RU2620288C1 - Method and device for determining orientation of space or air crafts - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: group of inventions relates to orientation control of the space (SC) and air crafts (AC) by means of sensing elements. The device comprises orientation sensors (S) relative to the inertial coordinate system and relative to the astronomical objects positioned on the base. Wherein the device is provided with one-dimensional or two-dimensional (or their combinations) S of angular measurement for each of the mentioned S. S of angular measurement comprises a radiation source and a radiation receiver mounted on the base, and a reflective element - at one of the S of determining orientation. These elements are mounted so that the planes of the incident and reflected radiation beams are not parallel. The angles are measured, for example, between the running axes of orientation S and the base. Management of these angles (in the data processing unit) is intended to eliminate the influence of errors in orientation S position in body-fixed coordinate axes (e.g., due to deformation of the structure) on the measured parameters of the craft orientation.

EFFECT: increased orientational accuracy of the spacecraft or aircraft without increasing the rigidity of their structure.

13 cl, 4 dwg

Description

FIELD OF THE INVENTION

The group of inventions relates to space and aviation technology, namely to technology for increasing the accuracy of determining the orientation of spacecraft (SC) and aircraft (LA) in an inertial coordinate system and with respect to certain celestial bodies of celestial bodies - astronomical objects, in particular such as the Sun, Earth, Moon, Venus, Mars, Jupiter, Saturn, etc.

State of the art

The prior art technical solutions that provide high-precision determination of the orientation of spacecraft or aircraft relative to the inertial coordinate system and relative to certain astronomical objects. These devices contain several sensors for determining the orientation of one or various types. Structurally, these devices can be in the form of monoblocks, in which all the sensors and the data processing unit are combined into a single design, and represent distributed systems where orientation sensors are installed in various places of the spacecraft or aircraft and are connected to the data processing unit using a cable network.

A solution is known from the prior art - a Hydra stellar orientation device from Sodern (France), in which 3 or 4 high-precision stellar orientation sensors with errors of the order of 1.5 arc seconds and a data processing unit are installed (All-Russian Scientific and Technical Conference modern problems of determining orientation and spacecraft navigation, Russia, Tarusa, September 22-25, 2008, http://www.iki.rssi.ru/books/2008tarusa.pdf) (Figs. 1 and 2).

The prior art solution is presented in patent US 6272432 B1 - (published on 08/07/2011, CL G01C 21/02), which proposed a device for determining the orientation, which includes a stellar orientation sensor and three uniaxial gyroscopic sensors.

A solution is known from the prior art - a device for orientation with respect to the Sun (determining the direction to the Sun) BOX-01, developed by Opteks (Russia), in which two high-precision two-coordinate slotted direction sensors for the Sun and a common data processing unit are installed (Second All-Russian Scientific Technical Conference "Modern Problems of Orientation and Navigation of Spacecraft", Tarusa, September 13-16, 2010, pp. 22-23 http://ofo.ikiweb.ru/publ/conf_2010_tez.pdf) (see. Fig. 3).

The prior art solution is known - a distributed orientation determination system installed on the Russian segment of the International Space Station (ISS). It includes a gyroscopic angular velocity vector meter (GIVUS) installed inside the ISS pressurized compartment, three BOKZ star sensors and one BOKS solar sensor installed on the outer surface of the Zvezda service module. GIVUS data, BOKZ and BOKS sensors are processed by computers of the onboard system of the ISS Russian segment.

However, all of the above orientation determining devices have been found to have a problem with the high accuracy of the orientation sensors. The presence of this problem was confirmed in a number of laboratory and field experiments [A.V. Nikitin, B.S. Dunaev, V.A. Krasikov, Mechanics, control and informatics №2. S. 62-69 (2011) and A.Yu. Karelin, Yu.N. Zybin, V.O. Knyazev, A.A. Pozdnyakov, Mechanics, Management, and Computer Science No. 19, P. 120-128 (2015)]. The experiments were as follows: two or more stellar sensors were installed next to each other, the optical systems of which were directed in approximately the same way. These sensors were simultaneously taken readings. The experimental results showed that the measurement error of each of the sensors during the entire experiment remained consistent with their technical characteristics (i.e. 1-3 seconds of arc), but their relative orientation changed by several arc seconds, and in some experiments by 10-20 arc seconds . The most likely cause of these deviations are thermal deformation and mechanical stress. The experimental results mean that orientation determining devices containing sensors with errors of less than 3-5 arc seconds give incorrect readings with a significant systematic error due to insufficient mechanical rigidity of the structures on which the sensors are installed.

A known method of solving this problem by increasing the rigidity of structures. This solution allows to reduce the magnitude of the described systematic error, but leads to a significant increase in the mass of the device for determining orientation, which in many space and aircraft is unacceptable. With the transition to orientation sensors with subsecond errors expected in the coming decades, solving this problem by increasing the rigidity of the mechanical structure is completely ineffective.

Disclosure of invention

The present invention is to develop a method and device for determining the orientation of spacecraft or aircraft, providing accurate determination of the orientation of the spacecraft or aircraft relative to the inertial coordinate system and / or relative to astronomical objects (in particular, such as planets, satellites and asteroids, for example the Sun, Earth , Moon, Venus, Mars, Jupiter, Saturn, etc.).

An astronomical object is understood to mean a celestial body - a material object that naturally formed in outer space.

The technical result of the invention is to reduce the error in determining the orientation of a spacecraft or aircraft relative to the inertial coordinate system and / or relative to astronomical objects by eliminating the systematic error associated with a change in the relative position of the orientation sensors under the influence of mechanical, thermal and other structural deformations on which the sensors are mounted.

