CN109470265B - Inertial navigation prism height difference calibration method and system - Google Patents
Inertial navigation prism height difference calibration method and system Download PDFInfo
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Abstract
The invention discloses a method and a system for calibrating height difference of an inertial navigation prism, and relates to the technical field of precise guidance and alignment of rocket aircrafts. The rocket core assembly inertial navigation system with the prism is fastened on the rotary table, the theodolite collimates and observes the horizontal azimuth angle and the pitch angle of each position of the inertial navigation prism by controlling the rotation of the rotary table at different positions, and then the horizontal azimuth angle and the height difference of a similar observation celestial body are calculated according to the rotary table angle, the horizontal azimuth angle and the pitch angle of each corresponding position, so that the installation deviation of the inertial navigation prism is calculated. The invention is based on the positioning principle of an astronomical navigation altitude difference method, realizes the accurate calibration of the installation deviation of the inertial navigation prism through the multi-position observation of the inertial navigation prism, has high precision and simple and convenient use, and has better social expansion application value and economic value.
Description
Technical Field
The invention belongs to the technical field of precise guidance and alignment of rocket aircrafts, and particularly relates to an inertial navigation prism height difference calibration method and system.
Background
The inertial navigation system is one of core components of a rocket aircraft control system and consists of an inertial component and an inertial navigation prism. The inertia assembly realizes the measurement of linear motion and rotational motion of the rocket aircraft relative to the inertia space and controls the rocket to fly to a specified target according to a preset trajectory. The inertial navigation prism is the basis of initial alignment of a rocket launching coordinate system and an inertial navigation coordinate system, realizes initial azimuth alignment of the rocket launching coordinate system and the inertial navigation coordinate system, accurately provides a launching initial attitude azimuth angle for the rocket, enables the inertial navigation coordinate system and the rocket launching coordinate system to be completely overlapped, and ensures that the rocket accurately flies to a target.
When the inertial navigation prism is installed relative to the inertial component, the edge line of the inertial navigation prism and an inertial navigation coordinate system can form installation deviation, and the deviation can be eliminated through calibration compensation. The existing equipment rockets in active service adopt an inertial navigation prism azimuth transfer alignment mode for compensation regardless of vertical launching or horizontal launching, and inertial navigation prism calibration methods are different in color, some need north references as references, are very poor in universality and inconvenient to use, and bring great difficulty to equipment user units in use and operation. In order to avoid the factors, calibration of an inertial navigation prism is even cancelled sometimes, great risk is brought to successful rocket flight, and the flight effect of the rocket is seriously influenced.
Disclosure of Invention
The invention aims to overcome the defects of the background technology, provides a method and a system for calibrating the height difference of an inertial navigation prism, overcomes the factors of difficult construction of a north reference and the like, and achieves the purposes of simple, practical and accurate calibration of the inertial navigation prism.
The invention provides a method for calibrating height difference of an inertial navigation prism, which comprises the following steps:
fastening an inertial navigation system of the rocket aircraft provided with the inertial navigation prism on a rotary table, and collimating and observing the inertial navigation prism in real time through a theodolite;
the rotation of the rotary table is automatically controlled by a control computer, so that the inertial navigation prism rotates to different positions, and the collimation of the theodolite and the inertial navigation prism is met;
the collimation connecting line of the theodolite and the inertial navigation prism is extended to an infinite distance and is regarded as an observation celestial body sigma in astronomical navigation positioning0The observation point of the theodolite is taken as a round point of a horizon coordinate system, and the collimation point sigma of the theodolite and the inertial navigation prism0' consider the projected point of a celestial body on the earth;
when the position of the theodolite is unchanged and the rotary table rotates to another position, the collimation connecting line of the theodolite and the inertial navigation prism is extended to an infinite distance, and the theodolite is regarded as another observation celestial body sigma in astronomical navigation positioning1Theodolite and inertial navigation prism collimation point sigma1' consider the projected point of a celestial body on the earth;
the position of the theodolite is unchanged, the rotary table rotates to a plurality of different positions, and the theodolite and the inertial navigation prism are regarded as a plurality of observation celestial bodies sigma in astronomical navigation positioning during collimation2…σiTheodolite and inertial navigation prism collimation point sigma2′…σi' consider the projected point of a celestial body on the earth;
according to collimation point sigma of inertial navigation prism'0…σ′iThe angle value of the rotary table, the pitch angle value and the horizontal azimuth angle value of the theodolite are used for calculating the sigma of the theodolite observation inertial navigation prism similar to the observation celestial body fixed star0′…σi' horizon azimuth and elevation difference;
and calculating the position of the edge line of the inertial navigation prism relative to the celestial body according to the horizon azimuth angle and the height difference of the similar observation celestial body of the inertial navigation prism observed by the theodolite, namely the installation deviation of the edge line of the inertial navigation prism relative to a rocket launching coordinate system.
On the basis of the scheme, the method for controlling the rotation of the turntable automatically through the control computer to enable the inertial navigation prism to rotate to different positions comprises the following steps:
leveling a rotary table fixedly provided with an inertial navigation system;
controlling the turntable to vertically align the inertial navigation prism with the theodolite, and reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
controlling the rotary table to enable the left side of the inertial navigation prism to rotate and be aligned with the theodolite, and reading a rotary table angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
and controlling the turntable to rotate the right side of the inertial navigation prism and align the inertial navigation prism with the theodolite, and reading the angle value of the turntable, the pitch angle value of the theodolite and the horizontal azimuth angle value.
