RU2784859C1 - Method for platform-free orientation of moving objects - Google Patents

Abstract

FIELD: moving objects strapdown orientation.

SUBSTANCE: claimed invention relates to a method for strapdown orientation of moving objects. For the orientation of moving objects, primary instrumental information is formed about the object's apparent acceleration vector based on the signals of a pre-calibrated non-orthogonal block of accelerometers, the vector of the resulting magnetic field strength from the signals of a pre-calibrated non-orthogonal block of magnetometers, the radius vector of the object's location point based on the signals of the satellite navigation system, as well as on the subsequent the processing of this complex magnetic-inertial-satellite information in order to determine the parameters of the orientation of the object in a certain way performs autonomous control, self-diagnosis, correction and normalization of the results obtained.

EFFECT: increased fault tolerance of the orientation system.

1 cl, 2 dwg, 6 tbl

Description

The invention relates to the field of on-board instrumentation and automation, can be used to solve problems of orientation and control of moving objects.

When controlling mobile objects (MO) in near-Earth space (ground and underground, floating and underwater, flying and ballistic, in-line and space), along with the task of navigation, it is necessary to solve the problem of spatial orientation. At the same time, along with the requirements of high accuracy, the software orientation systems are subject to requirements for ensuring high reliability in operation, as well as the requirement to ensure fault tolerance in order to implement the condition for the orientation systems to work in standby emergency modes (RAR).

An analysis of the existing methods for solving the tasks of strapdown software orientation in near-Earth space shows that most of the existing methods are focused on achieving, first of all, high accuracy in determining the orientation parameters and almost does not imply ensuring fault-tolerance and operability of systems in PAP [1-3].

Known strapdown method of inertial orientation software, which consists in determining the parameters of the orientation of objects by integrating the signals of triaxial units of gyroscopes (TBG) over time, taking into account predetermined parameters of the initial orientation software in prelaunch conditions [1, 2]. The method is autonomous, noise-resistant, highly reliable. The disadvantages of the method:

- low accuracy of solving the orientation problem due to the drift of gyroscope signals,

- limiting the time of active operation of the inertial orientation system and the need to perform system correction operations,

the absence of the fail-safe property of the inertial orientation system and the impossibility of its operation in the PAP in case of failures of gyroscopes in triaxial blocks. Thus, the method of inertial orientation of software with triaxial schemes for constructing blocks of gyroscopes does not provide the failsafe property of the orientation system.

There is a known method of offline strapdown orientation software on geophysical fields (HFP), which is free from the main drawback of the method of inertial orientation [3]. This method is based on the calculation of the PO orientation parameters from the readings of triaxial accelerometer units (TBA) and magnetometers (TBM). The essence of the method lies in the fact that, based on the readings of the TBA, parameters are calculated that characterize the deviations of the software from the horizon plane (roll angles (γ) and pitch angle ϑ according to the readings of the TBA, the angle of the magnetic heading ϕ is calculated.

The method of PO orientation by HFP is called the method of analytical horizon-compassing (AHK). Moreover, the computational operations of analytical compassing (AC) are carried out taking into account the results of previously performed operations of analytical leveling (AG). This shows the property of the connectedness of the operations AG and AK in the AGK method. At the same time, the errors characterizing the inaccuracy of the AG operations (Δγ; Δϑ) have a significant impact on the accuracy of determining the magnetic course ϕ at the AK stage.

The connection of the AG and AK channels in the AGK method leads to the fact that with any failure in the AG channel, the AK channel also becomes inoperable. This fact exacerbates the shortcoming of the AGK method associated with its lack of ability to adapt to failures.

движения ПО.The main disadvantage of the AGK method is that the method can only be implemented in the software shutdown mode (ZUPT mode) [3]. In the motion mode of the software, dynamic errors of the inertial channel appear due to the perturbation of the TBA from the side of accelerations

software movement.

With a three-axis block construction scheme (TBA, TBM), the AGK method does not provide conditions for adapting to failures of a strapdown orientation system (BSO).

There is a known method of analytical spatial orientation (APO) software in near-Earth space, which is free from the disadvantage of the AGC method, due to the connectivity of the channels of leveling and compassing [4].

