Calculation method for attitude precision index of patrol missile navigation system

Abstract

The invention relates to a method for calculating attitude precision indexes of a patrol missile navigation system, and solves the problem that the attitude precision indexes of the current patrol missile navigation system are mostly put forward by empirical values or analogy. Comprising the following steps: S1, coordinate system conversion; S2, dual-vector attitude determination and attitude angle calculation; and S3, attitude angle precision index calculation of a navigation system. According to the method, the attitude precision index of the patrol missile navigation system is quantitatively calculated and analyzed, and the method is more scientific and accurate compared with an existing frequently-adopted experience analogy method; coordinate system and attitude angle definition comes from actual engineering, and proposed index calculation requirements and methods are closer to engineering practice; the calculation method is simple, rotation and translation of a coordinate system are represented through a homogeneous transformation matrix, and calculation can be efficiently completed by using the strong matrix operation capability of MATLAB; the dual-vector attitude determination as a mature algorithm has been widely applied to spacecraft attitude control, and the attitude angle of the patrolling projectile can be calculated more reliably.

Description

Technical Field

[0001] The invention relates to a method for calculating an attitude accuracy index of a cruise missile navigation system, and belongs to the field of cruise missile navigation. Background Art

[0002] Cruise missiles generally have both reconnaissance and strike functions. During the project demonstration process of cruise missile development, it is necessary to propose accuracy index requirements for its navigation system, and then select appropriate navigation system products based on the proposed accuracy index. During the project demonstration process, considering that cruise missiles have long flight characteristics and generally have a flight time of more than 1 hour, the position accuracy of the navigation system mainly depends on the positioning accuracy of satellite navigation. For civil code signals, the horizontal accuracy is 10 meters and the elevation accuracy is 15 meters. Therefore, the focus of the demonstration of the navigation system accuracy index is the attitude accuracy index.

[0003] At present, there are error analysis methods for target positioning of airborne optoelectronic pods based on homogeneous coordinate transformation and Monte Carlo method, but they only analyze the errors of the longitude, latitude and geodetic height of the target obtained by the optoelectronic pod according to the target positioning calculation process through the azimuth and distance information of the target obtained by the airborne optoelectronic pod, the position and attitude information of the carrier obtained by the navigation system, and the installation error of the airborne optoelectronic pod. There is no method to calculate the attitude accuracy index of the navigation system based on the positioning accuracy requirements of the cruise missile for the target and the measurement accuracy of the optoelectronic pod.

[0004] In the above methods, the attitude accuracy indicators of the cruise missile navigation system are mostly proposed based on empirical values ​​or analogies, which cannot be analyzed and demonstrated quantitatively and rigorously. It is inevitable that the indicators are too high or do not meet the requirements, resulting in an increase in development costs. Summary of the invention

[0005] According to the requirements of the reconnaissance and positioning accuracy of the cruise missile on the target and the measurement accuracy of the optoelectronic pod, the present invention proposes a calculation method for the attitude accuracy index of the navigation system by adopting homogeneous coordinate transformation, dual-vector attitude determination and Monte Carlo method, which solves the problem that the attitude accuracy index of the cruise missile navigation system is currently proposed mainly based on empirical values ​​or analogies.

[0006] The present invention is achieved by the following technical solutions:

[0007] A method for calculating the attitude accuracy index of a cruise missile navigation system comprises the following steps:

[0008] S1: Coordinate system conversion

[0009] 1) The coordinates of the target in the base coordinate system

[0010] The carrier and the platform base are connected by a vibration absorber. During operation, the vibration of the vibration absorber causes the three axes of the base coordinate system to generate Δθ ba , Δψ ba Azimuth deviation, the base coordinate system fixed to the platform base is defined as the actual base coordinate system;

[0011] The coordinates of the target in the actual base coordinate system are expressed as

[0012]

[0013] Do the inverse transformation

[0014]

[0015] According to the 2-3-1 order, i.e. yaw, pitch, roll, first rotate around z b Axis rotation angle Δψ ba , transformation matrix:

[0016]

[0017] Then rotate around y b Axis rotation angle Δθ ba , transformation matrix:

[0018]

[0019] Finally, the rotation around x b Axis rotation angle Transformation matrix:

[0020]

[0021] Therefore, the coordinates of the target in the base coordinate system are

