An inertial navigation attitude angle calculation method based on extended Krawtchouk angle

Abstract

The application discloses an inertial navigation attitude angle calculation method based on extended Krylov angles, which comprises the following steps: determining the extended Krylov angles; calculating the values of the yaw angle, the pitch angle, the roll angle and the extended pitch angle at t k ; determining the angular velocity of the body coordinate system relative to the navigation coordinate system during rotation at t k ; performing soft variable structure angular velocity correction and integral updating calculation; updating the coordinate transformation matrix according to the integral updating calculation result, and supporting velocity updating and position updating, so as to improve the precision of the inertial navigation. The application takes the angular rate output by the gyroscope orthogonally installed on the body of the strapdown inertial system as input information, realizes the real-time updating of the inertial navigation attitude angle based on the soft continuous variable structure of the navigation calculation of the four extended Krylov angles, and makes the singular value not appear in the updating process of the attitude angle, so that the calculation precision is improved.

Description

Technical Field

[0001] This invention relates to a method for calculating the attitude angle of inertial navigation based on extended Krylov angles, belonging to the field of inertial technology. Background Technology

[0002] Inertial navigation is widely used in missiles, aircraft, ships, and weapons, primarily to determine the position, velocity, and attitude information of a vehicle relative to a navigation system in real time. Strapdown inertial systems are directly fixed to the vehicle, using gyroscopes to measure angular velocity and mathematically calculating the values ​​of three attitude angles.

[0003] Currently, methods for determining attitude information include direction cosine kinematics, Euler-Krylov angle kinematics, and quaternion kinematics. The disadvantage of direction cosine kinematics is that the transformation matrix has nine parameters and six relational equations, resulting in a large computational load and limited application in engineering. While quaternion kinematics provides a unique coordinate transformation matrix, there is no unique solution for determining attitude angles from the coordinate transformation matrix.

[0004] In contrast, the Euler-Krylov angle kinematic equations only have three. However, on page 46 of the book "Inertial Devices (Volume 1)" (China Aerospace Publishing House) in this technical field, it is argued that the kinematic equations described by Euler-Krylov angles contain singularities and degenerate. However, a Chinese patent (application number CN202010333184.9) proposes an attitude calculation method based on Krylov angles, which can achieve a full attitude motion description of the carrier. The problem is that when the pitch angle is 90°, the attitude calculation error is large during discretization, resulting in significant errors in the calculated velocity and position.

[0005] To address the singularity problem, existing technologies employ extended Krylov angles, characterized by four angles, to achieve a singularity-free full-attitude navigation solution ("Full-Attitude Navigation Solution Based on Extended Krylov Angles," Chinese Journal of Inertial Technology, Vol. 29 No. 5, 2021). The specific idea behind this method is to use different solution strategies in different regions, fixing one angle in each region and allowing the other three angles to participate in the attitude calculation. While this method solves the singularity problem in full-attitude navigation, it introduces the drawback of discontinuous angle changes, which is detrimental to flight control stability.

[0006] Therefore, it is necessary to study a new high-precision attitude angle calculation method based on extended Krylov angle to improve the accuracy of inertial navigation and flight control. Summary of the Invention

[0007] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and solve the problem of discontinuous attitude angle changes when calculating the attitude of a partitioned discrete variable structure.

[0008] The objective of this invention is achieved through the following technical solutions:

[0009] A method for calculating inertial navigation attitude angles based on extended Krylov angles includes:

[0010] In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, which include yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ.

[0011] During the navigation recursive solution process, the k-th time series t relative to time t0 is determined. k The attitude angles at any given time, including the yaw angle φ k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k , where t k = t0 + k × ΔT, where ΔT is the sampling time;

[0012] Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0013] Based on the yaw angle φ k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solve for t k The next moment t after moment k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 ;

[0014] Based on φ k+1 ψ k+1 γ k+1 and ξ k+1 Solve for t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment;

[0015] After performing integration based on apparent acceleration, gravitational acceleration, and the coordinate transformation matrix, the velocity update calculation is completed.

[0016] In one embodiment of the present invention, the position update calculation is completed based on the velocity update calculation result.

[0017] In one embodiment of the present invention, the calculation method is based on a strapdown inertial system fixed to the carrier. The body coordinate system corresponding to the strapdown inertial system is Ox′y′z′; the navigation coordinate system describing the carrier's motion attitude angle is Oxyz. The origins of the two coordinate systems coincide, and four Krylov angles are used to describe the relationship between the two coordinate systems. The navigation coordinate system reaches the body coordinate system after four rotations. The specific rotation process is as follows: the navigation coordinate system Oxyz rotates by an angle φ around the Oz axis to reach OLNz; OLNz then rotates by an angle ψ around the ON axis to reach OQNM; OQNM rotates by an angle γ around the OQ axis to reach OQy′P; finally, OQy′P rotates by an angle ξ around Oy′ to reach Ox′y′z′.