ПО и напряженности

результирующего магнитного поля, получаемой с помощью ТБА и ТБМ, соответственно, одновременно (непоэтапно) вычисляют параметры ориентации ПО в условиях функциональной избыточности информации. Следовательно, в способе АПО каналы АГ и АК не обособлены друг от друга, а объединены в один общий канал-канал АПО. К недостаткам способа АПО следует отнести следующее:The essence of the APO method lies in the fact that, based on two-vector magneto-inertial information about the apparent acceleration vectors

PO and tension

of the resulting magnetic field obtained with the help of TBA and TBM, respectively, at the same time (non-stage) calculate the orientation parameters of the software under conditions of functional redundancy of information. Therefore, in the APO method, the AG and AK channels are not isolated from each other, but are combined into one common channel, the APO channel. The disadvantages of the APO method include the following:

- the operability of the APS system is ensured only in the modes of AP stops or on low-maneuverable objects (as for the AGK method),

- at the hardware level, conditions are not provided for the implementation of the fault-tolerance property of the AFS system in PAP,

- the increased complexity of information processing algorithms imposes increased requirements on the computational characteristics of the calculator (the length of the bit grid, speed, information performance).

Thus, the AFS method eliminates many of the shortcomings of methods-analogues of platformless software orientation, but does not eliminate the main common drawback - the lack of a fail-safe property of the orientation system.

The property of functional fault tolerance (instrumental (hardware) and informational) can be implemented in terms of providing structurally or functionally redundant information [5, 6].

There is a method of strapdown orientation and software navigation based on the processing of multidimensional information obtained using blocks of vector sensors with non-orthogonally set sensitivity axes [7, p. 253]; [8, p. 216]. The non-orthogonal installation of vector sensors in the unit makes it possible to implement the conditions for structural (due to redundancy) and functional redundancy of information, which in turn contributes to an increase in the accuracy and reliability of the system, as well as giving them the properties of hardware (instrumental) fault tolerance and operability in the PAP.

The disadvantages of the method of strapdown autonomous software orientation based on the use of information from blocks with non-orthogonally installed vector sensors (accelerometers, magnetometers) include the lack of functional redundancy of information at the stage of processing the received primary instrument information (PIR)

There is a method of strapdown software orientation, based on the complex processing of magnetic-inertial-satellite information received from blocks of autonomous information (TBA, TBM) and satellite navigation system (SNS) [9]. This method is closest to the present invention and therefore taken as a prototype.

и напряженности магнитного поля

в осях базиса m, связанного с ПО, а на основе показаний СНС вычисляют проекции этих же векторов

на оси географического базиса q=NHE.The essence of the method lies in the fact that, based on the readings of autonomous blocks, information about the apparent acceleration vectors of the software is formed

and magnetic field strength

in the axes of the basis m associated with the software, and based on the readings of the SNS, the projections of the same vectors are calculated

on the axis of the geographical basis q=NHE.

составляют матричное уравнение, решение которого дает информацию о матрице ориентации А базиса m относительно базиса q.Then, based on the magneto-inertial information about the vectors

form a matrix equation, the solution of which gives information about the orientation matrix A of the basis m with respect to the basis q.

The disadvantages of this method of software orientation include the following:

- low accuracy of solving the orientation problem due to the perturbation of the magnetometric channel, due to the influence of the magnetic field of the software itself, which is not taken into account in the information processing method,

- low reliability of the orientation system that implements this method, because the failure of any sensor leads to an inoperable state of the entire system,

- lack of fault-tolerance and operability of the orientation system in PAP due to the lack of hardware and functional redundancy of information.

To eliminate these shortcomings, it is necessary to improve the magnetometric channel and create conditions for hardware and functional redundancy of information in all channels from the measurement process to calculations.

The objective of the present invention is to eliminate the shortcomings of the orientation method based on the processing of magnetic-inertial-satellite information.

The problem is solved by improving the magnetometric channel in the direction of taking into account technological destabilizing factors associated with the influence of the magnetic field of the object (MFO), errors in the assembly and installation of blocks, as well as by implementing the conditions for ensuring the structural and functional redundancy of information, achieved by using a non-orthogonal scheme installation in blocks of vector sensors and development of multivariant algorithms for processing combined information.

The present invention is illustrated by drawings (Fig. 1, 2). On FIG. Figure 1 shows a diagram of the installation of primary information vector sensors (PLI) in non-orthogonal blocks: an accelerometer block (NBA) and a magnetometer block (NBM). On FIG. 1 adopted the following designations:

XYZ - coordinate system (basis m) associated with the software,

- оси чувствительности одномерных ДПИ,

- sensitivity axes of one-dimensional DPI,

- углы ориентации осей чувствительности ДПИ относительно продольной оси ОХ связанного базиса m,X _t ; _βt

- angles of orientation of the DPI sensitivity axes relative to the longitudinal axis OX of the associated basis m,

v - number of DPI in the block (NBA or NBM).

