RU2483279C1 - Nongyroscopic inertial navigation system - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: quantity of used accelerometers (from 6 to 12) is increased. Mutual location and orientation of their sensitive axes provide for measurement of all basic navigation parameters. Extraction from the measured data of the basic parameters, angular speed components provides determination of angular orientation of the object based on single integration of readings of accelerometers. The proposed system provides reduction of growth rate of errors for determination of angular orientation and coordinates of the object.

EFFECT: improving the accuracy for determining angular orientation of the object and its coordinates.

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Description

Technical field

The invention relates to the field of inertial navigation and can be used to determine the current coordinates of the object and its angular orientation. The device can be used both autonomously and in combination with satellite radio navigation systems GPS and GLONASS.

State of the art

A device is known, described in US patent 2010/0268414 [1]. This device is designed to assess the angular velocity of a mobile object.

A device is known, described in US patent 2010/0114517 [2]. This device is designed to determine the spatial orientation of the object.

The disadvantages of these devices include the low accuracy of determining the spatial orientation of an object based on the readings of accelerometers.

The closest analogue of the present invention and adopted as a prototype is the device described in [3], which includes a module of six accelerometers, a unit for calculating the components of angular acceleration, an integrating unit, a unit for calculating the coefficients of the matrix of coordinate transformations, a unit for calculating accelerations in a connected coordinate system , unit for calculating accelerations in the Earth coordinate system, unit for calculating navigation parameters.

которых в подвижной системе координат и ориентация

их чувствительных осей заданы следующим образом:Moreover, a module of six accelerometers contains uniaxial accelerometers, coordinates

which in the moving coordinate system and orientation

their sensitive axes are defined as follows:

where r is the distance from the installation point of the accelerometer to the center of the moving coordinate system.

The determination of the navigation parameters of the object (coordinates and speed) at the current time using this device is as follows. The unit for calculating the components of angular acceleration determines the angular acceleration of the object based on the readings of six accelerometers. The integrating unit determines angular velocity values by integrating angular acceleration values. The block for calculating the coefficients of the matrix of coordinate transformations determines the angular orientation of the object based on the values of the angular velocity. The unit for calculating accelerations in the associated coordinate system performs the calculation of acceleration data based on the values of the components of the angular velocity and data taken from the accelerometers. The unit for calculating accelerations in the Earth's coordinate system determines the acceleration data by compensating the gravity vector from the values of the "apparent" acceleration. The unit for calculating navigation parameters calculates the speed and coordinates of the object by a single and 2-fold integration of accelerations in the Earth's coordinate system.

The disadvantage of the prototype is the low accuracy of determining the angular orientation of the object. This is due to the fact that to determine the angular orientation, double integration of angular acceleration, which is determined based on the readings of accelerometers, is necessary. In this case, double integration of the low-frequency noise of accelerometers occurs. Since the low-frequency component is practically a deterministic quantity, this leads to the fact that the error in determining the angular orientation has a monotonic increase and depends on time as ~ t ² . Because Since the coordinates of the object are determined on the basis of the subsequent double integration of the values of the angular orientation, the error in determining the coordinates monotonically increases and is estimated as ~ t ⁴ .

Disclosure of invention

The task of the invention is to increase the accuracy of determining the angular orientation of the object due to the transition from double to single integration of the readings of accelerometers. The technical result that allows us to complete the task is to reduce the frequency of integration of the readings of accelerometers and to reduce the growth rate of errors in determining the angular orientation and coordinates of the object.

The essence of this invention is to determine the angular velocity of an object based on "direct" readings of accelerometers, i.e. without performing the integration procedure. In this case, when determining the angular orientation, a single integration of the accelerometer readings will be used, which will lead to a decrease in the error growth to ~ t. To fulfill this condition, it is proposed to determine the basic navigation variables based on the readings of accelerometers (A _{accel, j} ), where j is the number of the accelerometer. In general, there are 12 basic navigation variables

,

,

- составляющие углового ускорения, W_X, W_Y, X_Z - составляющие угловой скорости. Выражение, связывающее значения акселерометров (A_accel,j) и базовых навигационных переменных (β), имеет следующий вид:where F _X , F _Y , F _Z - components of the "apparent" acceleration,

- components of angular acceleration, W _X , W _Y , X _Z - components of angular velocity. The expression connecting the values of accelerometers (A _{accel, j} ) and basic navigation variables (β) has the following form:

A _{accel, j} = Q _j · β, where

In this case, the Q matrix is completely determined by the accelerometer setup parameters: the coordinates of the accelerometers (R _{accel, j} ) and the orientation of their sensitive axes (θ _{accel, j} ). The values of β can be determined by solving a system of linear equations:

Since there are 12 basic navigation variables (β), it is proposed to use the readings of 12 accelerometers for their unambiguous identification based on the solution of the system of equations (2). The relative position of the accelerometers and the orientation of their sensitive axes are selected from the following conditions:

- the lack of degeneracy of the matrix Q;

- maximizing the value of the determinant of the matrix Q to reduce the error in calculating the value of β, since Q ^{-1 is} used in expression (2).

