RU2505785C1 - Method for determining parameters of model of measurement errors of accelerometers of driven inertial navigation system as per measurements of reference inertial navigation system - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: during movement there determined are parameters of a model of measurement errors of accelerometers of a driven inertial navigation system (INS) as per measurements of a reference INS based on measurement of apparent accelerations of a carrier object moving in inertial space and a separable object related to it. Those measurements are made by means of accelerometers of the reference inertial navigation system in a basic inertial system of coordinates (BISC) and by means of accelerometers of the driven inertial navigation system in an instrument inertial system of coordinates (IISC).

EFFECT: improving accuracy of calculation of mass centre trajectory of the separable object; improving accuracy of orientation of sensitivity axes of accelerometers of the driven INS of the separable object in BISC and prediction accuracy of trajectory of the separable object due to eliminating measurement errors of accelerometers of the driven INS.

Description

The invention relates to the field of navigation of various objects moving in an inertial space and having two inertial navigation systems (ANNs) on board, one of which is highly accurate, the other is relatively rough. The first is taken as a reference; the second is a navigation system, the parameters of the measurement errors of the accelerometers of which must be refined (specified) during the flight.

Objects equipped with such systems may include land and sea vehicles (cars, ships), as well as air and spacecraft (aircraft, launch vehicles, booster blocks, space vehicles), from which, at certain stages of flight, such as carriers, there is a separation of some objects. Carriers carry a high-precision inertial navigation system, which we will call the “reference”, and those that are separated from them are less accurate. For its designation we will use the term “slave”.

Known methods for calibrating sensitive elements (SE) during bench tests of W. Wrigley, W. Hollister, W. Denhard "Theory, design and testing of gyroscopes" ed. World, M., 1972; or I.E. Vinogradov, I.V. Gusev, A.I. Glazkov "Determination of calibration parameters of inertial measuring units (IIB) using a triaxial rotary table." Proceedings of FSUE SPCAP System and Control Devices No. 2 (8) 2009; “A method for calibrating CE BINS and a device for its implementation”, patent for invention No. 2334947, priority dated March 26, 2007 Makarchenko, S.A. Zaitsev, A.I. Kalinin, T.N. Rumyantsev.

The disadvantage of these methods is the inability to calibrate the SE of inertial navigation systems, including accelerometers, during movement.

There is a method of autonomously determining the initial orientation of the instrument coordinate system of the strapdown inertial block of a controlled object relative to the base (starting) coordinate system [1]. To achieve this result, the signals of the accelerometers determine the increment of the projections of the apparent velocity vector on the axis of the instrument coordinate system. Then determine the velocity vector and the acceleration vector, measure the angular velocity sensors of the strapdown inertial block (BIB). From the values of the measured accelerations and the angular velocity of the Earth’s rotation, the angular position of the instrument coordinate system relative to the base (starting) coordinate system, the latitude of the test site, the position of the axles of the cardan suspension relative to the base coordinate system and the projection of the angular velocity of the Earth on the axis of the cardan suspension are determined. Then carry out the calibration of the sensitive elements of the BIB and re-determine the initial orientation of the instrument coordinate system relative to the base coordinate system.

The disadvantage of this method is the possibility of its use only at a fixed point on the Earth, limiting its use, the more so the inability to determine the parameters of the model of errors of accelerometers during movement, in particular, in flight.

There is a method [2] for determining in flight coefficients of the model error of gyrostabilizers, including the model of error of accelerometers installed on a stabilized platform, by measuring signals at the output of accelerometers and gyro unit departures during special rotations of the gyrostabilized platform relative to its stabilization axes (one or more), determining projections of the angular velocity of rotation of the base in given directions, calculating linear accelerations and subtracting them from the signals coming from the output accelerometers, generating signals from the corrected signals of accelerometers, varying from the cycle of determining errors to the cycle during the rotation of the gyro-stabilized platform, forming the total output signals of the model from the obtained components, determining the error signal, including the error of the accelerometers, and then properly adjust the weight coefficients of the error model until an acceptable minimum of the difference between the signal generated in the model and the signal of total gyro blocks and accelerometer errors.

The method has practical meaning in those cases when it is possible to make fixed turns of a stabilized platform and to carry out necessary measurements for a long time under such conditions, including measurements of accelerometers.

In practice, these conditions are often not satisfied, for example, in active sections of the flight of a launch vehicle (LV) or booster block (RB) with main engines running, when special rotations of the stabilized platform are unacceptable, since they may contradict the solution of the main control problem.