On FIG. 2 shows a functional diagram of the extended magnetic-inertial non-orthogonal orientation (MINOR) method. On FIG. 2, the following designations are adopted:

1 - position corresponding to the performance of operations of metrological calibration, analytical adjustment and technological calibration of DPI and blocks (NBA, NBM),

и вектора напряженности

результирующего магнитного поля на оси чувствительностей датчиков, а также формированию многомерных векторов

в приборных базисах

2 - position corresponding to the process of measuring projections of the apparent acceleration vector with the help of NBA and NBM

and tension vector

the resulting magnetic field on the sensitivity axis of the sensors, as well as the formation of multidimensional vectors

in instrument bases

и

приведенных к осям связанного с объектом базиса m=XYZ,3 - position corresponding to the process of processing primary instrument information (PDI) and the formation of multivariate corrected vectors

and

reduced to the axes of the basis m=XYZ associated with the object,

4 - position corresponding to the process of processing magnetic-inertial-satellite information according to MINOR algorithms,

5 - position corresponding to the process of autonomous control and normalization (ACN) according to the algorithms of autonomous control, self-testing, correction and analytical diagnostics (CASCADE).

6 - satellite navigation system (SNS), which generates navigation information about the geographic latitude ϕ, longitude λ, height h and radius vector modulus

или информации о скалярных величинах (ϕ,λ,r). Двойными линиями обозначены потоки многомерной и многовекторной информации.Thin lines in the diagram (Fig. 2) indicate the flows of information about some vectors

or information about scalar quantities (ϕ,λ,r). Double lines indicate the flows of multidimensional and multivector information.

The MINOR method consists in the sequential execution of operations of technological calibrations, measurements, formation of PPI and its combined processing (Fig. 1, 2):

1. In advance (before the start of the software), the operations of metrological calibration, analytical adjustments and technological calibrations of the magnetometric and inertial measurement channels (pos. 1 in Fig. 2) are performed. Technological operations are performed according to the methodology described in the scientific and technical literature [10].

Processing of the received information is carried out according to the algorithms of technological support of the module (ATOM). At the output of the block (pos. 1 in Fig. 2), technological information (TI) is formed about the individual parameters of the DPI, NBA, NBM and the module.

с помощью НБА и вектора напряженности результирующего магнитного поля

с помощью НБМ формируют многомерные (v-мерные) векторы

и

в виде проекций

и

векторов

(Фиг. 1) на оси чувствительностей акселерометров и магнитометров (поз. 2, Фиг. 2).2. In the process of measuring the apparent acceleration vector

using the NBA and the vector of the resulting magnetic field

using NBM form multidimensional (v-dimensional) vectors

and

in the form of projections

and

vectors

(Fig. 1) on the sensitivity axis of accelerometers and magnetometers (pos. 2, Fig. 2).

- векторы кажущегося ускорения

ПО и напряженности магнитного поля Земли (МПЗ), отнесенные к географическому базису q=NHE,where

- apparent acceleration vectors

SO and strength of the Earth's magnetic field (EMF), referred to the geographical basis q=NHE,

- векторы

отнесенные к базису m=XYZ, связанному с ПО,

- vectors

referred to the m=XYZ basis associated with the software,

- многомерные приборные векторы (v х 1), компонентами которых являются показания блоков НБА и НБМ,

- multidimensional instrumental vectors (v x 1), whose components are the readings of the NBA and NBM units,

- абсолютное ускорение ПО и ускорение свободно падающего тела, отнесенные к связанному базису m=XYZ,

- absolute acceleration of the software and the acceleration of a freely falling body, referred to the associated basis m=XYZ,

- векторы напряженностей магнитных полей ПО (МПО) и электромагнитных помех (ЭМП) в связанном базисе m,

- vectors of strengths of magnetic fields PO (MPO) and electromagnetic interference (EMI) in the associated basis m,

A is the software orientation matrix.

S - matrix of Poisson's ratios,

E - identity matrix (3×3),

приборного базиса

относительно осей связанного базиса m,B, D - rectangular matrices (v × 3) characterizing the orientation of the axes

instrumental basis

with respect to the axes of the associated basis m,

And:

By using non-orthogonal measurement schemes in the NBA and NBM, the requirements of the instrumental (hardware) extension of the PPI are met due to the condition of functionally redundant information about the vectors

и матриц S, В, D находят при выполнении операций технологических калибровок (поз. 1, Фиг. 2)Vector Options

and matrices S, B, D are found during process calibration operations (pos. 1, Fig. 2)

It can be seen from expressions (1) and (2) that the NBM and NBA readings contain complex information: geophysical (GFI), instrumental, technological, operational, (including information about the orientation matrix A PO).

