RU2594631C1 - Method of determining spatial orientation angles of aircraft and device therefor - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: invention relates to instrument making of inertial navigation systems and can be used to determine angular orientation of aircraft of any type. Method comprises combined processing of measurements of overload sensors and measuring aircraft speed with a satellite navigation system (SNS) without angular velocity sensors. Angular velocity of aircraft is determined by parametric identification. Device implementing present method includes a unit of overload sensors, comprising three devices for measuring linear overloads, installed along longitudinal, transverse and vertical axes of aircraft, satellite navigation system, unit for determining linear accelerations, two integrators, unit for determining composite function, unit for generating matrix of guide cosines, minimising composite function, unit for determining angular velocities and unit for determining initial orientation angles, connected to each other in a certain manner.

EFFECT: technical result is simplification of method, reduced cost of its instrument implementation 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 undisturbed gyro-free vertical, presented in patent RU No. 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 disturbed by linear accelerations of the object , the formation of the above evaluations perturbing linear acceleration (north and east components α _N α, and _E, respectively) wasps fected according to satellite navigation receiver by numerical differentiation of the respective velocity or the method of least squares, converted these components in the projection α _x and α _y related coordinate system using the rate of the system object heading indication and is introduced continuously or discretely correction perturbed by these accelerations sensed by accelerometers 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 unperturbed gyro-free vertical that implements this method? contains a heading system, two linear accelerometers with a longitudinal and transverse orientation 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 in which perturbed object’s accelerations measure current angles of deviation of the associated axes coordinate systems and local verticals obtained using linear accelerometers are continuously adjusted by the values of these roots from the satellite navigation receiver and heading indicator.

However, the method described above has relatively low accuracy due to the need to restore accelerations by differentiating the components of the earth's speed measured by the satellite navigation system (SNA), which leads to an additional error in the measurement of angles. In addition, studies show poor observability in the roll and pitch measurement channel in the absence of vertical velocity from the SNA and in 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 a horizontal plane, according to which the projection of the earth's velocity on the vertical axis is additionally , normal overload n _y along the aircraft axis y, determine linear accelerations a _x , a _y , a _z and then, by integrating accelerations, determine linear speeds V _x , V _y , V _z along the axes connected coordinate system (SK), which are recalculated into normal terrestrial SK, make up the functional J from the difference of the three projections of the earth speed of the satellite navigation system (SSS) and the three components of the earth velocity obtained by integrating linear accelerations, taking into account the variance of the error of the speed meter R, determine the angular aircraft velocity ω _x, ω _y, ω _z parametrical identification method, determined initial angle γ _0, θ _0, ψ ₀ LA orientation from the measured sensor signals of the three linear accelerations, angles determined space orientation: 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 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 sensors linear overloads in the initial exhibition mode.

A device for determining the spatial orientation angles of an aircraft that implements this method, 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 an overload sensor block located along the vertical axis of the aircraft, series-connected linear acceleration determination unit, first integrator, matrix generation unit s of directional cosines, a functional determination unit, a functional minimization unit and an angular velocity determination unit, a unit for determining initial orientation angles and a second integrator connected in series, an output of an overload sensor unit is connected to an input of an initial orientation angle determination unit and to a first input of a linear acceleration determination unit, second the input of which is connected to the first output of the second integrator, and the third input of the linear acceleration determination unit is an input for a signal corresponding to the acceleration of gravity g, the second inputs of the first integrator and the functional determination unit are connected to the SNA output, and the third input of the functional determination unit is an input for signals corresponding to the values of the dispersion matrix of the errors of measurement of ground velocities R, the output of the angular velocity determination unit is connected to the third input of the first integrator and to the second input of the second integrator, the second output of which is connected to the second input of the block forming the matrix of guide cosines, and the third output second integrator is the output 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.

Projections of accelerations on the axis of the associated coordinate system are used to find the linear speeds of the aircraft. To do this, it is necessary to solve the system of differential equations

where the last terms in the right-hand sides take into account the rotation of the axes of the coupled coordinate system with angular velocities ω _x , ω _y , ω _z , the measurements of which are absent on board the aircraft. The initial conditions for differential equations (2) are calculated according to the satellite navigation system.

