RU2634083C1 - Navigation-piloting complex - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: navigation-piloting complex includes, at least, two strapdown navigation systems and an associated primary information processing unit, wherein the complex additionally comprises a navigation equation solving unit and a control unit, with the first input connected to the output of the navigation equation solving unit, and with the second and the third inputs connected to the first outputs of the strapdown navigation systems, wherein the primary information processing unit includes, in series connected calculating unit of variables b_i(k, r) in the signal direction, connected with the inputs to second outputs of the strapdown navigation systems, a calculating unit of measurements z_i, a calculating unit of residuals δ_i, a filtration unit of residuals δ_i, and a calculating unit of the orientation matrix, with the output connected to the first input of the navigation equation solving unit, and in series connected calculating unit of variables γ_i in the signal direction, with the inputs connected to the third outputs of the strapdown navigation systems, a filtration unit y_i and a calculating unit of the guide cosine matrix, with the output connected to the second input of the navigation equation solving unit.

EFFECT: increasing the accuracy of output information of the complex and the control depth of the systems that make up the complex.

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Description

The invention relates to navigation and aerobatic systems, combining several inertial navigation systems (ANN) to generate generalized output information about the location of the object, its orientation in space and its speeds, as well as using external information to correct the systems that make up the complex.

The prior art navigation and flight system VP-021 (see Fig. 1), including three strapdown inertial navigation systems (SINS) and a processing unit for their output information associated with the inputs of the SINS.

In the well-known navigation and aerobatic complex, inertial navigation systems are integrated by selecting the output information of inertial navigation systems (ANNs) according to a majority attribute, i.e. the most reliable information entering the complex from various systems is considered to be the information that has the least discrepancy, in particular, the system is selected for the correction of which external information is used to increase the accuracy of the output parameters of the system. Other systems that are part of the navigation complex, perform the functions of no more than a backup channel, providing increased reliability of the entire complex.

The technical task of the proposed navigation and flight complex is to increase the accuracy of the output information of the complex and the depth of control of the systems that make up the complex.

The specified technical problem is solved by means of a navigation and aerobatic complex, which includes at least two strap-on navigation systems and a unit for processing primary information associated with them, while the complex additionally includes a unit for solving navigation equations and a control unit connected to the output by the first input unit for solving navigation equations, and the second and third inputs connected to the first outputs of strapdown navigation systems, while the processing unit of the primary the formation includes a variable calculation unit b _i (k, r) connected in series to the second outputs of the strapdown navigation systems, a measurement calculation unit z _i , a residual calculation unit δ _i , a residual filtering unit δ _i and an orientation matrix calculation unit, output coupled to the first input of the navigation equations solutions and serially connected in the direction of signal flow calculation variables γ _i, inputs connected to third outputs strapdown navigating nnyh systems γ _i filtering unit and calculating unit matrix of the direction cosines, the output connected to the second input of the navigation equations solutions.

The specifics of solving the navigation problem using SINS is the lack of control signals of the moment sensors (DM) of the system. Therefore, in order to increase the accuracy of the output information of the complex and to increase the depth of control of the systems that make up the complex, it is proposed to combine several SINSs by pre-processing the primary information coming from the systems — the orientation and acceleration matrix in the axes of the accelerometers of the sensing element unit (BCE) - with the subsequent solution navigation equations based on processed primary information received from the systems included in the complex, with subsequent control coming from the system this in the information complex, which increases the depth of control of the systems that make up the complex (see Fig. 2). Consider the task of complex processing of primary information coming from several SINS (pos. 1, 2) in the form of an orientation matrix and accelerations (or increments of linear velocities) coming from the outputs of the first system integrators. The mutual orientation of the SINS block of sensors in solving the problem can be arbitrary and determined in the initial system exhibition mode as:

i = 1, 2, ..., N,

j = 1, 3, ..., N,

j ≠ i

Where

Ai ₀ , Aj ₀ - the initial value of the orientation matrices Ai, Aj;

N is the total number of SINS included in the complex.

Hereinafter, vectors and matrices are indicated in bold, transpose operations are indicated by the superscript “ ^t ”, matrices are denoted by the superscript “ ^-1 ”.

When solving the problem in the most general case, N orientation matrices Ai, 1 = 1, 2, ..., N, or equivalent course, roll and pitch angles are used as initial information.

, связанную с Ai соотношениями:Define the orientation matrix

related to Ai by the ratios:

Where

δ ^ i is the skew-symmetric matrix corresponding to the vector

малых углов поворота;

small rotation angles;

E is the identity matrix.

