RU2561003C1 - Integrated orientation and navigation system for objects with fast rotation about longitudinal axis - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: three receiving antennas of satellite navigation systems (SNS) with one specialised receiver having three inputs, each of which has one input for antenna connection are installed on the object; with that, the reference antenna along with a gimbal-free inertia measurement module (GIMM) on micromechanical sensors (MMS) is installed in the front part of the object along the rotation axis, and two other with maximum possible distance along longitudinal axis from the reference antenna are located in a circumferential direction with 180° displacement in transverse plane. Difference phase SNS measurements of the rotating object are used for evaluation of GIMM errors both for a roll angle and heading and pitch angles, as well as for evaluation of errors of scale coefficients of gyroscopes and accelerometers, including those installed along longitudinal axis of the object, about which fast rotation is performed.

EFFECT: improving accuracy and interference immunity.

14 dwg

Description

The invention relates to the field of navigation instrumentation of aircraft and spacecraft.

Currently, when solving problems of controlling small-sized moving objects (control objects - OS), gimballess inertial orientation and navigation systems are increasingly used. This is primarily due to progress in the development of inertial sensitive elements, electronics, a significant decrease in their overall dimensions and cost.

The creation of such gimballess inertial orientation and navigation systems is fraught with a number of problems. First of all, it is possible to single out the problem of achieving the required level of accuracy with inertial sensitive elements used in such systems, in particular with inertial micromechanical sensors (MMD). At the present stage of the development of MMD, the autonomous functioning of gimballess inertial systems for a long time while maintaining the required level of accuracy is not possible. The required level of accuracy is achieved by integrating information from gimballess inertial measuring modules (BI-IM) with the receiving equipment (PA) of satellite navigation systems (SNA), that is, by building integrated orientation and navigation systems (ISON) based on the BIIM, informationally and structurally integrated with PA SNS [1, 2].

To ensure also high noise immunity of such systems, their construction is carried out according to the so-called tightly coupled scheme [3].

In the considered patents [4, 5, 6, 7, 8], the required level of accuracy of the integrated system in determining the orientation parameters for objects with fast rotation around the longitudinal axis is not provided.

Methods for determining the orientation parameters of an object based on the use of phase measurements from antennas spaced at the object in the SNA PA are described in the description of the first domestic multi-antenna PA SNA MRK-11, developed by the Krasnoyarsk State Technical University and the Research Institute of Radio Engineering, as well as in [9, 10, eleven].

In the well-known schemes for constructing an ISON, for example, described in [12, 13], the multi-antenna PA SNA with phase measurements is used, which provides autonomous generation of object orientation parameters with a certain discreteness. This problem, as is known, requires solving the problem of ambiguity of phase measurements.

There are various ways to solve this problem [14]. All of them require simultaneous observation and processing of phase measurements from a constellation of navigation satellites (HC _i ), a rather complicated software.

Joint processing of BIIM and PA SNA data in the considered schemes for constructing ISON is performed at the level of orientation parameters.

However, in some cases, the problem of the relatively low level of accuracy of modern inertial MMDs (the errors of their scale factors are at the level of 1%) becomes so acute that without taking special measures it is not possible to achieve the required level of accuracy in solving the object orientation problem in the framework of constructing well-known ISON schemes. In particular, for objects with fast rotation around the longitudinal axis (1 ... 20 Hz), there is an acute problem associated with the error in the scale factor of the gyroscope standing along the axis of rotation. For such op-amps, the error in generating an ISON of the angle of rotation around the axis of rotation can be unacceptably large. The consequence of this may be the loss of control of the object.

There are ways to solve this problem. The main ones [15]:

- isolation of BIIM from rotation of the body of the object around the longitudinal axis;

- the use of an additional uniaxial gyrostabilizer along the longitudinal axis;

- the use of non-inertial measurements (from magnetometers, phase measurements from PA SNA, etc.);

- the use of forced precession of the object and the assessment of its parameters according to the testimony of specially installed accelerometers.

The patent [16] examined on this subject does not completely solve the problem of determining orientation parameters for objects with fast rotation around the longitudinal axis. Their implementation is associated either with the need to give the object the required movement, or with the need to use an additional set of independent meters, the proposed algorithms for processing the readings of which do not always provide the required level of accuracy of the integrated system.

Also known [17] is the construction scheme of the orientation and navigation system for objects with fast rotation around the longitudinal axis, which in its composition can also use BIIM. This system provides a solution to the problem of OS orientation by the angle and angular velocity of the roll using phase measurements of the SNA to four receiving antennas spaced around the circumference in the transverse plane of the object. In this case, a short antenna base of less than a wavelength is used, which eliminates the need to solve the problem of assessing the ambiguity of phase measurements. This scheme of building an integrated system is selected as a prototype.

List of drawings

In FIG. 1a shows a block diagram of an integrated system adopted as a prototype, in addition to receiving equipment of the SNA, according to the description of the patent, a small-sized gimballess inertial measuring module can be included to increase accuracy.

In FIG. 1b shows the location scheme on the object of the receiving antennas of the SNA, described in the prototype [17].

In FIG. 2a and 2b show a block diagram of the proposed ISON and an arrangement of receiving antennas A0, A1, A2 at the site.