[0018] In one embodiment of the present invention, the gyroscopes installed on the strapdown inertial system body are three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0019] In one embodiment of the present invention, t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of the four Krylov angles, at time t is:

[0020]

[0021] Where p represents the navigation coordinate system and b represents the body coordinate system.

[0022] In one embodiment of the present invention, the yaw angle, roll angle and extended pitch angle are all in the range of -180° to +180°, and the pitch angle is in the range of -90° to +270°.

[0023] In one embodiment of the present invention, the next time step t is calculated. k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The methods include:

[0024] Given the parameters k1 = -0.05 and k2 = -0.03 for the compliant variable structure, and the value of the radius Δβ of the singular circle centered at the singular point, determine the angular velocity correction value for the compliant variable structure:

[0025]

[0026] In the formula, (ψ1, γ1) = (90°, 0°), (ψ2, γ2) = (90°, 180°), (ψ3, γ3) = (90°, -180°), (ψ4, γ4) = (270°, 0°), (ψ5, γ5) = (270°, 180°), (ψ6, γ6) = (270°, -180°), (ψ7, γ7) = (-90°, 180°), (ψ8, γ8) = (-90°, 0°), (ψ9, γ9) = (-90°, -180°) are 9 singular points;

[0027] According to φ k ψ k γ k ξ k , Δω k and Determine φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0028]

[0029] In one embodiment of the present invention, the next time step t is calculated. k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The methods include:

[0030] Let the range of the "|" shaped active area be ψ. n ≤ψ≤ψ m , where ψ n ψ is the lower limit of the horizontal active area in the "|" shape. m The upper limit of the horizontal movement area of ​​the "|" shape; the value of the compliant variable structure parameter K is set to -4×10. -3 Determine the angular velocity correction value for the compliant structure:

[0031]

[0032] Where, when ψ m When <90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2=0°; when ψ n When >90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2 = 180°;

[0033] According to φ k , ψ k , γ k , ξ k , Δω k and determine φ k+1 , ψ k+1 , γ k+1 and ξ k+1 , the specific calculation formulas are as follows:

[0034]

[0035] In one embodiment of the present invention, solving for the four attitude angles φ at the next time instant t k+1 =t k +ΔT, ψ k+1 , ψ k+1 , γ k+1 and ξ k+1 comprises the following steps:

[0036] Set the I-shaped active region γ n ≤γ≤γ m , wherein γ n is the lower limit value of the I-shaped longitudinal active region, and γ m is the upper limit value of the I-shaped longitudinal active region; set the value of the compliant variable structure parameter K to -4×10 -3 , and determine the angular velocity correction value of the compliant variable structure:

[0037]

[0038] wherein, when γ n >0°, γ n and γ m satisfy (γ n +γ m ) / 2=90°; when γ m <0°, γ n and γ m satisfy (γ n +γ m ) / 2=-90°;

[0039] According to φ k , ψ k , γ k , ξ k , Δω k and determine φ k+1 , ψ k+1 , γ k+1 and ξ k+1 , the specific calculation formulas are as follows:

[0040]

[0041] In an embodiment of the present invention, solving for the four attitude angles φ at the next moment t k+1 =t k +ΔT k+1 , ψ k+1 , γ k+1 and ξ k+1 comprises the following steps:

[0042] Setting an I-shaped active region satisfying γ n1 ≤γ≤γ m1 and γ n2 ≤γ≤γ m2 , and γ m2 <γ<γ n1 and ψ n ≤ψ≤ψ m , wherein γ n1 is a lower limit value of a longitudinally upper active region of the I-shape, γ m1 is an upper limit value of the longitudinally upper active region of the I-shape, γ n2 is a lower limit value of a longitudinally lower active region of the I-shape, γ m2 is an upper limit value of the longitudinally lower active region of the I-shape, ψ n is a lower limit value of a transverse active region of the I-shape, ψ m is an upper limit value of the transverse active region of the I-shape; setting a value of a compliant variable structure parameter K as -4×10 -3 , and determining an angular velocity correction value of the compliant variable structure:

[0043]

[0044] wherein, for interval parameters, (γ n1 +γ m1 ) / 2=90°, (γ n2 +γ m2 ) / 2=-90°; when ψ m <90°, ψ n and ψ m satisfy (ψ n +ψ m ) / 2=0°; when ψ n >90°, ψ n and ψ m satisfy (ψ n +ψ m ) / 2=180°;