[0022] 2) From the base coordinate system to the carrier body coordinate system

[0023] Coordinate system of the circumferential machine body x a The axis is rotated 90° to obtain the base coordinate system, and the transformation matrix is:

[0024]

[0025] So there is The inverse transformation

[0026] 3) From the aircraft body coordinate system to the aircraft geographic coordinate system

[0027] The yaw angle of the aircraft is defined as ψ, and the north-east is positive; the roll angle of the aircraft is defined as γ, and the right roll is positive; the pitch angle of the aircraft is defined as , lift your head to be positive;

[0028] According to the 2-3-1 rotation sequence, first go around y s Axis rotation angle -ψ, transformation matrix:

[0029]

[0030] Then rotate around z s Axis rotation angle Transformation matrix:

[0031]

[0032] Finally, the rotation around x s Axis rotation angle γ, transformation matrix:

[0033]

[0034] therefore, The inverse transformation

[0035] 4) From the earth's rectangular coordinate system to the aircraft's geographic coordinate system

[0036] First, along z g Axis translation O g K(-N s e 2 sinλ s ), the translation matrix is ​​as follows:

[0037]

[0038] in, is the radius of curvature of the y-axis circle, a is the semi-major axis of the Earth, is the first eccentricity of the Earth reference ellipsoid, b is the Earth's semi-minor axis;

[0039] Then go around the moved y g The axis rotates -90°, and the rotation matrix is ​​as follows:

[0040]

[0041] Next, rotate around x g Axis rotation - (90°-α s ), the transformation matrix is ​​as follows:

[0042]

[0043] Next, rotate around z g Axis rotation -λ s , the transformation matrix is ​​as follows:

[0044]

[0045] Finally, the rotation around y g Axis translation h s +N s , the translation matrix is ​​as follows, where h s is the altitude of the aircraft above the ground,

[0046]

[0047] The conversion process from the earth rectangular coordinate system to the aircraft geographic coordinate system is as follows:

[0048]

[0049] The conversion process from the aircraft geographic coordinate system to the earth rectangular coordinate system is as follows:

[0050]

[0051] 5) From rectangular coordinate system to geodetic coordinate system

[0052] Conversion from geodetic coordinate system to geodetic rectangular coordinate system:

[0053]

[0054] Among them, B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height;

[0055] Conversion from geodetic rectangular coordinate system to geodetic coordinate system:

[0056]

[0057] in is the second eccentricity of the meridian ellipsoid;

[0058] S2: Dual vector attitude calculation attitude angle

[0059] The positions of target 1 and target 2 in the carrier body coordinate system are r a1 =[x a1 y a1 z a1 ] T and r a2 =[x a2 y a2 z a2 ] T , the positions of target 1 and target 2 in the aircraft geographic coordinate system are r s1 =[x s1 y s1 z s1 ] T and r s2 =[x s2 y s2 z s2] T According to the double vector attitude determination, the attitude transfer matrix from the carrier's geographic coordinate system to the carrier's body coordinate system can be obtained as follows:

[0060]

[0061] The attitude angles of the cruise missile relative to the geographic coordinate system of the carrier aircraft are the yaw angle ψ (north east is positive), the pitch angle and roll angle γ, then the attitude transfer matrix from the carrier's geographic coordinate system to the carrier's body coordinate system is

[0062] Therefore, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is

[0063]

[0064] Therefore, through the vector r a1 、r a2 、r s1 、r s2 And formula (2-2) can get the direction cosine matrix According to formula (2-3), the attitude angle of the cruise missile can be obtained: ψ, γ;

[0065] S3: Navigation system attitude angle accuracy index calculation

[0066] Given the measurement accuracy of the optoelectronic pod, GNSS positioning accuracy (under the earth rectangular coordinate system), platform base installation accuracy, and target reconnaissance positioning accuracy, the Monte Carlo simulation is used to calculate the attitude angle accuracy index of the navigation system. The process is as follows:

[0067] Under nominal conditions, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is

[0068] (1) The aircraft optoelectronic pod simultaneously measures and monitors two targets, denoted as target 1 and target 2. The corresponding spatial information is:

[0069]

[0070] The expressions of target 1 and target 2 in the actual base coordinate system are:

[0071]

[0072] The installation error of the platform base is Then the coordinates of target 1 and target 2 in the base coordinate system (x bi y bi z bi )(i=1,2) can be obtained by the following formula