FIG. 3 illustrates the interferometric principle of the formation of phase measurements in the SNA PA using the example of a single antenna base.

FIG. 4.1a, 4.1b characterize the parameters of the trajectory of the aircraft in the Earth’s atmosphere.

FIG. 4.2a ... 4.2g illustrate the simulation results in the MATLAB package (Simulink) of the algorithms of the proposed ISON, which includes the BIIM with a measuring unit on “rough” micromechanical gyroscopes (MMG) and accelerometers (MMA) and three SNA receivers with three antennas placed on the object according to FIG. 2b. In this case, the distances of the antennas A1, A2 relative to the reference antenna A0 were 0.3 m along the Y axis and ± 0.075 m along the X axis.

In FIG. 1a, the following notation is accepted:

1 - receiving equipment of satellite navigation systems, including one satellite receiver and four (or more) antennas - A1, A2, A3, A4, spaced on the corresponding antenna bases, the output of which receives the values:

,

- псевдодальность и псевдорадиальная скорость до i-го навигационного спутника HC_i (первичные навигационные параметры) или

,

- вектора координат и линейной скорости объекта соответственно, приведенные к месту расположения опорной антенны (навигационное решение);-

,

- pseudorange and pseudoradial speed to the i-th navigation satellite HC _i (primary navigation parameters) or

,

- vector coordinates and linear velocity of the object, respectively, reduced to the location of the reference antenna (navigation solution);

- φ _ji is the phase of the carrier signal from HC _i received at the j-th antenna;

,

- координаты или направляющие косинусы HC_i в осях гринвичского навигационного трехгранника (эфемеридная информация);-

,

- coordinates or direction cosines of HC _i in the axes of the Greenwich navigation trihedron (ephemeris information);

2 - a block of accelerometers, which is part of the measuring unit (IS) of a gimballess inertial measuring module;

3 - block gyroscopes IB BIIM;

4 - navigation calculator BIIM, generating according to the data of micromechanical sensors (blocks 2 and 3 of accelerometers and gyroscopes, respectively), the values of the following output parameters:

- K, ψ, θ - heading, pitch and roll values;

,

- координаты и вектор линейной скорости объекта в месте расположения ИБ БИИМ;-

,

- the coordinates and the linear velocity vector of the object at the location of the IB BIIM;

5 - a block for generating the first phase differences ∇φ _ji , (BVPRF) of HC _i signals at the carrier frequency received at the reference and jth antennas included in the computer of the integrated system;

6 - integrated information processing unit (BKOI), included in the computer of the integrated system, with a filter such as a Kalman filter, the output of which receives the values:

,

,

- оценки погрешностей ориентации по углам курса, тангажа и крена;-

,

,

- assessment of orientation errors in the corners of the course, pitch and roll;

,

- оценки погрешностей БИИМ по координатам и вектору линейной скорости объекта;-

,

- estimates of biomath errors by coordinates and linear velocity vector of an object;

7 - consumer receiving unit of the output parameters of the system.

The figure 1b adopted the following notation:

100 - a shell;

115 - axis of rotation;

120 - terminal body;

122 is the circle along which the antennas are located;

123 is a point on the axis of rotation relative to which the antennas are located;

151 ... 154 - four receiving antennas of the SNA;

X, Y, Z - the axis of the coordinate system associated with the terminal body.

In FIG. 2a, the following designations are adopted, other than the designations of FIG. 1a:

- in block 1: PA SNA, including one satellite receiver (receiver No. 1) with three inputs or three receivers (receiver No. 1, receivers No. 2 and 3, are indicated by a dotted line), each of which has one input for connecting the antenna, and three antennas: A0 - reference, A1, A2 - spaced on the corresponding antenna bases;

,

;- in block 8: a block for generating the difference between the calculated and measured values of the first or second phase measurement differences (BFRFI), additionally included in the calculator of the integrated system, for two antenna bases between the reference A0 receiving antenna of the SNA and the antennas A1, A2 separated from it -

,

;

- in block 6, outputs are additionally entered, from which the values are received:

,

- оценки погрешностей масштабных коэффициентов гироскопа и акселерометра, установленных по продольной оси объекта;-

,

- estimates of errors in the scale factors of the gyroscope and accelerometer installed along the longitudinal axis of the object;

- оценки остаточной «скачкообразной» неоднозначности фазовых измерений.-

- estimates of the residual “spasmodic” ambiguity of phase measurements.

In FIG. 2b, the following notation is accepted:

A0, A1, A2 - reference antenna and antennas spaced apart at respective antenna bases;

y ₀ is the longitudinal axis of the object.

In FIG. 3 adopted the following notation:

Aj is the jth antenna of the PA SNA;

A0 - reference antenna PA SNA;

Ox ₀ y ₀ z ₀ - coordinate system associated with the object;

- трехмерный вектор, характеризующий отстояние в системе координат Ox₀y₀z₀ j-ой антенны Aj относительно опорной А0;

- a three-dimensional vector characterizing the distance in the coordinate system Ox ₀ y ₀ z _{0 of the} jth antenna Aj relative to the reference A0;

- направление орта на навигационный спутник (HC_i) в точке приема;

- direction of the unit vector to the navigation satellite (HC _i ) at the receiving point;

β _ji is the angle between the jth antenna base and the direction to HC _i .