Thus, an increase in the number of accelerometers from 6 to 12 in the present invention, as well as an appropriate choice of the installation coordinates of the accelerometers and the relative orientation of their sensitive axes, provide a unique solution to the system of equations (2). In this case, based on the readings of 12 accelerometers, basic navigation parameters are calculated, from which the corresponding components of the angular velocity are distinguished. A single integration of the components of the angular velocity provides a more accurate (compared with the prototype) determination of the angular orientation of the object, defined by the matrix of coordinate transformations.

Brief Description of the Drawings

The figure shows a structural diagram of a gyro-free inertial navigation system consisting of blocks:

1 - module of the first six accelerometers;

2 - block calculation of the coefficients of the matrix coordinate transformation;

3 - unit for calculating accelerations in a connected coordinate system;

4 - unit for calculating accelerations in the Earth's coordinate system;

5 - block calculation of navigation parameters;

6 - module of the second six accelerometers;

7 - block calculation of basic navigation variables;

8 - block calculation of the components of the angular velocity.

The implementation of the invention

A gyro-free inertial navigation system containing a distributed set of accelerometers consists of an accelerometer module (1), a unit for calculating the coefficients of the coordinate transformation matrix (2), a unit for calculating accelerations in a connected coordinate system (3), a unit for calculating accelerations in the Earth coordinate system (4), unit for calculating navigation parameters (5), while the first six accelerometers have coordinates

in a connected coordinate system, where r is the distance from the installation point of the accelerometer to the center of the coordinate system.

To ensure increased accuracy in determining the angular orientation of the object, as well as navigation parameters: speed and coordinates of the object, the following are introduced into the device:

- module of the second six accelerometers (6);

- block calculation of basic navigation variables (7);

- unit for calculating the components of the angular velocity (8).

In this case, the orientation of the sensitive axes of the accelerometers (Θ) located in the module of the first six accelerometers (1) is specified in the associated coordinate system as

accelerometers disposed in the second module six accelerometers (6), have coordinates

in a connected coordinate system, and the orientation of their sensitive axes is specified in a connected coordinate system as

, которые содержат составляющие угловой скорости объекта.The module of the second six accelerometers (6) in combination with the module of the first six accelerometers provides the ability to highlight the basic navigation variables:

that contain the components of the angular velocity of the object.

The unit for calculating basic navigation variables (7) is designed to determine these components (β) based on the readings of accelerometers.

The unit for calculating the components of the angular velocity (8) is intended for calculating these components on the basis of basic navigation variables.

Blocks (7) and (8) can be implemented both hardware and software.

Communications between devices are as follows:

- the outputs of the module of the first six accelerometers (1) and the module of the second six accelerometers (6) are connected to the inputs of the unit for calculating basic navigation variables (7) and the unit for calculating accelerations in the associated coordinate system (3);

- the output of the block of basic navigation variables (7) is connected to the input of the block for calculating accelerations in the associated coordinate system (3) and to the input of the block for calculating the components of the angular velocity (8);

- the output of the block for calculating the components of the angular velocity (8) is connected to the input of the block for calculating the coefficients of the matrix of coordinate transformations (2);

- the output of the block for calculating the coefficients of the matrix of coordinate transformations (2) is connected to the input of the block for calculating accelerations in the Earth's coordinate system (4);

- the output of the unit for calculating accelerations in the associated coordinate system (3) is connected to the input of the unit for calculating accelerations in the Earth coordinate system (4);

- the output of the unit for calculating accelerations in the Earth's coordinate system (4) is connected to the input of the unit for calculating navigation parameters (5).

An example of a specific implementation.

The simulation showed that the maximum value of the determinant of the matrix Q, which minimizes the error in determining the basic navigation parameters, is performed by setting the coordinates of the accelerometers and the orientation of their sensitive axes, presented below in tables 1, 2.

Table 1 Accelerometer Installation Coordinates _Accel Acc 1 Acc 2 Ass 3 Acc 4 Acc 5 Acc 6 Acc 7 Acc 8 Acc 9 Acc 10 Acc 11 Acc 12 X 0 0 r r 0 0 -r -r 0 0 0 0 Y r r 0 0 -r -r 0 0 0 0 0 0 Z 0 0 0 0 0 0 0 0 -r -r r r

table 2 Orientation of the sensitive axes of accelerometers θ _accel Acc 1 Acc 2 Ass 3 Acc 4 Acc 5 Acc 6 Acc 7 Acc 8 Acc 9 Acc 10 Acc 11 Acc 12 X 0 0 0 -one -one 0 0 one one 0 0 0 Y 0 -one 0 0 0 one -one 0 0 0 one 0 Z one 0 -one 0 0 0 0 0 0 one 0 -one

и скорости

) в текущий момент времени (t_i) с помощью предлагаемого устройства выполняется следующим образом:Definition of navigation parameters of an object (coordinates

and speed

) at the current moment of time (t _i ) using the proposed device is performed as follows:

Accelerometer readings can be defined as:

, j∈1-12,

, j∈1-12,

where F is the "apparent" acceleration of the object in the moving coordinate system; R _j - coordinates of the installation of the accelerometer (see table 1); θ _{accel, j} is the orientation of the sensitive axes of the accelerometers (see table 2); W is the angular velocity of the object.