On the basis of the scheme, the inertial navigation prism is rotated to different positions by controlling the rotation of the turntable, and the method specifically comprises the following steps:
controlling the turntable to make the inertial navigation prism and theodolite vertically aligned to be regarded as celestial body sigma0And the angle value of the rotary table, the horizontal azimuth angle value of the theodolite and the pitch angle value are recorded as follows:
controlling the turntable to rotate to the right of the theodolite at equal intervals, aligning the inertial navigation prism with the theodolite, reading the angle value of the turntable, the pitch angle value and the horizontal azimuth angle value of the theodolite, and observing at the right side for not less than 3 positions; sequentially rotating the left side of the theodolite at equal intervals and ensuring clear imaging, reading the angle value of the turntable, the pitch angle value and the horizontal azimuth angle value of the theodolite, and observing the left side at no less than 3 positions;
when the turntable rotates to the ith position, the angle value of the turntable, the pitch angle value of the theodolite and the collimation of the inertial navigation prism and the horizontal azimuth angle value of the theodolite are recorded as:
on the basis of the scheme, the rotation control angle of the left side and the right side of the rotary table is 15 degrees relative to the minimum control deflection angle of the vertical collimation position of the inertial navigation prism and the theodolite.
On the basis of the scheme, the calculation method of the horizon azimuth angle of the theodolite observation inertial navigation prism relative to the celestial body is as follows:
the theodolite is erected and leveled at a point C and is vertically aligned with the inertial navigation prism, and the initial values of the angle of the rotary table, the horizontal azimuth angle of the theodolite and the pitch angle are recorded as follows:
rotating the turntable to a point A on the left side of the theodolite and collimating the inertial navigation prism, and recording observation values of the angle of the turntable, the horizontal azimuth angle and the pitch angle of the theodolite as follows:
rotating the turntable to a point B on the right of the theodolite and collimating the inertial navigation prism, wherein observed values of the turntable angle, the pitch angle of the theodolite and the horizontal azimuth angle are as follows:
according to the law of the normal line of the inertial navigation prism,
azimuth angle A of normal line of A-point inertial navigation prism relative to celestial body1Comprises the following steps:
A1＝180°-(VA-V0)-(θA-θ0) (5.4)
azimuth angle A of B point inertial navigation prism normal line relative to celestial body2Comprises the following steps:
A2＝180°-(VB-V0)-(θB-θ0) (5.5)
the horizontal azimuth angle A of the ridge line of the ith position inertial navigation prism relative to the celestial bodyiComprises the following steps:
Ai＝180°-(Vi-V0)-(θi-θ0) (5.6)。
on the basis of the scheme, the method for calculating the height difference of the edge lines of the inertial navigation prism comprises the following steps:
the vertical collimation observation inertial navigation prism ridge line high-low pitch angle of the theodolite is regarded as the celestial body top distance in the astronomical navigation positioning and is expressed as H0When the height difference of the position is equal to the celestial body top distance H0Minus 90 deg., expressed as Δ H0And so on, the height of the ridge line of the inertial navigation prism at the first position observed by the theodolite is H1Then the height difference at that position is Δ H1The height and the pitch angle of the ridge line of the inertial navigation prism at the second position observed by the theodolite are H2Then the height difference is Δ H2,., the height and pitch angle of the ridge line of the i-th position inertial navigation prism observed by the theodolite is HiThen the height difference is Δ Hi：
ΔH0＝H0-90° (6.1)
ΔH1＝H1-90° (6.2)
ΔH2＝H2-90° (6.3)
Observation of the ith position:
ΔHi＝Hi-90°(6.4)。
on the basis of the scheme, the position of the inertial navigation prism edge line, namely the installation deviation of the inertial navigation prism edge line relative to the rocket launching coordinate system is calculated by the following specific calculation method:
inertial navigation prism ridge line observation equation:
ΔHi＝X0cos Ai-Z0sin Ai(7.1)
both sides are simultaneously removed from-sin AiThen, there are:
-ΔHi·sec Ai＝-X0cot Ai+Z0(7.2)
suppose that:
h＝-ΔHi·sec Ai
A＝-cot Ai
then a linear equation can be established:
h＝A·X0+Z0﹙7.3﹚
linear regression was performed using the least squares method:
on the basis of the scheme, the rotation of the rotary table is automatically controlled by the control computer, so that the inertial navigation prism rotates to different positions.
The invention also provides an inertial navigation prism height difference calibration system, which comprises:
the rotary table is used for bearing an inertial navigation system provided with an inertial navigation prism;
the theodolite is used for observing an inertial navigation prism;
the control computer is used for controlling the rotary table to rotate so as to enable the inertial navigation prism to rotate to different positions; the control computer is also used for calculating the horizon azimuth angle and the height difference of the theodolite observation inertial navigation prism similar to the observation celestial body according to the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value when the inertial navigation prism rotates to different positions; and then, calculating the position of the edge line of the inertial navigation prism relative to the celestial body according to the horizon azimuth angle and the height difference of the similar observation celestial body of the theodolite observation inertial navigation prism, namely the installation deviation of the edge line of the inertial navigation prism relative to the rocket launching coordinate system.