выполняют операцию декомпозиции векторов

(поз. 3 на Фиг. 2). При этом формируют совокупность 8 пар оценок трехкомпонентных векторов

приведенных к осям связанного базиса m = XYZ:3. Based on the results of the formation of a multidimensional PPI

perform the operation of vector decomposition

(pos. 3 in Fig. 2). At the same time, a set of 8 pairs of estimates of three-component vectors is formed

reduced to the axes of the associated basis m = XYZ:

where T _i ; T _j ; T _k - readings of the three selected magnetometers (i-th, j-th, k-th), which are part of the NBM,

n _i ; n _j ; n _k - readings of the three selected accelerometers (i-th, j-th, k-th), which are part of the NBA,

- союзные матрицы (3×3), присоединенные к матрицам и B_μ и D_μ,

- union matrices (3×3) attached to the matrices and B _μ and D _μ ,

- обратные матрицы (33) для ц-ого варианта

- inverse matrices (33) for the i-th variant

detB _μ ; detD _μ - determinants of matrices and B _μ and D _μ

And:

являются неособенными:Algorithms (8)-(10) make it possible to obtain stable, non-degenerate solutions if the matrices B _μ and D _μ

are non-singular:

не повторяются.It is known that conditions (11) are satisfied if the rows or columns of these matrices are linearly independent, which is quite simple to implement in practice, since angles of non-orthogonal installation of DPI in blocks a _τ ; β _τ ; σ _τ ;

are not repeated.

To obtain detailed finite information processing algorithms, instead of formulas (8)-(10), the corresponding Cramer formulas can be used.

в условиях функциональной избыточности информации:Taking into account the results of the previously performed operations of technological preparation (item 1 in Fig. 2), an operation is performed to correct the estimates of the vectors

in conditions of functional redundancy of information:

оказываются свободными от влияния дестабилизирующих факторов со стороны МПО, ЭМП и технологических погрешностей монтажа модуля на ПО (М).After correction vectors

turn out to be free from the influence of destabilizing factors from the side of MPO, EMF and technological errors of mounting the module on software (M).

с использованием таблиц идентификации [6, с. 110].In the block (pos. 3 in Fig. 2), the operation of identifying failures of the DPI and determining the failed vector sensor are simultaneously performed. This operation is performed based on the comparison and estimates of the components of the vectors

using identification tables [6, p. 110].

The number 6 options for constructing measuring and computing three-loop channels (magnetometric and accelerometric) depends on the number v of vector LLIs that are part of the non-orthogonal blocks NBM, NBA:

значения числа 6 вариантов представлены в табл. 1.For

the values of the number of 6 options are presented in table. one.

From the technological, circuit-technical, economic and operational points of view, the most appropriate and efficient option is v=5 (for which δ=10), because usually implement in practice the number of channels δ, not exceeding ten (δ≤10).

обеспечивают условия адаптации БСО к отказам, свойства ее отказоустойчивости и работоспособности системы ориентации МИНОР в резервно-аварийных режимах (РАР) на аппаратном (инструментальном) уровне. При v=5 (табл. 1) допускаются отказы до четырех ДПИ (2 магнитометра + 2 акселерометра).By obtaining functionally redundant magneto-inertial information using 6 measuring and computing channels

provide the conditions for adapting the BSO to failures, the properties of its fault tolerance and the operability of the MINOR attitude control system in standby emergency modes (RAR) at the hardware (instrumental) level. With v=5 (Table 1), failures of up to four DPIs (2 magnetometers + 2 accelerometers) are allowed.

При этом одновременно программным путем производят в блоке (поз. 3 на Фиг. 2) операцию реконфигурации алгоритмов формирования измерительно-вычислительных каналов обработки комбинированной магнито-инерциальной информации.After the failure is identified, the failed DPI is programmatically disconnected from the information flow to the corresponding u-th measuring and computing channel

At the same time, the operation of reconfiguration of the algorithms for the formation of measuring and computing channels for processing the combined magnetic-inertial information is performed in the block (pos. 3 in Fig. 2) at the same time by software.

The operability of the BSO after the reconfiguration of the hardware measuring part of the system and the corresponding information processing algorithms remains at the same level [5, 6].