The relative orientation of the matrices Ai, Aj is defined as:

from where given

A ^-1 = A ^t - for orthogonal matrices,

(δ ^) ^m = -δ ^ - for skew-symmetric matrices,

справа, получаем:Multiplying (3) by

on the right, we get:

Denote:

Then:

ij = 1, 2, ..., N

i ≠ j

(6) does not provide an unambiguous solution. To confirm this statement, we consider the special case N = 3.

We have:

Multiplying (9) by C _ij on the right and adding with (8), we obtain:

Substituting (9) in (10), we obtain:

In (11), we have an uncertainty of the form 0/0, i.e. system (11) does not have a unique solution. In the general case, for N> 3, any triple of N selected equations will be linearly dependent, i.e. the rank of this system will not be maximum.

The geometric interpretation of the result is completely transparent. The point obtained by (11) is the intersection point of three-dimensional spherical surfaces of radius δ _i in 3N-dimensional space, where δ _i is the length of the vector δ _i , with the centers defined by the matrices A _i . Such a point can be determined by arbitrary specification of the vector δ _j ; all other vectors δ _i , i = 1, 2, ..., N, i ≠ j are determined by solving equations (11).

To obtain an unambiguous solution, we introduce the Gauss criterion:

Equating to zero the first partial derivatives of J with respect to δ _i , we obtain:

Summing (11) over i = 1, 2, ..., N, i ≠ j we get:

or taking into account (13):

Equating the upper off-diagonal elements in (15), we obtain the equations in scalar form:

Where

(in parentheses are the numbers of elements of the matrices C _ij , B _i and vectors δ _i , z _i ), or in vector form:

where the elements of the matrix B and the vector z are determined by (19) and (20).

The desired vector δ _i is defined as:

определяется как:Searched matrix

defined as:

where A _j is the orientation matrix of the jth SINS.

, определяемые как

и

(равно как и матрицы δ^i, δ^j), не являются тождественными и отличаются в общем случае начальной матрицей A_ij0 взаимной ориентации, что может оказаться важным в ряде приложений.It should be noted that the matrices

defined as

and

(as well as the matrices δ ^ i, δ ^ j), are not identical and differ in the general case by the initial matrix A _{ij0 of} mutual orientation, which may turn out to be important in a number of applications.

We note the specific application of criterion (12) in the construction of the algorithm. The standard Gauss criterion is used to obtain a solution to an overdetermined system (least squares method).

In the algorithm under consideration, criterion (12) was introduced to obtain a unique solution to the system of 3N equations with 3N unknowns. Generally speaking, one can obtain an overdetermined system by writing N equations (11) with i = 1, 2, ..., N. However, this approach will not give the desired result due to the complete identity of the written equations. Indeed, consider the system:

Substituting (26) in (25):

and multiplying on the right by C _ki , we obtain, taking into account C _ki C _kj = C _jj :

identical (24).

решалась выше с использованием критерия Гаусса (12). Задача может решаться с использованием критерия Чебышева:Definition task

was solved above using the Gauss criterion (12). The problem can be solved using the Chebyshev criterion:

In this case, solving a problem with criterion (29) reduces to solving a system of 3N equations with 2N unknowns, and criterion (29) reduces to:

or equivalent to it:

как точка в 3N-мерном пространстве, равноудаленная от трехмерных гиперплоскостей (22). Такой точкой является центр гиперсферы, вписанной в замкнутый симплекс-многогранник, образованный системой 3-мерных гиперплоскостей (22) в 3N-мерном пространстве, а условие (31) трансформируется в условие:Geometrically Solution

as a point in 3N-dimensional space equidistant from three-dimensional hyperplanes (22). Such a point is the center of the hypersphere inscribed in a closed simplex polyhedron formed by the system of 3-dimensional hyperplanes (22) in 3N-dimensional space, and condition (31) is transformed into the condition:

for all i, j = 1, 2, ..., N, equivalent to (29).

слева, получаем параметрическую систему алгебраических уравнений:Multiplying (32) by

left, we obtain a parametric system of algebraic equations:

solving which, we get the result δ _i equivalent to the result obtained earlier.

