RU2603767C1 - Method for self-compensation of gyroscopic device drifts independent of acceleration - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: invention relates to precision instrumentation and can be used during development and operation of navigation systems on the basis of gyroscopic devices (GD). Method for self-compensation of gyroscopic device drifts independent of acceleration, for estimation of which the current value of rated integral parameter N defined by mathematical processing of output signals of gyroscope, angle transducer readings and accelerometers is used. Forced turning of the frame around the axis, parallel to axis of the kinetic moment through the current rated correction angle of the frame turning, is performed when the current value achieves or exceeds the rated integral parameter N of a preset threshold, determined as a ratio of mean-square deviation (MSD) of maximum permissible direction storage error, caused by structural drifts to MSD of the drift uncertainty.

EFFECT: technical result is increased accuracy of a navigation system owing to reduced effect of structural drifts of GU on the basic direction storage error irrespective of law of the object motion.

4 cl, 2 dwg

Description

Description of the invention

Purpose and scope

The invention relates to the field of precision instrumentation and can be used in the creation and operation of navigation systems based on gyroscopic devices, for example, gyroscopes or angular velocity sensors, in marine, air, ground, downhole navigation, including those designed to study oil and gas trajectories , geothermal, iron ore and other wells.

State of the art

There are various methods of autocompensation of acceleration-independent drifts (hull drifts) of a gyroscopic device (GU), providing an increase in its accuracy when used (see the book "Autocompensation of instrumental errors of gyrosystems", authors S.M. Zel'dovich and other Publishing House "Shipbuilding" , 1976, UDC 531382, [1]).

The essence of any method of autocompensation is to give individual elements and nodes of the gyroscopic device additional mechanical movements that allow modulation of the departures of the gyroscopes and, ultimately, turn these departures from monotonic into periodic functions of time with a limited amplitude. These methods, in particular, include: forced movement of ball-bearing supports of suspensions of gyroscopic devices, for example, gyroscopes, forced rotation of gyroscopic sensitive elements, reversal of the kinetic moment vectors of gyroscopes, etc.

However, the proper movement of the object around an axis parallel to the axis of the autocompensation is superimposed on the aforementioned forced motion of the gyroscopic device (for example, a gyroscope), which leads to a decrease in the autocompensation operation efficiency, and, as a result, to an increase in the storage error of a given direction due to the fact that complete drift modulation occurs.

Closest to the claimed solution on the basis of the essential features selected as a prototype is a method of auto-compensation by forced rotation of the universal joint gimbal based on a gyroscope around the kinetic moment vector, disclosed in the aforementioned publication [1, p. 52]. In accordance with the solution disclosed in the prototype, a method for automatically compensating for hull drifts included in a navigation system installed on an object, a GU installed together with a triad of accelerometers on a rotary frame equipped with an engine and an angle sensor, so that the axis of rotation of the frame is parallel to the vector The kinetic moment of the PG is based on the forced rotation of the suspension of the PG around the vector of the kinetic moment. Moreover, when implementing this method, the base on which the bearings of the outer suspension ring of the PG are mounted based on a three-stage gyroscope is rotated by an engine with a constant angular velocity around an axis parallel to the initial orientation of the gyroscope kinetic moment vector. Thus, the body of the control unit is deployed at discrete time instants around an axis parallel to the vector of the kinetic moment of the control unit using a rotary frame connected to the engine with discrete fixation of positions.

The main disadvantage of this solution is that, in the framework of its implementation, the object’s motion around its center of mass is not taken into account, and, as a result, in the presence of such a movement, there is no complete modulation of the hull drifts of the PG (gyroscope) until its complete cessation (resonance phenomenon) . As a result, this method does not completely eliminate the influence of hull drifts of the GU on the error in storing the base direction, where the directions to the geographic or magnetic north are usually taken as base directions, but the direction along the arc of a large circle connecting the start and end points of the route can also be used. the direction of the bombing from the starting point to the target, or arbitrary horizontal directions forming a navigation coordinate system, for example, in polar regions.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is to propose a method of automatic compensation of acceleration-independent drifts (hull drifts) of a gyroscopic device (GU), providing modulation of the weight coefficients that determine the effect of these drifts on the storage error of a given direction during the operation of the navigation system on a moving object .

The technical result achieved by the claimed invention is to improve the accuracy of the navigation system by reducing the influence of hull drifts GU on the error in storage of the base direction, regardless of the law of movement of the object

_i+1, с обеспечением возможности компенсации корпусных дрейфов гироскопа, осуществляют при достижении или превышении текущим значением расчетного интегрального параметра N предустановленного порога N_max, определяемого как отношение среднеквадратичного отклонения (СКО) максимальной допустимой погрешности хранения направления σ_Amax, вызванной корпусными дрейфами, к СКО неопределенности этих дрейфов σ_τ, причем значение интегрального параметра N в каждый момент времени определяют путем математической обработки по формуле:The claimed technical result is achieved by using a method of auto-compensation of hull drifts of a PG installed together with a triad of accelerometers on a rotary frame equipped with an engine and an angle sensor, so that the axis of rotation of the frame is parallel to the vector of the kinetic moment of the PG, which consists in using the frame associated with the engine, the body of the PG is deployed at discrete moments of time around an axis parallel to the vector of the kinetic moment of the PG, with discrete fixation of positions. Moreover, the method according to the invention differs from the prototype in that feedback compensation is used, in which the software and hardware continuously monitor the level of suppression of body drifts, to evaluate which the current value of the calculated integral parameter N, determined by mathematical processing of the output signals of the gyroscope, is used, readings of the angle sensor and accelerometers, and the forced rotation of the frame around an axis parallel to the axis of the kinetic moment for the current calculation first rotational angle correction frame $$\beta$$