4. Perform the basic operations of processing MIS information in the block (pos. 4 in Fig. 2) according to the MINOR algorithms.

и

в географическом базисе q=NHE [11]:Taking into account the technological information (TI) and navigation information (ϕ, λ, r) obtained from blocks 1 and 6 (pos. 1 and 6 in Fig. 2), the components of the vectors are calculated

and

in the geographical basis q=NHE [11]:

Geomagnetic potential U:

относительно поверхности референц-эллипсоида с большой полуосью а равен:Radius-vector modulus

relative to the surface of the reference ellipsoid with the semi-major axis a is:

находят на основе основного уравнения гравиметрии [12]:Vector components

are found on the basis of the basic equation of gravimetry [12]:

The expression (15) is reduced to a scalar form:

Причем:

And:

In formulas (14)-(20), the following designations are accepted:

- градиент геомагнитного потенциала,gradU;

- geomagnetic potential gradient,

ϕ, λ; r, h - geographical coordinates of the observation point (latitude ϕ, longitude λ, radius r and height h),

- векторы абсолютного, относительного и кориолисова ускорений в географическом базисе q,

- vectors of absolute, relative and Coriolis accelerations in geographical basis q,

- коэффициенты Гаусса-Шмидта, [11],

- Gauss-Schmidt coefficients, [11],

- присоединенный полином Лежандра степени n порядка m,

- associated Legendre polynomial of degree n of order m,

α - eccentricity of the figure of the Earth,

q is the ratio of the centripetal acceleration at the equator to the acceleration of a freely falling body at the equator g _in

g _in \u003d 9.7803267715 m / s ² ;

Ω=7.292116557 * 10 ^-5 s ^-1 ,

R - average radius of the Earth, R=6378211 m,

r _ϕ ; r _λ - radii of curvature of the meridian and the parallel of the figure of the Earth at the point of observation,

a=6378245 m;

b=6356863 m;

h = r - R

- северная, вертикальная, восточная составляющие скорости движения ПО относительно Земли и соответствующие производные по времени.

- northern, vertical, eastern components of the speed of motion relative to the Earth and the corresponding time derivatives.

и производных получают на основе обработки навигационной информации от СНС (ϕ, λ, r).Numerical values of speed

and derivatives are obtained based on the processing of navigation information from the SNS (ϕ, λ, r).

геофизическая информация (ГФИ) может быть расширена за счет вычисления на основе способа восстановления векторной информации [13] компонент вектора

в связанном базисе m=XYZ.Based on vector information

geophysical information (GPI) can be extended by calculating, based on the vector information recovery method [13], the vector components

in the associated basis m=XYZ.

Further expansion of vector information can be achieved by calculating additional vectors in the related m=XYZ and geographic q=NHE bases [4]:

и дополнительных

векторов составляют матричное уравнение АПО в условиях функциональной избыточности информации [4]:Based on the calculated basic

and additional

vectors make up the APO matrix equation under conditions of functional redundancy of information [4]:

Or in compact form:

Based on the principle of decomposition, the matrix equation (26) is divided into particular matrix identification equations with square matrices of the form:

where P _k - instrument matrix (3×3) for the k-th option,

N _k - identification matrix (3×3) for the k-th option

Moreover, the matrices P _k and N _k (3×3) are formed on the basis of a set of any three rows of the matrix P (6×3) and the corresponding columns of the matrix N (3×6).

The maximum possible number (k _max ) of options for constructing matrix identification equations (28) is:

With δ=10 (for v=5, Table 1) we get:

For practical purposes, it is sufficient to use no more than 10 options for constructing identification equations

APO algorithms are obtained by inverting matrix identification equations (28) [4]:

where: P _k - instrument information matrix, (3×3),

- оценка матрицы ориентации ПО, (3×3),

- evaluation of the software orientation matrix, (3×3),

- союзная матрица (3×3),

- allied matrix (3×3),

detN _k - determinate of matrix N _k (3×3).

углов между ортами связанного m

и географического q

базисов:The orientation matrix of software A is determined using the direction cosines a _ij

angles between the unit vectors of the associated m

and geographical q

bases:

The condition of non-degeneracy of the identification matrix N _k is checked:

For example, for the identification matrix option:

condition (34) we specify:

Use the operation of calculating the average score of the software orientation matrix

Estimates of Euler angles are calculated using the formulas [4]:

определяют с помощью табл. 2-4.Euler angle estimates

determined using the table. 2-4.

