horizontal straight flight, a maneuver is performed, such as a “snake”, of coordinated or combat turns, after which the active phase of the optimal filtering procedure and identification of a discrete sequence of measurement signals are suspended and the filter identifier is transferred in the long-term mode - until the next session of correction, forecast with initial conditions determined by the values of the estimates at the time of completion of the active phase, and the current values eniyami model coefficients message (ANN model errors), the correction of the output parameters of the INS - geographic position coordinates and absolute linear velocity components, due to closeness and inaccessibility key management inputs INS correction channels implement open loop using current estimates of predicted values.

The main disadvantages of the closest analogue are:

- the absence in the ANN error model of a mathematical description of the coordinates of the relative placement of complexed systems;

- when forming the observation matrix, the error in calculating the angle of the azimuthal orientation of the supporting trihedron of the GP INS as a function of its small departure angles is not taken into account;

- when performing maneuvers traditional for the mode under consideration, such as a “snake”, coordinated or combat turns, instead of the expected, effective assessment of all state parameters and, first of all, weakly observed, such as the angle α _{z of the} azimuthal drift of the GP and the drift ε _{y of the} gyroscope the longitudinal channel, for the purpose of which the maneuver is carried out, there is an absolutely opposite picture of the divergence of the latter and violation of the convergence of the others;

- not typical for the procedure of optimal estimation of accuracy and speed, which indicates the inefficiency of the optimal processing and correction procedure as a whole.

The technical result of the invention is to increase the accuracy and speed of optimal estimation and correction of all measured ANN of navigation and aerobatic parameters in order to provide an effective solution to navigation, combat and special tasks.

The specified technical result is achieved due to the fact that:

,

,

,

,

,

,

,

,

,

, при этом коррекцию автономно счисленных значений географических координат

,

текущего местоположения и составляющих

,

абсолютной линейной скорости осуществляют в соответствии с общепринятыми выражениями, для чего используют текущие спрогнозированные значения оценок

,

,

,

и малых углов

,

,

, а для коррекции истинного курса рассчитывают откорректированное значение угла

азимутальной ориентации опорного трехгранника ГП в функции оцененных значений

и

и вычисляют откорректированное значение гироскопического курса

в функции оценок

и погрешности

измерения угла крена

, которую определяют расчетным путем в функции текущих, спрогнозированных значений оценок

,

и измеренных/откорректированных углов гироскопического курса ψ_г и тангажа υ, после чего рассчитывают истинный курс ψ_и, как сумму оценок

и

.1. In the method of estimating errors of inertial information and its correction by measuring the satellite navigation system, including the use of the traditional optimal filtering and Kalman identification procedure, for which measurement signals of the optimal filter-identifier are generated by comparing the geographical coordinates of the same location and the horizontal components of the absolute linear velocity in the projections on the axis of the reference trihedron of the GP ANNs of the calculated ANNs and formed by the measurements of the SNS, and its structure ru are synthesized in accordance with the error model traditional for the ANN, while the nature of the flight is methodically organized in such a way that, after 270 seconds of a straight horizontal flight, on which the gyro platform is precisely “graded” and the well-observed parameters of the ANN horizontal channels are estimated, maneuver , such as a "snake", coordinated or combat deployments, after which the active phase of the optimal filtering and identification procedure is suspended and the filter-identifier is switched to d mode long-term - until the next session of correction, forecast, for the implementation of which the measurement signals are zeroed, and the values of the estimates at the time of completion of the active phase of the estimation procedure are used as initial conditions in the forecast procedure, while the forecast itself is carried out in accordance with discrete equations for calculating a priori estimates of ANN errors , and the correction of the output parameters of the ANN — the geographical coordinates of the location and the components of the absolute linear velocity — is implemented in an open circuit of the ANN, for which they use predicting the predicted values of the estimates of the state parameters of the ANN, the ANN error model additionally used in solving such problems is expanded by including a mathematical description of the coordinates of its location relative to the antenna unit of the SNA, and they are presented in the form of a system of three interconnected differential equations of the first order in projections on the axis of the reference the trihedron of the GP INS, which simultaneously describe the kinematic components of the relative velocity d additively included in the high-speed measurement signals izheniya INS, and when forming the measurement signal and the observation matrix using kinematic equations relating Δφ errors, Δλ, Δχ numeral geographical coordinates of location and angle of the azimuthal orientation of the reference trihedron SE ANN errors withstand vertical α _x, α _y and an angle α _z azimuthal care GP ANN than, up to the second order with respect to such parameters as Δφ, Δλ, α _x, α _y, α _z, provide for determining the current values of the matrix elements and observation posts, and realize t chnoe and effective assessment and subsequent prognosis of such errors autonomous inertial notation as

,

,

,

,

,

,

,

,

,

while correcting autonomously calculated values of geographical coordinates

,

current location and components

,

absolute linear speed is carried out in accordance with generally accepted expressions, for which use the current predicted values of estimates

,

,

,

and small angles

,

,

, and to correct the true course, the corrected angle value is calculated

azimuthal orientation of the reference GP trihedron as a function of estimated values

and

and calculate the corrected value of the gyroscopic course

in the rating function

and errors

roll angle measurements

, which is determined by calculation in the function of current, predicted values of estimates

,

and the measured / corrected angles of the gyroscopic heading ψ _g and pitch υ, after which the true heading ψ _and , as the sum of the estimates, are calculated

and

.

относительной угловой скорости объекта, которое постоянно вычисляют с момента начала маневра, отсчет которого, в соответствии с циклограммой коррекции, начинают с 270-ой секунды после начала коррекции, при этом, если указанное среднее значение на выходе из маневра - начиная с 300-ой секунды, не превышает

рад/с (~3 град/мин), формируют команду «Маневр завершен» и, не прекращая процедуры оптимального оценивания, приводят текущие значения оценок

,

,

координат местоположения ИНС относительно АБ СНС к осям связанной с объектом системы координат, а получаемые при этом текущие значения оценок

,

,

в соответствии с рекуррентной процедурой нахождения среднего, осредняют на 3-секундном интервале времени, после чего осредненные значения оценок

,

,

сравнивают с хранящимися в БЦВМ конструктивными значениями указанных координат и при положительном исходе сравнения, когда их разница не превышает 1-2%, формируют признак «Оценка +», останавливают процедуру оптимального оценивания и переходят к режиму полноценного прогноза и коррекции, в противном случае - формируют признак «Оценка -» и после остановки оценивания прогноз не реализуют, а коррекцию текущих значений счисленных параметров осуществляют с использованием запомненных, на момент остановки оценивания значений оценок