_{i + 1} , with the possibility of compensating for hull gyro drifts, is carried out when the calculated integral parameter N exceeds or exceeds the current threshold value N _max , defined as the ratio of the standard deviation (SD) of the maximum permissible direction storage error σ _Amax caused by hull drifts to the standard deviation the uncertainties of these drifts σ _τ , and the value of the integral parameter N at each moment of time is determined by mathematical processing according to the formula:

, $${\rm N}=\sqrt{K_{\tau x}^2+K_{\tau y}^2}$$

,

и $$K_{\tau y}$$

- весовые коэффициенты, зависящие от угловых параметров движения объекта, определяемые путем математической обработки выходных сигналов гироскопа, показаний датчика угла (ДУ) и/или акселерометров по формуламWhere $$K_{\tau x}$$

and $$K_{\tau y}$$

- weighting coefficients depending on the angular parameters of the object’s movement, determined by mathematical processing of the output signals of the gyroscope, readings of the angle sensor (DU) and / or accelerometers according to the formulas

, $$\{\begin{array}{l}{K}_{\tau x}(t)={\displaystyle \underset{0}{\overset{t}{\int }}\frac{\sin (\Psi (t)+\beta (t))}{\sin \theta (t)}dt}\\ K_{\tau y}(t)={\displaystyle \underset{0}{\overset{t}{\int }}\frac{\cos (\Psi (t)+\beta (t))}{\sin \theta (t)}dt}\end{array}$$

,

и $$\Psi$$

- углы ориентации между корпусом объекта и горизонтной системой координат, $$\beta$$

- угол между ГУ и корпусом объекта, Where $$\theta$$

and $$\Psi$$

- orientation angles between the body of the object and the horizontal coordinate system, $$\beta$$

- the angle between the PG and the body of the object,

определяют в момент времени, когда N≥ $${\text{N}}_{\max }$$

путем математической обработки выходных сигналов гироскопа, показаний ДУ и/или акселерометров по формулам из следующей системы уравнений: and the current frame rotation angle $${\beta }_{i+\mathrm{one}}$$

determined at a point in time when N≥ $${\text{N}}_{\max }$$

by mathematical processing of the output signals of the gyroscope, the readings of the remote control and / or accelerometers according to the formulas from the following system of equations:

, (*) $$\{\begin{array}{l}\sin {\beta }_{i+\mathrm{one}}=\frac{\sin {\beta }_{i}K\mathrm{one}+\cos {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\\ \cos {\beta }_{i+\mathrm{one}}=\frac{\cos {\beta }_{i}K\mathrm{one}-\sin {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\end{array}$$

, (*)

where the parameters K1 and K2:

, а $$(N(t_i))=\sqrt{{(K_{\tau x}(t_i))}^2+{(K_{\tau y}(t_i))}^2}$$

- $$\{\begin{array}{l}K\mathrm{one}=K_{\tau y}(t_i)K_{\tau y}(t_k)+K_{\tau x}(t_i)K_{\tau x}(t_k)-{(}^N\\ K2=K_{\tau y}(t_i)K_{\tau x}(t_k)-K_{\tau x}(t_i)K_{\tau y}(t_k)\end{array}$$

, but $$(N(t_i))=\sqrt{{(K_{\tau x}(t_i))}^2+{(K_{\tau y}(t_i))}^2}$$

-

- момент времени вычисления текущего поправочного угла $${\beta }_{i+1}$$

, когда условие N ≥ N_max стало истиной, $${\beta }_i$$

- текущее значение угла между ГУ и корпусом объекта,wherein $$t_i$$

- time point for calculating the current correction angle $${\beta }_{i+\mathrm{one}}$$

when the condition N ≥ N _max becomes true, $${\beta }_i$$

- the current value of the angle between the PG and the body of the object,

- момент времени установки рамки в положение $${\beta }_i$$

. $$t_{i-\mathrm{one}}$$

- time frame setting $${\beta }_i$$

.

- момент времени наблюдения за движением объекта, удовлетворяющий следующему условию: $$t_{i-1}<t_k<t_i$$

, $$t_k$$

- the time moment of observation of the movement of the object, satisfying the following condition: $$t_{i-\mathrm{one}}<t_k<t_i$$

,

and N _max = σ _{Amax /} σ _τ .