The problem is solved in that the device for determining the orientation of spacecraft or aircraft contains a base, at least one sensor for determining the orientation relative to the inertial coordinate system and at least one sensor for determining the orientation relative to astronomical objects located on the base, as well as taken for each an orientation detection sensor, at least three one-dimensional angle measurement sensors, or at least two two-dimensional angle measurement sensors, or a combination of at least one one-dimensional and at least one two-dimensional angle measurement sensor, and a processing unit for receiving data from said sensors, wherein the angle measurement sensors include a radiation source, a radiation receiver and a reflective element, where the radiation source and radiation receiver are mounted on the base of the device or on one of the sensors for determining the orientation, and the reflecting element is mounted on one of the sensors for determining the orientation with the reception of the radiation beam from the reflecting element, while the radiation source, the radiation receiver and the reflecting element of the angle measuring sensors are installed to ensure the absence of parallelism of the planes determined by the incident and reflected radiation beam.

The sensor for determining the orientation relative to astronomical objects may be a sensor of direction to the Sun and / or a sensor of direction to the center of the Earth.

The distance measurement sensor may be an optical or electromechanical or interference sensor.

The sensor for determining the orientation relative to the inertial coordinate system may be a gyroscopic and / or star sensor.

Preferably, the device comprises three sensors for determining orientation relative to the inertial coordinate system, one sensor for astronomical objects, and eight two-dimensional or twelve one-dimensional angle measurement sensors.

Angle sensors can be configured to measure angles between orientation sensors and the base of the device.

At least three one-dimensional angle measurement sensors or at least two two-dimensional angle measurement sensors, or at least one one-dimensional and at least one two-dimensional angle measurement sensors can be configured to measure angles between orientation sensors and the base of the device, and the rest are made with the possibility of measuring angles between different sensors to determine the orientation.

The problem is also solved by the method of determining the orientation of spacecraft or aircraft using the aforementioned device and includes the following steps:

- measuring and transmitting readings of orientation sensors and angle measurement sensors to a data processing unit;

- determination of the orientation angle values of the orientation determining sensors relative to the structural coordinate system of the device based on the readings of the angle measurement sensors installed on each orientation determination sensor;

- converting the obtained angle values for the sensors for determining the orientation relative to the inertial coordinate system into a three-dimensional rotation matrix P _i , translating the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where i is the number of the orientation sensor;

- converting the obtained angle values for the sensors for determining the orientation relative to astronomical objects into a three-dimensional rotation matrix R _j , translating the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where j is the number of the orientation sensor and the number of the corresponding object;

- converting the readings of the sensor for determining the orientation relative to the inertial coordinate system into a three-dimensional rotation matrix S _i , translating the axis of the structural coordinate system of the sensor for determining the orientation in the axis of the inertial coordinate system, and the error in the readings of the sensor for determining the orientation relative to the inertial coordinate system in the error σ _{i of} the three-dimensional rotation matrix S _i ;

- conversion of the readings of each sensor for determining the orientation relative to astronomical objects into a unit vector of direction to the object in the structural coordinate system of the sensor V _j , where j is the number of the sensor for determining the orientation and the number of the corresponding space object;

- determining the orientation of the device by obtaining direction vectors for astronomical objects in the structural coordinate system of the device U _j according to the formula U _j = R _j × V _j ;

- calculation of the matrix of three-dimensional rotation Q, translating the axis of the structural coordinate system of the device in the axis of the inertial coordinate system;

- obtaining direction vectors for astronomical objects in the structural coordinate system of a spacecraft or aircraft O _j according to the formula

O _j = K × U _j ,

where K is the known matrix of three-dimensional rotation translating the axis of the structural coordinate system of the device in the axis of the structural coordinate system of a space or aircraft;

- obtaining direction vectors for astronomical space objects in the inertial coordinate system of the device E _j according to the formula

E _j = Q × U _j ;

- obtaining the orientation of the spacecraft or aircraft relative to the inertial coordinate system in the form of matrix A, according to the formula

A = K × Q.

The matrix Q can be calculated using two mathematical formulas.

The matrix Q can be calculated using Kalman filtering.

It is possible to calculate the Q matrix based on the data fusion method.

The determination of the orientation angle values of each orientation determination sensor relative to the structural coordinate system of the device is performed based on the readings of all the angle measurement sensors by solving a system of linear equations of mutual orientation of the orientation determination sensors and the device.

Brief Description of the Drawings

The invention is illustrated by drawings, where

in FIG. 1 shows a prototype device for determining the orientation of the star sensor Hydra company Sodern (France) with three optical heads;

in FIG. 2 shows a prototype of an orientation determining device - a Hydra star sensor from Sodern (France) with four optical heads;

in FIG. Figure 3 shows a prototype of a device for determining orientation — the BOKS-01 solar sensor, developed by Opteks (Russia), with two optical heads;

in FIG. 4 shows a diagram of an orientation determining apparatus.

The positions in figure 4 indicate: 1 - sensors for determining the orientation, 2 - data processing unit, 3 - sensors for measuring angles.

The implementation of the invention

A device for determining the orientation of spacecraft or aircraft, containing a base, at least one sensor for determining orientation relative to an inertial coordinate system and at least one sensor for determining orientation relative to astronomical objects (such as planets, satellites and asteroids, for example the Sun, Earth, Moon, Venus, Mars, Jupiter, Saturn) located on the base, as well as at least three one-dimensional angle measurement sensors or at least two two-dimensional angle measurement sensors, or a combination of at least one one-dimensional and at least one two-dimensional angle measurement sensor taken for each orientation determination sensor, and a processing unit for receiving data from said sensors.

Structurally, the device for determining the orientation can be a monoblock - a single device, or be a distributed device, parts of which are installed in various places of a space or aircraft. Sensors for determining the orientation are fixed in the design of the device for determining the orientation, but due to mechanical, thermal and other loads, they can deviate from the normal position by small angles.

The orientation detection sensors included in the device can be of two types:

1) the sensor (s) determining the orientation relative to the inertial coordinate system may be a gyroscopic (inertial) and / or star sensor (s).

2) the sensor (s) for determining the orientation relative to astronomical objects may be a sensor (s) of the direction to the Sun and / or a sensor of direction to the center of the Earth.

