RU2589495C1 - Method of determining spatial orientation angles of aircraft and device therefor - Google Patents

Abstract

FIELD: data processing; instrumentation.

SUBSTANCE: invention relates to inertial navigation systems and can be used for determining angular orientation of mobile objects of any type. Invention comprises combined processing of measurements of overload sensors and measurement of speed of mobile object using a satellite navigation system (SNS) without angular velocity sensors. Angular velocity is determined by parametric identification, minimising functional quality, which is formed from acceleration differences obtained by differentiation of flight-path velocities measured using SNS and accelerations, obtained by processing overload signals on three axes of aircraft. Device implementing present method comprises a unit of overload sensors, satellite navigation system, a unit for determining linear accelerations, unit for generating matrix of guide cosines, composite function determination unit, differentiation unit, unit for minimisation of composite function, angular velocity determination unit, unit for determining initial orientation angles and integrator, connected to each other in a certain manner.

EFFECT: simple method, reduced cost and high accuracy of determining angular orientation of object in absence of onboard devices for measuring angular velocities.

2 cl, 1 dwg

Description

The invention relates to the field of instrumentation of inertial navigation systems, in particular to the field of constructing angular coordinate sensors for automatic motion control systems, mainly as a vertical line, and can be used to determine the angular orientation of any type of aircraft. The technical result is to simplify the method, reduce the cost of its instrument implementation and increase the accuracy of determining the angular orientation of the object.

A known method and device for constructing an unperturbed gyro-free vertical, presented in the patent of the Russian Federation No.: RU 2258907, IPC G01C 19/44, published on 08.20.2005, adopted by us for the corresponding prototypes.

According to the above method of constructing an undisturbed gyro-free vertical of a moving object, including measuring the current angles of deviation of the axes of the associated coordinate system from the plane of the local horizon (vertical) — pitch and roll using two linear horizontal accelerometers with longitudinal and transverse orientations of their sensitivity axes, perturbed by linear accelerations of the object , the formation of the above evaluations perturbing linear acceleration (north and east components and α _N α _E respectively) wasp According to the data of the satellite navigation receiver, they are numerically differentiated by the corresponding speeds or by the least squares method, these components are recalculated in the projection α _x and α _{y of the} associated coordinate system using the course from the object’s heading system and correction is continuously or discretely introduced into the accelerometer measurements disturbed by these accelerations, than achieve the construction of an unperturbed vertical (pitch angles ϑ and roll γ) according to the formulas for linear accelerometers

A device for constructing an undisturbed gyro-free vertical that implements this method comprises a heading system, two linear accelerometers with longitudinal and transverse orientations of their sensitivity axes, an automatic motion control system, a satellite navigation receiver that generates estimates of the linear accelerations of the object, and a computing unit, for example, a microcomputer, which is perturbed by the object’s accelerations of measuring the current deviation angles of the axes of the associated coordinate system and local vertical, Obtained using linear accelerometers, they are continuously corrected by the values of these accelerations from the satellite navigation receiver and the direction indicator.

However, the method described above has relatively low accuracy. Studies show poor observability in the roll and pitch measurement channel in the absence of taking into account the vertical speed from the satellite navigation system (SSS) and the absence of a vertical accelerometer.

The aim of the proposed invention is to increase accuracy, simplify the method and reduce the cost of its implementation to determine the angular orientation of the aircraft in the absence of airborne angular velocity meters.

To achieve this goal, we propose a method for determining the spatial orientation angles of an aircraft (LA), including measuring linear overloads along the longitudinal axis n _x and the transverse axis n _{z of the} aircraft, measuring the projections of the earth's velocity on the horizontal plane, determining the accelerations of the aircraft by differentiating the measured SSS of the aircraft velocity projections in normal terrestrial coordinate system, further comprising measuring the earth projection speed on the vertical axis, the normal overload n _y along a vertical and LA, determine the linear acceleration _{a x, a y, a z} , are converted into the normal terrestrial coordinate system (SC) constitute functional J of the difference of three projections acceleration in the Earth's SC from SNA and the three components of acceleration derived from the three sensors linear accelerations based dispersions errors R-rate meter, the method of parametric identification determined angular LA ω _x speed, ω _y, ω _z, determined initial angle γ _0, θ _0, ψ ₀ orientation of the aircraft from the measured signals of three sensors of linear accelerations define angles space of orientation, the roll γ, pitch ϑ and yaw angle ψ, integrating the found angular velocities, in this case, if the signals from the SNA disappear, the aircraft is converted to horizontal flight at a constant speed (steady-state flight mode) and the roll and pitch angles are determined by the signals of three linear sensors overloads in the initial exhibition mode.