_i+1, зависящий от угловых параметров движения объекта, может быть определена на основании текущего значения весовых коэффициентов $$K_{\tau x}$$

и $$K_{\tau y}$$

и интегрального параметра N, а также соотношения N с предустановленным пороговым значением $${\text{N}}_{\max }$$

.The duration of the time interval between forced turns of the frame around an axis parallel to the vector of kinetic moment by the current correction angle of rotation of the frame $$\beta$$

_{i + 1,} depending on the angular parameters of the object’s movement, can be determined based on the current value of the weight coefficients $$K_{\tau x}$$

and $$K_{\tau y}$$

and the integral parameter N, as well as the relation N with a predefined threshold value $${\text{N}}_{\max }$$

.

In one embodiment of the invention, a biaxial TLS (angular velocity sensor) mounted on the frame so that the axis of its kinetic moment is parallel to the axis of rotation of the frame is used as a PG.

In yet another embodiment of the invention, two uniaxial TLSs are used as PGs, the sensitivity axes of each of which are orthogonal to the axis of rotation of the frame and to each other.

Brief Description of the Drawings

In order to better demonstrate the distinguishing features of the invention, as an example, not having any restrictive nature, one of the embodiments described below is described below:

FIG. 1 - coordinate system, where ENh is the horizontal coordinate system, XkYkZk is the coordinate system associated with the object, XpYpZp is the coordinate system associated with the frame;

FIG. 2 is an embodiment of a PG based on a biaxial CRS.

It should be noted that the accompanying drawings illustrate only one of the most preferred embodiments of the invention and cannot be construed as limiting its contents, which includes other embodiments.

Feasibility of the invention

As an example of the implementation of the solution according to the claimed invention, we consider a method of auto-compensation of hull drifts of the PG using the example of a gyroscopic inclinometer based on a biaxial TLS used as a PG. Moreover, in the considered embodiment, the gyroscopic inclinometer is considered as the object on which the TLS is installed (see figure 2). In this embodiment of FIG. 2, accelerometers 2 and CRS 1 are located on a rotating frame 3. Frame 3 has the ability to be installed in discrete positions relative to the longitudinal axis of the gyroscopic inclinometer 6 using engine 4. To measure the angle of rotation on the axis of the frame angle sensor 5 (remote control), for example, optical. ДУС 1 is installed so that the sensitivity axes are perpendicular to the axis of rotation of the frame 3. As a part of the considered GU, and the GU in any other design, as a rule, also includes a block of service electronic devices and an information processing unit, including at least a computer implemented on the basis of a microprocessor (not shown in FIG. 2), connected via communication lines, for example, telemetric communication, with an external or integrated control panel and a computer device (not shown in the drawings).

A block of service electronic devices, as a rule, includes at least a power supply unit, a control unit, amplifiers and analog-to-digital signal converters from sensitive sensors, accelerometers and an angle sensor, the current data of which are continuously transmitted to the information processing unit (calculator) for their subsequent processing by software and hardware and generating control signals for the corresponding GU element to correct their position. In the presence of an external control panel and a computer device, the current data from the GU sensors, accelerometers and an angle sensor can be transmitted via telemetry channels and / or any other wired or wireless communication known in the art to the corresponding information processing units for its conversion , processing according to predefined algorithms and generating control signals and commands on the GU, depending on the tasks being solved.

и $${\tau }_y$$

, углы между корпусом объекта и горизонтной системой координат - $$\theta$$

, $$\Psi$$

, а угол между ГУ и корпусом объекта - $$\beta$$

, погрешность азимута ∆А может быть определена следующим образом:According to the invention, when implementing the method of automatic compensation independent of the drift of the body of the gyroscopic device, the azimuth error ΔA caused by the body drifts of the SU (in the embodiment, the TLS) is taken as the storage error of the base direction. Denoting drifts of GU $${\tau }_x$$

and $${\tau }_y$$

, the angles between the body of the object and the horizontal coordinate system - $$\theta$$

, $$\Psi$$

, and the angle between the PG and the body of the object is $$\beta$$

, azimuth error ΔА can be determined as follows:

(1). $$\Delta A=-{\displaystyle \underset{0}{\overset{t}{\int }}\frac{{\tau }_x\sin (\Psi +\beta )}{\sin \theta }dt}-{\displaystyle \underset{0}{\overset{t}{\int }}\frac{{\tau }_y\cos (\Psi +\beta )}{\sin \theta }dt}$$

(one).

и $$K_{\tau y}$$

соответственно. Тогда погрешность азимута ∆А можно представить в виде следующего выражения:Given that the rate of change of drifts (drifts) τ_x, τ_y are slowly changing time functions in comparison with other factors of expression (1), they can be taken out of the signs of the integrals, and the remaining integral expressions are indicated as weight coefficients $$K_{\tau x}$$

 and $$K_{\tau y}$$

 respectively. Then the azimuth error ∆A can be represented as the following expression:

(2). $$\Delta A=-{\tau }_x\cdot K_{\tau x}-{\tau }_y\cdot K_{\tau y}$$

(2).