[0073]

[0074] The coordinates of target 1 and target 2 in the carrier body coordinate system (x ai y ai z ai )(i=1,2) can be obtained by the following formula

[0075]

[0076] (2) According to the target positioning accuracy requirements, the coordinates of target 1 and target 2 in the geodetic coordinate system

[0077] for

[0078] (L i +ΔL i B i +ΔB i H i +ΔH i )i=1,2(2-8)

[0079] The coordinates of target 1 and target 2 in the geodetic rectangular coordinate system are

[0080]

[0081] (3) Under nominal conditions, the position of the cruise missile in the geodetic rectangular coordinate system is (x m0 y m0 z m0 ), the GNSS plane positioning accuracy is 10m, and the elevation positioning accuracy is 15m, then the position error of the cruise missile in the geodetic rectangular coordinate system (Δx m Δy m Δz m ) is (10m 15m 10m), so the position coordinates of the cruise missile with errors (x m0 +Δx m y m0 +Δy m z m0 +Δz m ), and substituting it into equation (2-1) we can get the geodetic coordinates of the cruise missile with navigation position error (L ms ,B ms ,H ms ), substitute into matrices Q8 and Q 10 , Q 11 , Q 12 We can get Q8', Q1'0, Q1'1, Q1'2;

[0082] (4) The coordinates of target 1 and target 2 in the geographic coordinate system of the cruise missile carrier aircraft (x si y si z si ) can be obtained by the following formula

[0083]

[0084] (5) Through the above calculation, the coordinates of target 1 and target 2 in the carrier body coordinate system (x ai ,y ai ,z ai ), i = 1, 2 and the coordinates in the geographic coordinate system of the carrier (x si ,y si ,z si ),i=1,2, according to the dual-vector attitude determination algorithm in equations (2-2) and (2-3), the attitude angle of the aircraft body coordinate system relative to the aircraft geographic coordinate system can be obtained Further, the attitude angle error can be obtained

[0085]

[0086] (6) Repeat steps (1)-(5) 1000 times, and then calculate the attitude angle error The standard deviation of the attitude angle of the navigation system can be calculated to obtain the accuracy index.

[0087] Beneficial effects of the present invention:

[0088] 1. Quantitatively calculate and analyze the attitude accuracy index of the cruise missile navigation system, which is more scientific and accurate than the empirical analogy method commonly used at present;

[0089] 2. The coordinate system and attitude angle definitions are derived from actual engineering, and the proposed index calculation requirements and methods are closer to engineering reality;

[0090] 3. The calculation method is simple. The rotation and translation of the coordinate system are represented by the homogeneous transformation matrix. The powerful matrix operation capability of MATLAB is used to efficiently complete the calculation.

[0091] 4. As a mature algorithm, dual-vector attitude determination has been widely used in spacecraft attitude control and is more reliable for calculating the attitude angle of cruise missiles. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Geodetic coordinate system;

[0093] Figure 2 Geodetic rectangular coordinate system and aircraft geographic coordinate system;

[0094] Figure 3 Aircraft body coordinate system;

[0095] Figure 4 Base coordinate system. DETAILED DESCRIPTION

[0096] like Figure 1-4 As shown, the present invention proposes a method for calculating the accuracy index of the navigation system attitude information (carrier aircraft pitch angle, yaw angle, roll angle) based on the positioning information (target longitude, latitude, geodetic height) and accuracy requirements of the cruise missile to the target, the measurement information (target distance, azimuth, pitch angle) and accuracy index of the optoelectronic pod, and the installation error information of the optoelectronic pod, which solves the problem that the attitude accuracy index of the cruise missile navigation system is mainly based on empirical values ​​or analogies. It includes the following steps:

[0097] 1 Coordinate system conversion

[0098] 1.1 Coordinates of the target in the base coordinate system

[0099] Generally, the carrier and the platform base are connected by a vibration absorber. During operation, the vibration of the vibration absorber can cause the three axes of the base coordinate system to produce Δθ ba , Δψ ba , the base coordinate system fixed to the platform base is defined as the actual base coordinate system.