Based on 12 accelerometers, the basic navigation parameters β are determined as β = Q ^-1 · F _accel .

The unit for calculating basic navigation variables (3) provides the calculation of:

- элементы матрицы

(обратной Q_j), det(Q) - детерминант матрицы Q.Where

- matrix elements

(inverse Q _j ), det (Q) is the determinant of the matrix Q.

The unit for calculating the components of the angular velocity (4) performs the following transformation based on the obtained components of the basic navigation parameters:

The unit for calculating the coefficients of the coordinate transformation matrix (2) determines the angular orientation of the object based on the values of the angular velocity W (t _i ):

The unit for calculating accelerations in the associated coordinate system (3) calculates the data of accelerations based on the values of the components of the angular velocity and data taken from accelerometers:

The unit for calculating accelerations in the Earth coordinate system (4) determines the acceleration data by transferring the “apparent” acceleration from the gravity vector connected to the Earth coordinate system and compensating for it:

P _i = C _i · F _i ,

The unit for calculating navigation parameters (5) calculates the speed V (t,) and coordinates R (t _i ) by a single and 2-fold integration of accelerations:

V _i = V _i-1 + a _i · Δt, R _i = R _i-1 + V _i · Δt + 0.5 · a _i · Δt ² .

Let us estimate the error in determining the angular orientation and calculating the coordinates of the object. Since the angular orientation is determined on the basis of a single integration of the readings of the accelerometers, this leads to the fact that the error in determining the angular orientation is estimated as ~ t. Because the coordinates are determined on the basis of the subsequent double integration of the values of the angular orientation, the error in determining the coordinates also has a monotonous growth and is already estimated as ~ t ³ .

Comparison of error growth estimates for the prototype and the proposed device showed that the proposed device has a gain in the accuracy of determining the navigation parameters by reducing the error growth rate: if for the prototype the contribution to the orientation error and coordinates from the low-frequency noise of the accelerometers is ~ t ² ~ t ⁴ , accordingly, similar estimates for the prototype look like ~ t and ~ t ³ , respectively.

The use of this invention makes it possible to increase the accuracy of determining the angular orientation of the object, as well as the accuracy of determining its navigation parameters (coordinates and speed).

Information sources

1. US patent 2010/0268414, G06F 7/00 20060101, G06F 007/00.

2. US patent 2010/0114517, 702/92; 702/153.

3. Chao-Yu Hung, Chun-Min Fang, and Sou-Chen Lee "A Compensator to Advance Gyro-Free INS Precision", International Journal of Control, Automation, and Systems, vol. 4, no.3, p.351 -358, June 2006.

Claims (1)

A gyro-free inertial navigation system containing a distributed set of accelerometers, namely, an accelerometer module, a unit for calculating the coefficients of a matrix of coordinate transformations, a unit for calculating accelerations in a connected coordinate system, a unit for calculating accelerations in the Earth's coordinate system, a unit for calculating navigation parameters, the first six accelerometers having coordinates

in a linked coordinate system,
where r is the distance from the installation point of the accelerometer to the center of the coordinate system, while the output of the module of these accelerometers is connected to the input of the unit for calculating accelerations in a connected coordinate system, the output of the unit for calculating the coefficients of the matrix of coordinate transformations is connected to the input of the unit for calculating accelerations in the earth coordinate system, the output of the unit calculating accelerations in a connected coordinate system is connected to the input of the block for calculating accelerations in the earth coordinate system, the output of the block for calculating accelerations in the earth coordinate system is connected to a unit for calculating navigation parameters, characterized in that the system includes a module of the second six accelerometers, a unit for calculating basic navigation variables, a unit for calculating angular velocity components, and the orientation of the sensitive axes of the accelerometers (Θ) located in the module of the first six accelerometers is specified in related coordinate system as

accelerometers located in the module of the second six accelerometers have coordinates

in a connected coordinate system, and the orientation of their sensitive axes is specified in a connected coordinate system as

wherein the output of the module of the second six accelerometers is connected to the inputs of the unit for calculating the basic navigation variables and the unit for calculating accelerations in a connected coordinate system, the output of the module for the first six accelerometers is connected to the input of the unit for calculating the basic navigation variables, the output of the unit for calculating the basic navigation variables is connected to the inputs of the unit for calculating the accelerations in the connected coordinate system and the block for calculating the components of the angular velocity, and the output of the block for calculating the components of the angular velocity is connected to the input of the block the coefficients of the matrix coordinate transformation.