и $$\Psi$$

, входящих в подынтегральные выражения, в общем случае произвольный, определяемый из следующих известных соотношений:Moreover, taking into account that the law of change of orientation angles $$\theta$$

and $$\Psi$$

included in integrands, in the general case, arbitrary, determined from the following known relations:

; $$\theta =\arcsin \frac{\sqrt{a_x^2+a_y^2}}{a_z}$$

, где $$a_x,a_y,a_z$$

- выходные сигналы акселерометров, $$\beta$$

- выход датчика угла (угол между ГУ и корпусом объекта), очевидно, что при реализации способа автокомпенсации корпусных дрейфов ГУ согласно прототипу значения весовых коэффициентов $$K_{\tau x}$$

и $$K_{\tau y}$$

будут расти во времени, так как собственное движение прибора (определяемое значением угла ψ) складывается с принудительным движением рамки (определяемое значением угла $$\beta$$

), при этом, очевидным образом, не происходит полной модуляции дрейфов, и, как следствие, погрешность азимута возрастает. Таким образом, решение способа автокомпенсации корпусных дрейфов ГУ, раскрытое в прототипе, позволяет обеспечить модуляцию корпусных дрейфов ГУ в погрешности азимута только в случае соблюдения условия: $$\theta =c\text{onst}$$

и $$\Psi =const$$

. $$\psi +\beta =arctg\frac{a_x}{a_y}$$

; $$\theta =\arcsin \frac{\sqrt{a_x^2+a_y^2}}{a_z}$$

where $$a_x,a_y,a_z$$

- output signals of accelerometers, $$\beta$$

- the output of the angle sensor (the angle between the PG and the body of the object), it is obvious that when implementing the method of automatic compensation of the body drifts of the PG according to the prototype of the weight coefficient $$K_{\tau x}$$

and $$K_{\tau y}$$

will grow in time, since the proper movement of the device (determined by the value of the angle ψ) is added to the forced movement of the frame (determined by the value of the angle $$\beta$$

), in this case, obviously, there is no complete modulation of drifts, and, as a result, the azimuth error increases. Thus, the solution of the method for auto-compensation of hull drifts of the PG disclosed in the prototype allows modulating the hull drifts of the PG in the azimuth error only if the conditions are met: $$\theta =c\text{onst}$$

and $$\Psi =const$$

.

As mentioned earlier, the technical result achieved by the claimed invention is to increase the accuracy of the navigation system of the PG due to the modulation of weighting factors that determine the degree of influence of the hull drifts of the PG on the error of storage of the base direction, regardless of the movement of the object.

In the claimed invention, the self-compensation of the hull drifts of the PG is ensured by conducting the turns of the PG at discrete time instants around the kinetic moment vector. In this case, the value of the angle at which the PG frame is rotated using the engine and the angle sensor is determined based on the current values of the object orientation angles included in the expression of the azimuth error (1).

и $$K_{\tau y}$$

, входящих в зависимость, определенную формулой (1). При этом из чертежей, представленных на фиг. 1 и 2, следует, что при помощи двигателя 4 возможно управление только углом между ГУ и корпусом объекта $$\beta$$

. При установке (развороте) рамки ГУ в определенные положения, можно добиться поддержания значений весовых коэффициентов $$K_{\tau x}$$

и $$K_{\tau y}$$

в пределах, не превышающих заданного заранее установленного значения, при достижении которого производится разворот рамки на такой расчетный угол $$\beta$$

, который вызывает смену знака подынтегральных выражений, поэтому оба интеграла, определяющих зависимости весовых коэффициентов $$K_{\tau x}$$

и $$K_{\tau y}$$

, становятся из растущих функций убывающими. Таким образом, весовые коэффициенты $$K_{\tau x}$$

и $$K_{\tau y}$$

из неограниченно растущих со временем становятся ограниченными по величине независимо от закона движения, определяемого углами $$\theta$$

и $$\Psi$$

. An analysis of dependence (1) shows that in order to reduce the azimuth error ΔА, it is necessary to reduce the values of each of the weighting coefficients $$K_{\tau x}$$

and $$K_{\tau y}$$

included in the dependence defined by formula (1). Moreover, from the drawings shown in FIG. 1 and 2, it follows that with the help of engine 4 it is possible to control only the angle between the PG and the body of the object $$\beta$$

. When setting (turning) the GU framework in certain positions, it is possible to maintain the values of weight coefficients $$K_{\tau x}$$

and $$K_{\tau y}$$

within the limits not exceeding a predetermined predetermined value, upon reaching which the frame is rotated by such a calculated angle $$\beta$$

, which causes a change in the sign of integrands, therefore both integrals that determine the dependences of the weight coefficients $$K_{\tau x}$$

and $$K_{\tau y}$$

, become diminishing from growing functions. Thus, the weights $$K_{\tau x}$$

and $$K_{\tau y}$$

from unlimited growing over time become limited in size regardless of the law of motion defined by angles $$\theta$$

and $$\Psi$$

.

, можно добиться минимизации интегральных коэффициентов, а в пределе, их обнуления. Снижая тем самым влияние корпусных дрейфов ГУ на погрешность хранения базового направления. Thus controlling the angle $$\beta$$

, one can achieve the minimization of integral coefficients, and, in the limit, their zeroing. Reducing the effect of hull drifts of the GU on the error of storage of the base direction.