A device for determining the spatial orientation angles of an aircraft, including a block of overload sensors, comprising two linear overload meters along the longitudinal axis n _x and the transverse axis n _{z of the} aircraft and a satellite navigation system (SNA), further comprises a third linear overload meter n _y as part of the unit overload sensors located along the vertical axis of the aircraft, serially connected linear acceleration determination unit, the block forming matrix of the guide cosines, the determination unit fun a national, a functional minimization unit and an angular velocity determination unit, a differentiation unit whose input is connected to the SNA output, and the output is connected to the second input of the functional determination unit, and a series-connected initial orientation angle determination unit and an integrator, the second input of which is connected to the output of the determination unit angular speeds, the output of the overload sensor unit is connected to the input of the unit for determining the initial orientation angles and to the first input of the unit for determining linear accelerations, the second input of which the second and second input of the block forming the matrix of guide cosines are connected to the first output of the integrator, the third input of the linear acceleration determination unit is the input for the signal corresponding to the value of the gravitational acceleration g, the third input of the functional determination unit is the input for the signals corresponding to the values of the dispersion matrix of the Earth measurement errors speeds R, and the second output of the integrator is the output of the device.

The essence of the claimed invention is as follows.

The proposed method for estimating pitch, roll and yaw angles in flight is based on the joint processing of measurements of overload sensors and speed measurements of an aircraft by a satellite navigation system.

Consider mathematical models that establish relationships between different flight parameters. The projections of accelerations on the axis of the associated coordinate system are determined by the following expressions:

where n _x , n _y , n _z are the projections of the overloads on the axis of the associated coordinate system, measured by the overload sensors installed on board the aircraft;

ϑ, γ - pitch and roll angles to be evaluated;

g is the acceleration of gravity.

To find estimates of the angles of spatial orientation, we apply a system of differential equations to the input of which the angular velocities ω _x , ω _y , ω _z

where ϑ, γ, ψ are the angles of pitch, roll, yaw.

To use expressions (1) and (2), it is necessary to introduce a mathematical model that allows you to restore missing measurements of angular velocities. Consider a moving interval of 0.5 ... 1 s duration that runs through the entire flight data processing section. Since the duration of the interval is small, we approximate each angular velocity by a straight line segment

where t is the time from the beginning of the moving interval,

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

- величины угловых скоростей в начале скользящего интервала и коэффициенты, характеризующие углы наклона приращений угловых скоростей. $$C_{{\omega }_x}$$

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

- values of angular velocities at the beginning of the sliding interval and coefficients characterizing the angles of inclination of increments of angular velocities.

The determination of the initial angular position is divided into two processes: horizontal exhibition (roll and pitch) and azimuthal exhibition (course).

The initial values of the spatial orientation angles γ ₀ , ϑ ₀ , ψ ₀ , which are the initial conditions for differential equations (2), are determined by the signals of the overload sensors.

The horizontal exhibition is carried out according to the signals of three linear overload sensors, measuring on a fixed base the projection of the acceleration of gravity on their sensitivity axes in accordance with expression (1).

In this case, the numerical values of the measurements of the accelerometers will be equal

From the expression it follows that the roll and pitch angles can be found based on the signals of three accelerometers according to the formulas

In order to eliminate the influence of measurement noise present in the output signals of accelerometers, they are preliminarily averaged over a certain period of time.

The exhibition and further correction of the azimuth channel is carried out according to information from the magnetic course sensor. If there is information about the initial coordinates in accordance with the world model of the Earth’s magnetic field, the magnetic declination is found, which is taken into account when determining the true course from the magnetic.

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

производят методом параметрической идентификации.Estimation of unknown parameters $$C_{{\omega }_x}$$

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

produced by parametric identification method.

When numerically integrating equations (2), they substitute approximations of the angular velocities on the moving interval (3).

An overload sensor unit mounted on board provides the measurement of three linear aircraft overloads on the axis of the associated SC. They need to be projected onto the Earth’s normal coordinate system. As you know, the transition matrix from the Earth’s normal system to the connected one has the form

Accordingly, for the reverse transition, it is necessary to use the transposed matrix A ^T.

Then the projections of accelerations (1) in a coupled system are translated into the earth's normal system by the expression

where a _{x_g} , a _{y_g} , a _{z_g} are the projections of accelerations (4) on the axis of the earth's normal coordinate system.

So, expressions (1) - (7) make up the model of the object.