To find the spatial orientation angles ratings apply the system of differential equations, the input of which receives the angular velocities _{ω x, ω y, ω z} :

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

To use expressions (2) and (5), it is necessary to introduce a mathematical model that allows you to restore missing measurements of angular velocities. Consider a moving interval with a duration of 0.1 ... 1 s, running through the entire flight data processing section. Since the interval duration is short, 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 (3), are determined by the signals of three linear overload sensors.

The horizontal exhibition is carried out according to the signals of three accelerometers, measuring on a fixed base the projection of the acceleration of gravity on their axis of sensitivity in accordance with expression (1). In this case, the numerical values of the measurements of the accelerometers will be equal to:

a _x = g sin ϑ,

a _y = -g cos ϑ cos γ,

a _z = g cos ϑ sin γ.

From the expression it follows that the roll and pitch angles can be found based on the signals of three linear overload sensors 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.

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

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

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

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

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

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

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

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

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

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

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

determined by parametric identification method.

When numerically integrating equations (2) and (3), they substitute approximations of the angular velocities on the moving interval (4).

The onboard SNA provides the measurement of three projections of the speed of an aircraft on the axis of the earth's normal coordinate system. As is known, the matrix of guide cosines (OLS), i.e. transition from terrestrial normal SC to associated SC, has the form:

Accordingly, for the reverse transition, it is necessary to use the transposed matrix A ^T. Then the initial conditions for equations (2), which are projections of the velocity in a coupled system at the initial moment of time, are determined by the following expression:

where _{V x_g0, V y_g0, V z_g0} - projection aircraft velocity in normal terrestrial coordinate system at the initial time.

Similarly, the velocity projections in a coupled system, calculated according to equations (2), are translated into the Earth's normal system by the formula

where V _{x_g} , V _{y_g} , V _{z_g} are the projections of the aircraft speeds, determined by integrating the signals from the overload sensors, on the axis of the earth's normal coordinate system.

Expressions (1) - (7) make up the model of the object.

To obtain the observation model, we use the measured SNA projections of the aircraft velocity in the Earth’s normal coordinate system:

We use these quantities to form an observation model that takes the form:

,where quantities (9) are taken as elements of the observation vector $$\overline{z}\left(t_i\right)$$

,

ξ ^T (t _i ) = [ξ _x (t _i ) ξ _y (t _i ) ξ _z (t _i )] is the observation noise, which is a vector normal random sequence such as white noise with zero mean and the known dispersion matrix R ( t _i ).

The velocities in the right-hand sides of (10) 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 _i ) 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 (14) is a functional of the least squares method with a matrix of weight coefficients 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 (14), one of the modifications of the classical Newton method is used:

Where:

по формулам:Derivatives 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, with the exception of 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 |a _k+1-a _k|<δ|a _k|, где δ=0,005. При обработке в реальном масштабе времени целесообразно жестко задать число шагов, например пять, чтобы зафиксировать число итераций. Моделирование предложенного способа показало, что наименьшие погрешности оценивания углов ориентации имеют место в середине скользящего интервала, длительность которого составляет 0,1…1 с. При обработке участка полета произвольной длительности скользящий интервал перемещается по всему участку с малым шагом 0,01…0,125 с, а в качестве окончательных значений выбираются оценки углов и угловых скоростей, соответствующих середине скользящего интервала.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 the condition | a _{k + 1} - a _k | <δ | a _k |, 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 0.1 ... 1 s. When processing a flight section of arbitrary duration, the sliding interval moves over the entire section with a small step of 0.01 ... 0.125 s, and the final values are the estimates of the angles and angular velocities corresponding to the middle of the sliding interval.

In FIG. 1 shows a structural diagram of a device that implements this method of determining the angles of spatial orientation.

The device comprises an overload sensor unit 1, a satellite navigation system 2, a linear acceleration determination unit 3, a first integrator 4, a guide cosine matrix generation unit 5, a functional determination unit 6, a functional minimization unit 7, an angular velocity determination unit 8, an initial angle determination unit 9 orientation, the second integrator 10.

