RU2256154C1 - Method for measurement of flight vehicle attitudes - Google Patents

Abstract

FIELD: procedure of indirect measurements of flight vehicle attitudes.

SUBSTANCE: the method is based on the use of information from the receiver of the satellite navigation system measuring the light vehicle velocity components to the South, East and in altitude from three-coordinate angular velocity and linear acceleration transducers installed on board the flight vehicle. The flight vehicle attitudes are measured in compliance with the estimation algorithm realized in the computer, on the varying time interval.

EFFECT: enhanced accuracy of measurement of the bank, pitch angle and the flight vehicle heading in the conditions of maneuvering.

Description

The claimed invention relates to techniques for indirect measurements of the angular positions of aircraft (LA).

A known method of measuring the angular position of the aircraft [Dzhandzhgava GI, Chernodar A.V. Integrated primary information processing in strapdown inertial-satellite orientation and navigation systems. Materials of the 4th International Conference on Integrated Navigation Systems. St. Petersburg, 1997, p.52-58], according to which the roll, pitch and heading angles are measured in accordance with a three-level algorithm that combines information from the strapdown inertial navigation system (SINS) and from the satellite navigation system (SNA).

At the first level, projections of the projections of angular velocity onto the connected axes of the aircraft are performed by one time discretization step using the Levinson predictive filters.

At the second level, the estimates of the angular velocities obtained at the first level are smoothed using the Kalman filter, using the difference between the predicted values of the angular velocity and the angular velocity values measured using the angular velocity sensors as measurements.

At the third level, with the help of the Kalman filter, the estimates of the angular positions obtained at the second level from the information from the on-board receivers of satellite navigation are refined using, as measurements of the difference of the first and second orders of the matrices of directional cosines, determined using the SINS algorithm and using information from the on-board receivers SNA.

The disadvantage of this method is its low accuracy when maneuvering aircraft, which is due to:

- an increase in errors in predicting angular velocities at the first level of the algorithm when maneuvering an aircraft;

- an increase in the statistical uncertainty of the Kalman filter at the second level of the algorithm due to the inaccuracy of setting the correlation time constant and the rms value of the gyroscopic drift under conditions of maneuvering the aircraft;

- inaccuracy in the estimation of the matrix of guide cosines calculated in the strapdown inertial system, which is used at the third level of the algorithm and the estimation errors of which increase during maneuvering of the aircraft;

- accumulation of filtering errors, which takes place at the second and third levels due to the recurrent processing of measurement signals with inaccurate accounting of the statistical characteristics of the measurements used in maneuvering aircraft.

The purpose of the invention is to improve the accuracy of measurement of roll angles, pitch and aircraft course in conditions of maneuvering.

This goal is achieved due to the fact that according to the proposed method for measuring the angular positions of the aircraft, based on the use of information from the satellite navigation system and from angular velocity sensors, the measurement of the angular positions of the aircraft is carried out in accordance with the estimation algorithm implemented in the computing device, according to information from the receiver The SNA, which measures the speed components of the aircraft to the north, east, and altitude, and from three-coordinate angular velocity sensors (DLS) and linear acceleration sensors (DLU), is installed claimed on board aircraft, for sliding the observation time interval [t _0, t ₀ + T + τ], where:

t ₀ is the initial measurement time;

T is the length of the time interval of a single observation of the measurements of the SNA receiver;