и $$K_{\tau y}$$

в погрешность азимута, на основании вышеизложенного, может быть определен расчетный интегральный параметр N, следующим образом:For a total assessment of the contribution of weights $$K_{\tau x}$$

and $$K_{\tau y}$$

in the azimuth error, based on the foregoing, the calculated integral parameter N can be determined, as follows:

(3). $${\rm N}=\sqrt{K_{\tau x}^2+K_{\tau y}^2}$$

(3).

и $${\tau }_y$$

являются случайными некоррелированными константами с равными дисперсиями среднеквадратичного отклонения (СКО) $${\sigma }_{\tau }^{}$$

:Expression (3) for the integral calculated parameter N is obtained on the basis of the assumption that drift uncertainties $${\tau }_x$$

and $${\tau }_y$$

are random uncorrelated constants with equal variances of standard deviation $${\sigma }_{\tau }^{}$$

:

, то есть $${\sigma }_A^{}={\sigma }_{\tau }^{}\cdot N$$

, где σ_А - СКО погрешности хранения базового направления, вызванной корпусными дрейфами. $${\sigma }_A^2={\sigma }_{\tau }^2\cdot K_{\tau x}^2+{\sigma }_{\tau }^2\cdot K_{\tau y}^2$$

, i.e $${\sigma }_A^{}={\sigma }_{\tau }^{}\cdot N$$

, where σ _A is the standard deviation of the storage error of the base direction caused by hull drifts.

, определяемым из соотношения $${\sigma }_{A\max }^{}={\sigma }_{\tau }^{}\cdot {\text{N}}_{\max }$$

, где $${\sigma }_{A\max }^{}$$

- максимальное допустимое значение СКО погрешности хранения базового направления, вызванное корпусными дрейфами ГУ. Therefore, to limit the value of the standard deviation of the storage error of the base direction, it is sufficient to limit the value of the integral parameter N to the selected threshold value $${\text{N}}_{\max }$$

determined from the relation $${\sigma }_{A\max }^{}={\sigma }_{\tau }^{}\cdot {\text{N}}_{\max }$$

where $${\sigma }_{A\max }^{}$$

- the maximum permissible value of the standard deviation of the storage error of the base direction caused by hull drifts of the GU.

может быть определено как:Accordingly, the threshold value of the calculated integral parameter $${\text{N}}_{\max }$$

may be defined as:

, тогда, очевидно, что при $$\text{N}<{\text{N}}_{\max }$$

справедливо и $${\sigma }_A^{}<{\sigma }_{A\max }^{}$$

. $${\text{N}}_{\max }={\sigma }_{A\max }^{}/{\sigma }_{\tau }^{}$$

, then, obviously, for $$\text{N}<{\text{N}}_{\max }$$

fair and $${\sigma }_A^{}<{\sigma }_{A\max }^{}$$

.

предпочтительно выбирают из совокупности следующих условий: техническая реализуемость и малость прогнозируемой ошибки угла азимута.In general, the threshold value $${\text{N}}_{\max }$$

preferably selected from a combination of the following conditions: technical feasibility and the smallness of the predicted error of the azimuth angle.

выполняется условие $$\text{N}\ge {\text{N}}_{\max }$$

, для изменения знаков интегралов, ГУ относительно объекта необходимо установить в положение $${\beta }_{i+1}$$

. С учетом вышеизложенного, весовые коэффициенты для момента времени $$t_{i+1}$$

( $$t_{i+1}$$

- момент времени, когда будет выполнено условие $$K_{\tau x}=0$$

и $$K_{\tau y}=0$$

) могут быть определены следующим образом:Thus, if at time $$t_i$$

the condition is satisfied $$\text{N}\ge {\text{N}}_{\max }$$

, to change the signs of the integrals, the GU relative to the object must be set to $${\beta }_{i+\mathrm{one}}$$

. Based on the foregoing, weights for a point in time $$t_{i+\mathrm{one}}$$

( $$t_{i+\mathrm{one}}$$

- the point in time when the condition is met $$K_{\tau x}=0$$

and $$K_{\tau y}=0$$

) can be defined as follows:

(4). $$\{\begin{array}{l}{K}_{\tau x}(t_{i+\mathrm{one}})=K_{\tau x}(t_i)+{\displaystyle \underset{ti}{\overset{ti+\mathrm{one}}{\int }}\frac{\sin \Psi (t)\cos {\beta }_{i+\mathrm{one}}+\cos \Psi (t)\sin {\beta }_{i+\mathrm{one}}}{\sin \theta (t)}dt}\\ K_{\tau y}(t_{i+\mathrm{one}})=K_{\tau y}(t_i)+{\displaystyle \underset{ti}{\overset{ti+\mathrm{one}}{\int }}\frac{\cos \Psi (t)\cos {\beta }_{i+\mathrm{one}}-\sin \Psi (t)\sin {\beta }_{i+\mathrm{one}}}{\sin \theta (t)}dt}\end{array}$$

(four).

By entering the following notation:

(5). $$\begin{array}{l}{I}_s={\displaystyle \underset{ti}{\overset{ti+\mathrm{one}}{\int }}\frac{\sin \Psi (t)}{\sin \theta (t)}dt}\\ I_c={\displaystyle \underset{ti}{\overset{ti+\mathrm{one}}{\int }}\frac{\cos \Psi (t)}{\sin \theta (t)}dt}\end{array}$$

(5).