In FIG. 4.1 (a, b), 4.2 (a, g) the following notation is accepted:

nE, nN, nH - components of apparent acceleration (in geographic axes (ENH), respectively, [m / s ² ];

- nh _m - a given apparent acceleration in geographical axes, characterizing the movement of the object along the trajectory, [m / s ² ];

- t is the time, [s];

VE, VN, VH - components of the speed of the object in the geographical axes (ENH), respectively, [m / s];

- Vh _m - a given linear velocity in geographic axes, characterizing the movement of the object along the trajectory, [m / s];

-, Δψ, Δθ - orientation errors in pitch and roll angles (degrees);

- ΔK is the orientation error (degree);

- DMgi, DMai (i = x, y, z) - errors in estimating errors in the scale factors of the gyroscope and accelerometer installed along the longitudinal axis of the object;

- DDCf - errors of estimation of residual ambiguity of phase measurements.

The measured phase differences and the navigation solution from the PA SNS 1 receiver in the prototype (Fig. 1a) are processed in the Kalman filter (FC) implemented in the BKOI 6 unit of the integrated system calculator in order to obtain information about the angle and angular velocity of the roll. To obtain the initial information on the phase of the carrier, four SNA receiving antennas spaced around the circumference in the transverse plane of the object are used (Fig. 1b). In this case, a short antenna base (less than a wavelength) is used, which eliminates the need for a preliminary solution to the problem of assessing the ambiguity of phase measurements.

Data from sources of information unrelated to the SNA, for example, BIIM, are optimally processed in an integrated system calculator with PA SNA data in order to update the navigation solution and have additional information about heading and pitch angles.

.The interferometric principle of the formation of phase measurements in the SNA PA (Fig. 3) suggests that the signals from one HC _i in the form of a plane wave arrive at two antennas. The validity of the assumption of the planar nature of the wave is explained by the significant remoteness of the signal source compared with the length of the jth antenna base

.

Obviously, in units of range, the total phase difference of the signals received by the SNA PA at the locations of the antennas Aj, A0 (Fig. 3) is defined as

,where ∇r _ji is the distance difference ρ _ji to HC _i at the antenna base

,

λ _i is the wavelength of the emitted HC _i signal.

относительно антенной j-й базы

.) можно представить в видеIn the general case, taking into account the fact that the length of the antenna base exceeds the wavelength, measurements of the first phase difference from HC _i for j antenna bases (which is the measured value of the ortho directing cosine

relative to the antenna of the j-th base

.) can be represented as

- погрешность измерения разности псевдодальностей, обусловленная в основном различной нестабильностью опорных генераторов двух приемников СНС, размещенных в точках приема; η_ji - целое число длин волн, неоднозначность в фазовых измерениях;

- флуктуационная (шумовая) составляющая измерений.Where

- the error in measuring the difference of the pseudorange due mainly to the different instabilities of the reference generators of the two SNA receivers located at the receiving points; η _ji - integer number of wavelengths, ambiguity in phase measurements;

- fluctuation (noise) component of measurements.

In this case (in the prototype), when one specialized receiver is used with several inputs for connecting antennas and ensuring synchronization of phase measurements from several antennas, and also a short antenna base is used (Fig. 1b), less than the wavelength, expression (2) can be written as

The measurement data are generated in the calculator of the integrated system according to the output data ∇φ _ji , block BVPRF 5 (Fig. 1A).

от ПА СНС 1 или

от БИИМ 4, корректируемого в блоке БКОИ 6 (фиг. 1а) по данным навигационного решения от СНС, и известными эфемеридами

HC_i (от ПА СНС 1) в гринвичской системе координат, в вычислителе интегрированной системы рассчитываются направляющие косинусы орта

, соответственно,Having data on the Cartesian coordinates of the object

from PA SNS 1 or

from BIIM 4, corrected in the block BKOI 6 (Fig. 1A) according to the navigation solution from the SNA, and the known ephemeris

HC _i (from PA SNA 1) in the Greenwich coordinate system, the directional cosines of the unit vector are calculated in the calculator of the integrated system

accordingly

in Greenwich and geographic coordinate systems:

where C _{e, h} _ _pr (λ, φ) is the transition matrix from Greenwich to geographic axes, as a function of the coordinates of the object’s location.

направляющих косинусов вектора

в связанных с объектом осях определяются как:Values

guide cosines vector

in the axes associated with the object, they are defined as:

- декартовые координаты точки расположения антенн Aj, А0 относительно начала связанной с объектом системы координат.where [x _Aj , y _Aj , z _Aj ] ^T , $${[x_{A_o},y_{A_o},z_{A_o}]}^T$$

- Cartesian coordinates of the location of the antennas Aj, A0 relative to the origin of the coordinate system associated with the object.

To find the desired solution in the calculator of the integrated system, the well-known relation [14] is implemented:

where C _{o, h} (K, ψ, θ) is the desired orientation matrix as a function of angles K, ψ, θ.

Using information on heading and pitch angles, for example, from BIIM, the current values of the roll angle and the roll angular velocity are calculated. The BIIM data on the roll angle here (in the prototype) can be used in the BKOI 6 block to increase the accuracy and frequency of the roll angle output, providing information forecast between phase measurements.