Compared with the prior art, the invention has the following advantages:
the method is based on the technical principle of an astronomical navigation altitude difference method, realizes accurate calibration without installation deviation of a north reference inertial navigation prism, ensures that an inertial navigation coordinate system is overlapped with a rocket launching coordinate system through parameter compensation, reduces the alignment deviation of an initial azimuth angle of a rocket, improves the flying precision of the rocket, and has better expanded application value.
Drawings
FIG. 1 is a schematic view of a prism ridge projection for inertial navigation according to an embodiment of the present invention;
FIG. 2 is a spherical triangle of a celestial body for observing the edge line of an inertial navigation prism according to an embodiment of the present invention;
FIG. 3 is a diagram of dual celestial positioning of edges of inertial navigation prisms according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an inertial navigation prism calibration system according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the azimuth of the inertial navigation prism ridge line of the embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
Example 1:
referring to fig. 1, an embodiment of the present invention provides a method for calibrating a height difference of an inertial navigation prism, including the following steps:
fastening an inertial navigation system (inertial navigation system for short) provided with an inertial navigation prism on a rotary table, and collimating and observing the inertial navigation prism by an auto-collimation theodolite (theodolite for short);
the rotation of the rotary table is automatically controlled by a control computer, so that the inertial navigation prism rotates to different positions, and the collimation of the theodolite and the inertial navigation prism is met;
the collimation connecting line of the theodolite and the inertial navigation prism is extended to an infinite distance and is regarded as an observation celestial body sigma in astronomical navigation positioning0The observation point of the theodolite is taken as a circular point of a horizon coordinate system, and the collimation point of the theodolite and the inertial navigation prism is taken as an intersection point sigma 'of a celestial body and a ground surface'0I.e. as the projected point σ 'of celestial body on the earth'0；
When the position of the theodolite is unchanged and the rotary table rotates to another position, the collimation connecting line of the theodolite and the inertial navigation prism is extended to an infinite distance, and the theodolite is regarded as another observation celestial body sigma in astronomical navigation positioning1The theodolite and the inertial navigation prism collimation point are regarded as another intersection point sigma 'of the celestial body and the ground surface'1I.e. as the projected point σ 'of celestial body on the earth'1；
The position of the theodolite is unchanged, the rotary table rotates to a plurality of different positions, and the theodolite and the inertial navigation prism are regarded as a plurality of observation celestial bodies sigma in astronomical navigation positioning during collimation2···σiThe theodolite and the inertial navigation prism collimation point are taken as a plurality of intersection points sigma 'of the celestial body and the ground surface'2···σ′iI.e. as the projected point σ 'of celestial body on the earth'2···σ′i；
Collimating point sigma 'of theodolite and inertial navigation prism'0···σ′iIs regarded as a multipoint geographical position value and then is subjected to inertial navigation prism sigma'0···σ′iThe angle value of the turntable, the pitch angle value and the horizontal azimuth angle value of the theodolite are used for calculating sigma 'of a theodolite observation inertial navigation prism similar to observation celestial body star'0···σ′iHorizon azimuth and elevation difference;
and calculating the position of the edge line of the inertial navigation prism relative to the celestial body according to the horizon azimuth angle and the height difference of the similar observation celestial body of the inertial navigation prism observed by the theodolite, namely the installation deviation of the edge line of the inertial navigation prism relative to a rocket launching coordinate system.
The method for controlling the rotation of the rotary table to rotate the inertial navigation prism to different positions comprises the following steps:
controlling the turntable to vertically align the inertial navigation prism with the theodolite, and reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
controlling the rotary table to enable the left side of the inertial navigation prism to rotate and be aligned with the theodolite, and reading a rotary table angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
and controlling the turntable to rotate the right side of the inertial navigation prism and align the inertial navigation prism with the theodolite, and reading the angle value of the turntable, the pitch angle value of the theodolite and the horizontal azimuth angle value.
The method is characterized in that the inertial navigation prism is rotated to different positions by controlling the rotation of the turntable, and the method specifically comprises the following steps:
controlling the turntable to make the inertial navigation prism vertically aligned with the theodolite, and reading the angle value theta of the turntable0Pitch angle value V of theodolite0And the horizontal azimuth value H0Specifically, it is noted as:
controlling the direction of the rotary tableRotating the left side of the latitude instrument at equal intervals, aligning the inertial navigation prism with the theodolite, reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value, sequentially rotating at equal intervals, ensuring clear imaging, and reading the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value; the number of observation positions is not less than 3, and the rotary table controls the minimum angle and the vertical collimation rotary table angle theta0Is not less than 15.
Then, the turntable is controlled to rotate to the right of the theodolite at equal intervals, the inertial navigation prism is aligned with the theodolite, and the angle value of the turntable, the pitch angle value of the theodolite and the horizontal azimuth angle value are read; the number of observation positions is not less than 3, and the rotary table controls the minimum angle and the vertical collimation rotary table angle theta0Is not less than 15.