Usually, the orientation of a spacecraft or aircraft relative to large celestial objects: the Sun, Earth, Moon, Venus, Mars, Jupiter, Saturn, etc., is important. The listed objects vary greatly in their characteristics. Therefore, to determine the direction of them from small distances, when they look like extended bodies, at the same time, devices of various designs are required with high accuracy. Because of this, the direction to each object is determined by a specific sensor (or group of sensors).

Each orientation sensor has its own structural coordinate system. This is usually a Cartesian rectangular system. In optical sensors for determining orientation (star sensors, direction sensors to the Sun, Earth or Moon), usually one of the structural coordinate axes coincides with the axis of sight of the optical system of the sensor. For uniaxial gyroscopic sensors, one of the axes is usually directed parallel to the axis of the gyroscope.

With the device for determining the orientation as a whole associated with its own structural coordinate system. If the device is a monoblock, then usually the structural coordinate system is associated with the base of the device, with which it is attached to a spacecraft or aircraft. The structural coordinate system of a distributed orientation determining device may coincide with the structural coordinate system of the spacecraft or aircraft.

The result of measurements by the sensors to determine the orientation of the first type (relative to the inertial coordinate system) are the parameters of the rotation of the axes of the structural coordinate system of the sensor relative to the inertial coordinate system. These parameters can be represented in the form of three Euler angles, a quaternion of rotation, a matrix of three-dimensional rotation, etc. All these representations contain three independent parameters and any of them can be obtained from others.

The result of measurements by the sensors to determine the orientation of the second type (relative to the astronomical object) is the direction to a point on the corresponding space object (usually its center) in the structural coordinate system of the sensor. This direction can be represented by two angles, three guide cosines, etc. All these views contain two independent parameters.

In addition to the readings, orientation sensors can provide estimates of their errors. It is important to accompany each act of performing a measurement with an estimate of the errors if the error varies significantly depending on the position or condition of the space object, on the direction of the sensor in space, or changes over time. In cases where the error in the readings of the orientation sensor changes little, it can be determined in advance and considered a known characteristic of the sensor.

The results of the operation of the orientation determination device are:

1) determination of the parameters of the rotation of the axes of the structural coordinate system of the orientation determination device and the structural coordinate system of a space or aircraft relative to the inertial coordinate system;

2) determination of directions to astronomical space objects in the structural coordinate system of the orientation determining device, the structural coordinate system of a space or aircraft, and in the inertial coordinate system.

To determine the orientation of the spacecraft or aircraft and directions to astronomical objects in its coordinate system, it is necessary to know the transition matrix between the structural coordinate systems of the orientation determination device and the spacecraft. This matrix is either considered unchanged during the functioning of the spacecraft or aircraft and known (it is determined during installation of the device for determining orientation on board), or it is determined and controlled by the on-board systems of the device that are not related to the device for determining orientation.

In order to obtain the results of the operation of the device for determining the orientation, in addition to the readings of the sensors for determining the orientation included in the device, it is necessary to know the turns (orientation) of the sensors relative to the structural coordinate system of the device. In modern devices for determining orientation, these turns are considered known and are determined during assembly of the device or when installing it on board. It is assumed that the position and orientation of the sensors inside the orientation determining devices do not change during operation, and that this invariability is ensured by the mechanical rigidity of the structures of monoblock orientation determining devices or the rigidity of the structures of the spacecraft or aircraft for distributed devices.

However, as tests have shown, the mechanical rigidity of the structures allows you to keep the mutual orientation of the sensors inside the device for determining the orientation with an error of at least 3-5 arc seconds. If more accurate sensors are installed in the orientation determining device, then mechanical and thermal deformations of the device structures cause a systematic error of 3-5 arc seconds or more. Today, the most accurate gyroscopes, as well as stellar and solar orientation sensors, have such a small error. In the coming decades, the appearance of orientation sensors is expected with errors of about 0.1 arc second. For such precision, maintaining the relative position of the sensors in the device due to the rigidity of the mechanical structures will be completely insufficient.

Angle sensors can be one-dimensional or two-dimensional. A one-dimensional sensor measures one angle between certain structural elements of a device or orientation sensors. A two-dimensional sensor simultaneously measures two angles between the corresponding structural elements.

To solve this problem, the device must include at least three one-dimensional angle measurement sensors for each orientation sensor or at least two two-dimensional angle measurement sensors for each orientation sensor, or a combination of at least , one one-dimensional and at least one two-dimensional angle measurement sensors taken for each orientation determination sensor.

The real-time angle measurement sensors determine the rotation (orientation) of the coordinate systems of the sensors relative to each other or relative to the structural coordinate system of the orientation determination device. Knowing the real geometric configuration of the device for determining the orientation (i.e., the angular position of the sensors for determining the orientation included in it) allows, based on the readings of the sensors, to determine the orientation of the device with an error close to the error of the sensors included in it.

One of the possible design options for both a one-dimensional and a two-dimensional angle measurement sensor includes a radiation source, a radiation receiver and a reflective element; the radiation source and the radiation receiver are installed on the basis of the device or on one of the sensors for determining the orientation. A reflective element is mounted on the orientation detection sensor. The relative position of the radiation source and the reflecting element should ensure that the radiation beam reflected from the reflecting element hits the receiver with all permissible changes in the position of the reflecting element (the reflecting element is mounted on the orientation detection sensor to ensure that the radiation beam is received from the reflecting element). In a one-dimensional angle measurement sensor, both linear and matrix radiation detectors can be used; in a two-dimensional angle measurement sensor, only matrix ones.

For angle measurement sensors mounted on a specific orientation detection sensor, the installation of the above-mentioned structural elements is performed with the absence of parallelism of the planes determined by the incident and reflected radiation beam.

For the correct functioning of the device for determining the orientation, you only need to know the turn of the sensors for determining the orientation relative to the coordinate system of the device, their linear movement does not change the readings of the sensors for determining the orientation and does not affect the result of the operation of the device. Therefore, it is important for us only the angular position of the sensors to determine the orientation relative to the device. These angles can be measured directly using angle sensors.