The disadvantages of this scheme for constructing an integrated system include:

- phase measurements are used only to generate the angle and angular velocity along the roll;

- course errors in a number of applications with a long flight time of an object can reach significant values;

- a significant number of used SNA receiving antennas.

The objective of the invention is:

- the use of phase measurements to improve the accuracy of the development of course angles and pitch;

- minimizing the number of used SNA receiving antennas;

- the ability to use standard SNA receivers with one input for connecting the antenna while ensuring continuous calculation of the first differences in phase measurements under conditions of rapid rotation of the object around the longitudinal axis.

The technical result of the invention is to increase the accuracy of the development of the angle and angular velocity of the roll, as well as improving the noise immunity of the device.

The problem is solved in that:

- at least three SNA receiving antennas are installed at the facility with one specialized receiver having three inputs, or with three standard receivers, each of which has one input for connecting the antenna. In this case, the reference antenna together with the BIIM measuring unit on micromechanical sensors is installed in the bow of the object along the rotation axis, and the other two, with the maximum possible distance along the longitudinal axis from the reference antenna, are located around the circumference with an offset of 180 ° in the transverse plane;

- differential phase measurements of the SNA are used to estimate the biomath errors both in roll angle and in course and pitch angles, as well as to estimate errors in the scale factors of gyroscopes and accelerometers, including those installed along the longitudinal axis of the object around which rapid rotation is performed;

- the elimination of the ambiguity of the phase measurements of the PA SNA for the observed HC _{i is} carried out based on the BIIM data.

The implementation of these solutions is the main difference between the proposed device from the prototype.

The difference between PA SNA 1 (Fig. 2a) of the proposed ISON construction scheme from the prototype is to use either one specialized receiver having three inputs for connecting antennas, or three standard receivers, each of which has one input for connecting an antenna. At the same time, three antennas are installed on the object (Fig. 2b) (one - the support is installed in the bow of the object along the axis of rotation, and the other two, with the maximum possible distance along the longitudinal axis from the reference antenna, are located around the circumference with a shift of 180 ° in the transverse plane), and the reference antenna along with the measuring unit BIIM is located in the bow of the object along the axis of rotation.

Algorithmic software calculator BIIM 4 (Fig. 2A) is similar to the algorithms of BIIM prototype 4 (Fig. 1a).

,

расчетных и измеренных значений первых или вторых разностей фазовых измерений для двух антенных баз между опорной приемной антенной А0 и отстоящими от нее антеннами A1, А2. Выходные данные

,

которого поступают на дополнительный вход блока БКОИ 6.The difference between the block BKOI 6 (Fig. 2A) of the proposed scheme for constructing ISON from the prototype lies in the fact that it includes an additional block BFRFI 8 of the formation of differences

,

calculated and measured values of the first or second phase measurement differences for two antenna bases between the reference receiving antenna A0 and the antennas A1, A2 spaced from it. Output

,

which go to the additional input of the block BKOI 6.

In this case, the differences between the calculated and measured values of the first differences in phase measurements (it is sufficient to use phase measurements from one HC _i ) are formed in the BVPRF 5 unit using a specialized SNA receiver with three inputs for connecting antennas. Differences in the calculated and measured values of the second differences in phase measurements (it is necessary to use phase measurements from at least two HC _i ) are generated in the BFRFI 8 unit when three standard receivers are used as part of the SNA PA, each of which has one input for connecting the antenna.

The algorithmic support of the BKOI 6 block of the calculator of the proposed ISON is an implementation of the widely used Kalman filter algorithms similar to those used in the prototype.

The following measurements are used as input data of the BKOI 6 block for solving the Kalman filtering problem:

и радиальных скоростей

для каждого из наблюдаемых HC_i), либо готовых навигационных решений (по составляющим векторов координатам места

и линейной скорости объекта

соответственно);- the difference between the calculated and measured PA SNA values or primary navigation parameters (pseudorange

and radial speeds

for each of the observed HC _i ), or ready-made navigation solutions (based on the component coordinates of the location vector

and linear velocity of the object

respectively);

,

расчетных и измеренных ПА СНС значений первых или вторых разностей фазовых измерений для двух антенных баз.- difference

,

calculated and measured PA SNA values of the first or second differences of phase measurements for two antenna bases.

The output of the block BKOI 6 are:

,

,

- оценки погрешностей ориентации по углам курса, тангажа и крена;-

,

,

- assessment of orientation errors in the corners of the course, pitch and roll;

,

- оценки погрешностей по координатам и вектору линейной скорости объекта;-

,

- estimates of errors in the coordinates and the linear velocity vector of the object;

,

- оценки погрешностей масштабных коэффициентов гироскопов и акселерометров, в том числе установленных и по продольной оси объекта;-

,

- estimates of errors in the scale factors of gyroscopes and accelerometers, including those established along the longitudinal axis of the object;

- оценки остаточной «скачкообразной» неоднозначности фазовых измерений.-

- estimates of the residual “spasmodic” ambiguity of phase measurements.

,

, поступающих из блока БФРФИ 8 позволяет повысить точности выработки углов крена, курса и тангажа.Using additional differential phase measurements

,

coming from the BFRFI 8 block allows to increase the accuracy of the roll angle, course and pitch.