To take into account the degree of significance (priority) of certain measurements, a matrix of weighting coefficients is introduced into the quadratic Gaussian form. In the problem under consideration, the quadratic form and its derivatives will have the form:

Multiplying (15) by λ _i , i = 1, 2, ..., N, i ≠ j we obtain, taking into account (35):

Equating the upper off-diagonal elements in (36), we obtain the scalar equations (16), (17), (18), where

как результат однократной обработки исходных матриц ориентации A_i, i=1, 2, …, N, полученных на текущий момент времени. Для фильтрации случайных ошибок измерения результаты измерений осредняются на заданном временном интервале измерения построением линейного фильтра:Above, we constructed an algorithm for the unique determination of the vectors δ _i and the matrix

as a result of a single processing of the initial orientation matrices A _i , i = 1, 2, ..., N, obtained at the current time. To filter random measurement errors, the measurement results are averaged over a given measurement time interval by constructing a linear filter:

To construct filter (39), it is necessary to construct a transition matrix F, which describes the dynamics of changes in the estimated variables x, determine the measurement vector z, construct the coupling matrix H, and form the gain K in the filter feedback circuit.

The behavior of orientation matrices A _{i of} complexed SINSs is described by linear Poisson equations:

where ω _i ^ is the skew-symmetric matrix corresponding to the vector ω _{i of the} absolute angular velocities of the instrument trihedron of the ith SINS.

Due to linearity (40) and the principle of superposition, the behavior of the vector δ _i can be described by the kinematic equations of errors

и A_i в осях приборного трехгранника i-го БИНС, вызванные наличием некомпенсированных инструментальных ошибок (дрейфов) системы.where ν _i are the matrix divergence rates

and A _i in the axes of the instrument trihedron of the i-SINS caused by the presence of uncompensated instrumental errors (drifts) of the system.

Since the velocities ν _{i are} determined in the axes of the instrument trihedron, we can assume that these variables are independent of the absolute velocities ω _i .

Denote:

Then the structure of the matrix F in (39) will be determined by equations (41), (42):

Where

E is a unit matrix of size 3 × 3,

dt is the integration step.

The vector of small angles δ _{i is} used as a measurement.

Then the coupling matrix will be determined as:

where E is a 3 × 3 identity matrix.

The gain K can be calculated using the standard Kalman algorithm.

, которая состоит из последовательно соединенных блока вычисления переменных b_i (k, r) (поз. 4), где k, r - номера строк и столбцов матриц ориентации A(k, r) комплексируемых систем, блока вычисления измерений z_i (поз. 5), блока вычисления невязок δ_i (поз. 6), блока фильтрации невязок δ_i (поз. 7) и блока вычисления матрицы ориентации

(поз. 8).The block diagram (see Fig. 2) shows a structural diagram of the functional components of the primary information processing unit (item 3), which implements the calculation of the orientation matrix

, which consists of series-connected unit for computing variables b _i (k, r) (item 4), where k, r are the numbers of rows and columns of orientation matrices A (k, r) of complex systems, unit for calculating measurements z _i (item. 5), the residual calculator δ _i (pos. 6), the residual filtration block δ _i (pos. 7) and the orientation matrix calculator

(item 8).

The task of processing high-speed information is solved at the level of accelerations W _i (speed increments per clock cycle of the computer), defined in projections on the axis of the instrument trihedron (BEC). We form the vector of measurements as:

We get an overdetermined system which we will solve using the Gauss criterion:

where λ _i is the weight coefficient.

, получаем искомое решение (

в проекциях на оси сопровождающего трехгранника).Equating to zero partial derivatives with respect to

, we obtain the desired solution (

in projections on the axis of the accompanying trihedron).

используется в дальнейшем для решения навигационных уравнений.Received Vector

used in the future to solve navigation equations.

To use positional information at current coordinates and the course ϕ _i , λ _i , ε _i we define the matrix of guiding cosines of the i-SINS

where the indices in parentheses determine the elements of the matrix B _i . Performing operations on the direction cosine matrices B _i , similar to operations performed on the orientation matrices A _i :

where the elements of the matrix B _ij and the vector z are determined by (19) and (20), as:

(it is taken into account that the accompanying trihedra of all N SINS have the same orientation in the northern direction of the local meridian).

The desired vector γ _i is defined as:

определяется как:The required matrix of guide cosines

defined as:

We will use the elements γ _i (1), γ _i (2) of the vector γ _i calculated from (55) as measurements in the construction of the filter. The model of estimated errors is a dynamic group of error equations:

Where

δp ₁ , δp ₂ - speed pulses,

α ₁ , α ₂ - errors of vertical construction,

ε ₁ , ε ₂ - reduced scale errors of accelerometers,

ν ₁ , ν ₂ - departure rates, determined by the magnitude of uncompensated drift SINS,

ω ₀ ² - Schuler frequency.