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

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

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

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

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

. Для идентификации используют модификацию классического метода Ньютона (15, 16, 17, 18). Идентификации заканчивается по условию |a _k+1-a _k|<δ|a _k|, где δ=0,005. Используя идентифицированные параметры, в блоке 8 определения угловых скоростей определяют угловые скорости ω_x, ω_y, ω_z. Во втором интеграторе 10, интегрируя выражение (3), используя найденные угловые скорости и начальные значения от блока 9 определения углов γ₀, ϑ₀, ψ₀, согласно (5), определяют углы пространственной ориентации: крен γ, тангаж ϑ и угол рыскания ψ.The proposed device operates as follows. The signals from the block 1 of the overload sensors and the values of the orientation angles from the second integrator 10, taking into account the constant g in the block 3 of determining the accelerations determine linear accelerationsa _x,a _y, a _z according to expressions (1). Given the initial values of the velocity projections in the associated coordinate system from the SNA according to linear acceleration signals from block 3 and the angular velocities from the block 8 for determining angular velocities, taking into account the initial values of the velocity projections from the SNA 2, linear velocities V are determined in the first integrator 4_x, V_y, V_z. In this case, the expressions of system (2) are integrated. In block 5 of the formation of the least squares, the speeds are projected onto the Earth’s normal coordinate system using matrix A (6). Comparing the signals from the SNA 2 and from the block 5 of the formation of the least squares, in the block 6 determining the functional, taking into account the dispersion matrix R of the velocity error, find the functional J according to expression (14). In block 7 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 (15, 16, 17, 18). Identification ends by condition |a _{k + 1}-a _k| <δ |a _k|, where δ = 0.005. Using the identified parameters, in block 8 determining the angular velocities determine the angular velocity ω_x, ω_y, ω_z. In the second integrator 10, integrating expression (3), using the found angular velocities and initial values from block 9 for determining angles γ₀, ϑ₀, ψ₀, according to (5), the spatial orientation angles are determined: roll γ, pitch ϑ and yaw angle ψ.

If the signals from the SNA disappear, the aircraft is transferred to the 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.

The technical result of the proposed invention is to increase the accuracy of determining the angular orientation of the object in the absence of airborne angular velocity meters.

The invention can be used in all types of 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 the 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 a horizontal plane, characterized in that they additionally measure the projection of the earth's speed on the vertical axis, normal overload n _y along the y-axis of the aircraft, determine linear accelerations a _x , a _y , a _z and then, by integrating accelerations, determine linear speeds V _x , V _y , V _z along the axes of the associated coordinate system (SC), which are converted melt into a normal terrestrial SC, make up the functional J from the difference of the three projections of the terrestrial velocity of the satellite navigation system (SSS) and the three terrestrial velocity components obtained by integrating linear accelerations, taking into account the variance of the error of the speed meter determine the angular velocity of the aircraft ω _x , ω _y , ω _z parametrical identification method, determined initial angle γ _0, θ _0, ψ ₀ LA orientation from the measured sensor signals of the three linear accelerations are determined spatial orientation angles: γ roll, pitch p and the angle θ Scania ψ, the angular velocity by integrating results, while in the case of loss of signal from the SNA aircraft converted into horizontal flight at a constant rate (steady flight mode) and the angles of roll and pitch determined from the sensor signals of three linear accelerations in the initial alignment mode. 2. A device for determining the angles of spatial orientation of an aircraft (LA), including a block of overload sensors, containing 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 further comprising a third linear meter overload n _y in the composition overload sensor unit disposed along the aircraft vertical axis serially connected linear acceleration determining unit, a first integrator unit for forming ma direction cosines, functional determination unit, functional minimization unit and angular velocity determination unit, series-connected initial orientation angle determination unit and a second integrator, the output of the overload sensor unit is connected to the input of the initial orientation angle determination unit and to the first input of the linear acceleration determination unit, second the input of which is connected to the first output of the second integrator, and the third input of the linear acceleration determination unit is the input for the signal corresponding the beginning of the free fall acceleration g, the second inputs of the first integrator and the functional determination unit are connected to the SNA output, and the third input of the functional determination unit is an input for signals corresponding to the values of the dispersion matrix of the errors of measurement of ground velocities R, the output of the angular velocity determination unit is connected to the third input of the first integrator and to the second input of the second integrator, the second output of which is connected to the second input of the block forming the matrix of guide cosines, and the third to The output of the second integrator is the output of the device.

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