остаточной неоднозначности фазовых измерений, обеспечивающие его функционирование.In addition, the BFRFI 8 unit was connected with the output of the BVPRF 5 unit according to the current values of ∇φ _ji , the first phase differences of the HC _i signals at the carrier frequency received at the reference and jth antenna, with the inputs of the BKOI 6 unit according to the data from the SNA PA and BIIM , and the output of block BKOI 6 is estimated

residual ambiguity of phase measurements, ensuring its functioning.

,

погрешностей масштабных коэффициентов гироскопов и акселерометров, установленных в том числе и по продольной оси объекта, с соответствующим входом вычислителя БИИМ 4.An additional connection has also been introduced: the output of the BKOI 6 unit is estimated

,

errors of scale factors of gyroscopes and accelerometers, including those installed along the longitudinal axis of the object, with the corresponding input of the BIIM 4 calculator.

The differences in the algorithmic support of the calculator of the proposed ISON from the prototype are reduced, first of all, to the algorithmic support of the BFRFI 8 block.

The input data block BFRFI 8 (Fig. 2A) are:

- the values of the first phase differences of the HC _i signals from the BVPRF 5 block, measured according to the data of the SNA SNA 1;

- values of coordinates or guide cosines of HC _i from PA SNA 1;

- values of the coordinates of the place and the velocity vector of the object from the BIIM 4 computer;

- the values of the angles of the course, pitch and roll of the object from the calculator BIIM 4;

- evaluation of residual ambiguities of phase measurements from the block BKOI 6;

The output of the BFRFI 8 block is:

,

для двух антенных баз b1 и b2.- the difference between the calculated and measured values of the first or second phase differences of the signals HC _i

,

for two antenna bases b1 and b2.

направляющих косинусов орта

относительно антенных баз

, соответствующих согласно соотношению (2) текущим значениям ∇φ_ji измеренных первых разностей фаз сигналов HC_i, в блоке БФРФИ 8 (при использовании в составе ПА СНС нескольких приемников) формируются разности

измеренных значений направляющих косинусов для пары HC_i, соответствующие текущим значениям измеренных вторых разностей фаз сигналов HC_i:In addition to the measured values

ortho cosines

regarding antenna bases

corresponding, according to relation (2), to the current values ∇φ _{ji of the} measured first phase differences of the HC _i signals, in the BFRFI 8 block (when several receivers are used as part of the PA SNA), differences

the measured values of the guide cosines for the pair HC _i , corresponding to the current values of the measured second phase differences of the signals HC _i :

относительно антенных баз

для тех же наблюдаемых HC_i:The instrumental values of the ortho guiding cosines are calculated in the BFRFI block 8.

regarding antenna bases

for the same observed HC _i :

- вычисляются согласно соотношениям (4), (5); а матрица ориентации C_o,h__pr - по значениям углов K, ψ, θ от вычислителя БИИМ 4.where are the values of orth

- are calculated according to relations (4), (5); and the orientation matrix C _{o, h} _ _pr - according to the values of the angles K, ψ, θ from the calculator BIIM 4.

The calculated values for the second phase differences of the HC _i signals are also formed (when several receivers are used in the SNA PA 1):

из измерений (2).The formation of the second phase measurement differences is necessary to eliminate the influence of the discrepancy in the time scales of the reference generators of the SNA 1 receivers, i.e. to eliminate errors

from measurements (2).

Comparing the calculated and measured values of the first or second differences of phase measurements, difference measurements are formed in the BFRFI 8 block:

- or (when using a specialized receiver with three inputs in the PA SNA 1)

- or (when using several receivers with one input as part of the SNA PA 1)

относительно связанных с объектом осей, погрешности знания координат места объекта и HC_i, неоднозначности разностей фазовых измерений и шумы измерений, а также собственно шумы фазовых измерений ПА СНС.These measurements contain, with corresponding weights, mainly errors of the BIIM solution of the object orientation problem (errors ΔC _{o, h} _ _{pr of} the orientation matrix that are uniquely associated with errors in the analytical construction of the geographic accompanying trihedron: α, β, γ; where α is the error in the course, β, γ - errors in the construction of the vertical location), which include errors in the orientation of the antenna base

relative to the axes associated with the object, the error in the knowledge of the coordinates of the object’s location and HC _i , the ambiguity of the differences of the phase measurements and the measurement noise, as well as the noise of the phase measurements of the PA SNA.

Assuming that the biomass errors in navigation parameters and object orientation parameters are sufficiently small, which is ensured during the initial biomir measurements, the linearization of measurements is acceptable (11). In this case, the contribution of the BIIM errors to measurements (11) does not exceed half the wavelength of the emitted HC _i signal.

, то исключая целое число (η_i+1-η_i) из значения

и оставляя его дробную часть

, тем самым исключается из восстановленных измерений

неоднозначность фазовых измерений до уровня

. Остаточная неоднозначность фазовых измерений в пределах одной длины волны, как «скачкообразная» погрешность включается в число оцениваемых параметров.The preliminary processing of difference measurements (11) is performed in the BFRFI block 8 (Fig. 2a) and consists in eliminating the initial ambiguity of the phase measurements. Suppose, for example, that several receivers are used as part of a PA SNA. Because a priori it is known that useful information along with noise is less than one wavelength of the emitted HC _i signal in the values of the given measurement

, then excluding the integer (η _{i + 1} -η _i ) from the value

and leaving its fractional part

, thereby excluded from the reconstructed measurements

ambiguity of phase measurements to a level

. The residual ambiguity of phase measurements within the same wavelength, as a “spasmodic” error is included in the number of estimated parameters.