When the turntable rotates the ith position, the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value are recorded as:
the embodiment of the invention also provides an inertial navigation prism height difference calibration system, which comprises:
the rotary table is used for bearing an inertial navigation system provided with an inertial navigation prism;
the theodolite is used for observing an inertial navigation prism;
the control computer is used for controlling the rotary table to rotate so as to enable the inertial navigation prism to rotate to different positions; the control computer is also used for calculating the horizon azimuth of the celestial body observed by the theodolite and the height difference of the ridge line of the observation inertial navigation prism according to the angle value of the rotary table, the pitch angle value of the theodolite and the horizontal azimuth angle value when the inertial navigation prism rotates to different positions, calculating the position of the ridge line of the inertial navigation prism and calculating the installation deviation of the ridge line of the inertial navigation prism to the theodolite.
Example 2:
1. inertial navigation prism installation deviation
The inertial navigation system and rocket launching coordinate system XYZ are shown in FIG. 1, with the Z axis facing the sky vertically, the X axis as the direction, the Y axis as the yaw, L as the prism edge line, and Lxy as the prismThe ridges are projected on an XY plane, Lyz represents the ridges of the inertial navigation prism projected on a YZ plane, Lxz represents the ridges of the inertial navigation prism projected on an XZ plane, and the ridges of the inertial navigation prism projected on the XZ plane have no influence on the alignment and are ignored. Two parameters (X) for installation deviation of inertial navigation prism edge line in inertial navigation coordinate system0、Z0) To indicate. X0The mounting deviation of the prism edge line of the inertial navigation prism rotating around the Z axis represents the non-perpendicularity of the prism edge line of the inertial navigation prism and the X axis of the inertial navigation coordinate system, and the right-hand rule is that the prism edge line of the inertial navigation prism rotates anticlockwise to be positive; z0The installation deviation of the prism edge line of the inertial navigation prism rotating around the X axis represents the non-parallelism between the prism edge line of the inertial navigation prism and the Y axis of the inertial navigation coordinate system, and the right hand rule is that the prism edge line rotates in the counterclockwise direction to be positive.
2. Observation triangle creation
Assuming that a connecting line of collimation of a theodolite and an inertial navigation prism is extended to an infinite distance, the connecting line is regarded as an observation celestial body in astronomical navigation positioning, M point is a projection point of the celestial body on the earth (as shown in figure 2), an inertial navigation prism coordinate system is regarded as a celestial body equator coordinate system, an inertial navigation system coordinate system is regarded as a geographic coordinate system, and a theodolite observation coordinate system is regarded as a horizon coordinate system, the three are connected, and the variable quantity X of rotation of the inertial navigation system around a Z axis is0The variable quantity Z of the rotation of the inertial navigation system around the X axis is regarded as the 'geographic latitude' of the geographic coordinate system0The declination of the celestial body is regarded as the equatorial coordinate system of the celestial body, the elevation angle of the edge line of the transit prism observed by the theodolite is regarded as the zenith distance of the celestial body, and thus the spherical triangle delta P can be obtainedNMZ。
The three sides of the triangle are respectively:
PNZ＝90°-X0- -for measuring the observed geographic latitude, i.e. the angle of elevation of the prism ridge
PNM＝90°-Z0The rest declination of the edge line of the inertial navigation prism (or the rest geography longitude for the test observation), i.e. the yaw angle of the edge line of the inertial navigation prism
ZM is 90-h-the height of edge line margin of inertial navigation prism
The three vertex angles of the triangle are respectively:
∠MPNz-is a celestial bodyLocal time angle, i.e. deviation angle of edge line of inertial navigation prism
∠ZMPNIs the view angle of the theodolite and the inertial navigation prism
∠MPNZ is A-the azimuth angle of the horizon of the transit observation inertial navigation prism
The spherical triangle can solve the installation deviation (X) of the inertial navigation prism according to a sine formula, a cosine formula and a quadruple formula if the height angles and the horizontal azimuth angles of two or more celestial bodies are known0、Z0)。
3. Height difference method
The altitude difference method is characterized in that the relation between an inertial navigation prism ridge coordinate system and a theodolite observation horizon coordinate system is utilized, the height pitch angle of the theodolite observation inertial navigation prism ridge is regarded as the celestial body top distance of a celestial body, the angle obtained by subtracting 90 degrees is the celestial body height angle, the difference between the celestial body top distance and 90 degrees is regarded as the altitude difference, and the position of the inertial navigation prism ridge is calculated.
The altitude difference method only needs to rotate the two positions of the rotary table provided with the inertial navigation, the theodolite observes the vertical plate angle and the horizontal azimuth angle of the inertial navigation prism to obtain the position of the edge line of the inertial navigation prism, and the scheme adopts a multi-celestial observation method for ensuring the precision.