,

,

,

,

,

,

,

,

,

.2. In the method for estimating errors of inertial information and its correction according to measurements of the satellite navigation system according to claim 1, additionally after completing the maneuver and reaching the established post-maneuvering course, the fact of which is established by the value of the component averaged over a 5-second time interval

the relative angular velocity of the object, which is constantly calculated from the moment the maneuver begins, the countdown of which, in accordance with the correction sequence diagram, begins from the 270th second after the correction begins, moreover, if the indicated average value at the exit from the maneuver starts from the 300th second , does not exceed

rad / s (~ 3 deg / min), form the command “Maneuver is completed” and, without stopping the optimal estimation procedure, present the current values of the estimates

,

,

coordinates of the location of the ANN relative to the AB SNA to the axes of the coordinate system associated with the object, and the current values of the estimates obtained

,

,

in accordance with the recursive procedure for finding the average, averaged over a 3-second time interval, after which the averaged estimates

,

,

they are compared with the constructive values of the indicated coordinates stored in the digital computer and, with a positive outcome of the comparison, when their difference does not exceed 1-2%, the sign “Score +” is formed, the optimal estimation procedure is stopped and the mode of full-fledged forecast and correction is switched on, otherwise they form the sign “Evaluation -” and after the evaluation is stopped, the forecast is not realized, and the correction of the current values of the calculated parameters is carried out using the valuation values stored at the time the evaluation was stopped

,

,

,

,

,

,

,

,

,

.

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

,

и

, определяющие местоположение соответственно ИНС1, ИНС2 и ДИСС относительно начала (точка О) связанной с объектом системы координат (ССК) Oxyz.In FIG. 1 shows a diagram of the relative placement of ANN1, ANN2 and the antenna unit (AB) of the SNS at the facility. As parameters that determine the location of these systems on the object, vectors are taken

,

and

determining the location, respectively, of ANN1, ANN2 and DISS relative to the origin (point O) of the Oxyz coordinate system associated with the object (CCK).

и

, определяющие местоположение ИНС1 и ИНС2 соответственно относительно ДИСС, а также вектор

положения ИНС2 относительно ИНС1.The diagram also presents vectors

and

determining the location of ANN1 and ANN2, respectively, relative to the DISS, as well as the vector

provisions of ANN2 relative to ANN1.

By ANN2 is meant a backup ANN, which is introduced for general consideration.

- вектор путевой скорости объекта.

- vector of the ground speed of the object.

In FIG. Figure 2 shows the relative orientation of the geographic accompanying trihedron (GTS) ONHE and SSK Oxyz.

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

,

и

.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

,

and

.

,

и

их изменения является положительным.Referring to FIG. 2 reference direction of angles ψ _and , υ and γ and angular velocities

,

and

their change is positive.

In FIG. Figure 3 shows the mutual orientation of the support gyro platform trihedron (OGP) OξηζINS and SSK Oxyz.

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

,

и

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

,

and

.

,

и

является положительным.Referring to FIG. 3 reference direction of the angles ψ _g , υ and γ and angular velocities

,

and

is positive.

In FIG. Figure 4 shows the relative orientation of the Greenwich coordinate system (HSC) OX'Y'Z ', OGP OξηζINS and GTS ONHE.

Their mismatch is determined by the angles of geographic longitude λ, latitude ϕ and angle χ of the azimuthal orientation of the OTGP OξηζINS.

,

, и

.The transition from the axes of the HSC О X'Y'Z 'to the axes of the GTS ONHE and further to the axes of the OGP Оξηζ is carried out by successive rotations by the angles λ and ϕ and then by the angle χ (see Fig. 4) with angular velocities

,

, and

.

,

, и

их изменения следует считать положительным.Referring to FIG. 4 reference direction of angles λ, ϕ and χ and angular velocities

,

, and

their changes should be considered positive.

In order to disclose the physical essence and mathematical content of the proposed algorithmic and mathematical solutions, we present their detailed description.

But before - justification of the need for algorithmic accounting for the relative placement of the ANS and SNA information systems involved in inertial-satellite correction.

When developing an algorithm for optimal ANN correction by SNA measurements, the issue of methodological support for separate observation and estimation of all, without exception, state parameters of ANN and, first of all, weakly observable, such as the angle α _{z of} azimuthal mismatch between the real and the reference trihedra in the gyro platform, is extremely important. GP ANN and uncompensated departure - drift ε _{y of the} longitudinal channel gyroscope. In laboratory conditions and for the case of a stationary object, these parameters are unobservable and, as a result, are not separately evaluated.

Under the conditions of a moving object, to ensure their observability, there is no need to implement any additional methodological solutions. And this is due solely to the fact that the object’s movement itself is a rather effective tool that allows controlling the dynamics of changes in the errors of the ANN output parameters from all, without exception, state parameters and, as a consequence, their observability.

At the same time, in order to ensure the maximum efficiency of the connections of all state parameters with the ANN output signals, such as the geographical latitude ϕ and longitude λ, and the horizontal components V _x , V _{y of} absolute speed, it is necessary to perform maneuvers such as a coordinated turn, “snake” or combat U-turn.

Performing the above-mentioned maneuvers, accompanied by a fairly intense change in the angular and spatial orientation of the object and, as a result, a highly dynamic change in its angular and ground speed components, with different structural arrangements of the information systems involved in the correction modes under consideration, lead to the appearance of so-called kinematic components in the measurement signals speed.

The indicated components of the velocity, being mathematically not described, and, as a result, algorithmically unaccounted for, and this is true, instead of the methodologically justified and expected estimation of weakly observed parameters lead to a completely opposite result, namely, the divergence of the procedure for their estimation.

Ignoring the specifics of this phenomenon leads to such conclusions, such as: “exchange rate errors are well evaluated when there are two correction sections of 5 ... 10 min each, separated by a speed and / or course maneuver” (see Scientific and Technical Journal Engineering Physics No. 12 / 2012, p. 49, 16 line above).

In fact, the exchange rate error is estimated well if it is estimated in 0.5-1 minutes of one of the maneuvers mentioned above.

Moreover, “the presence of two correction sections of 5 ... 10 min each” has no physical explanation.

For a qualitative assessment of the parameters of the ANN horizontal channels, a correction section is required, lasting no more than 4-4.5 minutes, after which a maneuver is carried out, which ensures the estimation of the azimuthal error and does not worsen, which is especially important, the results of the "leveling".

In the case presented above from Engineering Physics, the maneuver not only does not provide an estimate of the azimuthal error, but even worsens the results of the “leveling” carried out in the first 5 ... 10-minute correction section.

And, in order to somehow smooth out the consequences of the maneuver, it was obvious that a second 5 ... 10-minute correction section was required.

Now, from the general physical concepts, we obtain a mathematical model that describes the geometry of the relative placement of the main information systems on the object, such as an airplane or a helicopter, and show that this model also describes the kinematic components of speed mentioned above.