вместе с известными [18] разностными измерениями по навигационным параметрам поступают на вход блока БКОИ 6 вычислителя интегрированной системы (фиг. 2а) для последующей обработки с использованием алгоритмов фильтра Калмана.Measurements

together with the known [18] difference measurements with respect to navigation parameters, they are input to the BKOI block 6 of the integrated system calculator (Fig. 2a) for subsequent processing using Kalman filter algorithms.

The estimates worked out in the BKOI 6 block are fed back to the BIIM 4 computer to correct errors of the inertial module in the generation of orientation parameters and navigation parameters. And also for the correction of errors of scale factors of the gyroscope and accelerometer installed along the longitudinal axis of the object. This allows you to increase the allowable time interval for the operation of ISON in stand-alone mode by the time of “failures” of the PA SNA 1. In addition, estimates of the residual ambiguity of phase measurements are received at one of the inputs of the BFRFI 8 unit.

Analysis of the accuracy of the proposed solution

Measurement Formation

- Difference navigation measurements

As in the prototype when using BIIM in its composition, differential measurements are formed by navigation parameters:

и радиальным скоростям

для каждого из наблюдаемых HC_i either by pseudo-range

and radial speeds

for each of the observed HC _i

,

- измеренные ПА СНС 1 и

,

- расчетные по данным БИИМ и эфемеридной информации HC_i значения), либо по координатам места и составляющим вектора линейной скорости объекта(

,

- measured PA SNS 1 and

,

- calculated according to the BIIM and ephemeris information HC _i values), or according to the coordinates of the place and the components of the linear velocity vector of the object

- Difference phase measurements

могут быть представлены в следующем виде:For the case of using several receivers in the PA SNA, linearized difference measurements (11b) for two antenna bases

can be represented as follows:

Where

,

,

- направляющие косинусы вектора антенной базы

в географических осях, т.е. элементы векторов

; s_ij, s_(i+1)j, (j=E, N, H) - элементы орта

(направляющие косинусы орта

HC_i относительно географических осей), формируемые согласно соотношениям (4), (5); ΔCf_(i+1)-i - остаточная неоднозначность фазовых измерений в пределах одной длины волны; v_zi - шумы измерений, включающие шумы измерений фазы несущей ПА СНС 1 и составляющие, обусловленные погрешностями знания координат места объекта и эфемеридной информации HC_i, а также погрешностями привязки антенных баз к осям объекта.α, β, γ - errors (α - at the heading, β, γ - in the construction of the vertical of the place characterizing errors in the pitch and roll angles) of the orientation problem in the construction of the geographic trihedron ENH, i.e. calculations in BIIM orientation matrix C _{o, h} _ _pr ;

,

,

- directing cosines of the antenna base vector

in geographic axes, i.e. vectors elements

; s _ij , s _{(i + 1) j} , (j = E, N, H) - elements of the unit vector

(directing cosines of the orth

HC _i relative to the geographic axes) formed according to the relations (4), (5); ΔCf _{(i + 1) -i} is the residual ambiguity of phase measurements within the same wavelength; v _zi are the measurement noise, including the measurement noise of the carrier phase of the PA SNA 1 and the components caused by errors in the knowledge of the coordinates of the object’s location and ephemeris information HC _i , as well as errors in the binding of antenna bases to the axes of the object.

, вторые пол-оборота - для второй

.It should be noted that when the object rotates due to HC _i shadowing, the first half-turn uses phase measurements for the first antenna base

, the second half-turn - for the second

.

Calculation model of errors

In the formation of the computational model of ISON errors, the following approximations were used:

и ММА

, изменения систематических составляющих погрешностей масштабных коэффициентов ММГ ΔM_gi и акселерометров ΔM_ai от запуска к запуску и их изменчивость в пуске были аппроксимированы (из-за отсутствия достоверных данных об их спектральном составе) соответствующими винеровскими процессами;- displacements of zeros of MMG

and MMA

, changes in the systematic components of the errors of the MMG scale factors ΔM _gi and accelerometers ΔM _ai from launch to launch and their variability in the launch were approximated (due to the lack of reliable data on their spectral composition) by the corresponding Wiener processes;

ПА СНС (смещения соответственно шкалы времени в единицах дальности и частоты опорного генератора в единицах радиальной скорости для опорной антенны в ПА СНС относительно данных HC_i) были представлены расчетной моделью

,

, где коэффициент k2, характеризующий дрейф частоты опорного генератора, был аппроксимирован соответствующим винеровским процессом;- errors δD,

PA SNA (offsets, respectively, of the time scale in units of range and frequency of the reference oscillator in units of radial velocity for the reference antenna in PA SNA relative to HC _i data) were presented by the calculation model

,

where the coefficient k2, characterizing the frequency drift of the reference generator, was approximated by the corresponding Wiener process;

- the errors ΔCf _{(i + 1) -i} were also approximated by the corresponding Wiener processes;

- measurement noises v _{zi are} approximated by discrete white noises with known variances at the measurement frequency;

- when forming phase measurements, one pair of HC _{i is used} .