The error in measuring the angles should be on the order of the error in the sensors for determining the orientation, i.e. no more than 1-3 arc seconds for modern stellar sensors and gyroscopes and no more than 0.1-0.3 arc seconds for high-precision sensors for determining the orientation of the next generation. These values determine the permissible errors of the angle sensors.

The type of angle measurement sensor does not matter. Mechanical, interference, electromechanical (capacitive, magnetic, inductive, etc.), optical and other types of angle sensors with the required error can be used. The choice of type of sensor may be affected by the requirements for operation in space or flight conditions, weight or energy restrictions, as well as the effect of sensors on other on-board equipment.

For measurement, the angles between the individual orientation determination sensor and the reference part of the orientation device (for example, the base of the device) can be selected, in which case the coordinate system of this sensor relative to the coordinate system of the device is directly determined from the results of these measurements.

Another option for determining the orientation of the sensors in the coordinate system of the device for determining the orientation is to measure both the angles between the sensors and the reference part of the device for determining the orientation, and between pairs of sensors.

Those. at least three one-dimensional angle measurement sensors or at least two two-dimensional angle measurement sensors, or at least one one-dimensional and at least one two-dimensional angle measurement sensors are configured to measure angles between the orientation sensors and the base devices, and the rest are made with the possibility of measuring angles between different sensors to determine the orientation.

In this case, the measurement of the angles relative to the reference part of the orientation determining device must be performed for at least three one-dimensional angle measurement sensors or at least two two-dimensional angle measurement sensors, or at least one one-dimensional and at least one two-dimensional angle measurement sensors. Based on the obtained set of measurement of the angles, the rotation of the coordinate system of each of the sensors relative to the coordinate system of the orientation determination device is determined. Those. angle measurement sensors are configured to measure angles between orientation sensors and the base of the device, and the rest are configured to measure angles between different orientation sensors in the device.

The preferred design of the device for determining the orientation of spacecraft or aircraft contains three sensors for determining orientation relative to the inertial coordinate system, one sensor for determining orientation with respect to the astronomical object and eight two-dimensional or twelve one-dimensional sensors for measuring angles, which will reduce the error in determining the orientation of the spacecraft or aircraft with respect to astronomical objects.

A method for determining the orientation of spacecraft or aircraft using the aforementioned device includes:

a) measuring and transmitting the readings of orientation sensors and angle sensors to the data processing unit.

Indications from orientation sensors and angle sensors, measure and transmit to the data processing unit. Sensors for determining the orientation of the first type (relative to the inertial coordinate system) determine the orientation parameters of the sensor relative to the inertial coordinate system. These parameters can be represented in several equivalent ways, for example, in the form of a three-dimensional rotation matrix, which translates the axes of the structural coordinate system in the axis of the inertial coordinate system. Sensors for determining the orientation of the second type (relative to a certain astronomical space object) determine the direction to a certain point of the corresponding astronomical space object (usually to its center) in the structural coordinate system of the sensor. Additionally, both types of sensors can provide an estimate of the error of the obtained orientation parameters;

b) determining the orientation angles of the orientation determining sensors relative to the structural coordinate system of the device based on the readings of the angle measurement sensors installed on each orientation determining sensor (i.e., determining the direction of the axes of the structural coordinate system of each of the sensors relative to the structural coordinate system of the device) based on the sensors measuring the angles mounted on each orientation sensor.

Reflection elements (mirrors, reflective prisms, etc.) are installed on each orientation detection sensor. Based on the device for determining the orientation or other sensors for determining the orientation, radiation sources (lasers, laser diodes, etc.) are installed that emit narrow collimated radiation beams and coordinate-sensitive radiation receivers (for example, matrix or linear CCDs or CMOS radiation detectors. CCDs - charge-coupled device; CMOS - a complementary metal-oxide semiconductor). The radiation beam from the first radiation source is directed so that it hits the first reflective element, and after reflection from it falls approximately at the center of the first radiation receiver. Similarly to the second and subsequent angle measuring sensors, the beam is reflected from the corresponding reflective element and enters approximately the center of the corresponding radiation receiver. At least one one-dimensional angle measurement sensor, or at least two two-dimensional angle measurement sensors, or at least one one-dimensional and one two-dimensional angle measurement sensors must be installed on one orientation detection sensor. Each of these sensors includes one radiation source and receiver and one reflective element. When the angular position of the orientation determination sensor changes, the image of the beams at the radiation detectors is shifted. If the distance from the reflective element to the radiation receiver is 0.3 m, then the rotation of the sensor by 1 arc second leads to a displacement of the beam image by 1.5 μm. This offset is 1 / 10-1 / 3 pixels of industrially produced CCDs and CMOS matrices or rulers and is easily detected with the current level of technology.

If the planes that specify the rays (before and after reflection) are not parallel to each other, then by shifting the image of two rays on two matrix radiation detectors, it is possible to determine changes in all three parameters of the sensor’s orientation relative to the coordinate system of the orientation determination device.

The described design of the angle measurement sensor is designed to register small displacements of orientation sensors relative to a certain initial position, which is fully consistent with the solution of the problem. The positions of the sensors are determined by the design of the device for determining the orientation, the initial values of the orientation parameters of the sensors are determined during the assembly of the device;

c) converting the obtained angle values for the sensors for determining the orientation relative to the inertial coordinate system into a three-dimensional rotation matrix P _i that translates the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where i is the number of the orientation sensor;

d) converting the obtained angle values for the sensors for determining the orientation relative to astronomical objects into a three-dimensional rotation matrix R _j that translates the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where j is the number of the orientation sensor and the number of the corresponding object;

d) the conversion of the readings of the sensor for determining the orientation relative to the inertial coordinate system into a matrix of three-dimensional rotation S _i , which translates the axis of the structural coordinate system of the sensor for determining the orientation in the axis of the inertial coordinate system, and the errors of the readings of the sensor for determining the orientation relative to the inertial coordinate system in the errors of the matrix of the three-dimensional rotation S _i ;

f) converting the readings of each sensor for determining the orientation relative to astronomical objects into a unit vector of direction to the object in the structural coordinate system of the sensor V _j , where j is the number of the sensor for determining the orientation and the number of the corresponding space object;

g) obtaining direction vectors for astronomical objects in the structural coordinate system of the device U _j according to the formula

U _j = R _j × V _j ;

h) the calculation of the matrix of three-dimensional rotation Q, translating the axis of the structural coordinate system of the device in the axis of the inertial coordinate system;

The calculation of the matrix Q can be performed in the following ways:

i) If the readings of the ith orientation sensor are accompanied by an estimate of the measurement error σ _i and the values of these errors are different, then the matrix Q is calculated by the formula

where N is the number of orientation sensors in the device.

ii) If the errors of the sensors are approximately the same, then the matrix Q is calculated by the formula

.