Referring to fig. 3, the position 1 of the inertial navigation prism observed by the theodolite frame is extended to a point P, which is regarded as a first celestial body sigma1Celestial body height angle difference delta H from theodolite to inertial navigation prism1As the height intercept, the vertical line of the end point of the over intercept is taken as the edge line l of the inertial navigation prism1(ii) a The observation inertial navigation prism position 2 extends to the N point, which is regarded as the second celestial body sigma2Celestial body height angle difference delta H from theodolite to inertial navigation prism2As the height intercept, the vertical line of the end point of the over intercept is taken as the edge line l of the inertial navigation prism2The intersection point M of the two ridge lines is the true position of the ridge line of the inertial navigation prism, and the distance from the M point to the O point is called the installation deviation (X) of the ridge line of the inertial navigation prism0、Z0). The positioning method in view of such a height intercept is called a height difference method.
4. Method for positioning edge line of inertial navigation prism
The edge line of the inertial navigation prism is positioned by adopting an astronomical navigation multi-celestial body (or double-celestial body) positioning method. Taking the dual celestial body positioning as an example in fig. 3, the observation equations of the two inertial navigation prism edge lines are:
ΔH1＝X0cosA1-Z0sinA1
ΔH2＝X0cosA2-Z0sinA2
combining two observation equations, knowing the azimuth angle of the horizon of the celestial body observed by the theodolite and the altitude angle of the edge line of the inertial navigation prism, the installation deviation X of the edge line of the inertial navigation prism in the inertial navigation coordinate system can be solved0、Z0。
Assuming that the inertial navigation prism is observed at multiple points, the following are provided:
ΔH3＝X0cosA3-Z0sinA3
∙∙∙∙∙∙
ΔHi＝X0cosAi-Z0sinAi
thus, a plurality of observation equations can be combined to calculate the installation deviation X of the prism edge line of the inertial navigation in the inertial navigation coordinate system0、Z0The accuracy will be higher.
Example 3:
the inertial navigation prism height difference calibration system comprises a position speed rotating platform (hereinafter referred to as a rotating platform), a theodolite, a control computer and the like. Controlling the computer to control the position of the turntable to rotate, observing an inertial navigation prism by the theodolite, placing an inertial navigation system provided with the inertial navigation prism on the table surface of the turntable, enabling the Y axis of the inertial navigation system to be close to a vertical state towards the edge line of the inertial navigation prism vertically, enabling the X, Z axis to be in a horizontal state, controlling the computer to control the turntable to enable the inertial navigation prism to be vertically aligned with the theodolite, and reading the angle value of the turntable, the pitch angle value of the theodolite and the horizontal azimuth angle value; secondly, controlling a computer to control a rotary table, aligning an inertial navigation prism with the left side of the theodolite, and reading a rotary table angle value, a theodolite pitch angle value and a horizontal azimuth angle value; and controlling the computer to control the rotary table to horizontally rotate the rotary table, aligning the inertial navigation prism with the right side of the theodolite, reading the angle value of the rotary table, the pitch angle value and the horizontal azimuth angle value of the theodolite, and observing the inertial navigation prism for multiple times in order to improve the test precision.
The specific process is as follows: controlling the computer to control the turntable to make the inertial navigation prism vertically aligned with the theodolite, and reading the angle value theta of the turntable0Pitch angle value V of theodolite0And the horizontal azimuth value H0(ii) a Specifically, it is noted as:
controlling a computer to control a turntable to rotate 15 degrees to the left side of a theodolite, enabling an inertial navigation prism to be aligned with the theodolite, reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value, sequentially rotating at equal intervals, ensuring clear imaging, and reading the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value; then controlling the computer to control the turntable to rotate to the right of the theodolite at equal intervals and enable the inertial navigation prism to be aligned with the theodolite, wherein the minimum angle is 15 degrees, reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value, and respectively recording the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value as thetai、Vi、HiI is expressed as the i-th position of the turntable rotation, and is specifically noted as:
calculation of the azimuth A