To reveal the physical essence of the indicated velocity components, we present the derivation of differential equations that describe the nature of the change in their relative coordinates in the projections on the axis of the geographic accompanying GST ONHE trihedron and the reference trihedron of the OTGP ANN Оξηζ gyro platform.

To do this, we use the above scheme of relative placement on the object ANN1, ANN2 and SNS (Fig. 1).

,

и

_. Это означает, что при векторе угловой скорости

вращения объекта вокруг его ЦТ будут иметь место линейные перемещения ИНС1, ИНС2 и СНС со скоростями вида:In this diagram, the origin of the Oxyz coordinate system associated with the object is aligned with the center of gravity of the CT, and the location of ANN1, ANN2, and the SNS antenna unit is determined by the vectors, respectively

,

and

_. This means that with the angular velocity vector

the rotation of the object around its central point will be linear displacements ANN1, ANN2 and SNS with velocities of the form:

- вектор предписанной заданием путевой скорости объекта.Where

is the vector of the prescribed target speed of the object.

In accordance with FIG. 1 by vector triangles O-INS1-SNA and O-INS2-SNA, we write the following useful matrix equalities:

,

- вектора местоположения ИНС1 и ИHC2 соответственно относительно антенного блока (АБ) СНС.Where

,

- the location vector of ANN1 and INC2, respectively, relative to the antenna unit (AB) of the SNS.

,

перемещения ИНС1 и ИНС2 со скоростью

АБ СНС приведет к выражениям вида:Obviously speed comparison

,

displacement of ANN1 and ANN2 with speed

AB SNA will lead to expressions of the form:

и

движения ИНС1 и ИНС2 относительно АБ СНС однозначно определяются угловой скоростью вращения Ω' объекта вокруг его ЦТ и местоположением ИНС1 и ИНС2 относительно АБ СНС Δr₁, Δr₂ (2).It follows from the above expressions that

and

the movements of ANN1 and ANN2 relative to the ABS of the SNA are uniquely determined by the angular velocity of rotation Ω 'of the object around its central heating center and the location of ANN1 and ANN2 relative to the ABS of the SNS Δr ₁ , Δr ₂ (2).

представлена, как угловая скорость вращения объекта вокруг ЦТ. Но этого абсолютно недостаточно для полной характеристики рассматриваемой скорости, поскольку, не ясно, относительно какой системы координат следует рассматривать вращение объекта, а посему непонятна процедура ее расчета.Above

presented as the angular velocity of rotation of an object around a central heating system. But this is absolutely not enough to fully characterize the speed in question, since it is not clear with respect to which coordinate system the rotation of the object should be considered, and therefore the procedure for its calculation is not clear.

вращения объекта и абсолютную угловую скорость

вращения географического сопровождающего трехгранника ГСТ ONHE.To answer these questions, we introduce the absolute angular velocity

object rotation and absolute angular velocity

rotation of the geographic accompanying trihedron of the GTS ONHE.

и

- это угловые скорости вращения объекта и ГСТ ONHE относительно инерциальной системы отсчета.The concept of absolute angular velocity of rotation means the rotation of something relative to an inertial coordinate system. In the case under consideration

and

are the angular velocities of the rotation of the object and the ONHE GTS relative to the inertial reference system.

и

:Obviously, the angular velocity of rotation of the object relative to the GTS ONHE will be equal to the difference in angular velocities

and

:

,

,

, жестко связанные с объектом, изменяют свои проекции на оси ГСТ ONHE, исключительно только за счет вращения связанной с объектом системы координат oxyz, относительно ГСТ ONHE, угловая скорость которого определяется выражением (4), то, очевидно, справедливы следующие выражения для их производных:Given that the vectors

,

,

, rigidly connected with the object, change their projections on the axis of the ONHE GTS, solely due to the rotation of the oxyz coordinate system associated with the object relative to the ONHE GTS, the angular velocity of which is determined by expression (4), then the following expressions are true for their derivatives:

Comparing the 1st and 2nd derivatives with the 3rd (5), we obtain the expressions:

which, taking into account (2), can be written in the following form:

Comparing the obtained vector expressions (7) with those obtained earlier (3), and combining them, we can write the following generalized expressions of the form:

If we present the obtained expressions in a scalar form, in projections on the axis of the geographic accompanying trihedron of the GTS ONHE, then they will acquire a form that is quite acceptable for their algorithmic use.

We give it:

,

,

и

,

,

- проекции векторов

и

(2) на оси ГСТ ONHE.Where

,

,

and

,

,

- projections of vectors

and

(2) on the axis of the GTS ONHE.

The resulting expressions have the form of first-order differential equations presented in the normal Cauchy form, which, by the way, is necessary to describe the original system — the message model in the traditional optimal estimation procedure. This is when viewed from the left.

On the other hand, if we look at (9) and (10) from the right, then these are expressions for calculating the components of the speed of movement of ANN1 (9) and ANN2 (10) relative to the ABSNS.

In some cases, instead of equations / expressions (9), (10) presented in the projections on the ONHE GTS axis, it is advisable to use similar equations / expressions, but in the projections on the axis of the supporting trihedron of the OTGP ANS gyro platform Oξηζ.

Obviously, these equations / expressions, by analogy with (9), (10), will have the following form:

where Δξ ₁ , Δη ₁ , Δζ ₁ and Δξ ₂ , Δη ₂ , Δζ ₂ are the current values of the coordinates of the location of ANN1 / BINS1 and ANN2 / BINS2 relative to AB SNA in the projections on the OTGP axis ANN Оξηζ, a ΔV _1ξ , ΔV _lη , ΔV _1ζ and ΔV _2ξ , ΔV _2η , ΔV _2ζ are the kinematic components of the speed of the ANN1 / BINS1 and ANN2 / BINS2 in the projections on the OTGP axis of the ANN Oξηζ.

In the procedure for optimal filtering and identification of ANN errors by SNA measurements, the above differential equations (11), (12) are used as an integral part of traditional models of ANN or SINS errors, developed on the basis of a rigorous mathematical description of their functioning and in full accordance with the fundamental principle of the unperturbed acceleration measurements.

The extended ANN error model obtained in this way describes not only the parameters traditional for the ANN and their relationships, but also those kinematic components of the measurement signals that were not previously taken into account.

The extension of the ANN error model allows us to eliminate the main cause of the algorithmic inconsistency of all known correction algorithms, which consists in an incorrect mathematical description of the original system, and thereby ensure fast and stable convergence of all and, first of all, weakly observable state parameters, such as α _z , ε _y , Δn _i (Δξ _i ), Δn _i (Δζ _i ), Δe _i (Δη _i ).