.

iii) A method for computing the Q matrix based on Kalman filtering, [Zhang N., Sang N., Shen X., Adaptive Federated Kalman Filtering Attitude Estimation Algorithm for Double-FOV Star Sensor, Journal of Computational Information Systems 6: 10 (2010) 3201-3208];

iv) A method for computing the Q matrix based on the data fusion method [Chiang Y.-T., Chang FR, Wang LS, Jan YW, Ting LH, Data fusion of three attitude sensors, SICE 2001. Proceedings of the 40th SICE Annual Conference . International Session Papers, P. 234-239 (2001) and Uhlmann JK, General Data Fusion for Estimates with Unknown Cross Covariances, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, V. 2755, 1996, P. 536-547 ];

i) obtaining direction vectors for astronomical objects in the structural coordinate system of a spacecraft or aircraft O _j according to the formula

O _j = K × U _j ,

where K is the known matrix of three-dimensional rotation translating the axis of the structural coordinate system of the device in the axis of the structural coordinate system of the spacecraft or aircraft.

The matrix K is considered known or transmitted to the device for determining the orientation by the on-board systems of the apparatus on which the device is installed. Information about the rotation matrix K depends on which name unit and in which place the device is installed, and this matrix cannot be autonomously determined by the proprietary means of the orientation determining device. Therefore, the latter action is not typical for orientation determining devices and is performed onboard systems by most space and aircraft;

_j ) obtaining direction vectors for astronomical space objects in the inertial coordinate system of the device E _j according to the formula

E _j = Q × U _j ;

k) obtaining the orientation of the spacecraft or aircraft relative to the inertial coordinate system in the form of matrix A, according to the formula

A = K × Q.

When using the device, when the angle measurement sensors are configured to measure angles between the orientation sensors and the base of the device, the determination of the orientation angle values of each orientation determination sensor relative to the structural coordinate system of the device is performed based on the readings of the angle measurement sensors installed on this orientation determination sensor.

When using the device, when at least three one-dimensional sensors for measuring angles or at least two two-dimensional sensors for measuring angles, or at least one one-dimensional and at least one two-dimensional sensors for measuring angles are configured to measure angles between the orientation sensors and the base of the device, and the rest are made with the possibility of measuring the angles between different sensors to determine the orientation, determining the values of the orientation angles of each sensor to determine the orientation relative to truktsionnoy device coordinate system is performed based on readings of angle measurement sensors by solving a system of linear equations relative orientation of the sensors and determine the orientation of the device.

This group of inventions allows to reduce the errors in determining the orientation of a spacecraft or aircraft relative to the inertial coordinate system and / or relative to astronomical objects by eliminating the systematic error associated with a change in the relative position of the orientation sensors under the influence of mechanical, thermal and other structural deformations on which the sensors are installed. The mathematical justification of the method

Let the device contain N sensors for determining the orientation relative to the inertial coordinate system, i = 1 ... N are the numbers of sensors and M sensors for determining the orientation with respect to space bodies, j = 1 ... M are the numbers of sensors of this type. In the initial unperturbed state of the device, the angular position of the ith orientation determination sensor relative to the inertial coordinate system is described by a three-dimensional rotation matrix P ⁽⁰⁾ _i that translates the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device. The readings of the sensors for determining the orientation with respect to the inertial coordinate system can be represented in the form of a matrix of a three-dimensional rotation S _i that translates the axis of the structural coordinate system of the i-th sensor for determining the orientation in the axis of the inertial coordinate system.

The orientation of the device relative to the inertial coordinate system is described by a three-dimensional rotation matrix Q, translating the axis of the structural coordinate system of the device in the axis of the inertial coordinate system. Suppose that the sensors for determining the orientation have zero error (the values of the matrices S _{i are} absolutely accurate), and the sensors themselves are in the initial unperturbed positions P ⁽⁰⁾ _i . In this case, the matrix Q can be obtained from the readings of any of the sensors, all of them give matching results:

In real conditions, the readings of the sensors have some error σ _i , in this case, the readings of the i-th sensor can be represented as S _i = S ⁽⁰⁾ _i + δS _i , where S ⁽⁰⁾ _i is the true three-dimensional rotation matrix describing the orientation of i -th sensor, δS _i is a small three-dimensional rotation matrix describing the deviation of the readings matrix of the i-th sensor S _i from the true orientation matrix S ⁽⁰⁾ _i , caused by the measurement error. The products S _i × P _i in the formula (1) will give different values for different sensors. In this case, the statistically most reliable value of the matrix is calculated by the formula

The orientations S _i × P _i determined from the readings of individual sensors will deviate from Q by a value of the order of σ _i , and the average error Q will be <σ> / N ^1/2 (here <σ> is the weighted average of the errors σ _i ).

This formula was derived under the assumption that all the sensors for determining the orientation with respect to the inertial coordinate system are in the initial unperturbed positions, i.e. the matrices P ⁽⁰⁾ _{i are} known exactly. The formula remains valid as long as the deviations of the sensors from the initial positions remain small compared with the errors of the orientation sensors σ _i themselves.