τ is the length of the time interval for predicting the angular positions of the aircraft with respect to the last measurement of the SNA on a moving time interval;

t ₀ + T + τ = t is the current moment of real time,

and first, for the time moment t ₀ from the measurements of the TLS, DLO and SNA on the time interval [t ₀ , t ₀ + T], three projections of the aircraft speed on the axis of the associated coordinate system are estimated and the pitch, roll and yaw angles are estimated by iteratively solving the algebraic system equations compiled by the method of sensitivity functions, the solution of which minimizes the root-mean-square value of the discrepancy between the velocity measurements using the SNA and velocity estimates using the TLS and DLU, which are calculated by solving the differential system equations for the derivatives of the projections of the aircraft speed on the axis of the connected coordinate system with recalculation of the associated velocities on the axis of the local planar rectangular earth coordinate system and differential equations for the derivatives of pitch, roll and yaw angles, and then for time t according to the measurements of the TLS and DLO on the moving interval of time, the pitch, roll and yaw angles are estimated by solving differential equations for the derived pitch, roll and yaw angles, after which the yaw angle is converted to the course angle, When the shift interval in a sliding direction of increasing time value τ measuring angular positions of aircraft in accordance with an algorithm of estimation repeated estimation of pitch angle, roll rate, and produce in each discrete real time, which differs from the previous by the amount τ.

When implementing the proposed method for indirect measurement of the angular positions of aircraft, measurements of TLS and DLU are performed in the associated coordinate system of the aircraft OX ₁ Y ₁ Z ₁ . The SNA receiver receives satellite signals and calculates the components of the velocity vector V _N , V _E , V _H in the directions to the north, east and in height [Soloviev Yu.A. Satellite navigation systems. - M .: ECO-TRENDZ, 2000, p. 56, p. 59].

,

,

в местной плановой прямоугольной системе координат OXYZ, в которой ось ОХ направлена на север, ось OZ направлена на восток, а ось OY направлена по местной вертикали вверх. Ошибками приближения можно пренебречь при относительно небольших величинах Т и τ, при которых траекторию полета ЛА можно достаточно точно рассматривать в местной плановой прямоугольной системе координат.For all SNA measurements for one position of the moving interval, it is assumed that the velocities V _N , V _E , V _{H are} approximately equal to the velocities

,

,

in the local plan rectangular coordinate system OXYZ, in which the OX axis is directed to the north, the OZ axis is directed to the east, and the OY axis is directed upward in the local vertical. Approximation errors can be neglected for relatively small values of T and τ, at which the flight path of the aircraft can be fairly accurately considered in the local planar rectangular coordinate system.

Denote a is a vector containing three components of the speed of the aircraft in a connected coordinate system and three angles of orientation of the aircraft:

here the index T denotes the transposition operation;

V _x , V _y , V _z - projection of the speed of the aircraft on the axis of the associated coordinate system;

ϑ, γ, ψ are the pitch, roll, and yaw angles, respectively.

The estimation algorithm is iterative and has the form:

Step 1. The initial number of iterations k = 1 and the initial approximation of the vector a _k-1 (t ₀ ) = a ₀ (t ₀ ) are specified, in which one condition is used, namely that the speed of the aircraft along the longitudinal axis of the associated coordinate system is not equal to zero:

here V _x0 is the a priori value of the estimation of the velocity component V _x in the coupled coordinate system, which is determined by the type of aircraft.

Step 2. Start a cycle of N iterations, in which steps 2-7 of the algorithm are solved. The integration of a system of differential equations of the 6th order on the time interval [t ₀ , t ₀ + T], which consists of two systems of equations of the 3rd order:

The right-hand sides of the systems of equations (1), (2) are substituted with measurements of the overloads n _x , n _y , n _z , which are signals of the DLU in units of g, and measurements of angular velocities, which are signals of the SLD. The system of equations (1) follows from the well-known fact that the DLU signal is equal to the projection on its measuring axis of the difference between the absolute acceleration of the sensor installation point and the acceleration of gravity [Belotserkovsky S.М. et al. Introduction to aeroelasticity. - M .: Science. Ch. ed. Phys.-Math. lit., 1980, p. 109].

In the system of equations (1) we have:

- проекции вектора абсолютной скорости на связанные оси OX₁, OY₁, OZ₁;

- projections of the absolute velocity vector on the associated axes OX ₁ , OY ₁ , OZ ₁ ;

(-g sinϑ), (-g cosϑ cosγ), (g cosϑ sinγ) are the projections of the acceleration of gravity on the connected axes OX ₁ , OY ₁ , OZ ₁ .