As shown in FIG. 5, the theodolite is erected, leveled and vertically aligned to the inertial navigation prism, and the initial values of the angle of the turntable, the horizontal azimuth angle and the pitch angle of the theodolite are recorded as (theta)0、V0、H0) Rotating the turntable to the point A on the left side of the theodolite and collimating the inertial navigation prism, wherein the observation values of the angle of the turntable, the horizontal azimuth angle and the pitch angle of the theodolite are (theta)A、VA、HA) Rotating the turntable to the point B on the right side of the theodolite and collimating the inertial navigation prism, wherein the observation values of the angle of the turntable, the pitch angle of the theodolite and the horizontal azimuth angle are (theta)B、VB、HB) According to the law of the normal line of the inertial navigation prism, the horizontal azimuth angle A of the normal line of the A point inertial navigation prism1Comprises the following steps:
A1＝180°-(VA-V0)-(θA-θ0)
ΔVA＝VA-V0
ΔθA＝θA-θ0
horizontal position angle A of B point inertial navigation prism normal line2Is composed of
A2＝180°-(VB-V0)-(θB-θ0)
ΔVB＝VB-V0
ΔθB＝θB-θ0
Similarly, the observation of the ith position includes:
Ai＝180°-(Vi-V0)-(θi-θ0)
ΔVi＝Vi-V0
Δθi＝θi-θ0
height difference calculation
The vertical collimation observation inertial navigation prism ridge line high-low pitch angle of the theodolite is regarded as the celestial body top distance in the astronomical navigation positioning and is expressed as H0When the height difference of the position is equal to the celestial body top distance H0Minus 90 deg., expressed as Δ H0And so on, the height of the ridge line of the inertial navigation prism at the first position observed by the theodolite is H1Then the height difference at that position is Δ H1The height and the pitch angle of the ridge line of the inertial navigation prism at the second position observed by the theodolite are H2Then the height difference is Δ H2,., the height and pitch angle of the ridge line of the i-th position inertial navigation prism observed by the theodolite is HiThen the height difference is Δ Hi：
ΔH0＝H0-90°
ΔH1＝H1-90°
ΔH2＝H2-90°
Observation of the ith position:
ΔHi＝Hi-90°
data processing
Inertial navigation prism ridge line observation equation:
ΔHi＝X0cosAi-Z0sinAi
both sides were simultaneously removed by-sinAiThen, there are:
-ΔHi·secAi＝-X0cotAi+Z0
suppose that:
h＝-ΔHi·secAi
A＝-cotAi
then a linear regression equation can be established:
h＝A·X0+Z0
linear regression was performed using the least squares method:
test examples
The theodolite observation inertial navigation prism carries out 11 positions in total, positive and negative mirror observation is carried out on each position, and specific test data are shown in a table 1;
table 1: original data table for theodolite observation
In order to eliminate the influence of the index difference of the theodolite, the height and pitch angle H of the theodolite is as follows:
H＝(Hright side-HLeft side of)/2
In order to eliminate the influence of the sighting axis difference of the theodolite, the horizontal angle V of the theodolite is as follows:
V＝(Vright side+VLeft side of-180°)/2
Then, the test data in table 1 are calculated according to the elevation angle and the horizontal angle of the theodolite and the formulas 5.6 and 6.4 in the claims, and the elevation angle, the horizontal angle, the altitude difference and the azimuth angle of the observation position of the inertial navigation prism are shown in table 2.
TABLE 2 inertial navigation prism height pitch angle, horizontal angle, altitude difference and azimuth angle
| Serial number | High-low pitch angle H | Horizontal angle V | Height difference Δ H | Azimuth |
| Datum | ||||
| 90°0'0.6" | 179°34'1.4" | 0.6" | 0°0'0.0" | |
| 1 | 89°59'57.7" | 177°29'10.1" | -2.3" | 158°4'51.3" |
| 2 | 89°59'58.1" | 177°29'12.1" | -1.9" | 160°4'49.3" |
| 3 | 89°59'58.0" | 177°29'12.3" | -2.0" | 162°4'49.1" |
| 4 | 89°59'58.4" | 177°59'17.1" | -1.6" | 164°34'44.3" |
| 5 | 89°59'58.9" | 177°59'19.6" | -1.1" | 166°34'41.8" |
| 6 | 90°0'3.4" | 180°59'46.2" | 3.4" | 199°34'15.2" |
| 7 | 90°0'2.9" | 181°46'18.3" | 2.9" | 197°47'43.1" |
| 8 | 90°0'3.9" | 181°46'18.5" | 3.9" | 195°47'42.9" |
| 9 | 90°0'4.7" | 181°46'21.7" | 4.7" | 193°47'39.7" |
| 10 | 90°0'3.3" | 181°46'24.5" | 3.3" | 191°47'36.9" |
Take the 1 st position as an example, according to the formula
ΔHi＝X0cosAi-Z0sinAi
Then there are:
0.6＝X0cos(158°4′51.3″/180°)-Z0sin(158°4′51.3″/180°)
2.988533646＝-0.829664263X0+Z0
by analogy, another 9 position equations of the inertial navigation prism are:
2.446394253＝-0.81108061X0+Z0
2.55230907＝-0.792824317X0+Z0
2.019813362＝-0.770462021X0+Z0
1.388625814＝-0.770468169X0+Z0
-3.79832258＝-0.498028501X0+Z0
-3.23773786＝-0.49647347X0+Z0
-4.40387＝-0.524487226X0+Z0
-5.33868287＝-0.538744867X0+Z0
-3.77125312＝-0.553173507X0+Z0
these 10 equations are taken in accordance with claims (7.4), (7.5):
X0＝-22.87"Y0＝-15.97"
the technical scheme depends on the technical principle of an astronomical navigation altitude difference method, realizes that the installation deviation of the inertial navigation prism does not need to be accurately calibrated by a north reference, ensures the coincidence of an inertial navigation coordinate system and a rocket launching coordinate system through parameter compensation, reduces the alignment deviation of the initial azimuth angle of the rocket, improves the hit precision of the rocket, and has better expanded application value.
Various modifications and variations of the embodiments of the present invention may be made by those skilled in the art, and they are also within the scope of the present invention, provided they are within the scope of the claims of the present invention and their equivalents.
What is not described in detail in the specification is prior art that is well known to those skilled in the art.