, получим следующую систему уравнений, с учетом принятых в (5) обозначений:Equating to zero weight coefficients at time $$t_{i+\mathrm{one}}$$

, we obtain the following system of equations, taking into account the notation adopted in (5):

(6). $$\{\begin{array}{l}{K}_{\tau x}(t_{i+\mathrm{one}})=K_{\tau x}(t_i)+I_s\cos {\beta }_{i+\mathrm{one}}+I_c\sin {\beta }_{i+\mathrm{one}}=0\\ K_{\tau y}(t_{i+\mathrm{one}})=K_{\tau y}(t_i)+I_c\cos {\beta }_{i+\mathrm{one}}-I_s\sin {\beta }_{i+\mathrm{one}}=0\end{array}$$

(6).

и $$\cos {\beta }_{i+1}$$

позволяет получить следующую систему зависимостей:Solution of a system of equations for $$\sin {\beta }_{i+\mathrm{one}}$$

and $$\cos {\beta }_{i+\mathrm{one}}$$

allows you to get the following system of dependencies:

(7). $$\{\begin{array}{l}\sin {\beta }_{i+\mathrm{one}}=\frac{K_{\tau y}(t_i)I_s-K_{\tau x}(t_i)I_c}{I_s^2+I_c^2}\\ \cos {\beta }_{i+\mathrm{one}}=\frac{-K_{\tau x}(t_i)I_s-K_{\tau y}(t_i)I_c}{I_s^2+I_c^2}\end{array}$$

(7).

At the same time, the following conditions are satisfied for the expression specified in the divider:

$$I_s^2+I_c^2={(K_{\tau x}(t_i))}^2+{(K_{\tau y}(t_i))}^2={(N(t_i))}^2$$

и $$K_{\tau y}$$

достигнут нуля.provides the minimum time for which weights $$K_{\tau x}$$

and $$K_{\tau y}$$

reached zero.

(где $$t_r$$

- время работы навигационной системы ГУ, $$t_{i-1}$$

- момент времени, когда ГУ относительно объекта был установлен в положение $${\beta }_i$$

) закон изменения углов ориентации, а как следствие и закон изменения $$K_{\tau x}(t)$$

и $$K_{\tau y}(t)$$

можно считать неизменным. Тогда, выбрав интервал наблюдения от $$t_k$$

до $$t_i$$

( $$t_{i-1}<t_k<t_i$$

), система уравнений для весовых коэффициентов может быть представлена следующим образом:Since, when $$t_{i+\mathrm{one}}-t_{i-\mathrm{one}}<<t_r$$

(Where $$t_r$$

- the operating time of the navigation system GU, $$t_{i-\mathrm{one}}$$

- the point in time when the PG relative to the object was set to $${\beta }_i$$

) the law of change of orientation angles, and as a consequence, the law of change $$K_{\tau x}(t)$$

and $$K_{\tau y}(t)$$

can be considered unchanged. Then, by choosing the observation interval from $$t_k$$

before $$t_i$$

( $$t_{i-\mathrm{one}}<t_k<t_i$$

), the system of equations for weights can be represented as follows:

(8). $$\{\begin{array}{l}{K}_{\tau x}(t_i)=K_{\tau x}(t_k)+{\displaystyle \underset{tk}{\overset{ti}{\int }}\frac{\sin \Psi (t)\cos {\beta }_i+\cos \Psi (t)\sin {\beta }_i}{\sin \theta (t)}dt}\\ K_{\tau y}(t_i)=K_{\tau y}(t_k)+{\displaystyle \underset{tk}{\overset{ti}{\int }}\frac{\cos \Psi (t)\cos {\beta }_i-\sin \Psi (t)\sin {\beta }_i}{\sin \theta (t)}dt}\end{array}$$

(8).

By entering the following notation:

(9). $$\{\begin{array}{l}{f}_s={\displaystyle \underset{tk}{\overset{ti}{\int }}\frac{\sin \Psi (t)}{\sin \theta (t)}dt}=\cos {\beta }_i(K_{\tau x}(t_i)-K_{\tau x}(t_k))-\sin {\beta }_i(K_{\tau y}(t_i)-K_{\tau y}(t_k))\\ f_c={\displaystyle \underset{tk}{\overset{ti}{\int }}\frac{\cos \Psi (t)}{\sin \theta (t)}dt}=\sin {\beta }_i(K_{\tau x}(t_i)-K_{\tau x}(t_k))+\cos {\beta }_i(K_{\tau y}(t_i)-K_{\tau y}(t_k))\end{array}$$

(9).

and determining the conditions for normalization as follows:

(10). $$I_s=k{f}_s,I_c=k{f}_c$$

(10).