Let us now consider the most general case when the readings of the sensors have errors (as in the previous case), and the sensors themselves deviate from their original positions. In this case, the matrix describing the position of the ith sensor relative to the device will have the form P _i = P ⁽⁰⁾ _i + δP _i , where δP _i is the matrix of small three-dimensional rotation describing the deviation of the sensor from the initial position described by the matrix P ^{(0 )} _i . Denote the angle of small deviation of the i-th sensor by π _i . In this case, the matrix Q is calculated by the formula

The average error of the matrix Q calculated by this formula will be ((<σ> ² + <π> ² ) / N) ^1/2 , where <π> is the weighted average of the deviations of the sensors π _i . It can be seen that while <π><<σ> the error is determined by orientation sensors and formula (2) is valid for the matrix Q. If <π>><σ>, and especially in the case of <π>>><σ>, the orientation error is determined by the deformations of the device structures. In this case, a further increase in the accuracy of orientation sensors becomes meaningless, since it does not increase the accuracy of the device as a whole.

Angle measurement sensors included with the device make it possible to measure sensor deviations with a certain error and determine the rotation matrix ΔP _i which is an approximation of the matrix δP _i . The difference between these two matrices δP _i -ΔP _i = dP _{i is} also a small three-dimensional rotation matrix, and the angle of this rotation is approximately equal to the error of the angle measuring sensors ε.

The method described in the invention proposes to substitute in the formula (3) not P _i , but (P _i -ΔP _i ). In this case, for the matrix Q, the following expression is obtained

In this case, the error of the matrix Q will be ((<σ> ² + ε ² ) / N) ^1/2 and does not depend on the magnitude of the deviations of the sensors from the initial positions <π> if they exceed the error in measuring the angle of deviation of the sensors ε.

For sensors for determining the orientation relative to space objects, their initial unperturbed positions relative to the device are described by three-dimensional rotation matrices R ⁽⁰⁾ _j , where j is the number of the sensor for determining the orientation and the number of the space object, the direction to which is determined. The perturbed positions differ from the initial ones and have the form R ⁽⁰⁾ _j = R _j + δR _j , where δR _j is the small three-dimensional rotation matrix describing the deviation of the jth sensor from the unperturbed position. The angle of this rotation is, respectively, α _j .

The results of the operation of the sensors for determining the orientation with respect to space objects can be represented as a unit vector V _{j of the} direction to the space object (for extended objects - to some point of them, most often - to the center). The error of the sensor leads to the fact that the direction of the vector V _j differs from the true direction to the object by a small angle ψ _j .

The matrix R _j allows you to determine the coordinates of a unit direction vector to the j-th space object in the structural coordinate system of the device according to the formula

In this coordinate system, the direction to the object will deviate from the true direction to the object by an average angle (α _j ² + ψ _j ² ) ^1/2 . Subsequently, the vector U _{j is} transformed into the vector E _{j of the} direction to the object in the inertial coordinate system according to the formula E _j = Q × U _j . The error of the matrix Q is added to the error of the vector U _j in the inertial coordinate system, and the average deviation of the vector E _j from the true one will be (<σ> ² + α _j ² + ψ _j ² ) ^1/2 .

If the angle of deviation of the orientation determination sensor from the initial position α _{j is} large, then increasing the accuracy of the orientation sensor will not lead to an increase in the accuracy of the device as a whole. Angle measurement sensors included with the device make it possible to measure sensor deviations with some error and determine the rotation matrix ΔR _j which is an approximation of the matrix δR _j . The difference of these two matrices δR _j -ΔR _j = dR _{j is} also a small three-dimensional rotation matrix, and the angle of this rotation is approximately equal to the error of the angle measuring sensors ε.

The method described in the invention proposes to substitute in the formula (5) not R _j , but (R _j -ΔR _j ). In this case, for the vectors U _{j the} following expression is obtained

In this case, the errors (deviation angles) of the vectors U _j will be (ε ² + ψ _j ² ) ^1/2 , and the vectors E _j , respectively, (<σ> ² + ε ² + ψ _j ² ) ^1/2 and not will depend on the magnitude of the deviations of the sensors from the initial positions α _j if they exceed the error in measuring the angle of deviation of the sensors ε.

EXAMPLES

Example 1. A method and apparatus for determining the orientation of spacecraft or aircraft

An orientation determining device includes a device base, three stellar orientation sensors and one directional sensor to the Sun mounted on the base, eight two-dimensional angle measurement sensors measuring angles between the orientation sensors and the device base, and a data processing unit. The indications of star sensors are the quaternion of the orientation of the structural coordinate system of the sensor relative to the inertial coordinate system, and the readings of the direction sensor to the Sun are two spherical angles that determine the components of the direction to the Sun in the structural coordinate system of the sensor. The readings of the sensors for determining the orientation are accompanied by estimates of measurement errors. Angle measurement sensors consist of a reflective element, a source of a narrow beam of radiation and a matrix radiation receiver. The reflecting element is mounted on the orientation detection sensor (stellar orientation sensor or directional sensor on the Sun), and the radiation source and receiver - on the basis of the device. Each orientation sensor has two reflective elements. At the same time, their installation is made in such a way that: 1) the beam emitted by the radiation source after reflection from the reflecting element falls approximately in the middle of the radiation matrix receiver and 2) the planes defined by the reflected radiation beams directed to the reflecting element for two reflecting elements mounted on the same orientation sensor, were not parallel. The angular errors of orientation sensors and angle sensors do not exceed a few angular seconds.

In the initial undeformed state, orientation sensors occupy a certain initial position. This position is determined by three Euler angles characterizing the rotation of the structural coordinate system of the sensor relative to the structural coordinate system of the device associated with the base of the device. In the initial state, the radiation beams reflected from the reflecting elements fall into certain places of the matrix radiation detectors. A change in the position of the orientation sensor relative to the base of the device leads to a shift in the position of the reflected radiation beam at the matrix receiver in the general case simultaneously in two directions - along the rows and along the columns of the matrix. The shift of the position of the radiation beams at the receivers of two two-dimensional angle measurement sensors, the reflective elements of which are mounted on a specific orientation sensor, make it possible to determine (small) changes in the Euler angles of this orientation sensor.