[0100] The target is in the actual base coordinate system (such as Figure 4 ) can be expressed as

[0101]

[0102] Can do inverse transformation

[0103]

[0104] According to the 2-3-1 (yaw, pitch, roll) rotation sequence, first around z b Axis rotation angle Δψ ba , transformation matrix:

[0105]

[0106] Then rotate around y b Axis rotation angle Δθ ba , transformation matrix:

[0107]

[0108] Finally, the rotation around x b Axis rotation angle Transformation matrix:

[0109]

[0110] Therefore, the coordinates of the target in the base coordinate system are

[0111] 1.2 From base coordinate system to aircraft body coordinate system

[0112] Coordinate system of the circumferential machine body x a The base coordinate system can be obtained by rotating the axis 90°, and the transformation matrix is:

[0113]

[0114] So there is The inverse transformation

[0115] 1.3 From the aircraft body coordinate system to the aircraft geographic coordinate system

[0116] The yaw angle of the aircraft is defined as ψ, and the north-east is positive; the roll angle of the aircraft is defined as γ, and the right roll is positive; the pitch angle of the aircraft is defined as Looking up is positive.

[0117] According to the 2-3-1 rotation sequence, first go around y s Axis rotation angle -ψ, transformation matrix:

[0118]

[0119] Then rotate around z s Axis rotation angle Transformation matrix:

[0120]

[0121] Finally, the rotation around x s Axis rotation angle γ, transformation matrix:

[0122]

[0123] therefore, The inverse transformation

[0124] 1.4 From Earth's Cartesian Coordinate System to Aircraft's Geographic Coordinate System

[0125] like Figure 2 As shown in the figure, the transformation from the earth rectangular coordinate system to the aircraft geographic coordinate system is:

[0126] First, along z g Axis translation O g K(-N s e 2 sinλ s ), the translation matrix is ​​as follows:

[0127]

[0128] in, is the radius of curvature of the y-axis circle, a is the semi-major axis of the earth, which can be 6378137m. is the first eccentricity of the earth reference ellipsoid, b is the semi-minor axis of the earth, and can be taken as 6356752m.

[0129] Then go around the moved y g The axis rotates -90°, and the rotation matrix is ​​as follows:

[0130]

[0131] Next, rotate around x g Axis rotation - (90°-α s ), the transformation matrix is ​​as follows:

[0132]

[0133] Next, rotate around z g Axis rotation -λ s , the transformation matrix is ​​as follows:

[0134]

[0135] Finally, the rotation around y g Axis translation h s +N s , the translation matrix is ​​as follows, where h s is the altitude of the aircraft above the ground,

[0136]

[0137] The conversion process from the earth rectangular coordinate system to the aircraft geographic coordinate system is as follows:

[0138]

[0139] The conversion process from the aircraft geographic coordinate system to the earth rectangular coordinate system is as follows:

[0140]

[0141] 1.5 From rectangular coordinate system to geodetic coordinate system

[0142] Conversion from geodetic coordinate system to geodetic rectangular coordinate system:

[0143]

[0144] Among them, B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height.

[0145] Conversion from geodetic rectangular coordinate system to geodetic coordinate system:

[0146]

[0147] in is the second eccentricity of the meridian ellipsoid.

[0148] 2 Double vector attitude determination and attitude angle calculation process

[0149] The process of calculating the attitude angle by dual-vector attitude determination is to obtain the three attitude angles of the cruise missile relative to the geographic coordinate system of the carrier aircraft based on the known position information of target 1 and target 2 in the carrier aircraft's body coordinate system.

[0150] The positions of target 1 and target 2 in the carrier body coordinate system are r a1 =[x a1 y a1 z a1 ] T and r a2 =[x a2 y a2 z a2 ] T , the positions of target 1 and target 2 in the aircraft geographic coordinate system are r s1 =[x s1 y s1 z s1 ] T and r s2 =[x s2 y s2 z s2 ] T According to the double vector attitude determination, the attitude transfer matrix from the carrier's geographic coordinate system to the carrier's body coordinate system can be obtained as follows:

[0151]

[0152] The attitude angles of the cruise missile relative to the geographic coordinate system of the carrier aircraft are the yaw angle ψ (north east is positive), the pitch angle and roll angle γ, then the attitude transfer matrix from the carrier's geographic coordinate system to the carrier's body coordinate system is

[0153] Therefore, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is

[0154]

[0155] Therefore, through the vector r a1 、r a2 、r s1 、r s2And formula (2-2) can get the direction cosine matrix According to formula (2-3), the attitude angle of the cruise missile can be obtained: ψ, γ.