(11),Where $$k^2=\frac{{(K_{\tau x}(t_i))}^2+{(K_{\tau y}(t_i))}^2}{f_s^2+f_c^2}=\frac{{(N(t_i))}^2}{f_s^2+f_c^2}$$

(eleven),

, в который необходимо установить рамку:with subsequent substitution of (10) into (7), we obtain the following expressions for the trigonometric functions of the angle $${\beta }_{i+\mathrm{one}}$$

in which you want to set the frame:

, (12) $$\{\begin{array}{l}\sin {\beta }_{i+\mathrm{one}}=\frac{\sin {\beta }_{i}K\mathrm{one}+\cos {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\\ \cos {\beta }_{i+\mathrm{one}}=\frac{\cos {\beta }_{i}K\mathrm{one}-\sin {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\end{array}$$

, (12)

where the parameters K1 and K2 are determined from the following relationships:

(13). $$\begin{array}{l}K\mathrm{one}=K_{\tau y}(t_i)K_{\tau y}(t_k)+K_{\tau x}(t_i)K_{\tau x}(t_k)-{(}^N\\ K2=K_{\tau y}(t_i)K_{\tau x}(t_k)-K_{\tau x}(t_i)K_{\tau y}(t_k)\end{array}$$

(13).

позволяет реализовать способ автокомпенсации корпусных дрейфов гироскопа с обратной связью с осуществляемым постоянным отслеживанием текущего, уже достигнутого уровня компенсации данных дрейфов, в котором момент времени, когда необходимо выполнить разворот и угол, в который необходимо установить рамку, зависят от угловых параметров движения прибора.Thus, the obtained dependence for calculating the angle $${\beta }_{i+\mathrm{one}}$$

allows you to implement a method of automatic compensation of hull gyroscope drifts with feedback with ongoing monitoring of the current, already achieved level of compensation for these drifts, in which the moment of time when you need to make a turn and the angle at which you want to set the frame depend on the angular parameters of the movement of the device.

The implementation of the method is as follows.

вновь происходит новый расчет значения угла, в который необходимо установить ГУ, и осуществляется следующий разворот рамки из текущего положения. Далее цикл повторяется. Поскольку интегральный параметр N осуществляет непрерывное отслеживание уже достигнутого уровня компенсации корпусных дрейфов ГУ, вырабатываемые при этом оценки позволяют рассчитать угол, на который необходимо развернуть рамку при достижении порогового значения, что позволяет ограничить погрешность выработки азимута, вызванную корпусными дрейфами ГУ в режиме постоянного наблюдения, независимо от закона движения объекта.If the condition N <N _max is satisfied, then the PG relative to the body of the object is stationary. For N ≥ N _max, from the equations (12) the value of the angle is calculated at which it is necessary to establish the PG relative to the body of the object. After performing this operation, the PG turns to this position around the axis parallel to the axis of the kinetic moment. Since, regardless of the position of the frame, the calculation of N continues, one can observe a decrease in this parameter with time (to 0 in this case), and then its growth. Upon reaching the condition $$N\ge {\text{N}}_{\text{max}}$$

again, a new calculation of the value of the angle at which it is necessary to set the PG occurs, and the next frame is rotated from the current position. Next, the cycle repeats. Since the integral parameter N continuously monitors the already achieved level of compensation of the hull drifts of the PG, the estimates generated in this case allow one to calculate the angle by which the frame must be rotated when the threshold value is reached, which allows limiting the error in the azimuth caused by the hull drifts of the PG in the constant observation mode, independently from the law of motion of the object.

It should be noted that all calculations are carried out on the basis of objectively obtained measurements of the angle sensor, accelerometers and PG, which are transmitted in real time to the ground control panel and processed by a personal computer or similar devices connected to the ground control panel with generation based on the calculations and transmission of control signals to the gyroscopic device. Similarly, these operations can be carried out when implementing the information processing unit integrated in the GU, the control panel and the computer, based on microprocessor devices. With any of the options, control systems or current information processing systems or modules are implemented, the method of auto-compensation of gyroscopic devices independent of accelerations of drifts, according to the claimed invention, can be carried out automatically in a hardware-software manner.

The embodiment described above, as indicated earlier, related to the longitudinal arrangement of the gyroscopic inclinometer, however, it is obvious that the self-compensation method implemented in the present invention can be applied to any other gyroscopic devices, since in this case, the main object of observation is the gyroscope itself and the ability to control the rotation of the frame to compensate for the body drifts of the gyroscope.

Without loss of quality of the method of auto-compensation according to the invention, as a GU can be used:

- one biaxial TLS installed so that the axis of its kinetic moment is parallel to the axis of rotation of the frame.

When using a biaxial TLS as a PG, the TLS measures two projections of angular velocity. Values of angular velocities will contain errors, including hull drifts, to which the method of auto-compensation is valid, all the above conclusions remain valid for this embodiment of the invention.

- two uniaxial TLS, the sensitivity axes of which are orthogonal to each other and the axis of rotation of the frame.

When using two uniaxial TLS as a control unit, two projections of the angular velocity are measured, while the angular velocity values will contain errors, including hull drifts, to which the auto-compensation method described above and corresponding to the claimed invention is valid.

Thus, the claimed method of auto-compensation of acceleration-independent drifts of PGs will significantly improve the accuracy of the navigation system of the PGs by modulating the weight coefficients that determine the degree of influence of the hull drifts of the PGs on the storage error of the base direction, regardless of the movement of the object.