The system of equations (2) contains the known equations for the derivatives of the pitch, roll and yaw angles [Krasovsky A.A. Automatic flight control systems and their analytical design. - M .: Science. Ch. ed. Phys.-Math. lit., 1973, p.27].

The solution of differential equations (1), (2) is performed with the initial conditions:

Step 3. A column vector is calculated for the estimates of SNA measurements from the TLS, DLU measurements

where V _NT , V _ET , V _HT are row vectors of estimates of the components of the earth's speed to the north, east, and in height.

Where:

The dimension of row vectors V _NT , V _ET , V _HT is equal to the number N _CHC of SNA measurements in the time interval [t ₀ , t ₀ + T].

Here T _CHC - discreteness of measurements of the SNA;

N _CHC - the number of samples of measurements of the SNA in the time interval [t ₀ , t ₀ + T];

A = [e] _ij is the matrix of directional cosines, dimension (3.3), which describes the transition from a connected to a local planned earth coordinate system, the elements of which are calculated using estimates of pitch, roll and yaw angles obtained by solving the system of equations (1) , (2) using known relations [Krasovsky A.A. Automatic flight control systems and their analytical design. - M .: Science. Ch. ed. Phys.-Math. lit., 1973, p.26]:

Step 4. The matrix F of dimension (3 · N _CHC , 6) of the sensitivity functions of the SNA measurements to the increments of the components of the vector a _k-1 (t ₀ ) is calculated.

For this, the system of equations (1) is solved 6 times, with different initial conditions equal to:

Here ΔV _x , ΔV _y , ΔV _z , Δυ, Δγ, Δψ are given fixed small increments.

From the obtained 6 solutions of system (1), 6 column vectors of the form are formed:

where the column vectors: z _{T1, k-1} , z _{T2, k-1} , z _{T3, k-1} , z _{T4, k-1} , z _{T5, k-1} , z _{T6, k-1} are formed in the same way as described by relations (4), (5), (6).

A matrix of sensitivity functions F is formed, which is a matrix of partial derivatives, which are approximately replaced by the ratio of increments:

Here Δa (t ₀ ) is the vector of fixed small increments specified for the approximate calculation of partial derivatives. More details:

Matrix F contains 6 columns, each of which has (3 · N _CHC ) rows.

Step 5. An overdetermined system of linear algebraic equations of the form is compiled and solved:

which follows from the method of parametric identification based on sensitivity functions [Reference on the theory of automatic control. Ed. A.A. Krasovsky. - M .: Science. Ch. ed. Phys.-Math. lit., 1987].

Here Δa _k (t ₀ ) is the vector of the desired increments relative to the approximation a _k-1 (t ₀ );

z _T is the vector of measurements of the ground speed of the aircraft using SNA;

Z _{T, k-1} is the vector of estimates of the measurements of the earth's speed, calculated in step 3;

F is the matrix of sensitivity functions.

The difference Z _T - Z _{T, k-1} is the residual vector between the velocity measurements using the SNA and the estimates of these measurements obtained using the TLS and DLU.

System of equations (9) consists of 3 · N _CHC equations and has 6 unknowns, which are increments of the components of the vector Δa _k (t ₀ ).

The system of linear algebraic equations (9) is solved by the least squares method

or is solved by any other known method of solving algebraic equations, which is not fundamental. A solution exists if the matrix (F ^T F) is not degenerate. The number of equations in the system of equations (9) must be at least six. When solving, the increments Δa _k (t ₀ ) are determined, which minimize the mean-square value of the residual.

Step 6. The values of the vector of initial conditions are replaced by its next approximation in the indicated correspondence with the method of sensitivity functions:

Step 7. The number of iterations performed is checked. If it is less than N, then the counter of the number of iterations k: = k + 1 is increased and proceeds to step 2. If the number of iterations is N, then it is assumed that the estimate of the vector a is found for the moment t ₀ , which is delayed relative to real time t by T + τ.