In this case, the calculated model of errors of ISON will have the form

Where

is the state vector of the system,

where ΔV _E , ΔV _N , ΔV _H are the errors in the development of the components of the vector of the relative linear velocity of the object in projections on the geographic axes; Δφ, Δλ, Δh - errors in the development of the geographical coordinates of the place (in latitude, longitude and height); Ф _{k + 1 / k} is the transition matrix of the system state at the step T _{z of the} measurement discreteness; Г _{k + 1} ≅ Ф _{k + 1} · dT - matrix that determines the influence of the input noise vector w _k with covariances Q _k ; H _{k + 1} is the measurement matrix corresponding to equations (12) and (13); v _{k + 1} - measurement noise.

The results of simulation of algorithms for the operation of ISON in the MATLAB package (Simulink)

Modeling was carried out with the following initial data:

- characteristics of the Earth and the gravitational field

R = 6378163 - average equatorial radius of the Earth, (m);

U _e = 7.2921151467 · 10 ^-5 , (rad / s); t _gr0 = 0;

- accelerations from gravity -

,

,

- квадрат первого эксцентриситета эллипсоида вращения Земли; α₃=(a-b)/а - сжатие; а=6378136 (м); α₃=1/298.25784 - параметры общеземного эллипсоида ПЗ-90;where g ₀ = 9.78049 is the acceleration of gravity at the equator of the earth's ellipsoid (m / s ² ); β = 0.005317 (dimensionless quantity, has the order of smallness α ₃ ); a , b - major and minor semiaxis of the ellipsoid of rotation of the Earth;

- the square of the first eccentricity of the ellipsoid of rotation of the Earth; α ₃ = ( a -b) / a - compression; a = 6378136 (m); α ₃ = 1 / 298.25784 - parameters of the all-terrestrial ellipsoid PZ-90;

MMG errors in projections on the axis x _b y _b z _b IS:

- ΔMgx, ΔMgy, ΔMgz - instability of scale factors MMG - random variables with a level of (1σ);

,

,

- систематические составляющие дрейфов ММГ в проекциях на оси x_by_bz_b ИБ, которые характеризуют смещение нулей от пуска к пуску - случайные величины с уровнем (1σ);-

,

,

- the systematic components of MMG drifts in projections on the axis x _b y _b z _b IS, which characterize the shift of zeros from start to start - random variables with a level of (1σ);

- Δω _xb , Δω _yb , Δω _zb are the random components of MMG drifts that characterize the zero drift at start-up - first-order Markov processes σ1 _gi , μ _gi (i = x _b , y _b , z _b );

- fluctuation components of MMG drifts in the projections on the IB axis - discrete white noise at the operating frequency σ2 _gi ;

- α _xy , α _xz , α _yx , α _yz , α _zx , α _zy - orthogonalization errors of the sensitivity axes of gyroscopes - random variables with a level of (1σ) 10 arc.s .;

Errors of linear accelerometers in projections on the axis x _b y _b z _b IS:

- ΔMax, ΔMay, ΔMaz - instability of the scale factors of linear accelerometers - random variables with a level of (1σ);

,

,

- смещение нулей линейных акселерометров - случайные величины с уровнем (1σ);-

,

,

- displacement of zeros of linear accelerometers - random variables with a level of (1σ);

- Δ a _xb , Δ a _yb , Δ a _zb - drifts of zeros of linear accelerometers - Markov processes of the first order σ1 _ai , μ _ai ;

- fluctuation components of the errors of accelerometers in projections on the x _b y _b z _b axis; IS - discrete white noises at the operating frequency σ2 _ai .

PA SNS:

- measurement noise (1σ)

- according to the coordinates of the place - 10 (m);

- according to the components of the linear velocity vector - 0.1 (m / s).

Characteristics of IS Biim on MMD:

- MMA error model

ΔM a x = -1 * 1e-2; ΔM a y = 1 * 1e-2; M a z = 1 * 1e-2;

σ1 _ai = 0.01 (m / s ² ); µ _ai = 0.01 (s ^-1 ); σ2 _ai = 0.02 / sqrt (dt), (m / s ² ); (i = x _b , y _b , z _b )

- Model of errors of gyroscopes (MMG)

ΔMgx = 1 * 1e-2; ΔMgy = -1 * 1e-2; ΔMgz = 1 * 1e-2;

σ1 _gi = 30 * 5e-6 (rad / s); µ _gi = 0.01 (s ^-1 ); σ2 _gi = 36 * 5e-6 / sqrt (dt), (rad / s) or 0.01 ° / s / Hz½; (i = x _b , y _b , z _b );

- errors of the initial exhibition of BIIM (t = 0)

α ₀ = -0.2 ° * pi / 180; β ₀ = 0.1 ° * pi / 180; γ ₀ = -0.1 ° * pi / 180;

ΔV _E0 = 0.1 (m / s); ΔV _N0 = -0.1 (m / s); ΔV _H0 = 0.1 (m / s);

Δφ ₀ = 3 m / R; Δλ ₀ = -3m / (R * cos (fio * pi / 180)); Δh ₀ = 3 m;

Operating frequencies for simulation

dt = 0.001 s; - discreteness of simulation modeling of the object along the trajectory (1 kHz);

dT = 0.001 s - discreteness of operation of the BIIM algorithms (1 kHz);

dT1 = dT - discreteness of the covariance channel of the FC;

Tz = 0.03 s is the discreteness of measurement processing in the FC (discreteness of the SNA data).