,

,

относительной угловой скорости вращения объекта. Приведем возможные математические процедуры расчета рассматриваемых угловых скоростей.For the algorithmic use of the above differential equations (11), (12), it is necessary to know the current values of the input parameters for the specified equations, namely, the components

,

,

relative angular velocity of rotation of the object. We give possible mathematical procedures for calculating the angular velocities under consideration.

,

,

изменения углов эволюции объекта. При этом угловые скорости

,

,

и

,

,

вращения объекта относительно ГСТ ONHE и ОТГП Oξηζ могут быть определены путем приведения компонент

,

,

, и

,

,

к осям ГСТ и ОТГП соответственно. Очевидно, они будут равны (см. фиг. 2, 3):Obviously, the angular velocities of rotation of the SSK Oxyz relative to the ONHE GTS are determined by the angular velocities

,

,

changes in the angles of evolution of the object. In this case, the angular velocity

,

,

and

,

,

the rotation of the object relative to the ONHE GTS and the OTG Oξηζ can be determined by bringing the components

,

,

, and

,

,

to the axes of the GTS and OTGP, respectively. Obviously, they will be equal (see Fig. 2, 3):

In expressions (13), (14) and below, “s” should be understood as the sine of the angle, and by “c” - the cosine.

The above expressions can be used to calculate the required components of the angular velocity.

,

,

,

целесообразно определять методом численного дифференцирования с дискретом 0,1 сек.Moreover, derivatives

,

,

,

it is advisable to determine by numerical differentiation with a discrete of 0.1 sec.

Expressions (13), (14) can be used for their purpose both in measurements of ANNs and in measurements of SINS.

In practice, another approach to calculating the considered components of the angular velocity of the object can be used, but it can be implemented only by measuring SINS. It seems to be somewhat more complicated, but its advantage is the absence of the need to perform operations of numerical differentiation, which is important.

The indicated option for calculating the considered components of the angular velocity of the object is based on the determination of the relative angular velocity and requires knowledge of both the absolute angular velocity of rotation of the object and the absolute angular velocity of rotation of the GTS and TGP. In this case, the desired angular velocities are found as the differences in the absolute angular velocity of the object and, accordingly, the second two. Due to the fact that the absolute angular velocity of an object is measured exclusively by systems, such as SINS, this approach can only be used for their correction.

Considering that the components of the absolute angular velocity of the object, measured by SINS, are output in projections on the axis of the connected coordinate system, their preliminary transformation along the axes of the GTS ONHE and OGP Oξηζ is necessary.

To this end, we write forward and inverse matrix transformations for the coordinate systems shown in FIG. 2 and FIG. 3:

и

для реализации указанных процедур. Они, очевидно, имеют следующий вид:In accordance with FIG. 2 and FIG. 3, we present the transposed matrices

and

to implement these procedures. They obviously have the following form:

In accordance with the matrix (16), the expressions for the components of the absolute angular velocity of the object in the projections on the axis of the GTS ONHE will have the following form:

Similar expressions in the projections on the OTGP axis Oξηζ will be equal to:

To determine the absolute angular velocity components of the GTS ONHE and OGP Oξηζ, we use the mutual orientation of the GSC OX'Y'Z ', GTS ONHE and OGP Oξηζ shown in FIG. four.

To find the absolute angular velocity of rotation of the GTS ONHE, we first write down the expressions for its angular velocity relative to the GSC OX'Y'Z 'associated with the Earth in the projections on the axis of the GTS ONHE. In accordance with FIG. 4, they will obviously be equal:

where the following obvious notation is accepted:

,

- северная и восточная составляющие путевой скорости объекта,Where

,

- the northern and eastern components of the ground speed of the object,

R _N , R _E - the main radii of curvature of the earth's ellipsoid of revolution.

Obviously, the sought absolute components of the angular velocity of the GTS rotation will be equal to the sum of the components (19) and the corresponding projections due to the daily rotation of the Earth, namely:

where the components u _N and u _H are equal

a u is the Earth's daily rotation speed.

Therefore, the required components of the angular velocity of the object relative to the ONHE GTS will be equal to:

where Ω _N , Ω _H , Ω _{E are} defined by expressions (17), and ω _N , ω _H , ω _{E are} expressed by expressions (21).

,

,

произведенных поворотов на углы λ, ϕ, χ к осям ОТГП Oξηζ. В результате получим:In order to determine the components of the relative angular velocity of the OGP Oξηζ, in accordance with FIG. 3, we present all three angular velocities

,

,

rotations by angles λ, ϕ, χ to the axes of the OGP Oξηζ. As a result, we get:

и

представлены выше (20).Expressions for

and

presented above (20).

Obviously, the expressions for the components of the absolute angular velocity of the GTP will be equal to the sum of the components (24) and the corresponding components of the angular velocity of the daily rotation of the Earth:

where u _N , u _{H are} determined by expressions (23).

The expressions for the desired components of the angular velocity of rotation of the object relative to the OGP Oξηζ will be equal to:

where Ω _ξ , Ω _n , Ω _{ζ are} determined by expressions (18), and ω _ξ , ω _η , ω _ζ are determined by expressions (25).

Thus, it is shown that a correct description of the initial system is achieved by expanding the traditional ANN error model by including in it non-traditional differential equations describing the nature of the change in the coordinates of its installation on the object relative to the information system that performs the functions of a meter or ANN corrector. The latter is considered the SNA.

The necessity of this extension is due to the fact that only in this case, algorithmic accounting and elimination of all undesirable consequences that lead to the kinematic velocity components that occur during the maneuver of the object and due to the geometry of the relative placement of the information systems involved in the considered modes can be provided simply and effectively.

Next, we consider the most important operations for the developed algorithm, which determine the physical essence of the proposed engineering solution.

When developing (deriving) an ANN error model, the form of representing its output signals by speed is important. The indicated form not only determines the form of the observation matrix, but the ANS error model itself also substantially depends on it.

Without citing or analyzing all possible forms of this representation, it should be noted that the most analytically developed and acceptable for solving the problem under consideration is a representation of the form:

,

,

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

Components (27) in their physical essence are purely inertial and do not explicitly include kinematic velocity components. Although they are implicitly present, both in components (27) and in the velocity components formed by measurements of the SNA.

In explicit form, these speed components will be presented when comparing the horizontal components of the absolute speed (27) and similar components formed from the current measurements of the SNA. As will be shown below, as a result of this comparison, the so-called communication equations will be obtained from which the desired measurement signals can be formed quite simply and all elements of the observation matrix for the considered estimation and correction procedure can be determined.

Before proceeding to the consideration of these issues, it should be noted that in this case we will use the known kinematic relations connecting the errors Δϕ, Δλ, Δχ of the autonomous inertial numbering of the main navigation parameters with errors α _x , α _y keeping the vertical ANN and the angle α _{z of} azimuthal departure its GP and similar relations for the errors Δυ, Δγ, Δψ _{g of} measuring the angles of evolution of the object.