To obtain a model of observations, we differentiate the measured SNA projections of the aircraft speed in the Earth's normal coordinate system. For numerical differentiation, well-known methods are used that have good smoothing properties. In this case, we obtain the acceleration estimates in the Earth's normal system, calculated from satellite measurements

We use these quantities to form the observation model (8), which takes the form

where quantities (8) are taken as elements of the observation vector z (t _i ),

- шум наблюдений, представляющий собой векторную нормальную случайную последовательность типа белого шума с нулевым математическим ожиданием и известной дисперсионной матрицей R(t_i). $${\xi }^T(t_i)=[{\xi }_x(t_i){\xi }_y(t_i){\xi }_z(t_i)]$$

- observation noise, which is a vector normal random sequence such as white noise with zero mathematical expectation and the known dispersion matrix R (t _i ).

The accelerations in the right-hand sides of (7) are determined by the model of the object (1) - (7), which includes unknown values of the angular velocities at the beginning of the sliding interval and coefficients characterizing the inclination angles of the increments of angular velocities

The above models of the object and observations can be represented in the following general vector form:

where y (t), u (t) are the vectors of output and input signals of dimensions n and m, respectively,

z (t _t ) is the observation vector of dimension r,

a is a vector of unknown parameters to be identified,

ξ (t _i ) is the observation noise, which is a vector normal random sequence such as white noise with zero mathematical expectation and the well-known dispersion matrix R (t _i ).

.Observation noises are normal and independent random variables. Therefore, their joint probability distribution density is equal to the product of densities for each moment t _i , $$i=\overline{\mathrm{one,}N}$$

.

It is known that the maximum likelihood function under the above assumptions about the properties of noise leads to unbiased and effective estimates. The maximum likelihood functional is as follows:

It is easy to see that (12) is the least squares functional with the weight coefficient matrix R (t _i ) ^-1 . Thus, under the above assumptions about the properties of noise, the maximum likelihood functional coincides with the weighted functional of the least squares method.

To minimize (12), use one of the modifications of the classical Newton method

Where

по формуламDerivatives of the forecast estimates are determined numerically for times t _i , $$i=\overline{\mathrm{one,}N}$$

according to the formulas

where e _j is a vector of dimension p, all of whose elements are equal to zero except for the j-th element, which is equal to 1; ε is a small number, usually set at the level of 0.001 ... 0.1% of the nominal value of the parameters.

определяют численным решением уравнений объекта и наблюдений при η(t_i)=0. Идентификацию заканчивают по условию $$\left|a_{k+1}-a_k\right|<\delta \left|a_k\right|$$

, где δ=0,005. При обработке в реальном масштабе времени целесообразно жестко задать число шагов, например пять, чтобы зафиксировать число итераций.Estimates z (t _i , a), $$i=\overline{\mathrm{one,}N}$$

determined by numerical solution of the equations of the object and observations when η (t _i ) = 0. Identification is completed by condition $$\left|a_{k+\mathrm{one}}-a_k\right|<\delta \left|a_k\right|$$

where δ = 0.005. When processing in real time, it is advisable to rigidly set the number of steps, for example, five, to fix the number of iterations.

Modeling of the proposed method showed that the smallest errors in the estimation of orientation angles occur in the middle of the moving interval, the duration of which is 0.5 ... 1 s. When processing a flight section of arbitrary duration, the moving interval moves across the entire area with a small step of 0.03 ... 0.125 s, and the final values are the estimates of angles and angular velocities corresponding to the middle of the moving interval.

A device for determining the spatial orientation angles of an aircraft that implements this method comprises a block 1 of overload sensors, a satellite navigation system 2, a block 3 for determining linear accelerations, a block 4 for generating a matrix of guide cosines (MNCs), a block 5 for determining the functional, a block 6 for minimizing the functional, block 7 determining angular velocities, differentiation unit 8, block 9 for determining initial orientation angles, and integrator 10.

The proposed device operates as follows.