There is a method [3] for determining the trajectory of motion of moving objects in a basic inertial coordinate system (BISC) by numerically integrating the basic equation of inertial navigation with respect to information about the components of the apparent acceleration vector supplied by a triple of non-coplanar carrier ANN accelerometers. In parallel, a similar numbering of the navigation trajectory is performed using the readings of the accelerometers of the ANN of the object, which should subsequently be separated from the carrier.

Before the reckoning of the trajectories, the axes of each system are displayed in the BISK. The initial starting coordinate system is usually taken as a BISK. An exhibition driven by ANN is carried out on the basis of measurements exclusively of its own sensitive elements. At the same time, the accuracy of the exhibition of the driven ANN due to the relatively low accuracy of its sensitive elements, as well as possible dynamic disturbances caused, for example, by wind actions on the object during the pre-launch exhibition, is insufficient to solve the control problems of the separated object. The orientation error of the driven ANN with respect to the reference will be characterized by the matrix M of the _PBC .

The orientation error of the reference ANN in the BISK is assumed to be negligible. Therefore, the _KPB matrix M characterizes the error in the knowledge of the position of the sensitivity axes of the accelerometers of the driven ANN with respect to the BISK, in which the navigation problems are solved by both ANNs.

The disadvantage of this method, adopted as a prototype, is the inability to determine in flight the parameters of the errors of the accelerometers of the driven ANN in the presence of even minor errors of knowledge of the orientation of the latter.

The consequence of this is the insufficient accuracy of the solution of the navigation problem after the start of the independent movement of the detached object, and, ultimately, the insufficient accuracy of the control task. This situation is typical, for example, for the flight of the upper stage, when, after separation from the launch vehicle, it performs the task of delivering payloads to the target orbits, especially when this happens for a considerable time.

,

,

и независящих

,

,

от перегрузки параметров модели погрешностей измерений акселерометров ведомой ИНС. Параметры

характеризуют ошибки масштабных коэффициентов измерений акселерометров,

- ошибки нулей измерений акселерометров. Величины параметров полагаем ограниченными, так что:The proposed method is intended to improve the accuracy of determining the trajectory of the center of mass, increase the accuracy of the orientation of the sensitivity axes of accelerometers in the base inertial coordinate system and the accuracy of predicting the trajectory of a detached object, including after switching to an independent solution of navigation and control problems by determining (refinement) during the joint movement of the carrier and the detachable object depending

,

,

and independent

,

,

from overloading the model parameters of the measurement errors of the accelerometers of the slave ANN. Options

characterize the errors of scale factors for measuring accelerometers,

- errors of zero measurements of accelerometers. We consider the parameter values limited, so that:

;

, j=1, 2, 3,

;

, j = 1, 2, 3,

и

- заданные константы.Where

and

- given constants.

It is assumed that the ANN of the detached object contains at least three accelerometers with an unplanar arrangement of the sensitivity axes, the orientation of which with respect to the sensitivity axes of the accelerometers of the reference inertial system is known with an error characterized by the matrix M of the _CPB .

The problem is achieved by the fact that in the known method adopted as a prototype, determining the predicted in the base (initial start) inertial coordinate system of the trajectory of the center of mass, including measuring the vectors of the apparent acceleration of the carrier object moving in inertial space and the detachable object rigidly connected with it, produced by accelerometers of the reference inertial navigation system in the BISC and the slave ANN in the instrument inertial coordinate system (PISC), which is formed by the axes sensitive STI accelerometers ANN detachable object, transmitting with a certain frequency measurement accelerometers reference ANN carrier results in the computing device (slave) detachable object, during movement, after a certain time t _i, the measurements accelerometers ANN detachable object accumulate apparent velocity before the vector unit achieve an apparent velocity readings obtained by this accelerometers ANN setpoint, at which point t _{i + 1} is fixed in a detachable VU object components apparent vectors ck growth accumulated in the interval [t _i, t _{i + 1]} on indications INS of the carrier and on indications ANN detachable object, this data is determined and stored in the slave detachable object:

- differences of the same components of these vectors

- differences of modules of vectors

where w _et (t _i , t _{i + 1} ) and w _ved (t _i , t _{i + 1} ) are the apparent velocity vectors accumulated in the interval [t _i , t _{i + 1} ] according to the readings of the accelerometers of the reference and driven ANN, respectively;

Δw of _leads (t _i , t _{i + 1} ) is the vector of differences of the components of the apparent speeds or, in other words, the vector of the total errors of the components of the apparent speed accumulated in the considered interval [t _i , t _{i + 1} ], due to the whole set of measurement errors of the driven ANN (ANN of the separated object);