[0156] 3. Calculation process of attitude angle accuracy index of navigation system

[0157] The process of calculating the attitude angle accuracy index of the navigation system by Monte Carlo simulation is based on the known measurement accuracy of the optoelectronic pod, GNSS positioning accuracy (under the earth rectangular coordinate system), platform base installation accuracy and target reconnaissance positioning accuracy.

[0158] Under nominal conditions, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is

[0159] (1) The aircraft optoelectronic pod simultaneously measures and monitors two targets, denoted as target 1 and target 2. The corresponding spatial information is:

[0160] (R i +ΔR i λ i +Δλ i α i +Δα i )i=1,2(2-4)

[0161] The expressions of target 1 and target 2 in the actual base coordinate system are:

[0162]

[0163] The installation error (accuracy) of the platform base is Then the coordinates of target 1 and target 2 in the base coordinate system (x bi y bi z bi )(i=1,2) can be obtained by the following formula

[0164]

[0165] The coordinates of target 1 and target 2 in the carrier body coordinate system (x ai y ai z ai )(i=1,2) can be obtained by the following formula

[0166]

[0167] (2) According to the target positioning accuracy requirements, the coordinates of target 1 and target 2 in the geodetic coordinate system

[0168] for

[0169] (L i +ΔLi B i +ΔB i H i +ΔH i )i=1,2(2-8)

[0170] The coordinates of target 1 and target 2 in the geodetic rectangular coordinate system are

[0171]

[0172] (3) Under nominal conditions, the position of the cruise missile in the geodetic rectangular coordinate system is (x m0 y m0 z m0 ), the GNSS plane positioning accuracy is 10m, and the elevation positioning accuracy is 15m, then the position error of the cruise missile in the geodetic rectangular coordinate system (Δx m Δy m Δz m ) can be taken as (10m 15m10m), so the position coordinates of the cruise missile with errors (x m0 +Δx m y m0 +Δy m z m0 +Δz m ), and substituting it into equation (2-1) we can get the geodetic coordinates of the cruise missile with navigation position error (L ms ,B ms ,H ms ), substitute into matrices Q8 and Q 10 , Q 11 , Q 12 Q8', Q1'0, Q1'1, Q1'2 can be obtained.

[0173] (4) The coordinates of target 1 and target 2 in the geographic coordinate system of the cruise missile carrier aircraft (x si y si z si ) can be obtained by the following formula

[0174]

[0175] (5) Through the above calculation, the coordinates of target 1 and target 2 in the carrier body coordinate system (x ai ,y ai ,z ai ), i = 1, 2 and the coordinates in the geographic coordinate system of the carrier (x si ,y si ,z si),i=1,2, according to the dual-vector attitude determination algorithm in equations (2-2) and (2-3), the attitude angle of the aircraft body coordinate system relative to the aircraft geographic coordinate system can be obtained Further, the attitude angle error can be obtained

[0176]

[0177] (6) Repeat steps (1)-(5) 1000 times, and then calculate the attitude angle error The standard deviation of the attitude angle of the navigation system can be used to prove the accuracy index.

[0178] In the present invention, the coordinate system is defined as follows:

[0179] 1. Geodetic coordinate system

[0180] Geodetic coordinate system C(O C -X C Y C Z C ) The origin is the center of mass of the Earth, X C The axis direction is defined as the point from the origin to the intersection of the Greenwich meridian and the Earth's equator, Z C The axis direction is defined as the origin pointing to the North Pole of the Earth, C The axis is defined as perpendicular to the X C O C Z C Planar and same Z C Axis, X C The coordinates of any point P in the geodetic coordinate system can be expressed as (B, L, H), which represents the geodetic latitude, longitude and geodetic height of point P.

[0181] 2. Geodetic rectangular coordinate system

[0182] Geodetic rectangular coordinate system G(O g -X g Y g Z g ) coordinates are completely coincident with the three axes of the geodetic coordinate system. The geodetic coordinate system and the geodetic rectangular coordinate system differ only when they represent a point in space. The coordinates of a point P in the geodetic rectangular coordinate system can be expressed as (x g ,y g ,z g ), where x g ,y g 、z g They are OP (see Figure 1 ) In the geodetic rectangular coordinate system, X g Axis, Y g Axis and Z g The projection value on the axis.