могут быть получены на основе использования формул Крамера [4].Algorithms for calculating estimates of Euler angles

can be obtained based on the use of Cramer's formulas [4].

5. Control and normalizing operations are performed using complex algorithms for self-testing and combined autonomous diagnostics (CASKAD) (pos. 5 in Fig. 2):

Similarly perform control operations on additional vectors (23)-(25).

The verification of the correctness of the calculation of estimates of the orientation parameters of the SW is performed according to the following algorithms [4]:

Based on the results of the checks, operations are performed to correct and normalize the intermediate and final results of calculations (Fig. 2).

The practical implementation of the proposed method of strapdown software orientation in the near-Earth space can be performed based on the use of imported or domestic element base (Tables 5, 6).

с допустимыми погрешностями, не превышающими 1^II, необходимо обеспечитьNumerical analysis shows that in order to perform calculations of Euler angle estimates

with permissible errors not exceeding 1 ^II , it is necessary to ensure

с помощью НБМ с точностью до 2 знака после запятой

- vector component measurements

using NBM with an accuracy of 2 decimal places

с помощью НБА с точностью до 4…5 знака после запятой (Δn_доп=5 ⋅ 10^-5g);- vector component measurements

using NBA with an accuracy of 4 ... 5 decimal places (Δn _add =5 ⋅ 10 ^-5 g);

- calculation of Euler angles and their trigonometric functions up to 6...7 decimal places.

Such requirements for the accuracy of measurements and calculations are provided when the length of the bit grid in the calculator is 24 bits. Specified in table. 6 calculators allow you to operate with numbers with a bit grid length of 32 bits.

The frequency of updating information of the BSO that implements the MINOR method is determined by the maneuverability of the software and the permissible errors in the calculation of angles.

For example, for the most dynamic software orientation channel (roll channel y), for the step frequency of information update, we have:

The cyclic update rate of information in the navigation channel SNS is v _c =1...5 Hz. Therefore, the necessary condition for matching the information update rates in the orientation (v _m ) and navigation (v _c ) channels is met:

For low-maneuverable software, the step frequency v _m can be reduced to v _m =100 Hz.

The clock frequency v _T for performing computational operations is provided based on the condition:

МГц.For calculators listed in Table. 6, clock frequency

MHz.

The design of the BSO based on the implementation of the MINOR method can be made in the form of a monoblock, a block diagram, or a combined diagram. BSO MINOR operating modes:

- technological preparation mode,

- regular mode,

- self-monitoring and autonomous self-diagnosis mode,

- backup emergency modes (modes of adaptation to failures).

Thanks to the implementation of such a set of operating modes, the BSO provide conditions both for improving the accuracy and reliability of the system, and for giving it a new property - survivability in operation.

Sources of information

1. Orientation and navigation of moving objects. Modern information technologies / Ed. ed. B.S. Aleshina, K.K. Veremeshko, A.I. Chernomorsky. - M.: Fizmatlit, 2006. - 424 p.

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Claims (1)

Method for strapdown orientation of moving objects, based on the formation of primary instrumental information about the apparent acceleration vector n of the object according to the signals of a pre-calibrated non-orthogonal block of accelerometers, the vector of the resulting magnetic field

according to the signals of a pre-calibrated non-orthogonal block of magnetometers, radius-vector

object location points according to the signals of the satellite navigation system, as well as on the subsequent processing of this complex magnetic-inertial-satellite information in order to determine the object's orientation parameters, characterized in that, first, extended two-vector multidimensional information is formed

based on the readings of pre-calibrated non-orthogonal blocks of v accelerometers (v≥4) and v magnetometers (v≥4) in non-orthogonal multi-axis instrument bases р=X _k

then perform the operation of decomposition of the obtained multidimensional two-vector primary instrumental information

by forming δ populations

estimates of three-coordinate vectors

obtained on the basis of a sample of readings of accelerometer triples and magnetometer triples, with their subsequent reduction to the axes of the associated basis m=XYZ, then, taking into account the results of previously performed operations of technological calibrations, the generated sets of vector estimates are corrected

and compute δ pairs of adjusted vectors

in the associated basis m=XYZ, then, based on the use of navigation information from the satellite navigation system, vectors are calculated

and their vector product in the geographical basis q=NHE and, finally, using the calculated vectors corrected and reduced to the bases m and q, determine the estimates of the object orientation matrices and estimates of the Euler angles under conditions of functionally redundant information, and also perform autonomous control, self-diagnostics, correction and normalization of the obtained results.

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