[0045] According to φ k , ψ k , γ k , ξ k , Δω k and Determine φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0046]

[0047] In one embodiment of the present invention, the next time step t is calculated. k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The methods include:

[0048] Let the "H"-shaped activity area ψ n1 ≤ψ≤ψ m1 And ψ n2 ≤ψ≤ψ m2 , and ψ m1 <γ<ψ n2 And γ n ≤γ≤γ m , where ψ n1 ψ is the lower limit of the horizontal left-side active area of ​​the "H" shape. m1 This represents the upper limit of the horizontal movement area on the left side of the "H" shape; ψ n2 ψ is the lower limit of the horizontal right-side active area of ​​the "H" shape. m2 The upper limit of the horizontal movement area on the right side of the "H" shape; γ n γ is the lower limit value of the "H"-shaped vertical activity area. m This represents the upper limit of the "H"-shaped longitudinal active region; the given value of the compliant variable structure parameter K is -4 × 10⁻⁴. -3 Determine the angular velocity correction value for the compliant structure:

[0049]

[0050] Among them, the interval parameter (ψ) n1 +ψ m1 ) / 2=0°、(ψ n2 +ψ m2 ) / 2=180°; when γ n When >0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=90°; when γ m When <0°, γ n and γ m Satisfy (γ) n +γ m ) / 2 = -90°;

[0051] According to φ k ψ k γ k ξ k , Δω k and Determine φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0052]

[0053]

[0054] In one embodiment of the present invention, the next time step t is calculated. k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The methods include:

[0055] Let the active region γ be shaped like a "+". n ≤γ≤γ m or ψ n ≤ψ≤ψ m , where γ n γ is the lower limit of the "+" shaped vertical activity area. m This represents the upper limit of the "+" shaped vertical activity area; ψ n ψ is the lower limit of the "+" shaped horizontal movement area. m This represents the upper limit of the "+" shaped lateral movement region; the given value of the compliant variable structure parameter K is -4 × 10. -3 Determine the angular velocity correction value for the compliant structure:

[0056]

[0057] Where, when γ n When >0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=90°; when γ m When <0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=-90°; when ψ m When <90°, ψ n and ψ m Satisfy (ψ) n +ψm ) / 2=0°; when ψ n When >90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2 = 180°;

[0058] According to φ k ψ k γ k ξ k , Δω k and Determine φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0059]

[0060]

[0061] In one embodiment of the present invention, the next time step t is calculated. k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The methods include:

[0062] Let the active region γ be in the shape of a "#". n1 ≤γ≤γ m1 or γ n2 ≤γ≤γ m2 or ψ n1 ≤ψ≤ψ m1 or ψ n2 ≤ψ≤ψ m2 , where ψ n1 ψ is the lower limit of the horizontal left-hand active area of ​​the "#" shape. m1 This represents the upper limit of the horizontal movement area to the left of the "#" shape; ψ n2 ψ is the lower limit of the horizontal right-hand active area of ​​the "#" shape. m2 This represents the upper limit of the horizontal movement area to the right of the "#" shape; γ n1 γ is the lower limit value of the upper vertical active area of ​​the "#" shape. m1 γ represents the upper limit of the vertical upper region of the "#" shaped activity area. n2 γ is the lower limit value of the vertical lower part of the "#" shaped active area. m2 This represents the upper limit of the vertical lower part of the "#" shaped active area; the given value of the compliant variable structure parameter K is -4 × 10. -3 Determine the angular velocity correction value for the compliant structure:

[0063]

[0064] Wherein, the interval parameter γ n2 <γ m2 <γ n1 <γ m1 , ψ n1 <ψ m1 <ψ n2 <ψ m2 , and (γ n1 +γ m1 ) / 2=90° and (γ) n2 +γ m2 ) / 2=-90° and (ψ n1 +ψ m1 ) / 2=0° and (ψ n2 +ψ m2 ) / 2 = 180°;

[0065] According to φ k ψ k γ k ξ k , Δω k and Determine φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0066]

[0067] Compared with the prior art, the present invention has the following advantages:

[0068] (1) This invention overcomes the problem of discontinuous attitude angle changes during partitioned discrete variable structure attitude calculation, and realizes real-time continuous representation of attitude angles, which is beneficial to the smoothness of flight control.

[0069] (2) This invention fully covers the situation where the four attitude angles are in any quadrant. Near the singular point, the possibility of the running trajectory approaching the singular point is overcome by the soft obstacle avoidance control method, thereby realizing the full attitude adaptability of the strapdown system inertial navigation.