The indicated ratios have the following form:

It should be noted that the above ratios are valid only for the autonomous inertial numbering mode and in no way can be extended to such autonomous modes as the Kurodoppler KDR or the airborne CWR numeration modes.

The ANN output signals for the horizontal components of the absolute linear velocity in the projections on the axis of the reference trihedral of the GP Оξηζ are represented by expressions (27).

We form similar expressions for the SNA measurements using the calculated ANN of the current value of the angle χ of the azimuthal orientation of the GP ANN.

,

,

и их идеальных значений ϕ, λ, χ - Очевидно, что связывающие их соотношения имеют вид:Hereinafter, we will use the following notation for the calculated ANN parameters

,

,

and their ideal values ϕ, λ, χ - Obviously, the relations connecting them have the form:

It should be noted that for the numbering errors Δϕ, Δλ, Δχ included in (29), the above relations (28) are valid.

We will also assume that all navigation parameters formed from the SNA measurements are equal to their ideal values, additively mixed with normal uncorrelated noise of the corresponding intensity.

,

путевой скорости достаточно просто могут быть сформированы соответствующие составляющие абсолютной линейной скорости

,

:Obviously, knowing the current values of the geographical latitude ϕ ^s with the SNA, as well as the horizontal components

,

ground speed quite simply can be formed corresponding components of the absolute linear velocity

,

:

where: u is the angular velocity of the Earth's daily rotation; R _E is one of the main radii of the earth's ellipsoid of revolution.

,

:Designing the components (30) on the axis of the supporting trihedron of the GP INS, we obtain the following expressions for calculating the components

,

:

приводит к следующим выражениям для составляющих

,

:It is quite simple to show that the substitution in (31) of the value

leads to the following expressions for the constituents

,

:

,

абсолютной линейной скорости приняты следующие обозначения:where for the constituents

,

absolute linear velocity the following notation:

,

,

,

(31) равны соответствующим составляющим V_ξ V_η выражений (27).Obviously, up to random noise, the measurements that make up

,

(31) are equal to the corresponding components V _ξ V _{η of} expressions (27).

,

:Substituting in (32) instead of Δχ its value determined by relation (28), we obtain the following expression for

,

:

,

, и V_ξ, V_η получим следующие уравнения связи:Subtracting the corresponding components (33) from the velocity components (27) and remembering the proximity of the components noted above

,

, and V _ξ , V _η we obtain the following communication equations:

- составляющие ΔV_ξ, ΔV_η кинематической скорости (12).where: W ₃ , W ₄ - measurement noise mentioned above;

- components ΔV _ξ , ΔV _{η of the} kinematic velocity (12).

Denote the left sides of equations (34) by Z ₃ and Z ₄ :

,

, сформированным по измерениям СНС (33).where Z ₃ , Z ₄ are the designations traditionally accepted in the optimal filtering procedure for measurement signals, which are found by comparing the components of the velocity V _x , V _y , measured by the ANN (27), and the components

,

formed by measurements of the SNA (33).

On the right side of the communication equations (34), which in the matrix representation, as a rule, are written in the form:

the elements of the row matrices H ₃ and H _{4 of the} observation are determined.

To determine them, we present the form of the state parameter vector of the extended system for the case of correction according to the SNA measurements.

In accordance with the study, the vector x under consideration has the dimension [13 × 1] and should include the following state parameters:

where all the state parameters above have already been presented, with the exception of the uncompensated components ε _x , ε _y , ε _{z of the} departure of the corresponding gyroscopes.

Measurement signals generated from measurements of the coordinates of the current location of the object can be obtained by comparing the geographical coordinates calculated by the inertial system and the measured SNA.

If the second of them is written as:

then the first - inertial coordinates, obviously, will be equal:

Where

the location coordinates of the ANN relative to the AB SNA. The accuracy of their representation is determined by second-order smallness values with respect to such state parameters (37) as Δξ, Δη, Δλ, α _z .

A comparison of the location coordinates calculated by the inertial system (39) and the measured SNA (38) will lead to the following communication equations:

where W ₁ , W ₂ - normal noise measurements of known intensity.

Taking the left sides of equations (41) as measurement signals Z ₁ and Z ₂ :

on the right-hand sides, in accordance with (41), the corresponding elements of the observation matrix can be obtained.

The indicated matrix, in accordance with (34), (41) and (37), will have the following form:

Given that the procedure for optimal correction of all parameters of the ANN state in the classical version of its execution with evaluation and control in accordance with the one presented in the monograph by A.A. Krasovsky "Analytical design of control circuits of aircraft", "Engineering", Moscow, 1969 [3] a separation theorem, for modern ANNs is impossible, due to their closeness and lack of access to the main control points of the measuring channels of the systems in question, therefore, nothing more acceptable remains as its software implementation in an open circuit, or in a computer complex.

Before proceeding to its mathematical description, we will present the optimal estimation procedure preceding it and the cyclogram of its implementation.

To evaluate all errors of the ANN, the mathematical description of which is presented in the form of an extended system of interconnected differential equations of the first order, it is necessary to provide two sections of the flight.

In the first horizontal section of a straight flight without accelerations, the so-called “horizontalization” of the gyro platform is carried out with the evaluation of well-observed parameters of the ANN horizontal channels, such as ΔV _x , ΔV _y , α _x , α _y , ε _x and a coordinated (inseparable) estimation of poorly observed parameters, such as α _z , ε _y . The duration of this correction section is no more than 4-4.5 minutes, at the end of which, for the purpose of accurately assessing poorly observed parameters, a maneuver is performed, such as a “snake”, coordinated or combat turns.

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

As a result of its implementation, an accurate assessment of state parameters such as α _z , ε _y , Δξ, Δη, Δζ, as well as the refinement of the estimate of the drift ε _{z of the} azimuthal gyroscope is carried out. Accurate estimation of the coordinates Δξ, Δη, Δζ of the location of the ANN relative to the AB SNA is an indicator of the quality of the assessment and is necessary for the algorithmic accounting of the kinematic components of speed.

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

After that, the filter-identifier is transferred to the long-term mode - until the next correction session, the forecast of the received estimates.

A feature of its operation 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 for the whole time of the forecast are also taken equal to zero.

Moreover, as the initial values of the estimates in the forecast procedure, their values obtained at the end of the maneuver are used, and all values of the coefficients that weight the considered estimates are calculated in accordance with their analytical representation in the extended ANN error model. In this case, for their calculation, the current values of autonomously calculated / adjusted parameters are used.