Claims (3)

The method of auto-compensation of body drifts of a gyroscopic device (PG) installed together with a triad of accelerometers on a rotary frame equipped with an engine and an angle sensor, so that the axis of rotation of the frame is parallel to the vector of the kinetic moment of the PG, which consists in using a frame associated with the engine , the PG case is deployed at discrete moments of time around an axis parallel to the vector of the kinetic moment of the PG, with discrete fixation of positions, characterized in that they use reverse compensation an ide, in which the software-hardware method continuously monitors the level of suppression of hull drifts, which is estimated using the current value of the calculated integral parameter N, determined by mathematical processing of the output signals of the gyroscope, the readings of the angle sensor and accelerometers, and the forced rotation of the frame around the axis parallel to the kinetic axis moment for the current estimated correction angle of rotation of the frame $$\beta$$

_{i + 1} , with the possibility of compensating for hull gyro drifts, is carried out when the calculated integral parameter N exceeds or exceeds the current threshold value N _max , defined as the ratio of the standard deviation (SD) of the maximum permissible direction storage error σ _Amax caused by hull drifts to the standard deviation the uncertainties of these drifts σ _τ , and the value of the integral parameter N at each moment of time is determined by mathematical processing according to the formula:
$${\rm N}=\sqrt{K_{\tau x}^2+K_{\tau y}^2}$$

,
Where $$K_{\tau x}$$

and $$K_{\tau y}$$

- weighting coefficients depending on the angular parameters of the object’s movement, determined by mathematical processing of the output signals of the gyroscope, readings of the angle sensor (DU) and / or accelerometers according to the formulas
$$\{\begin{array}{l}{K}_{\tau x}(t)={\displaystyle \underset{0}{\overset{t}{\int }}\frac{\sin (\Psi (t)+\beta (t))}{\sin \theta (t)}dt}\\ K_{\tau y}(t)={\displaystyle \underset{0}{\overset{t}{\int }}\frac{\cos (\Psi (t)+\beta (t))}{\sin \theta (t)}dt}\end{array}$$

,
Where $$\theta$$

and $$\Psi$$

- orientation angles between the body of the object and the horizontal coordinate system, $$\beta$$

- the angle between the PG and the body of the object,
and the current frame rotation angle $${\beta }_{i+\mathrm{one}}$$

determined at a point in time when N≥ $${\text{N}}_{\max }$$

by mathematical processing of the output signals of the gyroscope, the readings of the remote control and / or accelerometers according to the formulas from the following system of equations:
$$\{\begin{array}{l}\sin {\beta }_{i+\mathrm{one}}=\frac{\sin {\beta }_{i}K\mathrm{one}+\cos {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\\ \cos {\beta }_{i+\mathrm{one}}=\frac{\cos {\beta }_{i}K\mathrm{one}-\sin {\beta }_{i}K2}{N(t_i)\sqrt{{(K_{\tau x}(t_i)-K_{\tau x}(t_k))}^2+{(K_{\tau y}(t_i)-K_{\tau y}(t_k))}^2}}\end{array}$$

, (*)
where the parameters K1 and K2:
$$\{\begin{array}{l}K\mathrm{one}=K_{\tau y}(t_i)K_{\tau y}(t_k)+K_{\tau x}(t_i)K_{\tau x}(t_k)-{(}^N\\ K2=K_{\tau y}(t_i)K_{\tau x}(t_k)-K_{\tau x}(t_i)K_{\tau y}(t_k)\end{array}$$

, but $$(N(t_i))=\sqrt{{(K_{\tau x}(t_i))}^2+{(K_{\tau y}(t_i))}^2}$$

-
wherein $$t_i$$

- time point for calculating the current correction angle $${\beta }_{i+\mathrm{one}}$$

when the condition N ≥ N _max becomes true, $${\beta }_i$$

- the current value of the angle between the PG and the body of the object,
$$t_{i-\mathrm{one}}$$

- time frame setting $${\beta }_i$$

.
$$t_k$$

- the time moment of observation of the movement of the object, satisfying the following condition: $$t_{i-\mathrm{one}}<t_k<t_i$$

,
and N _max = σ _{Amax /} σ _τ .

2. The method according to p. 1, characterized in that the duration of the time interval between forced turns of the frame GU around the axis parallel to the vector of kinetic moment at the current correction angle of rotation of the frame $$\beta$$

_{i + 1,} depending on the angular parameters of the object’s movement, is determined based on the current value of the weight coefficients $$K_{\tau x}$$

and $$K_{\tau y}$$

and the calculated integral parameter N, as well as the ratio of N with a predefined threshold value $${\text{N}}_{\max }$$

. 3. The method according to any one of paragraphs. 1 and 2, characterized in that as the GU use one biaxial TLS installed so that the axis of its kinetic moment is parallel to the axis of rotation of the frame. 4. The method according to any one of paragraphs. 1 and 2, characterized in that as the GU use two uniaxial TLS, the sensitivity axis of each of which are orthogonal to the axis of rotation of the frame and to each other.

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