Claims (6)
1. A method for calibrating height difference of an inertial navigation prism is characterized by comprising the following steps:
fastening an inertial navigation system of the rocket aircraft provided with the inertial navigation prism on a rotary table, and collimating and observing the inertial navigation prism in real time through a theodolite;
the rotation of the rotary table is automatically controlled by a control computer, so that the inertial navigation prism rotates to different positions, and the collimation of the theodolite and the inertial navigation prism is met;
the collimation connecting line of the theodolite and the inertial navigation prism is extended to an infinite distance and is regarded as an observation celestial body sigma in astronomical navigation positioning0The observation point of the theodolite is taken as a round point of a horizon coordinate system, and the collimation point sigma 'of the theodolite and the inertial navigation prism'0Regarding the projection point of the celestial body on the earth;
when the position of the theodolite is unchanged and the rotary table rotates to another position, the collimation connecting line of the theodolite and the inertial navigation prism is prolonged to be freeDistance limit, which is regarded as another observation celestial body sigma in astronomical navigation positioning1Theodolite and inertial navigation prism collimation point sigma'1Regarding the projection point of the celestial body on the earth;
the position of the theodolite is unchanged, the rotary table rotates to a plurality of different positions, and the theodolite and the inertial navigation prism are regarded as a plurality of observation celestial bodies sigma in astronomical navigation positioning during collimation2…σiTheodolite and inertial navigation prism collimation point sigma'2…σ'iRegarding the projection point of the celestial body on the earth;
the theodolite is erected and leveled at a point C and is vertically aligned with the inertial navigation prism, and the initial values of the angle of the rotary table, the horizontal azimuth angle of the theodolite and the pitch angle are recorded as follows:
rotating the turntable to a point A on the left side of the theodolite and collimating the inertial navigation prism, and recording observation values of the angle of the turntable, the horizontal azimuth angle and the pitch angle of the theodolite as follows:
rotating the turntable to a point B on the right of the theodolite and collimating the inertial navigation prism, wherein observed values of the turntable angle, the pitch angle of the theodolite and the horizontal azimuth angle are as follows:
according to collimation point sigma of inertial navigation prism'0…σ'iThe angle value of the rotary table, the pitch angle value and the horizontal azimuth angle value of the theodolite and the normal law of the inertial navigation prism are used for calculating sigma 'of the theodolite for observing the inertial navigation prism similar to the star of the observation celestial body'0…σ'iAzimuth of horizon:
azimuth angle A of normal line of A-point inertial navigation prism relative to celestial body1Comprises the following steps:
A1＝180°-(VA-V0)-(θA-θ0) (1.4)
azimuth angle A of B point inertial navigation prism normal line relative to celestial body2Comprises the following steps:
A2＝180°-(VB-V0)-(θB-θ0) (1.5)
the horizontal azimuth angle A of the ridge line of the ith position inertial navigation prism relative to the celestial bodyiComprises the following steps:
Ai＝180°-(Vi-V0)-(θi-θ0) (1.6)；
the vertical collimation observation inertial navigation prism ridge line height and pitch angle of the theodolite are regarded as the celestial body top distance in the astronomical navigation positioning and are expressed as H0When the height difference of the position is equal to the celestial body top distance H0Minus 90 deg., expressed as Δ H0And so on, the height of the ridge line of the inertial navigation prism at the first position observed by the theodolite is H1Then the height difference at that position is Δ H1The height and the pitch angle of the ridge line of the inertial navigation prism at the second position observed by the theodolite are H2Then the height difference is Δ H2,., the height and pitch angle of the ridge line of the i-th position inertial navigation prism observed by the theodolite is HiThen the height difference is Δ Hi：
ΔH0＝H0-90° (1.7)
ΔH1＝H1-90° (1.8)
ΔH2＝H2-90° (1.9)
Observation of the ith position:
ΔHi＝Hi-90° (1.10)；
establishing an inertial navigation prism ridge line observation equation according to the horizon azimuth angle and the height difference of a theodolite observation inertial navigation prism similar to an observation celestial body:
ΔHi＝X0cosAi-Z0sinAi(1.11)
both sides were simultaneously removed by-sinAiThen, there are:
-ΔHi·secAi＝-X0cotAi+Z0(1.12)
suppose that:
h＝-ΔHi·secAi
A＝-cotAi
then a linear equation can be established:
h＝A·X0+Z0(1.13)
linear regression was performed using the least squares method:
wherein, X0For deviation of the mounting of the edges of the inertial navigation prism rotating about the Z-axis, Z0Is the installation deviation of the prism edge line of the inertial navigation rotating around the X axis,
and calculating the position of the edge line of the inertial navigation prism relative to the celestial body, namely the installation deviation of the edge line of the inertial navigation prism relative to the rocket launching coordinate system.
2. The method of claim 1, wherein: the method comprises the following steps of automatically controlling the rotation of the turntable through a control computer to enable the inertial navigation prism to rotate to different positions:
leveling a rotary table fixedly provided with an inertial navigation system;
controlling the turntable to vertically align the inertial navigation prism with the theodolite, and reading a turntable angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
controlling the rotary table to enable the left side of the inertial navigation prism to rotate and be aligned with the theodolite, and reading a rotary table angle value, a theodolite pitch angle value and a horizontal azimuth angle value;
and controlling the turntable to rotate the right side of the inertial navigation prism and align the inertial navigation prism with the theodolite, and reading the angle value of the turntable, the pitch angle value of the theodolite and the horizontal azimuth angle value.