The initial values of the Euler angles for each orientation sensor and the initial position of the radiation beams on the matrix receivers of all angle measurement sensors are determined during the pre-flight calibrations of the device and stored in the data processing unit. The transition coefficients from the displacements of the beam positions on the matrix radiation detectors to the Euler angle corrections are calculated based on the relative position of the elements of the angle measurement sensors on the basis of the device and on the orientation sensors (i.e., based on the device design), are refined during pre-flight device calibrations, and also stored in the data processing unit.

During operation, the device experiences mechanical and thermal influences that lead to deformation of the device. As a result of these deformations, orientation sensors deviate from their original positions. Simultaneously with the change in the positions of the sensors, the positions of the reflecting elements mounted on them change, which leads to a shift in the positions of the reflected radiation beams on the matrix radiation detectors. The readings from all angle measuring sensors, consisting of the displacements of the positions of the radiation beams along the rows and along the columns of the matrix radiation detectors, and from three star sensors and from the direction sensor to the Sun, are measured (taken) and transmitted to the data processing unit.

Then, based on these offsets, using the coefficients determined during the pre-flight calibration, the corrections to the Euler angles for each orientation sensor are calculated. Corrections are added to the original Euler angles, which determines the current position of the orientation sensors relative to the base of the device. For each stellar orientation sensor, a three-dimensional rotation matrix Pi is calculated from its Euler angles, which translates the axes of the structural coordinate system of the sensor in the axis of the structural coordinate system of the device, where i = 1, 2, or 3 is the number of the stellar orientation sensor. For a direction sensor to the Sun, a three-dimensional rotation matrix R is calculated from its Euler angles, which translates the axes of the structural coordinate system of the sensor in the axis of the structural coordinate system of the device.

In turn, the readings of each of the stellar sensors are converted into a three-dimensional rotation matrix Si, which translates the axes of the structural coordinate system of the stellar sensor into the axis of the inertial coordinate system, and the error of readings is the error σi of the three-dimensional rotation matrix Si.

The readings of the direction sensor on the Sun are converted into a unit vector V of the direction on the Sun in the structural coordinate system of the sensor. Then, the unit direction vector to the Sun U is determined in the structural coordinate system of the device by multiplying the vector V and the matrix R using the formula U = R × V.

Then, the matrix of the three-dimensional rotation Q, which translates the axis of the structural coordinate system of the device in the axis of the inertial coordinate system, is calculated by the formula

After calculating the matrix Q, the following actions are performed:

- obtaining the direction vector to the Sun in the structural coordinate system of a spacecraft or aircraft O according to the formula

O = K × U.

Here K is the well-known matrix of three-dimensional rotation translating the axis of the structural coordinate system of the device in the axis of the structural coordinate system of a space or aircraft;

- getting the direction vector to the Sun in the inertial coordinate system of device E according to the formula

E = Q × U;

- obtaining the orientation of the spacecraft or aircraft relative to the inertial coordinate system in the form of matrix A, by the formula:

A = K × Q.

After completing these steps, the data processing unit transmits the matrix A and the vectors O and E to the control unit of the spacecraft or aircraft.

Example 2. Tests and checks using computer simulation

Before making the existing system, tests and verification of the operation of the device for determining the orientation of space or flying using computer simulation are carried out. Computer modeling tools can also be used as part of the process of planning the actual motion of a spacecraft or an aircraft in space.

For computer simulation, it will be necessary to develop a virtual model of the device for determining orientation as a whole, as well as its constituent star sensors, a direction sensor to the Sun and two-dimensional angle measurement sensors. Additionally, we need a minimal model of the spacecraft or aircraft on which the device is installed, as well as a model of external conditions (including power and thermal effects) that allows you to set or determine the deformation of the device.

Computer simulation is used to test and verify the operability of the device for determining orientation and its individual subsystems, as well as the effectiveness of the method of its use.

Example 3. Tests and checks using physical modeling

Tests and verification of the operation of the device for determining the orientation of the spacecraft or aircraft are performed using physical models or real equipment to verify the results of computer simulation. Tests on physical models are carried out on special ground-based laboratory stands.

The laboratory test bench includes simulators of space objects used as landmarks, namely three simulators of the starry sky and one simulator of the Sun.

The starry sky simulator is a computer screen (LCD or LED) on which, using a control computer, an image of a fragment of the starry sky and a projecting optical system is displayed. The dimensions of the fragment slightly exceed the field of view of the stellar sensor. The optical system and the screen are installed along the axis of sight of the stellar sensor. The projection system is set so that the sharp image of the sky on the screen is located at infinity. Fragments of the starry sky displayed on the screens should correspond to the relative position of the optical axes of the stellar sensors. Simulation of the rotation of the device for determining the orientation relative to the starry sky (i.e., relative to the inertial coordinate system) is carried out by changing the images on the screens without real rotation of the device and moving the simulators of the starry sky on the stand.

The Sun Simulator is a powerful light source with angular dimensions of 0.5 °. The sun simulator is mounted on a movable bracket, allowing it to be installed at various points in the upper hemisphere above the orientation determining device. Changing the position of the Sun relative to the device under test is carried out by moving the simulator.

In addition to simulators, the laboratory bench includes thermal and mechanical loading devices. Thermal loading is carried out by asymmetric (one-sided) irradiation of the tested device with visible or infrared radiation. For mechanical loading, a change in the position of the device in the Earth's gravitational field (device tilts) and the suspension of small calibrated loads to various parts of the device are used.

A laboratory model of an orientation determination device was assembled, which included two stellar orientation sensors, one direction sensor to the Sun, six two-dimensional angle sensors (two for each of the orientation sensors) and a data processing unit. The layout was assembled on an optical table, which played the role of the base of the device. Two simulators of the starry sky and a simulator of the Sun were installed on the same table. The measurements showed that the random errors of stellar sensors are 3 arc seconds, the error of the direction sensor on the Sun is 5 arc seconds, and the relative orientation of these devices in the unloaded state is preserved with an error of 1 arc second, which is equal to the error of two-dimensional angle measurement sensors. As a result, in the unloaded state, the random error in determining the orientation of the device as a whole relative to the inertial coordinate system was 3.2 arc seconds, and the direction to the Sun relative to the inertial coordinate system was 6 arc seconds.