,

,

,

,

…, а счисленные значения инерциальных параметров, как

,

,

, V_x, V_y ….Further, the values of the estimates obtained as a result of the forecast will be denoted in the same way as 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 parameters.

,

,

определяются выражениями (29). Тогда, располагая значениями оценок

и

, выражения для расчета откорректированных географических координат местоположения будут иметь вид:When correcting the geographical coordinates of the location and the true course, we assume that the calculated values

,

,

are determined by expressions (29). Then, having the values of the estimates

and

, expressions for calculating the corrected geographical coordinates of the location will look like:

To correct the true course, we use the expression in accordance with which it is calculated:

- счисленное значение угла азимутальной ориентации опорного трехгранника ГП ИНС, а

- измеренный гироскопический курс.Where

- the calculated value of the azimuthal orientation angle of the supporting trihedron of the GP INS, and

- measured gyroscopic course.

и ошибки измерения гироскопического курса

.From the expression (45) it follows that in order to correct the true course, it is obviously necessary to first write off the errors of the reckoning angle

and gyroscopic heading measurement errors

.

осуществляется в соответствии с соотношениями:Corrected Corrected Angle Value Procedure

carried out in accordance with the ratios:

,

- оцененные/спрогнозированные значения оценок угла α_z азимутального ухода ГП ИНС и ошибки счисления географической долготы, а

- откорректированное значение географической широты (44).Where

,

- estimated / forecasted values of the estimates of the angle α _{z of the} azimuthal drift of the GP INS and the errors of calculating geographic longitude, and

- adjusted value of geographical latitude (44).

осуществляют в соответствии со следующей цепочкой соотношений:In this case, the correction of the angle of the gyroscopic course

carried out in accordance with the following chain of ratios:

,

,

оцененные/спрогнозированные значения малых углов рассогласования реального и опорного трехгранников ГП ИНС.Where

,

,

estimated / predicted values of small mismatch angles of the real and reference trihedra of the INS GP.

, в соответствии с (45) будет равно:Therefore, the corrected true rate value

, in accordance with (45) will be equal to:

To correct the components V _x , V _{y of the} absolute linear velocity, we use expressions (27).

,

,

,

,

, в соответствии с упомянутыми выше выражениями (27), достаточно просто могут быть рассчитаны текущие откорректированные значения составляющих

,

абсолютной линейной скорости.Knowing the current forecasted valuation values

,

,

,

,

, in accordance with the above expressions (27), the current corrected values of the components can be calculated quite simply

,

absolute linear speed.

The expressions for their calculation are:

,

абсолютной линейной скорости могут быть использованы в качестве входных параметров при реализации алгоритма автономного инерциального счисления. При этом в качестве начальных значений координат ϕ, λ, χ используются их откорректированные значения (44), (46).The indicated values of the horizontal components

,

absolute linear velocity can be used as input parameters when implementing the algorithm of autonomous inertial numbering. In this case, their adjusted values (44), (46) are used as the initial values of the coordinates ϕ, λ, χ.

(14), (26), вычисляемой в соответствии с рекуррентным выражением вида:Additionally, in order to implement an effective quality control procedure for assessing the parameters of the ANN state, after completing the maneuver and reaching the established post-maneuvering course, this is determined by the value of the component averaged over a 5-second time interval

(14), (26), calculated in accordance with a recurrence expression of the form:

- предыдущее и последующее значения осредненной скорости;

- текущее входное значение осредняемой величины после выхода на установившийся послеманевренный курс - спустя 30 сек после начала маневра и при выполнении неравенства вида:Where

- previous and subsequent values of the averaged speed;

- the current input value of the averaged value after reaching the steady post-maneuvering course - 30 seconds after the start of the maneuver and when inequalities of the form are fulfilled:

,

,

координат местоположения ИНС относительно АБ СНС к осям связанной с объектом системы координат.When this inequality is fulfilled, the command “Maneuver is completed” is formed and, without stopping the optimal estimation procedure, the current values of the estimates are given

,

,

coordinates of the location of the ANN relative to the AB SNA to the axes associated with the object coordinate system.

,

,

осредняют на 3-секундном интервале времени, в соответствии с приведенной выше рекуррентной процедурой нахождения среднего (50), и сравнивая полученные осредненные значения оценок

,

,

с хранящимися в БЦВМ конструктивными значениями указанных координат, при положительном исходе сравнения, когда их разница не превышает 1-2%, формируют признак «Оценка+», останавливают процедуру оценивания и переходят к режиму полноценного прогноза и коррекции.The resulting current valuation values

,

,

averaged over a 3-second time interval, in accordance with the above recursive procedure for finding the average (50), and comparing the obtained averaged estimates

,

,

with the constructive values of the indicated coordinates stored in the digital computer, with a positive outcome of the comparison, when their difference does not exceed 1-2%, the sign “Score +” is formed, the evaluation procedure is stopped and the mode of full-fledged forecasting and correction is switched on.

,

,

,

,

,

,

,

,

,

.Otherwise, the sign “Evaluation-” is formed and after the evaluation is stopped, the forecast is not realized, and the correction of the current values of the calculated / measured parameters is carried out using the valuation values stored at the time of the evaluation stop.

,

,

,

,

,

,

,

,

,

.

The feasibility of using indirect quality control of optimal estimation of all parameters of the ANN state, including the slightly observable, such as the angle α _{z of the} azimuthal drift of the GP ANN and the drift ε _{y of the} longitudinal channel gyroscope, can be confirmed by theoretical and experimental studies, as well as the results of bench and field tests, during which the main of the fact that in the present invention agaetsya as technical result.

In the course of the aforementioned works, additional comprehensive studies were conducted to assess:

- the effect of the intensity of the performed maneuver on the accuracy and speed of the ANN parameter estimation;

- the dependence of the specified indicators of the quality of assessment on the accuracy of the reference information, the frequency of its updating and the time delay.

The main conclusion of the conducted research and full-scale tests is that without accurate estimation of the coordinates of the relative location of the navigation measuring systems involved in the integrated processing of information, it is impossible to qualitatively solve problems such as the initial exhibition and correction of the ANN under the specific conditions of a disturbed and maneuverable aircraft flight.

Accurate estimation of the relative coordinates of the location of the navigation systems involved in the joint processing of information is a necessary and sufficient condition for the accurate estimation of all parameters of the ANN state, including the weakly observed ones.

The inventive method of estimating errors of inertial information and its correction by measuring the satellite navigation system is implemented as follows.

1. The optimal estimation of inertial information errors is carried out on the basis of the classical procedure of optimal filtering and Kalman identification and in exact accordance with the mathematical model of ANN errors traditional for the considered estimation mode.

2. The input signals of the optimal filter identifier are formed by comparing the geographical coordinates of the same location and the horizontal components of the absolute linear velocity of the object in the projections on the OTGP axis of the ANN, measured by the ANN and formed from the SNS measurements, and the filter identifier is synthesized in full accordance with the mathematical description of the ANN .