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

. Для идентификации используют модификацию классического метода Ньютона (14, 15, 16, 17). Идентификацию заканчивают по условию выполнения $$\left|a_{k+1}-a_k\right|<\delta \left|a_k\right|$$

, где δ=0,005. Используя идентифицированные параметры, в блоке 7 определения угловых скоростей определяют угловые скорости ω_x, ω_y, ω_z. В интеграторе 10, интегрируя выражение (2), используя найденные угловые скорости и начальные значения от блока 9 определения начальных углов γ₀, ϑ₀, ψ₀, согласно (5), определяют углы пространственной ориентации крен γ, тангаж ϑ и угол рыскания ψ.The signals from block 1 of the overload sensors and the values of the orientation angles from the integrator 10, taking into account the constant g, in block 3 of determining the accelerations determine linear accelerations a _x , a _y , a _z , according to expressions (1). In block 4 of the formation of OLSs, linear accelerations are projected onto the Earth’s normal coordinate system using matrix A (6). From the values of the speeds from the SNA 2 by their differentiation in block 8, linear accelerations are obtained. Comparing linear accelerations from differentiation block 8 and from block 4 of OLS formation, in block 5 of determining the functional, taking into account the dispersion matrix R of the acceleration errors, find the functional J according to expression (12). In block 6 of minimizing the functional, minimizing the functional J, unknown parameters are identified $$C_{{\omega }_x}$$

, $$C_{{\omega }_y}$$

, $$C_{{\omega }_z}$$

, $$K_{{\omega }_x}$$

, $$K_{{\omega }_y}$$

, $$K_{{\omega }_z}$$

. For identification, a modification of the classical Newton method is used (14, 15, 16, 17). Identification is completed by the condition of fulfillment $$\left|a_{k+\mathrm{one}}-a_k\right|<\delta \left|a_k\right|$$

where δ = 0.005. Using the identified parameters, in block 7 determining the angular velocities determine the angular velocity ω _x , ω _y , ω _z . In integrator 10, integrating expression (2), using the found angular velocities and initial values from block 9 for determining the initial angles γ ₀ , ϑ ₀ , ψ ₀ , according to (5), determine the spatial orientation angles of the roll γ, pitch ϑ and yaw angle ψ .

The technical result of the proposed invention is to simplify the method, reduce the cost of its instrument implementation and increase the accuracy of determining the angular orientation of the object in the absence of on-board angular velocity meters.

The invention can be used in all types of moving objects and aircraft. For implementation, accelerometers and satellite receivers widely used in aircraft can be used. Integration and parameter determination blocks can be implemented on standard computer elements.

Claims (2)

1. The method of determining the angles of spatial orientation of the aircraft (LA), including measuring linear overloads along the longitudinal axis n _x and the transverse axis n _{z of the} aircraft, measuring the projections of the earth's speed on the horizontal plane, determining the accelerations of the aircraft by differentiating the measured SNA projections of the speed of the aircraft in the normal earth coordinate system, characterized in that they additionally measure the projection of the earth's velocity on the vertical axis, the normal overload n _y along the vertical axis y of the aircraft, determine linear accelerations a _x , a _y , a _z, which are recalculated into the normal Earth coordinate system (SC), make up the functional J from the difference of the three projections of accelerations in the Earth SC from the SSS and the three components of the accelerations obtained from three linear acceleration sensors, taking into account the variances of the errors of the R speed meter, using the parametric identification method, determine the angular velocity of the aircraft ω _x , ω _y , ω _z , determine the initial angles γ ₀ , ϑ ₀ , ψ _{0 of the} aircraft orientation from the measured signals of the three linear overload sensors, determine the spatial orientation angles of the roll γ, pitch ϑ and ugo yaw ψ, integrating the found angular velocities, in this case, in the case of loss of signals from the SNA, the aircraft is transferred to horizontal flight at a constant speed (steady-state flight mode) and the roll and pitch angles are determined by the signals of three linear overload sensors in the initial exhibition mode. 2. A device for determining the spatial orientation angles of an aircraft (LA), including a block of overload sensors, comprising two linear overload meters along the longitudinal axis n _x and the transverse axis n _{z of the} aircraft and a satellite navigation system (SNA), characterized in that it additionally meter comprises a third linear accelerations n _y in the composition overload sensor unit disposed along the vertical axis of the aircraft, connected in series determination unit linear accelerations guide forming unit matrix osines, functional determination unit, functional minimization unit and angular velocity determination unit, differentiation unit, the input of which is connected to the SNA output, and the output is connected to the second input of the functional determination unit, and the initial orientation angle determination unit and the integrator, the second input of which is connected in series with the output of the unit for determining angular velocities, the output of the unit for overload sensors is connected to the input of the unit for determining the initial orientation angles and to the first input of the unit for determining linear accelerations, the second input of which and the second input of the block forming the matrix of guide cosines are connected to the first output of the integrator, the third input of the linear acceleration determination unit is the input for the signal corresponding to the value of the gravitational acceleration g, the third input of the functional definition unit is the input for signals corresponding to the values dispersion matrix of errors of measurement of terrestrial velocities R, and the second output of the integrator is the output of the device.