[0183] 3. Aircraft geographic coordinate system

[0184] The carrier geographic coordinate system S(O s -X s Y s Z s ) origin O s Defined in the space where the center of mass of the carrier is located, X s The direction is due north of the aircraft, Y s The direction is the zenith direction of the aircraft, Z s The direction is due east of the position of the carrier aircraft. Figure 2 (North Sky East), where α s is the aircraft longitude, λ s is the aircraft latitude.

[0185] Note: The "carrier aircraft" described in this patent can be a drone or a cruise missile in actual engineering practice.

[0186] 4. Aircraft body coordinate system

[0187] Aircraft body coordinate system A(O a -X a Y a Z a ) origin O a Fixed to the center of mass of the aircraft, X a The axis is forward along the reference axis of the fuselage, also known as the longitudinal axis; Z a The axis perpendicular to the plane is symmetrical to the right, also known as the horizontal axis; Y a The axis is perpendicular to the plane of symmetry X a Axis, also known as vertical axis, see Figure 3 .

[0188] 5. Base coordinate system

[0189] Base coordinate system B(O b -X b Y b Z b ) The origin O is fixed to the center of mass of the aircraft, X b The Y axis is forward along the fuselage reference axis; b Axis vertical plane symmetrical facing right; Z b The axis is perpendicular to the plane of symmetry X b Axis downward. Where R is the distance between the projectile and the target, λ is the target pitch angle, and α is the target azimuth angle.