3. The method of claim 2, wherein: the method is characterized in that the inertial navigation prism is rotated to different positions by controlling the rotation of the turntable, and the method specifically comprises the following steps:
controlling the turntable to make the inertial navigation prism and theodolite vertically aligned to be regarded as celestial body sigma0And the angle value of the rotary table, the horizontal azimuth angle value of the theodolite and the pitch angle value are recorded as follows:
controlling the turntable to rotate to the right of the theodolite at equal intervals, aligning the inertial navigation prism with the theodolite, reading the angle value of the turntable, the pitch angle value and the horizontal azimuth angle value of the theodolite, and observing at the right side for not less than 3 positions; sequentially rotating the left side of the theodolite at equal intervals and ensuring clear imaging, reading the angle value of the turntable, the pitch angle value and the horizontal azimuth angle value of the theodolite, and observing the left side at no less than 3 positions;
when the turntable rotates to the ith position, the angle value of the turntable, the pitch angle value of the theodolite and the collimation of the inertial navigation prism and the horizontal azimuth angle value of the theodolite are recorded as:
4. the method of claim 3, wherein: the minimum control deflection angle of the left and right rotation control angles of the rotary table relative to the vertical collimation position of the inertial navigation prism and the theodolite is 15 degrees.
5. The method of claim 1, wherein: the rotation of the rotary table is automatically controlled by a control computer, so that the inertial navigation prism rotates to different positions.
6. An inertial navigation prism height difference calibration system is characterized by comprising:
the rotary table is used for bearing an inertial navigation system provided with an inertial navigation prism;
the theodolite is used for observing an inertial navigation prism;
a control computer for controllingRotating the rotation table to rotate the inertial navigation prism to different positions; the control computer is also used for calculating the horizon and azimuth angle of a similar observation celestial body of the theodolite observation inertial navigation prism according to the turntable angle value, the theodolite pitch angle value and the horizontal azimuth angle value when the inertial navigation prism rotates to different positions and the inertial navigation prism normal law, wherein the theodolite is erected and leveled at a point C and vertically collimates the inertial navigation prism, and the initial values of the turntable angle, the theodolite horizontal azimuth angle and the pitch angle are recorded as: (theta)0、V0、H0) Rotating the turntable to a point A on the left side of the theodolite and collimating the inertial navigation prism, and recording observation values of the turntable angle, the horizontal azimuth angle and the pitch angle of the theodolite as follows: (theta)A、VA、HA) Rotating the turntable to a point B on the right of the theodolite and collimating the inertial navigation prism, wherein observed values of the turntable angle, the pitch angle of the theodolite and the horizontal azimuth angle are as follows: (theta)B、VB、HB)，
Then the horizontal position angle A of the normal line of the A point inertial navigation prism1Comprises the following steps:
A1＝180°-(VA-V0)-(θA-θ0) (6.1)
horizontal position angle A of B point inertial navigation prism normal line2Comprises the following steps:
A2＝180°-(VB-V0)-(θB-θ0) (6.2)
horizontal position angle A of ridge line of ith position inertial navigation prismiComprises the following steps:
Ai＝180°-(Vi-V0)-(θi-θ0) (6.3)；
the vertical collimation observation inertial navigation prism ridge line height and pitch angle of the theodolite are regarded as the celestial body top distance in the astronomical navigation positioning and are expressed as H0When the height difference of the position is equal to the celestial body top distance H0Minus 90 deg., expressed as Δ H0And so on, the height of the ridge line of the inertial navigation prism at the first position observed by the theodolite is H1Then the height difference at that position is Δ H1The height and the pitch angle of the ridge line of the inertial navigation prism at the second position observed by the theodolite are H2Then the height difference is Δ H2,., longitude and latitudeThe height and the pitch angle of the ridge line of the inertial navigation prism at the ith position observed by the instrument are HiThen the height difference is Δ Hi：
ΔH0＝H0-90° (6.4)
ΔH1＝H1-90° (6.5)
ΔH2＝H2-90° (6.6)
Observation of the ith position:
ΔHi＝Hi-90° (6.7)；
then, establishing an inertial navigation prism ridge line observation equation according to the horizon azimuth angle and the height difference of the theodolite observation inertial navigation prism similar to the observation celestial body:
ΔHi＝X0cosAi-Z0sinAi(6.8)
both sides were simultaneously removed by-sinAiThen, there are:
-ΔHi·secAi＝-X0cotAi+Z0(6.9)
suppose that:
h＝-ΔHi·secAi
A＝-cotAi
then a linear equation can be established:
h＝A·X0+Z0(6.10)
linear regression was performed using the least squares method:
wherein, X0For deviation of the mounting of the edges of the inertial navigation prism rotating about the Z-axis, Z0Is the installation deviation of the prism edge line of the inertial navigation rotating around the X axis,
and calculating the position of the edge line of the inertial navigation prism relative to the celestial body, namely the installation deviation of the edge line of the inertial navigation prism relative to the rocket launching coordinate system.
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| CN112146681B (en) * | 2020-09-12 | 2023-03-10 | 中国运载火箭技术研究院 | Method and device for testing installation error of inertial group prism and computer storage medium |
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| CN113624252B (en) * | 2021-06-30 | 2023-09-12 | 北京自动化控制设备研究所 | Inertial navigation prism azimuth installation deviation calibration method and inertial navigation system |
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