RU2215994C1 - Method of initial alignment of inertial navigational system - Google Patents

Abstract

FIELD: initial alignment of inertial navigational systems. SUBSTANCE: gyro- stabilized platform of inertial navigational system is immovably stabilized relative to inertial coordinate system. Signal from accelerometers are measured at initial period of time and measurement is repeated after small interval. Elements of matrix of direction cosines are calculated between inertial and normal coordinate systems. On base of elements of matrix of direction cosines thus calculated orientation of inertial coordinate system connected with gyrostabilized platform is determined relative to normal coordinate system. EFFECT: enhanced accuracy; reduced duration of alignment procedure.

Description

 The invention relates to the field of inertial navigation systems (ANN) and can be used to implement the mode of their initial exhibition.

 There is a method of the initial exhibition of platform ANNs (for example, a semi-analytical ANN), which consists in physically bringing the gyrostabilized platform (GSP) into the horizon plane (leveling) and subsequent gyrocompassing based on the measured signals from accelerometers and GSP control by means of gyroscope moment sensors [1, p. 354-371].

 As is known, the accuracy of calculating the output parameters of the ANN depends on the accuracy of the initial exhibition. It is obvious that the use of moment sensors of gyroscopes is an inevitable source of errors in the initial exhibition. The reason for this is the non-ideal electromechanical characteristics of the torque sensors. In addition, the procedure of physical leveling of the GSP increases the time of the initial exhibition, and the error of the “analytical” gyrocompassing, based on the calculation of the azimuthal angle, is determined by many factors that depend on the errors of horizontalization of the GSP [1, p. 371, last paragraph].

 To increase the accuracy of the initial exhibition of the platform ANN and reduce its duration, it is proposed to use the platform ANN in an uncontrolled mode of operation of gyroscopes, in which the GPS is stabilized motionless in inertial space, and there is no procedure for the physical leveling of the GPS. In this case, the ANS operating mode of the analytical type is implemented [2, p. 142, 2 paragraph above; from. 178].

где М - матрица направляющих косинусов между нормальной X_gУ_gZ_g и инерциальной X_iY_iZ_i системами координат; ось Y_g направлена на север, ось X_g - на восток, ось Z_g - по местной вертикали вверх.This technical result is achieved by the fact that the GPS of the inertial navigation system is stabilized motionless relative to the inertial coordinate system, then the signals from the accelerometers are measured at the initial time t ₀ , then at the times t = t ₀ + δt, where δt is a small fixed time interval, and determine the orientation of the inertial coordinate system associated with the gyrostabilized platform relative to the normal coordinate system using the matrix relation

where M is the matrix of guide cosines between normal X _g Y _g Z _g and inertial X _i Y _i Z _i coordinate systems; the y _g axis is directed north, the x _g axis is east, the z _g axis is upward in the local vertical.

Для решения задачи начальной выставки ИНС необходимо определить матрицу М в виде ее элементов m_ij (i, j=1, 2, 3) с тем, чтобы в дальнейшем эту информацию можно было использовать в рабочем режиме ИНС. Это можно сделать на основе измерений сигналов с акселерометров в два фиксированных момента времени по следующим формулам:

m₂₁ = m₃₂m₁₃-m₁₂m₃₃;
m₂₂ = m₁₁m₃₃-m₃₁m₁₃; (1)
m₂₃ = m₃₁m₁₂-m₁₁m₃₂,
где A₀₁, A₀₂, A₀₃ - сигналы, измеренные с акселерометров, расположенных на ГСП соответственно по осям Х_i, Y_i, Z_i, в начальный момент времени t₀,
g - ускорение свободного падения (g=const для заданного местоположения системы),

малый фиксированный интервал времени, Ω- угловая скорость вращения Земли, φ- широта местоположения навигационной системы;

A₁₁, A₁₂, A₁₃ - сигналы, измеренные с акселерометров в момент времени t= t₀+δt;
a = Ω²cosφsinφ; b = Ω²cos²φ.
Таким образом, связь между нормальной системой координат и инерциальной будет иметь вид:

Соотношение (2) полностью решает задачу начальной выставки инерциальной навигационной системы, поскольку однозначно определяет взаимную ориентацию инерциальной системы координат, физически реализуемой с помощью ГСП, и нормальной системы координат с направлениями осей на север, восток и по местной вертикали вверх.Consider the standard coordinate systems: the normal X _g Y _g Z _g , the two orthogonal axes of which are connected to the horizon plane and are oriented to the north Y _g and east X _g , and the third is directed upward along the local vertical Z _g , and the inertial coordinate system X _i Y _i Z _i associated with the axes of the SHG [3, p. 38]. Define a matrix of guide cosines between these two coordinate systems

To solve the problem of the initial ANN exhibition, it is necessary to determine the matrix M in the form of its elements m _ij (i, j = 1, 2, 3) so that in the future this information can be used in the ANN operating mode. This can be done based on measurements of signals from accelerometers at two fixed points in time according to the following formulas:

m ₂₁ = m ₃₂ m ₁₃ -m ₁₂ m ₃₃ ;
m ₂₂ = m ₁₁ m ₃₃ -m ₃₁ m ₁₃ ; (1)
m ₂₃ = m ₃₁ m ₁₂ -m ₁₁ m ₃₂ ,
where A ₀₁ , A ₀₂ , A ₀₃ - signals measured from accelerometers located on the SHG along the axes X _i , Y _i , Z _i , at the initial time t ₀ ,
g is the acceleration of gravity (g = const for a given location of the system),

small fixed time interval, Ω is the angular velocity of the Earth's rotation, φ is the latitude of the location of the navigation system;

A ₁₁ , A ₁₂ , A ₁₃ - signals measured from accelerometers at time t = t ₀ + δt;
a = Ω ² cosφsinφ; b = Ω ² cos ² φ.
Thus, the relationship between the normal coordinate system and the inertial will look like:

Relation (2) completely solves the problem of the initial exhibition of an inertial navigation system, since it uniquely determines the mutual orientation of the inertial coordinate system physically realized using GPS, and the normal coordinate system with the directions of the axes to the north, east, and local vertical up.

The method of the initial exhibition of an inertial navigation system is implemented as follows: the GPS of an inertial navigation system (for example, in a four-axis gimbal) is stabilized motionless in an inertial space, signals from accelerometers are measured at the initial time t ₀ , then the measurements are repeated for time t = t ₀ + δt with a small fixed time interval δt (for example, 5 s), calculate by the formulas (1) the elements of the matrix of guide cosines M and determine the orientation of the inertial coordinate system flax normal coordinate system by means of the matrix equation (2).

Sources of information
1. Gyroscopic systems. Gyroscopic devices and systems: Textbook. for universities for special. "Gyroscope, instruments and devices" / D.S. Pelpor, I.A. Mikhalev, V.A. Bauman and others; under the editorship of D.S. Pelpora. - M .: Higher. Shk., 1988 .-- 424 p.

 2. Bromberg P.V. Theory of inertial navigation systems. - M .: Science. The main edition of the physical and mathematical literature, 1979. - 296 p.

 3. Mikeladze V. G., Titov V. M. The basic geometric and aerodynamic characteristics of aircraft and missiles: a Handbook. - M.: Mechanical Engineering, 1990. - 144 p.

Claims (1)

A method for the initial exhibition of an inertial navigation system, including measurements from accelerometers mounted on a gyro-stabilized platform, characterized in that the gyro-stabilized platform of the inertial navigation system is stabilized motionless relative to the inertial coordinate system, signals from accelerometers are measured at the initial time t ₀ , and then at time t = t ₀ + δt, where δt is a small fixed time interval, and the orientation of the inertial coordinate system associated with gyrostabilization is determined platform with respect to the normal coordinate system using the matrix relation

where M is the matrix of guide cosines between the normal X _g Y _g Z _g and inertial X _i Y _i Z _i coordinate systems; the y _g axis is directed north, the x _g axis is east, the z _g axis is upward in the local vertical.