The layout was loaded by suspending small loads from the structural elements so that the average deviation of the stellar and solar sensors from the initial position was 15 arc seconds. As a result, in the loaded state, without taking into account the readings of the angle measurement sensors, the average error in determining the orientation of the device as a whole relative to the inertial coordinate system was 16 arc seconds, and the direction to the Sun relative to the inertial coordinate system was 17 arc seconds.

When taking into account the readings of angle measurement sensors according to the method proposed in the present invention, the error in determining the orientation of the device as a whole relative to the inertial coordinate system decreased to 3.8 arc seconds, and the direction to the Sun relative to the inertial coordinate system to 6.5 arc seconds, which allows to conclude that a technical result has been achieved.

Claims (32)

1. A device for determining the orientation of spacecraft or aircraft, comprising a base, at least one sensor for determining orientation relative to an inertial coordinate system and at least one sensor for determining orientation with respect to astronomical objects located on the base, as well as at least one sensor for determining orientation at least three one-dimensional angle measurement sensors, or at least two two-dimensional angle measurement sensors, or a combination of at least one one-dimensional and at least one two-dimensional angle measurement sensors, and a processing unit for receiving data from said sensors, wherein the angle measurement sensors include a radiation source, a radiation receiver and a reflective element, the radiation source and the radiation receiver being installed on the basis of the device or on one of the orientation determination sensors and the reflecting element is mounted on one of the sensors for determining the orientation with the reception of the radiation beam from the reflecting element, while the radiation source, the radiation receiver and a reflective element angle measurement sensors mounted with ensuring a lack of parallelism of the planes defined by the incident and reflected radiation beams. 2. The device according to p. 1, characterized in that the sensor for determining the orientation relative to astronomical objects is a direction sensor to the Sun and / or a direction sensor to the center of the Earth. 3. The device according to claim 1, characterized in that the angle measurement sensor is an optical, or electromechanical, or interference sensor. 4. The device according to p. 1, characterized in that the sensor determines the orientation relative to the inertial coordinate system is a gyroscopic and / or star sensor. 5. The device according to p. 1, characterized in that it contains three sensors for determining orientation relative to the inertial coordinate system, one sensor for astronomical objects and eight two-dimensional or twelve one-dimensional angle measurement sensors. 6. The device according to p. 1, characterized in that the angle measurement sensors are configured to measure angles between the orientation sensors and the base of the device. 7. The device according to claim 1, characterized in that at least three one-dimensional sensors for measuring angles, or at least two two-dimensional sensors for measuring angles, or at least one one-dimensional and at least one two-dimensional sensors for measuring angles the angles between the orientation sensors and the base of the device, and the rest are made with the possibility of measuring angles between different sensors to determine the orientation. 8. A method for determining the orientation of spacecraft or aircraft using the device according to claim 1, including - measuring and transmitting readings of orientation sensors and angle measurement sensors to a data processing unit; - determination of the orientation angle values of the orientation determining sensors relative to the structural coordinate system of the device based on the readings of the angle measurement sensors installed on each orientation determination sensor; - converting the obtained angle values for the sensors for determining the orientation relative to the inertial coordinate system into a three-dimensional rotation matrix P _i , translating the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where i is the number of the orientation sensor; - converting the obtained angle values for the sensors for determining the orientation relative to astronomical objects into a three-dimensional rotation matrix R _j , translating the axis of the structural coordinate system of the corresponding sensor in the axis of the structural coordinate system of the device, where j is the number of the orientation sensor and the number of the corresponding object; - converting the readings of the sensor for determining the orientation relative to the inertial coordinate system into a three-dimensional rotation matrix S _i , translating the axis of the structural coordinate system of the sensor for determining the orientation in the axis of the inertial coordinate system, and the error in the readings of the sensor for determining the orientation relative to the inertial coordinate system in the error σ _{i of} the three-dimensional rotation matrix S _i ; - conversion of the readings of each sensor for determining the orientation relative to astronomical objects into a unit vector of direction to the object in the structural coordinate system of the sensor V _j , where j is the number of the sensor for determining the orientation and the number of the corresponding space object; - determining the orientation of the device by obtaining direction vectors for astronomical objects in the structural coordinate system of the device U _j according to the formula U _j = R _j × V _j ; - calculation of the matrix of three-dimensional rotation Q, translating the axis of the structural coordinate system of the device in the axis of the inertial coordinate system; - obtaining direction vectors for astronomical objects in the structural coordinate system of a spacecraft or aircraft O _j , according to the formula O _j = K × U _j , where K is the known matrix of three-dimensional rotation translating the axis of the structural coordinate system of the device in the axis of the structural coordinate system of a space or aircraft; - obtaining direction vectors for astronomical space objects in the inertial coordinate system of the device E _j according to the formula E _j = Q × U _j ; - obtaining the orientation of the spacecraft or aircraft relative to the inertial coordinate system in the form of matrix A according to the formula A = K × Q. 9. The method for determining the orientation of spacecraft and aircraft according to claim 8, characterized in that the matrix Q is calculated by the formula

where N is the number of sensors for determining the orientation relative to the inertial coordinate system in the device. 10. The method for determining the orientation of spacecraft and aircraft according to claim 8, characterized in that the matrix Q is calculated by the formula

, where N is the number of sensors for determining the orientation relative to the inertial coordinate system in the device. 11. The method for determining the orientation of spacecraft and aircraft according to claim 8, characterized in that the matrix Q is calculated using Kalman filtering. 12. The method for determining the orientation of spacecraft and aircraft according to claim 8, characterized in that the matrix Q is calculated based on the data fusion method. 13. The method for determining the orientation of spacecraft and aircraft according to claim 8, characterized in that when using the device according to claim 7, the determination of the orientation angles of each orientation determination sensor relative to the structural coordinate system of the device is performed based on the readings of all angle measurement sensors by solving a linear system mutual orientation equations of orientation sensors and devices.

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