3. The estimation of inertial information errors is methodically organized in such a way that after 270 seconds of a straight horizontal flight, on which exact “leveling” is realized with the well-observable parameters of ANN horizontal channels being evaluated, a highly dynamic maneuver, such as a “snake”, of coordinated or combat turns, is carried out , which assesses the observable parameters of the ANN, such as the azimuthal drift α _{z of} its GP and uncompensated drift ε _{at the} longitudinal channel gyroscope.

4. At the end of the maneuver, the active phase of the optimal filtering of the ANN parameters is stopped and the filter identifier is transferred to the long-term mode until the next session of the optimal estimation of ANN errors and the forecast of the obtained estimates.

5. For its implementation, the measurement signals and the optimal gain of the filter-identifier are reset, previously stopping the procedure of their recursive calculation, and the values of the estimates at the time of completion of the active phase of the optimal estimation are used as initial conditions in the procedure for their prediction.

6. In this case, the forecast of optimal estimates is carried out in accordance with the discrete equations used in the optimal estimation procedure for calculating a priori estimates.

,

,

,

и счисленные значения навигационных параметров

,

,

,

.7. Correction of the output parameters of the ANN - the geographical coordinates of the location and the horizontal components of the absolute linear velocity is implemented in an open loop, for which the current predicted estimates are used

,

,

,

and calculated values of navigation parameters

,

,

,

.

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

8. The traditional ANN error model developed for solving such problems is expanded by including a mathematical description of the coordinates of its location relative to the antenna unit of the SNA, which is represented as a system of three interconnected differential equations of the first order in the projections on the axis of the reference trihedron of the GP ANN, which are simultaneously they also describe the components of the kinematic velocity of the ANN that are additively included in the measurement signals of the optimal filter-identifier.

The rationale for expanding the ANN error model and deriving the differential equations of its motion relative to the ABS of the SNA is given in the section of the invention and is represented by expressions (1) ÷ (12), where the equations themselves, and at the same time, the expressions for the components of the kinematic speed of the ANN relative to the ABS of the SNA, have view (11), (12).

,

,

относительной угловой скорости объекта, которые являются входными параметрами дифференциальных уравнений (11), (12), представлен выражениями (13)÷(26).In this case, the derivation of the calculated expressions for the components

,

,

the relative angular velocity of the object, which are the input parameters of the differential equations (11), (12), is represented by the expressions (13) ÷ (26).

,

,

,

,

,

,

,

,

,

.9. When generating the input signals of the optimal filter identifier and the observation matrix, kinematic relations (28) are used, connecting errors Δϕ, Δλ, Δχ, calculating the geographical coordinates of the location and the azimuthal orientation angle of the reference AN IN trihedral with vertical errors α _x , α _y and the angle α _{z of the} azimuthal drift of the INS GP, which, up to the second order of smallness with respect to such parameters as Δϕ, Δλ, α _x , α _y , α _z , provide the determination of the values of the elements of the message matrix and ning, which provides an efficient in accuracy and speed of estimation and subsequent long-term forecast of such errors of autonomous inertial reckoning as

,

,

,

,

,

,

,

,

,

.

A detailed description of the procedure for generating positional (41) and high-speed (34) communication equations and deriving expressions based on them for calculating measurement signals by coordinates (42) and speed (35) and observation matrix (43) is presented in the corresponding section of the invention, in which presents the output of the mentioned signals and the observation matrix (28) ÷ (43).

,

, осуществляют в соответствии с общепринятыми выражениями (44), в которых используют текущие спрогнозированные значения оценок

,

, а коррекцию горизонтальных составляющих V_x, V_y абсолютной линейной скорости реализуют в соответствии с выражениями (49). Для чего используют текущие значения спрогнозированных оценок

,

,

,

,

и расчетные значения составляющих V_x и V_y (27).10. Correction of geographic coordinates of location calculated by inertial system

,

are carried out in accordance with generally accepted expressions (44), in which the current predicted values of estimates are used

,

and the correction of the horizontal components V _x , V _{y of the} absolute linear velocity is realized in accordance with expressions (49). Why use the current values of the predicted estimates

,

,

,

,

and the calculated values of the components V _x and V _y (27).

объекта реализуют в соответствии с физическим определением углов ψ_г и χ, его определяющих (45), (48).11. True course correction

the object is implemented in accordance with the physical definition of the angles ψ _r and χ, which determine it (45), (48).

азимутальной ориентации опорного трехгранника ГП ИНС (46), используя текущие спрогнозированные значения оценок

,

и откорректированное значение широты

(44).To do this, calculate the corrected angle

azimuthal orientation of the reference trihedron of the GP INS (46), using the current predicted estimates

,

and adjusted latitude

(44).

погрешности счисления угла

используют соответствующее кинематическое соотношение связи Δχ с α_z и Δλ (28).In this case, to calculate the estimate

margin error

using the corresponding kinematic relationship of the relationship Δχ with α _z and Δλ (28).

рассчитывают в соответствии с цепочкой соотношений, представленной выражениями (47). Для этого используют текущие спрогнозированные значения оценок

,

,

и измеренные/откорректированные значения текущих углов тангажа

, крена

и гироскопического курса

. При этом сама процедура расчета (47) основана на кинематических соотношениях связи ошибок Δυ, Δγ, Δψ_г измерения углов эволюции объекта с малыми углами α_х, α_y, α_z рассогласования реального и опорного трехгранников ГП ИНС (28).Current adjusted gyro rate value

calculated in accordance with the chain of ratios represented by expressions (47). To do this, use the current forecasted valuation values

,

,

and measured / corrected values of the current pitch angles

roll

and gyroscopic course

. In this case, the calculation procedure (47) is based on the kinematic relations of the error relation Δυ, Δγ, Δψ _{g of} measuring the evolution angles of the object with small angles α _x , α _y , α _{z of the} mismatch between the real and the reference trihedra of the INS GP (28).

рассчитывают, как сумму откорректированных значений

(46) и

(47).Corrected true course value

 calculated as the sum of the adjusted values

(46) and

 (47).

Additionally, to control the quality of assessment and implementation of a useful decision-making scheme, the following is carried out:

относительной угловой скорости объекта (5), которое постоянно вычисляют с момента начала маневра, отсчет которого, в соответствии с циклограммой коррекции, начинают с 270-ой секунды после начала коррекции.12. After completing the maneuver and reaching the established post-maneuverable course, the fact of which is established by the value of the component averaged over a 5-second time interval

the relative angular velocity of the object (5), which is constantly calculated from the moment the maneuver begins, the countdown of which, in accordance with the correction sequence diagram, begins from the 270th second after the start of correction.