[0070] (3) The present invention can directly and accurately give the attitude angle of the body coordinate system relative to the navigation coordinate system, while quaternions can only be given indirectly through the coordinate transformation matrix.

[0071] (4) The method of the present invention has a simple structure and is easy to implement in engineering. Attached Figure Description

[0072] Figure 1This is a flowchart of the steps of the inertial navigation attitude angle calculation method based on the extended Krylov angle of the present invention;

[0073] Figure 2 This is a schematic diagram illustrating the relationship between the body and the navigation coordinate system in a strapdown inertial system, described by Krylov angles.

[0074] Figure 3 These are the four attitude angles calculated during the three rolls of an aircraft, described by the four Krylov angles of the partitioned discrete variable structure attitude solution.

[0075] Figure 4 To avoid singularities, a phase plane diagram is used during partitioned discrete variable structure attitude calculation;

[0076] Figure 5 Implementation method one is based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0077] Figure 6 A phase plane diagram for calculating the attitude of a compliant continuous variable structure that avoids singularities in Implementation Method 1;

[0078] Figure 7 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method 1;

[0079] Figure 8 Implementation method two is based on the four attitude angles of the aircraft during the three rolls described by the four Krylov angles;

[0080] Figure 9 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "|"-shaped orbit in implementation method 2 to avoid singularities;

[0081] Figure 10 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method 2;

[0082] Figure 11 Implementation method three is based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0083] Figure 12 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "I"-shaped track in implementation method three to avoid singularities;

[0084] Figure 13 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method 3;

[0085] Figure 14 Implementation method four is based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0086] Figure 15 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "I"-shaped track in implementation method four to avoid singularities;

[0087] Figure 16 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method 4;

[0088] Figure 17 Implementation method five is based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0089] Figure 18 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "H"-shaped orbit in implementation method five to avoid singularities;

[0090] Figure 19 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method 5;

[0091] Figure 20 Implementation method six is ​​based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0092] Figure 21 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "+" shaped orbit in implementation method six to avoid singularities;

[0093] Figure 22 The three-dimensional trajectory of aircraft motion calculated for navigation based on the attitude angles calculated in Implementation Method Six;

[0094] Figure 23 Implementation method seven is based on the four attitude angles during the three-roll process of an aircraft, described by four Krylov angles;

[0095] Figure 24 Phase plane diagram for calculating the compliant continuous variable structure attitude of the "#" shaped orbit in implementation method seven to avoid singularities;

[0096] Figure 25 The three-dimensional trajectory of the aircraft motion is calculated for navigation based on the attitude angles calculated in Implementation Method Seven. Detailed Implementation

[0097] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0098] Implementation Method 1:

[0099] like Figure 1 In this embodiment, the inertial navigation attitude angle calculation method based on extended Krylov angles includes:

[0100] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0101] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0102] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0103] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation compliant attitude angle calculation method based on extended Krylov angle are as follows:

[0104] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0105] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0106] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψk+1 γ k+1 and ξ k+1 The solution steps are as follows

[0107] (3.1) Given the values ​​of the compliant variable structure parameters k1, k2, and Δβ, calculate the angular velocity correction value of the compliant variable structure based on the given information.

[0108]

[0109] In the formula, (ψ1, γ1) = (90°, 0°), (ψ2, γ2) = (90°, 180°), (ψ3, γ3) = (90°, -180°), (ψ4, γ4) = (270°, 0°), (ψ5, γ5) = (270°, 180°), (ψ6, γ6) = (270°, -180°), (ψ7, γ7) = (-90°, 180°), (ψ8, γ8) = (-90°, 0°), (ψ9, γ9) = (-90°, -180°) are 9 singular points.

[0110] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0111]

[0112] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0113]

[0114] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0115] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0116] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0117] In step (5), the updated coordinate transformation matrix will be used. And apparent acceleration and gravitational acceleration As the velocity differential equation The input is integrated to obtain the updated velocity V. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0118] Based on the above implementation methods, the following is an explanation through a set of comparative examples.

[0119] Example of Implementation Method 1:

[0120] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0121] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0122] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0123]

[0124] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0125]

[0126] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0127] Secondly, using the compliant continuous variable structure attitude calculation method of the present invention, the compliant variable structure parameter k1 = -5 × 10 -2 k2 = -3 × 10 -2 Δβ = 30°, the four attitude angles calculated are as follows Figure 5As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 6 As shown in the figure, -180° and 180° of γ are the same point; -90° and 270° of ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps, and it avoids 9 singular points during operation, realizing full attitude calculation, which is beneficial to flight control.