The parameters of the trajectory of the object are shown in figures 4.1a and 4.1b.

According to the orientation parameters of the object, the following traffic conditions were adopted:

- at the rate: K = Ko = 90 °;

- by pitch: change of angle on the flight path from + 50 ° to -20 °;

, при f_θ=1 Гц, θ₀=0°.- roll: rotation with constant angular velocity

, at f _θ = 1 Hz, θ ₀ = 0 °.

Errors ISON

Errors in the generation of orientation parameters without using phase measurements are shown in figures 4.2a, 4.2b (Fig. 4.2b shows a graph of Fig. 4.2a in a time-magnified scale at the time of launch). Similar errors, but using phase measurements are shown in FIG. 4.2c, 4.2g (in Fig. 4.2g there is a graph of Fig. 4.2c in a time-enlarged scale at the time of launch). In FIG. 4.2e and 4.2e, errors in the estimation of errors in the scale coefficients of MMD are given. In FIG. 4.2g errors of estimation of the ambiguity of phase measurements are given.

Mathematical modeling and the results of solving the problem of orientation of the object in the proposed scheme for constructing ISON, shown in Fig. 4.2a-4.2zh, confirm the effectiveness of this solution. Moreover, the proposed solution allows for interruptions in the receipt of data from the PA SNA and allows you to effectively ensure the rejection of false measurements.

Bibliography

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Claims (1)

An integrated orientation and navigation system for objects with fast rotation around the longitudinal axis, containing the receiving equipment of the satellite navigation system (SNA), including at least three SNA receiving antennas spaced at the respective antenna bases on the object, one SNA receiver with at least three inputs for connecting antennas or at least three SNA receivers, each with one input for connecting an antenna, a gimballess inertial measuring module (BIIM), including a measuring unit (IS) with blocks and gyroscopes and accelerometers, for example micromechanical gyroscopes and accelerometers, and a navigation calculator, the first and second inputs of which are connected to the outputs of the block of accelerometers and the block of gyroscopes, as well as an integrated system calculator, including a block for generating the first phase differences (BPRF) of navigation satellite signals at the carrier frequency , a complex information processing unit (BCOI) with a Kalman filter type filter, while the input or inputs of the BVPRF block are connected to the third output or third outputs of the CH receivers for measuring the phase of the carrier, and the output of the BVPRF block is connected to the first input of the BKOI block, the second and third inputs of which are connected respectively to the first and second outputs of the SNA receivers according to the measured values of the pseudorange, pseudo-radial speed to the navigation satellites or according to the coordinates of the object’s location, its linear velocity vector , the fourth input of the BKOI block is connected to the fourth output of one of the SNA receivers by the coordinates or the direction cosines of the navigation satellites, the fifth input of the BKOI block is connected to the first output BIIM calculator at the corners of the course, pitch and roll, and its sixth input is connected to the second output of the BIIM calculator according to the location coordinates and the linear velocity vector of the object, while the first output of the BKOI block according to estimates of the errors of the angle of the course, pitch and roll is connected to the third input of the BIIM calculator , its second output, according to the estimates of the errors in the coordinates of the place and the components of the linear velocity vector of the object, is connected to the fourth input of the BIIM computer, and the first and second outputs of the BIIM computer, respectively, in the angles of course, pitch, roll and location points, the linear velocity vector of the object are also connected to the consumer interface, characterized in that the integrated system calculator additionally has a unit for generating the difference between the calculated and measured values of the first or second phase measurement differences (BFRFI) for two antenna bases between the A0 reference antenna of the SNA and A1, A2 antennas separated from it, the first input of which is connected to the output of the BWPRF unit according to the measured values of the first phase differences of the signals of the navigation satellites, the second input of the block The RFBR is connected to the fourth input of the BKOI block at the coordinates or the direction cosines of the navigation satellites, its third input is connected to the fifth input of the block BKOI at the corners of the course, pitch and roll, the fourth input of the block BFRC is connected to the sixth input of the block BKOI at the coordinates of the object’s location, and its fifth the input is connected to the additional fourth output of the BKOI block according to estimates of residual ambiguities of the phase measurements, the output of the BFRFI block is connected to the additional seventh input of the BKOI block, the additional third output of the BKOI is estimated to be inaccurate of the scale coefficients of gyroscopes and accelerometers, including those installed along the longitudinal axis of the object, is connected to the fifth input of the BIIM calculator, while the reference receiving antenna (AO) of the SNA together with the BIIIM information security device are installed in the bow of the object along the rotation axis, and two other antennas (A1, A2) SNAs are placed with the greatest possible distance along the longitudinal axis from the reference antenna and are located circumferentially with an offset of 180 ° in the transverse plane of the object.

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