Δ _w w (t _i , t _{i + 1} ) is the difference between the modules of the accumulated vectors of the apparent speed or, in other words, the error of the module of the apparent speed accumulated in the interval [t _i , t _{i + 1} ] according to the readings of the accelerometers of the slave ANN;

- the relative projections of the apparent velocity vectors accumulated on the interval [t _i , t _{i + 1} ] separately along the sensitivity axis of each accelerometer of the slave ANN, onto the vector of the apparent speed acquired from the reference ANN

where (•, •) is the designation of the scalar product of vectors,

- единичный вектор вектора кажущейся скорости в БИСК, накапливаемой на интервале [t_i,t_i+1] по показаниям эталонной ИНС,

is the unit vector of the apparent speed vector in the BISC accumulated in the interval [t _i , t _{i + 1} ] according to the indications of the reference ANN,

w _{ved (j)} (t _i , t _{i + 1} ) is the apparent velocity vector in the BISC, obtained on the interval [t _i , t _{i + 1} ] according to the readings of the j-th accelerometer of the driven ANN,

- проекция единичного вектора

- projection of a unit vector

на

,

on

,

w _{Ved (j)} (t _i , t _{i + 1} ) = w _{Ved (j)} (t _i , t _{i + 1} ) j,

where j is the orth of the sensitivity axis of the jth accelerometer of the driven ANN in projections on the BISC axis.

, отличающимся малыми значениями ускорений и достаточной продолжительностью

.Such actions are repeated several times: at least twice on the intervals of active movement, characterized by significant overloads and mutually noncollinear directions of the apparent velocity vectors accumulated on them for given moduli of these vectors, and at least once in the section

characterized by small acceleration values and sufficient duration

.

According to the above, the intervals of active movement are characterized by the conditions:

- единичный вектор кажущейся скорости, накапливаемой на интервале

(i=1, 3, 5) активного движения,Where

is the unit vector of the apparent velocity accumulated in the interval

(i = 1, 3, 5) of active movement,

ℜ _w is a given positive constant that determines the minimum allowable modulo angle of different parallelism of the apparent velocity vectors accumulated on the considered intervals,

w ^ak is the selected constant.

, характеризуется следующими условиями:Interval of movement with small congestion, denoted as

characterized by the following conditions:

,moreover

,

- абсолютное значение ν-й компоненты вектора кажущегося ускорения

, ν=x, y, z - оси БИСК,Where

is the absolute value of the νth component of the apparent acceleration vector

, ν = x, y, z are the BISC axes,

- модуль гравитационного ускорения,

- module of gravitational acceleration,

w ^min is some constant. You can take w ^min = w ^ak ,

- например, некоторый интервал участка орбитального полета разгонного блока, характеризующийся движением РБ с выключенными маршевыми двигателями, но при возможных периодических срабатываниях двигателей стабилизации.

- for example, a certain interval of the orbital flight section of the booster block, characterized by the movement of the RB with the main engines off, but with possible periodic triggering of the stabilization engines.

выполняется неравенствоIn view of (6) on

inequality holds

при матрице ошибок ориентации М_КПБ, элементы (компоненты вектора поворота) которой соответствуют угловым ошибкам порядка единиц градусов, справедливо:Whence it follows that for the interval of motion

when the orientation error matrix M is the _CPB , the elements (components of the rotation vector) of which correspond to angular errors of the order of units of degrees, it is true:

- определяемый по формуле (1) вектор суммарных ошибок компонент кажущейся скорости, обусловленных влиянием на интервале

погрешностей измерений ведомой ИНС;Where

- the vector of the total errors of the components of the apparent speed determined by formula (1), due to the influence on the interval

measurement errors of the driven ANN;

- интеграл от функции влияния независящей составляющей

ошибки измерений j-го акселерометра на погрешность компоненты

вектора

кажущейся скорости в проекции на ось чувствительности данного акселерометра.

- integral of the influence function of the independent component

measurement errors of the j-th accelerometer to the component error

of vector

apparent velocity in projection onto the sensitivity axis of this accelerometer.

, характеризующихся условиями (4), (5), с учетом найденных с помощью (8) параметров

из системы линейных уравненийAccording to the values (2) of the apparent velocity modulus errors accumulated at intervals

characterized by conditions (4), (5), taking into account the parameters found using (8)

from a system of linear equations

.determine the parameters

.

и

- определяемые с использованием (3) интегралы от функций влияния параметров соответственно

и

на ошибку модуля вектора кажущейся скорости, накапливаемой по показаниям акселерометров ведомой ИНС на интервале

.AT 9):

and

- integrals determined using (3) of the influence functions of the parameters, respectively

and

to the error of the module of the vector of the apparent speed accumulated by the readings of the accelerometers of the driven ANN in the interval

.