[0128] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 7 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0129] Implementation Method Two:

[0130] like Figure 1 In this embodiment, the inertial navigation attitude angle "|"-shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0131] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0132] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0133] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0134] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "|" shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0135] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0136] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0137] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The solution steps are as follows

[0138] (3.1) Given the value of the compliant variable structure parameter k, and the "|"-shaped active region ψ n ≤ψ≤ψ m Calculate the angular velocity correction value of the compliant variable structure.

[0139]

[0140] Where, when ψ m When <90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2=0°; when ψ n When >90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2 = 180°;

[0141] (3.2) Based on the measured φ k ψ k γk ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0142]

[0143] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0144]

[0145] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0146] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0147] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0148] In step (5), the updated coordinate transformation matrix will be used. And apparent acceleration and gravitational acceleration As the velocity differential equation The input is integrated to obtain the updated velocity V. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0149] Example of Implementation Method Two:

[0150] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0151] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0152] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0153]

[0154] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0155]

[0156] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0157] Secondly, the "|"-shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, and the compliant variable structure parameter k = -4 × 10 -3 ψ n =-45°, ψ m =45°; the four attitude angles calculated are as follows Figure 8 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 9 As shown in the figure, -180° and 180° of γ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps. ψ is restricted to the interval between -45° and 45°, and nine singular points are avoided during operation, achieving full attitude calculation, which is beneficial to flight control.

[0158] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 10 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0159] Implementation Method 3:

[0160] like Figure 1 In this embodiment, the inertial navigation attitude angle "I"-shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0161] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0162] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0163] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0164] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "I"-shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0165] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0166] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0167] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γk+1 and ξ k+1 The solution steps are as follows

[0168] (3.1) Given the value of the compliant variable structure parameter K, and the "I"-shaped active region γ n ≤γ≤γ m Calculate the angular velocity correction value of the compliant variable structure.

[0169]

[0170] Where, when γ n When >0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=90°; when γ m When <0°, γ n and γ m Satisfy (γ) n +γ m ) / 2 = -90°;

[0171] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0172]

[0173] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0174]

[0175] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0176] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0177] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0178] In step (5), the updated coordinate transformation matrix will be used. And apparent acceleration and gravitational acceleration As the velocity differential equation The input is integrated to obtain the updated velocity V. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0179] Example of Implementation Method 3:

[0180] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0181] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0182] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0183]

[0184] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0185]

[0186] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0187] Secondly, the "I"-shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, and the compliant variable structure parameter k = -4 × 10 -3 γ n =45°, γ m =135°; the four attitude angles calculated are as follows Figure 11 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 12As shown in the figure, -180° and 180° of ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps. γ is limited to the range of 45° and 135°, and nine singular points are avoided during operation, achieving full attitude calculation, which is beneficial to flight control.

[0188] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 13 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0189] Implementation Method Four:

[0190] like Figure 1 In this embodiment, the inertial navigation attitude angle "I"-shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0191] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0192] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0193] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0194] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "I"-shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0195] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k The values ​​at time φ are respectively k ψ k γ k and ξ k ;

[0196] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0197] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The solution steps are as follows

[0198] (3.1) Given the value of the compliant variable structure parameter k, and the "I"-shaped active region γ n1 ≤γ≤γ m1 And γ n2 ≤γ≤γ m2 , and γ m2 <γ<γ n1 And ψ n ≤ψ≤ψ m Calculate the angular velocity correction value of the compliant variable structure.

[0199]

[0200] Among them, the interval parameter (γ) n1 +γ m1 ) / 2=90°、(γ n2 +γ m2 ) / 2=-90°; when ψ m When <90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2=0°; when ψ n When >90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2 = 180°;

[0201] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0202]

[0203]

[0204] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0205]

[0206] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0207] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0208] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0209] In step (5), the updated coordinate transformation matrix will be... And apparent acceleration and gravitational acceleration As the velocity differential equation The input is integrated to obtain the updated velocity V. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0210] Example of Implementation Method Four:

[0211] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0212] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0213] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0214]

[0215] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0216]

[0217] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0218] Secondly, the "I"-shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, with the compliant variable structure parameter k = -4 × 10 -3 γ n1 =45°, γ m1 =135°, γ n2 =-135°, γ m2 =-45°, ψ n =-45°, ψ m =45°; the four attitude angles calculated are as follows Figure 14 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 15 As shown in the figure, -180° and 180° for φ, γ, and ξ are the same point, and -90° and 270° for ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps, and it avoids 9 singular points during operation, realizing full attitude calculation, which is beneficial to flight control.