Step 8. The system of 3rd order differential equations (2) is integrated on the time interval [t ₀ , t ₀ + T + τ] with the initial conditions

when substituting into it the measurements of n _x , n _y , n _z , ω _x , ω _y , ω _z from the sensors of the TLS and DLU.

As a result, the roll, pitch and yaw angles are estimated for the instant t = t ₀ + T + τ.

Step 9. The angle of the course is calculated, which is uniquely associated with yaw and, taking into account the accepted direction of the axis of the OX of the earth's coordinate system to the north, is 2π-ψ.

The condition for solving the algorithm is to ensure that the system of equations (9) is not degenerate, which requires at least two samples of SNA measurements for time T.

Since each SNA measurement contains 3 velocity components V _N , V _E , V _H , for two samples of SNA measurements, there are 6 scalar measurements of velocity components, equal to the number of unknowns in the system of equations (9).

The specific values of the parameters T, τ, N are determined by modeling errors and verified by experimental data.

Thus, the proposed method allows for indirect measurement of the angular positions of the aircraft with increased accuracy in terms of maneuvering.

Improving the accuracy of estimating the angular positions of the aircraft is achieved by:

- coordination of the set of measurements of the projections of the speed of the aircraft using the SNA on a moving time interval with the set of projections of the speed of the aircraft, which are calculated from the measurements of the TLS and DLA;

- elimination of the accumulation of estimation errors due to the use of a finite set of measurements for a single determination of orientation angles and rejection of recurrent processing procedures such as a Kalman filter with this drawback;

- the use of computational procedures that do not use the statistical characteristics of measurements, and, thus, eliminating the influence of errors in setting a priori statistics of measurement errors.

Claims (1)

A method of measuring the angular positions of an aircraft (LA), based on the use of information from a satellite navigation system (SNA) and from angular velocity sensors, characterized in that the measurement of the angular positions of the aircraft is carried out in accordance with an estimation algorithm implemented in a computing device, according to information from SNA receiver, which measures the speed components of the aircraft to the north, east and in height, and from three-coordinate angular velocity sensors (DLS) and linear acceleration sensors (DLU) installed on board the aircraft, the moving observation time interval [t ₀ , t ₀ + T + τ], where t ₀ is the initial measurement time; T is the length of the time interval of a single observation of the measurements of the SNA receiver; τ is the length of the time interval for predicting the angular positions of the aircraft with respect to the last measurement of the SNA on a moving time interval; t ₀ + T + τ = t is the current moment of real time, moreover, for the time point t _o according to measurements of the TLS, DLU and SNA on the time interval [t ₀ , t ₀ + T], three projections of the aircraft speed on the axis of the associated coordinate system are estimated and the pitch, roll and yaw angles are estimated by iteratively solving the system of algebraic equations compiled by the method of sensitivity functions, the solution of which minimizes the root-mean-square value of the discrepancy between velocity measurements using the SNA and velocity estimates using the TLS and DLU, which are calculated by solving the system of differential equations Aviation for Derivative Projections of the Aircraft Speed on the Axis of a Linked Coordinate System with Recalculation of Associated Velocities on the Axis of a Local Planar Rectangular Earth Coordinate System and Differential Equations for Derivatives of Pitch, Roll and Yaw Angles, and then for Time t by Measurement of TLS and DLA on a Moving Time Interval the pitch, roll and yaw angles are estimated by solving the differential equations for the derivatives of pitch, roll and yaw, after which the yaw angle is converted to the angle of the course, when shifting the moving interval in the direction of increasing time by the value of τ, the measurements of the angular positions of the aircraft in accordance with the estimation algorithm are repeated, the pitch, roll and course angles are estimated at each discrete real-time moment that differs from the previous one by the value of τ.