, характеризующимся малыми значениями перегрузок по осям БИСК и достаточной продолжительностью участка, определяют в ВУ отделяемого объекта ошибки кажущейся скорости по осям чувствительности каждого акселерометра ведомой ИНС, вызванные совокупным влиянием погрешностей измерений этой ИНС. Значение ошибки каждого акселерометра делят на величину интеграла от функции влияния погрешности измерений соответствующего акселерометра, независящей от перегрузки, на погрешность накапливаемой на интервале

по оси чувствительности данного акселерометра кажущейся скорости, тем самым определяют и запоминают параметры погрешностей измерений каждого акселерометра, независящие от перегрузки. Из запомненных ошибок модулей измеренной кажущейся скорости, полученных не менее чем на трех интервалах активного движения, характеризующихся значительными перегрузками, вычитают результаты умножений значений параметров погрешностей, независящих от перегрузки, на величины интегралов от функции влияния данного параметра каждого акселерометра ведомой ИНС на ошибку модуля кажущейся скорости, набранной на соответствующем интервале активного движения, и определяют тем самым значения правых частей системы линейных уравнений для параметров погрешностей измерений акселерометров, зависящих от перегрузки. Решают линейную систему, определяют из нее и запоминают значения параметров погрешностей измерений акселерометров, зависящих от перегрузки. По найденным значениям независящих и зависящих от перегрузки параметрам погрешностей каждого акселерометра ведомой ИНС уточняют получаемые от этих акселерометров текущие значения кажущихся ускорений и используют их при численном интегрировании в реальном масштабе времени основного уравнения инерциальной навигации навигационной траектории отделяемого объекта.Thus, we propose a method for determining the parameters of the model of measurement errors of accelerometers of a driven inertial navigation system (INS) from measurements of a reference ANN, which includes measurements of the apparent accelerations of a carrier object moving in inertial space and a detachable object rigidly connected with it, made by accelerometers of the reference inertial navigation system of the object carrier in the base inertial coordinate system (BISC) and accelerometers of the driven inertial navigation system department the object to the instrument in the inertial coordinate system (vocalization) is formed axes accelerometer sensitivity driven ANN transmission with a certain periodicity measurements accelerometers INS reference carrier in a computing device (slave) separated object. During the movement, starting from a certain point t _i , according to the measurements of the accelerometers of the reference ANN and the driven ANN, the apparent speeds are accumulated until the vector module reaches the apparent speed obtained from the readings of the accelerometers of the driven ANN of the specified value. At this moment t _{i + 1, the} components of the apparent velocity vectors accumulated over the interval [t _i , t _{i + 1} ] according to the readings of the reference ANN and the driven ANN are fixed in the VU of the object to be separated. According to these data, the apparent module velocity vector module error caused by measurement errors of the driven inertial navigation system and the relative projections of the three apparent velocity vectors, formed according to the readings of each separate accelerometer of the driven ANN, onto the unit velocity of the apparent speed accumulated by the accelerometers readings are determined and stored in the VU of the separated object reference ANN. Such actions are repeated at least on two intervals of active motion, characterized by mutually noncollinear directions of the apparent velocity vectors accumulated on them and on the first interval. According to the readings of the accelerometers of the reference ANN of the carrier object and the driven ANN of the detached object accumulated in at least one traffic area

, characterized by small values of overloads along the BISC axes and a sufficient duration of the section, determine the apparent velocity errors in the axis of the detached object along the sensitivity axes of each accelerometer of the driven ANN caused by the combined influence of the measurement errors of this ANN. The error value of each accelerometer is divided by the integral of the function of the influence of the measurement error of the corresponding accelerometer, independent of overload, on the error accumulated over the interval

along the sensitivity axis of a given accelerometer of apparent speed, thereby determining and storing the measurement error parameters of each accelerometer, independent of overload. From the stored errors of the measured apparent speed modules obtained at least three intervals of active motion, characterized by significant overloads, the results of multiplying the error parameter values independent of the overload by the integrals of the function of the influence of this parameter of each accelerometer of the driven ANN on the apparent speed module error are subtracted typed on the corresponding interval of active movement, and thereby determine the values of the right parts of the system of linear equations for param measurement errors ditch accelerometers dependent overload. They solve a linear system, determine from it and remember the values of the parameters of the measurement errors of the accelerometers, depending on the overload. Based on the found values of the error-independent and overload-dependent error parameters of each accelerometer of the slave ANN, the current values of apparent accelerations obtained from these accelerometers are clarified and used for real-time numerical integration of the basic inertial navigation equation of the navigation path of the separated object.