When integrating these equations into the right-hand side, we substitute the values of the angles δ _i and the departures ν _i obtained by the algorithm described above and redesigned on the axis of the accompanying trihedron:

As a result, we obtain an autonomous system of equations for estimation errors:

Δγ ₁ '= Δδr ₁ + ω ₃ Δγ ₂

,

,

переменных γ_i, δp_i, α_i, получаемой на выходе фильтра.where Δγ _i , Δδp _i , Δαi i = 1, 2 are the estimation errors

,

,

variables γ _i , δp _i , α _i obtained at the output of the filter.

When determining the gain in the filter feedback loop, we neglect the weak cross-links between the channels of the system, which will not lead to a violation of the stability of the system, but only to a shift of the roots of its characteristic equation. As a result, we obtain two identical systems of third-order equations:

i = 1, 2

or in vector form:

Where

with measurement:

and communication matrix:

, и векторы x, (64). Компоненты γ_i векторов x, i=1, 2 используются для коррекции матрицы направляющих косинусов:The output parameters of the algorithm are the vector δ _i , which is used to calculate the corrected value of the orientation matrix

, and vectors x, (64). The components γ _{i of the} vectors x, i = 1, 2 are used to correct the matrix of guide cosines:

Where

The components δp _i are used to calculate the corrected speeds.

The block diagram of the functional components of the processing unit of the primary information coming from the SINS output, which implements the calculation of the linear velocity increment matrix W _i , is shown in FIG. 2 in the form of three series-connected blocks (Fig. 2) - a calculation unit according to (47) - (55) of the variables γ _i (item 9), a filtration unit γ _i (item 10) and a calculation unit according to (56) of the matrix B guide cosines (pos. 11). At the output of the block (item 3), we obtain the corrected values of the linear velocities of the object V ₁ , V ₂ and the matrix of guide cosines.

в осях приборного трехгранника и скорости V₁, V₂, полученные в блоке обработки первичной информации.In the block for solving navigation equations (item 12), standard navigation equations are solved and the orientation matrix A is integrated by solving standard Poisson equations. The input quantities for integrating the navigation equations and the orientation matrix in this block are matrices

in the axes of the instrument trihedron and the speeds V ₁ , V ₂ obtained in the primary information processing unit.

The block for solving navigation equations (pos. 12) is connected to the input of the control unit (pos. 13), the other inputs of which are connected to the SINS outputs (pos. 1, 2), which are part of the complex.

We will build an indicator for monitoring high-speed information. Let us determine the difference in the increment of velocities coming from the outputs of the integrators of the i-th and j-th SINS in projections on the axis of the j-th SINS:

We introduce the scalar product as an indicator:

Substituting (70) in (71), we obtain:

Similarly, to control the output information coming from the outputs of the SINS laser gyroscopes, we introduce the scalar product as an indicator:

Where

и

представляют собой матрицы размера 3×3.Indicators

and

are 3 × 3 matrices.

, или первых интеграторов для

) по соответствующему каналу - элемент матриц, стоящий на пересечении второй строки и третьего столбца определяет степень расхождения соответствующего устройства по первому каналу; элемент матриц, стоящий на пересечении первой строки и третьего столбца определяет степень расхождения соответствующего устройства по второму каналу; элемент матриц, стоящий на пересечении второй строки и первого столбца определяет степень расхождения соответствующего устройства по третьему каналу.The magnitude of the elements of these matrices determines the degree of discrepancy between the output signals of the ith and jth SINS (laser gyroscopes for

, or the first integrators for

) on the corresponding channel - the matrix element at the intersection of the second row and the third column determines the degree of discrepancy of the corresponding device along the first channel; the matrix element at the intersection of the first row and the third column determines the degree of divergence of the corresponding device on the second channel; the matrix element at the intersection of the second row and the first column determines the degree of divergence of the corresponding device on the third channel.

Claims (1)

Navigation and flight complex, which includes at least two strapdown inertial systems and a unit for processing primary information associated with them, characterized in that the complex additionally includes a block for solving navigation equations and a control block, the first input connected to the output of the block for solving navigation equations, and the second and third inputs connected to the first outputs of the strapdown inertial systems, while the primary information processing unit includes a series connection the data in the direction of the signal is the variable calculation unit b _i (k, r), the inputs connected to the second outputs of the strap-on navigation systems, the measurement calculation unit z _i , the residual calculation unit δ _i , the residual filtering unit δ _i and the orientation matrix calculation unit connected to a first input unit navigation equations solutions and serially connected in the direction of signal flow calculation variables γ _i, inputs connected to third outputs strapdown navigation systems, filtering block γ _i and block Comput Lenia direction cosine matrix, the output connected to the second input of the navigation equations solutions.

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