[0219] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 16 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0220] Implementation Method 5:

[0221] like Figure 1 In this embodiment, the inertial navigation attitude angle "H"-shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0222] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0223] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0224] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0225] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "H"-shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0226] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0227] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0228] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The solution steps are as follows

[0229] (3.1) Given the value of the compliant variable structure parameter k, and the "H"-shaped active region ψ n1 ≤ψ≤ψ m1 or ψ n2 ≤ψ≤ψ m2 , or ψ m1 <γ<ψ n2 And γ n ≤γ≤γ m Calculate the angular velocity correction value of the compliant variable structure.

[0230]

[0231] Among them, the interval parameter (ψ) n1 +ψ m1 ) / 2=0°、(ψ n2 +ψ m2 ) / 2=180°; when γ n When >0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=90°; when γ m When <0°, γ n and γ m Satisfy (γ) n +γ m ) / 2 = -90°;

[0232] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0233]

[0234]

[0235] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0236]

[0237] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0238] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0239] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0240] In step (5), the updated coordinate transformation matrix will be... And apparent acceleration and gravitational acceleration As the velocity differential equation The input is used to solve the equation, and the updated velocity V is obtained after integration. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0241] Example of Implementation Method 5:

[0242] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0243] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0244] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0245]

[0246] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0247]

[0248] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0249] Secondly, the "H"-shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, with the compliant variable structure parameter k = -4 × 10 -3 ψ n1 =-45°, ψ m1 =45°, ψ n2 =135°, ψ m2 =225°, γ n1 =45°, γ m1 =135°; the four attitude angles calculated are as follows Figure 17 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 18 As shown in the figure, -180° and 180° for φ, γ, and ξ are the same point, and -90° and 270° for ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps, and it avoids 9 singular points during operation, realizing full attitude calculation, which is beneficial to flight control.

[0250] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference]. Figure 19 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0251] Implementation Method Six:

[0252] like Figure 1 In this embodiment, the inertial navigation attitude angle "+" shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0253] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0254] like Figure 2 As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as O-XYZ′, which is the moving frame. Here, the OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0255] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0256] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "+" shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0257] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0258] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0259] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The solution steps are as follows

[0260] (3.1) Given the value of the compliant variable structure parameter k, and the "+" shaped active region γ n ≤γ≤γ m or ψ n ≤ψ≤ψ m Calculate the angular velocity correction value of the compliant structure.

[0261]

[0262] Where, when γ n When >0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=90°; when γ m When <0°, γ n and γ m Satisfy (γ) n +γ m ) / 2=-90°; when ψ m When <90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2=0°; when ψ n When >90°, ψ n and ψ m Satisfy (ψ) n +ψ m ) / 2 = 180°;

[0263] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0264]

[0265]

[0266] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0267]

[0268] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0269] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0270] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0271] In step (5), the updated coordinate transformation matrix will be... And apparent acceleration and gravitational acceleration As the velocity differential equation The input is used to solve the equation, and the updated velocity V is obtained after integration. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0272] Example of Implementation Method Six:

[0273] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0274] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0275] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0276]

[0277] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0278]

[0279] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0280] Secondly, the "+" shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, and the compliant variable structure parameter k = -4 × 10 -3 γ n =45°, γ m =135°, ψ n =-45°, ψ m =45°; the four attitude angles calculated are as follows Figure 20 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 21 As shown in the figure, -180° and 180° for φ, γ, and ξ are the same point, and -90° and 270° for ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps, and it avoids 9 singular points during operation, realizing full attitude calculation, which is beneficial to flight control.

[0281] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 22 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0282] Implementation Method Seven:

[0283] like Figure 1 In this embodiment, the inertial navigation attitude angle "#" shaped trajectory compliance calculation method based on extended Krylov angle includes:

[0284] In this embodiment, the Krylov angle is extended. This describes the relationship between the navigation coordinate system and the body coordinate system. The navigation coordinate system arrives at the body coordinate system after four rotations, and the rotation angles corresponding to the four rotations are denoted as yaw angles. Pitch angle ψ, roll angle γ, and extended pitch angle ξ. Among these, yaw angle... The pitch angle ψ, roll angle γ, and extended pitch angle ξ all range from -180° to +180°.