и зависящих

от перегрузки параметров модели погрешностей измерения акселерометров ведомой ИНС и учет их в текущих показаниях акселерометров, что обеспечивает более точное формирование компонент вектора кажущегося ускорения, а, значит, и более точное счисление траектории движения отделяемого объекта с помощью численного интегрирования основного уравнения инерциальной навигации с уточненными значениями входящих в него компонент кажущегося ускорения. Одновременно это обеспечивает повышение точности ориентации осей чувствительности акселерометров ведомой ИНС в БИСК за счет устранения из элементов матрицы М_КПБ составляющих, обусловленных ошибками измерений акселерометров.The technical result of the proposed method is the determination during the movement of independent

and dependent

from overloading the model parameters of the measurement errors of the accelerometers of the slave ANN and taking them into account in the current readings of the accelerometers, which ensures more accurate formation of the components of the apparent acceleration vector, and, therefore, more accurate calculation of the trajectory of the separated object using numerical integration of the basic inertial navigation equation with specified values its component component of apparent acceleration. At the same time, this provides an increase in the accuracy of orientation of the axes of sensitivity of the accelerometers of the slave ANN in the BISK by eliminating the components from the matrix elements M of the _CPB due to measurement errors of the accelerometers.

Literature

1. 3 application: 2008150507/28, 12.19.2008. Patent holder: FSUE "NPTSAP" (RU).

2. Application: 98109135/09, 05/13/1998. (43) Date of publication of the application: 03.20.20003.

3. Statistical dynamics and control optimization of aircraft. A.A. Lebedev, V.T. Bobronnikov, M.N. Krasilshchikov, V.V. Malyshev. - M.: Mechanical Engineering, 1985, pp. 85-87.

Claims (1)

A method for determining model parameters of measurement errors of accelerometers of a driven inertial navigation system (INS) from measurements of a reference ANN, including measurements of the apparent accelerations of a carrier object moving in inertial space and a detachable object rigidly connected with it, made by accelerometers of a reference inertial navigation system of a carrier object in a base inertial coordinate system (BISK) and accelerometers of the driven inertial navigation system of a detached object in the instrument and ertsialnoy coordinate system (vocalization) is formed axes of sensitivity of the accelerometer driven ANN transmission with a certain periodicity measurements accelerometers reference ANN carrier in a computing device (slave) detachable object, characterized in that during the movement, after a certain time t _i, for the measurements of the accelerometers of the reference ANN and the slave ANN accumulate apparent speeds until the module reaches the apparent speed obtained from the readings of the accelerometers of the driven ANN given by eniya at this point t _{i + 1} is fixed in a slave detachable object vector components apparent velocity accumulated in the interval [t _i, t _{i + 1]} on indications reference ANN and driven INS, according to these data is determined and stored in the slave detachable object error the apparent velocity vector module caused by measurement errors of the driven inertial navigation system, and the relative projections of the three apparent velocity vectors, formed according to the readings of each individual slave accelerometer of the driven ANN, onto the unit velocity of the apparent speed accumulated by the knowledge of the accelerometers of the reference ANN, repeat such actions on at least two intervals of active movement, characterized by mutually noncollinear directions of the apparent velocity vectors accumulated on them and on the first interval, according to the readings of the accelerometers of the reference ANN of the carrier object and the driven ANN of the detached object accumulated at least on one section of traffic

characterized by small values of overloads along the BISC axes and a sufficient duration of the section, the apparent velocity errors are determined in the VU of the detached object along the sensitivity axes of each accelerometer of the driven ANN, caused by the combined influence of the measurement errors of this ANN, the error value of each accelerometer is divided by the integral of the function of the influence of the measurement error of the corresponding accelerometer, independent of overload, for the error accumulated in the interval

along the sensitivity axis of the given accelerometer of apparent speed, thereby determining and storing the measurement error parameters of each accelerometer, independent of overload, from the stored errors of the measured apparent speed modules obtained at least three intervals of active movement, characterized by significant overloads, subtract the results of multiplication of parameter values of errors independent of the overload on the values of the integrals of the influence function of this parameter of each accelerometer is known ANN on the error of the apparent speed modulus typed in the corresponding interval of active movement, and thereby determine the values of the right-hand sides of the system of linear equations for the error parameters of the measurement of accelerometers depending on the overload, solve the linear system, determine from it and store the values of the measurement error parameters of the accelerometers, which depend from overload, according to the found values that are independent of and depending on the overload, the error parameters of each accelerometer of the slave ANN are specified by of these accelerometers are the current values of apparent accelerations and use them for real-time numerical integration of the basic equation of inertial navigation of the navigation path of a detached object.