Claims

1. A method for calculating the attitude accuracy index of a cruise missile navigation system, characterized by: The following steps are involved: S1: Coordinate system conversion 1) The coordinates of the target in the base coordinate system The carrier and the platform base are connected by a vibration absorber. During operation, the vibration of the vibration absorber causes the three axes of the base coordinate system to generate Δθ ba , Δψ ba Azimuth deviation, the base coordinate system fixed to the platform base is defined as the actual base coordinate system; The coordinates of the target in the actual base coordinate system are expressed as Do the inverse transformation According to the 2-3-1 order, i.e. yaw, pitch, roll, first rotate around z b Axis rotation angle Δψ ba , transformation matrix: Then rotate around y b Axis rotation angle Δθ ba , transformation matrix: Finally, the rotation around x b Axis rotation angle Transformation matrix: Therefore, the coordinates of the target in the base coordinate system are 2) From the base coordinate system to the carrier body coordinate system Coordinate system of the circumferential machine x a The axis is rotated 90° to obtain the base coordinate system, and the transformation matrix is: So there is The inverse transformation 3) From the aircraft body coordinate system to the aircraft geographic coordinate system The yaw angle of the aircraft is defined as ψ, and the north-east is positive; the roll angle of the aircraft is defined as γ, and the right roll is positive; the pitch angle of the aircraft is defined as θ, and the head-up is positive; According to the 2-3-1 rotation sequence, first go around y s Axis rotation angle -ψ, transformation matrix: Then rotate around z s Axis rotation angle θ, transformation matrix: Finally, the rotation around x s Axis rotation angle γ, transformation matrix: therefore, The inverse transformation 4) From the earth's rectangular coordinate system to the aircraft's geographic coordinate system First, along z g Axis translation O g K(-N s e 2 sinλ s ), the translation matrix is ​​as follows: in, is the radius of curvature of the y-axis circle, a is the semi-major axis of the Earth, is the first eccentricity of the Earth reference ellipsoid, b is the Earth's semi-minor axis; Then go around the moved y g The axis rotates -90°, and the rotation matrix is ​​as follows: Next, rotate around x g Axis rotation - (90°-α s ), the transformation matrix is ​​as follows: Next, rotate around z g Axis rotation -λ s , the transformation matrix is ​​as follows: Finally, the rotation around y g Axis translation h s +N s , the translation matrix is ​​as follows, where h s is the altitude of the carrier aircraft, The conversion process from the earth rectangular coordinate system to the aircraft geographic coordinate system is as follows: The conversion process from the aircraft geographic coordinate system to the earth rectangular coordinate system is as follows: 5) From rectangular coordinate system to geodetic coordinate system Conversion from geodetic coordinate system to geodetic rectangular coordinate system: Among them, B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height; Conversion from geodetic rectangular coordinate system to geodetic coordinate system: in is the second eccentricity of the meridian ellipsoid; S2: Dual vector attitude calculation attitude angle The positions of target 1 and target 2 in the carrier body coordinate system are r a1 =[x a1 y a1 z a1 ] T and r a2 =[x a2 y a2 z a2 ] T , the positions of target 1 and target 2 in the aircraft geographic coordinate system are r s1 =[x s1 y s1 z s1 ] T and r s2 =[x s2 y s2 z s2 ] T According to the double vector attitude determination, the attitude transfer matrix from the carrier's geographic coordinate system to the carrier's body coordinate system can be obtained as follows: The attitude angles of the cruise missile relative to the carrier aircraft's geographic coordinate system are yaw angle ψ (north east is positive), pitch angle θ and roll angle γ, then the attitude transfer matrix from the carrier aircraft's geographic coordinate system to the carrier aircraft's body coordinate system is: Therefore, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is Therefore, through the vector r a1 、r a2 、r s1 、r s2 And formula (2-2) can get the direction cosine matrix C s a , and then according to formula (2-3), we can get the attitude angles θ, ψ, and γ of the cruise missile; S3: Navigation system attitude angle accuracy index calculation Given the measurement accuracy of the optoelectronic pod, GNSS positioning accuracy (under the earth rectangular coordinate system), platform base installation accuracy, and target reconnaissance positioning accuracy, the Monte Carlo simulation is used to calculate the attitude angle accuracy index of the navigation system. The process is as follows: Under nominal conditions, the attitude angle of the cruise missile relative to the geographic coordinate system of the carrier aircraft is (-ψ0, θ0, γ0); (1) The aircraft optoelectronic pod simultaneously measures and monitors two targets, denoted as target 1 and target 2. The corresponding spatial information is (R i +ΔR i λ i +Δλ i α i +Δα i ) i=1,2 (2-4) The expressions of target 1 and target 2 in the actual base coordinate system are: The installation error of the platform base is Then the coordinates of target 1 and target 2 in the base coordinate system (x bi y bi z bi )(i=1,2) can be obtained by the following formula The coordinates of target 1 and target 2 in the carrier body coordinate system (x ai y ai z ai )(i=1,2) can be obtained by the following formula (2) According to the target positioning accuracy requirements, the coordinates of target 1 and target 2 in the geodetic coordinate system For (L i + ΔL i B i + ΔB i H i + ΔH i ) i = 1, 2 (2 - 8) The coordinates of target 1 and target 2 in the geodetic rectangular coordinate system are (3) Under nominal conditions, the position of the cruise missile in the geodetic rectangular coordinate system is (x m0 y m0 z m0 ), the GNSS plane positioning accuracy is 10m, and the elevation positioning accuracy is 15m, then the position error of the cruise missile in the geodetic rectangular coordinate system (Δx m Δy m Δz m ) is (10m 15m 10m), so the position coordinates of the cruise missile with errors (x m0 +Δx m y m0 +Δy m z m0 +Δz m ), and substituting it into equation (2-1) we can get the geodetic coordinates of the cruise missile with navigation position error (L ms ,B ms ,H ms ), substitute into matrices Q8 and Q 10 , Q 11 , Q 12 We can get Q8', Q1'0, Q1'1, Q1'2; (4) The coordinates of target 1 and target 2 in the geographic coordinate system of the cruise missile carrier aircraft (x si y si z si ) can be obtained by the following formula (5) Through the above calculation, the coordinates of target 1 and target 2 in the carrier body coordinate system (x ai ,y ai ,z ai ), i = 1, 2 and the coordinates in the geographic coordinate system of the carrier (x si ,y si ,z si ), i = 1, 2, according to the dual-vector attitude determination algorithm in equations (2-2) and (2-3), the attitude angle (ψ, θ, γ) of the carrier body coordinate system relative to the carrier geographic coordinate system can be obtained, and the attitude angle error can be further obtained (6) Repeat steps (1) to (5) n times, and then calculate the standard deviation of the attitude angle error (Δψ, Δθ, Δγ) to obtain the accuracy index of the navigation system attitude angle.

2. The method for calculating the attitude accuracy index of a cruise missile navigation system according to claim 1 is characterized by: In S3, the GNSS positioning accuracy is the positioning accuracy in the geodetic rectangular coordinate system.

3. The method for calculating the attitude accuracy index of a cruise missile navigation system according to claim 1 is characterized by: In S3 (6), repeat steps (1) to (5) for no less than 1000 times.

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