[0285] like Figure 2As shown, the body coordinate system corresponding to the strapdown inertial system is denoted as OX′Y′Z′, which is the moving frame. The OX′ axis represents the longitudinal axis of the carrier, the OZ′ axis represents the transverse and longitudinal axes of the carrier, and the OY′ axis, along with the OX′ and OZ′ axes, forms a right-handed coordinate system. The navigation coordinate system describing the carrier's attitude angles is denoted as O-XYZ, which is the fixed frame. Initially, the OX axis points east, the OY axis points north, and the OZ axis points upwards. The origins of the body coordinate system OX′Y′Z′ and the navigation coordinate system O-XYZ coincide, both originating from the geometric center of the strapdown inertial system.

[0286] Preferably, the rotation process from the navigation coordinate system to the body coordinate system is as follows: the navigation coordinate system O-XYZ rotates around the OZ axis. Arrive at coordinate system O-LNZ; coordinate system O-LNZ rotates ψ about the ON axis to arrive at coordinate system O-QNM; coordinate system O-QNM rotates γ about the OQ axis to arrive at coordinate system O-QY′P; coordinate system O-QY′P rotates ξ about the OY′ axis to arrive at the body coordinate system OX′Y′Z′.

[0287] During the rotation, the angular velocity of the strapdown inertial system relative to the navigation coordinate system is: The implementation steps of the inertial navigation "#" shaped trajectory compliance attitude angle calculation method based on extended Krylov angle are as follows:

[0288] (1) The attitude angles φ, ψ, γ and ξ are calculated at t k φ at time 1 and 2 respectively k ψ k γ k and ξ k ;

[0289] (2) Based on the angular velocity output by the gyroscope installed on the strapdown inertial system, the value at t is obtained. k angular velocity of the body relative to the navigation frame at any moment

[0290] (3) Let the sampling time be ΔT, then at the next time t k+1 =t k The four attitude angles φ of +ΔT k+1 ψ k+1 γ k+1 and ξ k+1 The solution steps are as follows

[0291] (3.1) Given the value of the compliant variable structure parameter k, and the "#" shaped active region γ n1 ≤γ≤γ m1 or γ n2 ≤γ≤γ m2 or ψ n1 ≤ψ≤ψ m1 or ψn2 ≤ψ≤ψ m2 Calculate the angular velocity correction value of the compliant variable structure.

[0292]

[0293] Wherein, the interval parameter γ n2 <γ m2 <γ n1 <γ m1 , ψ n1 <ψ m1 <ψ n2 <ψ m2 , and (γ n1 +γ m1 ) / 2=90°、(γ n2 +γ m2 ) / 2=-90°、(ψ n1 +ψ m1 ) / 2=0°、(ψ n2 +ψ m2 ) / 2 = 180°.

[0294] (3.2) Based on the measured φ k ψ k γ k ξ k and and angular velocity correction value Δω k Calculate φ k+1 ψ k+1 γ k+1 and ξ k+1 The specific calculation formula is as follows:

[0295]

[0296]

[0297] (4) Put φ k+1 ψ k+1 γ k+1 and ξ k+1 Substitute into the following formula and solve for t. k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is:

[0298]

[0299] (5) Based on the integral update solution, the coordinate transformation matrix is ​​updated, and velocity and position updates are supported to improve the accuracy of inertial navigation.

[0300] In step (1), the yaw angle φ, pitch angle ψ, roll angle γ and extended pitch angle ξ range from -180° to +180°, and the pitch angle ψ ranges from -90° to +270°.

[0301] The gyroscopes installed on the strapdown inertial system body are either three single-degree-of-freedom gyroscopes or two two-degree-of-freedom gyroscopes.

[0302] In step (5), the updated coordinate transformation matrix will be used. And apparent acceleration and gravitational acceleration As the velocity differential equation The input is integrated to obtain the updated velocity V. The updated velocity V is then used as the position differential equation. The input is integrated to obtain the updated position r.

[0303] Example of Implementation Method Seven:

[0304] The attitude angles of an aircraft during a certain full-attitude motion were calculated using strapdown inertial navigation (“Full-attitude navigation calculation method based on extended Krylov angle”, Journal of Chinese Inertial Technology, Vol.29 No.5, 2021).

[0305] First, a causal-constrained partitioned discrete variable structure attitude calculation method is adopted. This method is characterized by dividing the phase plane formed by the pitch angle ψ and roll angle γ into two regions. In region 1 (… or ) contains singularities, while region 2 (condition is) It does not contain singularities.

[0306] To avoid the trajectory of motion in region 1 approaching a singularity, ψ = 0 is set when calculating the attitude. The calculation method is as follows:

[0307]

[0308] In region 2, φ = 0 is achieved through state transition, and the solution method is as follows:

[0309]

[0310] The four attitude angles calculated are as follows Figure 3 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 4 As shown, the curves for the four attitude angles are discontinuous, which is detrimental to flight control.