на выходе из маневра - начиная с 300-ой секунды не превышает

рад/с (~3 град/мин) (51), формируют команду «Маневр завершен» и, не прекращая процедуры оптимального оценивания, приводят текущие значения оценок

,

,

координат местоположения ИНС относительно АБ СНС к осям связанной с объектом системы координат, а получаемые при этом значения оценок

,

,

, в соответствии с рекуррентной процедурой нахождения среднего (50), осредняют на 3-секундном интервале времени, после чего осредненные значения оценок

,

,

сравнивают с хранящимися в БЦВМ конструктивными значениями указанных координат и при его положительном исходе, когда их разница не превышает 1-2%, формируют признак «Оценка +», останавливают процедуру оптимального оценивания и переходят к режиму прогноза и коррекции, в противном случае формируют признак «Оценка -» и после остановки оценивания прогноз не реализуют, а коррекцию текущих значений счисленных параметров осуществляют с использованием запомненных, на момент остановки оценивания, значений оценок

,

,

,

,

,

,

,

,

,

.Moreover, if the indicated average value

at the exit from the maneuver - starting from the 300th second it does not exceed

rad / s (~ 3 deg / min) (51), form the “Maneuver is completed” command and, without stopping the optimal estimation procedure, present the current values of the estimates

,

,

coordinates of the location of the ANN relative to the AB of the SNA to the axes of the coordinate system associated with the object, and the resulting evaluation values

,

,

, in accordance with the recursive procedure for finding the average (50), averaged over a 3-second time interval, after which the averaged estimates

,

,

they are compared with the constructive values of the indicated coordinates stored in the digital computer and, with a positive outcome, when their difference does not exceed 1-2%, the sign “Score +” is formed, the optimal estimation procedure is stopped and the prognosis and correction mode are switched on, otherwise the sign “ Evaluation - ”and after the evaluation is stopped, the forecast is not realized, and the correction of the current values of the calculated parameters is carried out using the estimated values at the time the evaluation was stopped

,

,

,

,

,

,

,

,

,

.

The rationale for the feasibility and feasibility of implementing the specified evaluation control scheme is given in the final part of the section of the invention.

From the presented description of the proposed method for estimating errors of inertial information and its correction by measuring the satellite navigation system, it follows that the technical result of the invention is achieved.

Claims (2)

1. A method for estimating errors of inertial information and its correction from measurements of a satellite navigation system, including the use of the traditional optimal filtering and Kalman identification procedure, for which measurement signals of the optimal filter-identifier are generated by comparing the geographical coordinates of the same location and the horizontal components of the absolute linear velocity in projections on the axis of the reference trihedral of the gyro platform (GP) of the inertial navigation system (ANN) of the calculated ID C and formed by measurements of the satellite navigation system (SNA), and its structure is synthesized in accordance with the error model traditional for the ANN, while the nature of the flight is methodically organized in such a way that after 270 seconds of a straight horizontal flight, on which the gyro platform is precisely “horizontized” and evaluate the well-observed parameters of the ANN horizontal channels, carry out a maneuver, such as a “snake”, of coordinated or combat turns, after which the active phase of the optimal filter procedure radios and identifications are suspended and the filter identifier is transferred to the long-term mode - until the next correction session, the forecast, for which the measurement signals are reset, and the valuation values at the time the active phase of the estimation procedure is completed are used as initial conditions in the forecast procedure, while the forecast itself carried out in accordance with discrete equations for calculating a priori estimates of ANN errors, and the correction of the output parameters of the ANN - the geographical coordinates of the location and the components of the absolute linear linear velocity, they are implemented in an open-circuit ANN, for which they use the current predicted estimates of the state parameters of the ANN, characterized in that the ANS error model used in solving such problems is expanded by including a mathematical description of the coordinates of its location relative to the antenna unit (AB) SNA and represent them in the form of a system of three interconnected differential equations of the first order in the projections on the axis of the supporting trihedron of the GP INS, which are simultaneously described additively in odyaschie in speed measurement signals kinematic components of the relative velocity of the INS motion, and when forming the measurement signal and the observation matrix using kinematic equations relating Δφ errors, Δλ, Δχ numeral geographical coordinates of location and angle of the azimuthal orientation of the reference trihedron SE ANN errors withstand vertical α _x, α _y and the angle α _{z of the} azimuthal drift of the INS GP, than, up to the second order of smallness with respect to such parameters as Δϕ, Δλ, α _x , α _y , α _z , provide They determine the current values of the elements of the message and observation matrices and thereby realize an accurate and effective estimation and subsequent forecast of such errors of autonomous inertial numbering as

,

,

,

,

,

,

,

,

,

while correcting autonomously calculated geographic coordinates

,

the current location and the components V _x , V _{y of the} absolute linear velocity are carried out in accordance with generally accepted expressions, for which the current predicted estimates are used

,

,

,

and small angles

,

,

, and to correct the true course, the corrected angle value is calculated

azimuthal orientation of the reference GP trihedron as a function of estimated values

and

and calculate the corrected value of the gyroscopic course

in the rating function

and errors

roll angle measurements

, which is determined by calculation in the function of current, predicted values of estimates

,

and the measured / corrected angles of the gyroscopic heading ψ _g and pitch υ, after which the true heading ψ is calculated _and as the sum of the estimates

and

. 2. The method for estimating errors of inertial information and its correction by measuring the satellite navigation system according to claim 1, characterized in that after completing the maneuver and reaching the established post-maneuvering course, the fact of which is established by the value of the component averaged over a 5-second time interval

the relative angular velocity of the object, which is constantly calculated from the moment the maneuver begins, the countdown of which, in accordance with the correction sequence diagram, begins from the 270th second after the correction begins, moreover, if the indicated average value at the exit from the maneuver starts from the 300th second , does not exceed

rad / s (~ 3 deg / min), form the command “Maneuver is completed” and, without stopping the optimal estimation procedure, present the current values of the estimates

,

,

coordinates of the location of the ANN relative to the AB SNA to the axes of the coordinate system associated with the object, and the current values of the estimates obtained

,

,

, in accordance with the recursive procedure for finding the average, averaged over a 3-second time interval, after which the averaged estimates

,

,

they are compared with the constructive values of the indicated coordinates stored in the on-board digital computer (BCM) and, with a positive outcome of the comparison, when their difference does not exceed 1-2%, the sign “Score +” is formed, the optimal estimation procedure is stopped and the regime of full-fledged forecast and correction is stopped otherwise, the “Evaluation -” sign is formed, and after the evaluation is stopped, the forecast is not realized, and the correction of the current values of the calculated parameters is carried out using the time of stopping estimating the values of the estimates

,

,

,

,

,

,

,

,

,

.

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