[0311] Secondly, the "#"-shaped track compliant continuous variable structure attitude calculation method of the present invention is adopted, and the compliant variable structure parameter k1 = -4 × 10 -3 γ n1=30°, γ m1 =150°, γ n2 =-150°, γ m2 =-30°, ψ n1 =-60°、ψ m1 =60°, ψ n2 =120°, ψ m2 =240°; the four attitude angles calculated are as follows Figure 23 As shown, the trajectories of pitch angle ψ and roll angle γ in the phase plane are as follows: Figure 24 As shown in the figure, -180° and 180° of γ are the same point; -90° and 270° of ψ are the same point. It can be seen that the change process of the four attitude angles is a continuous curve without jumps, and it avoids 9 singular points during operation, realizing full attitude calculation, which is beneficial to flight control.

[0312] The speed and position navigation deviations caused by the aforementioned attitude angle errors are small (position error less than 20m) and can be ignored. Based on this, the roll angle γ, pitch angle ψ, and yaw angle... The three-dimensional trajectory of the aircraft motion calculated by the extended pitch angle ξ navigation solution is shown in [reference needed]. Figure 25 As can be seen, the high-attack, high-maneuverability motion of the aircraft is reproduced very well.

[0313] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0314] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Set compliant structural parameters k 1 = -0.05 k 2 = -0.03, given the radius Δ of the singular circle centered at the singular point. β The value is used to determine the angular velocity correction value for the compliant variable structure: In the formula, ( ψ 1, γ 1) = (90°, 0°), ( ψ 2, γ 2) = (90°, 180°), ( ψ 3, γ 3) = (90°, -180°), ( ψ 4, γ 4) = (270°, 0°), ( ψ 5, γ 5) = (270°, 180°), ( ψ 6, γ 6) = (270°, -180°), ( ψ 7, γ 7) = (-90°, 180°), ( ψ 8, γ 8) = (-90°, 0°), ( ψ 9, γ 9) = (-90°, -180°) are 9 singular points; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

2. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Let the range of the "|" shaped active area be... ψ n ψ ψ m ,in, ψ n This is the lower limit value of the horizontal active area of ​​the "|" shape. ψ m Set the upper limit of the horizontal movement area of ​​the "|" shape; set the compliant variable structure parameters. K The value is -4 10 -3 Determine the angular velocity correction value for the compliant structure: Among them, when ψ m <90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=0 ;when ψ n >90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=180 ; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

3. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: setting an "I-shaped" movable area γ n γ γ m , wherein, γ n is a lower limit value of the longitudinal "I-shaped" movable area, γ m is an upper limit value of the longitudinal "I-shaped" movable area; setting a compliant variable structure parameter K has a value of -4 10 -3 to determine an angular velocity correction value of the compliant variable structure: Among them, when γ n >0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=90 ;when γ m <0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=-90 ; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

4. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Set an "I-shaped" movable area γ n1 γ γ m1 and γ n2 γ γ m2 , and γ m2 < γ < γ n1 and ψ n ψ ψ m , wherein: γ n1 is the lower limit value of the longitudinal upper movable area of the "I-shape", γ m1 is the upper limit value of the longitudinal upper movable area of the "I-shape", γ n2 is the lower limit value of the longitudinal lower movable area of the "I-shape", γ m2 is the upper limit value of the longitudinal lower movable area of the "I-shape", ψ n is the lower limit value of the transverse movable area of the "I-shape", ψ m is the upper limit value of the transverse movable area of the "I-shape"; a compliance variable structure parameter is given K has a value of -4 10 -3 , and the angular velocity correction value of the compliance variable structure is determined as: Among them, the interval parameter ( γ n1 + γ m1 ) / 2=90 、( γ n2 + γ m2 ) / 2=-90 ;when ψ m <90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=0 ;when ψ n >90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=180 ; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

5. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Set up an "H"-shaped activity area ψ n1 ψ ψ m1 and ψ n2 ψ ψ m2 ,and ψ m1 < γ < ψ n2 and γ n γ γ m ,in, ψ n1 This is the lower limit value of the horizontal left-side active area of ​​the "H" shape. ψ m1 This is the upper limit of the horizontal movement area on the left side of the "H" shape; ψ n2 This is the lower limit value of the horizontal right-side active area of ​​the "H" shape. ψ m2 This is the upper limit of the horizontal movement area on the right side of the "H" shape; γ n This is the lower limit value of the "H"-shaped vertical activity area. γ m The upper limit of the "H"-shaped longitudinal active region; given compliant variable structure parameters. K The value is -4 10 -3 Determine the angular velocity correction value for the compliant structure: Among them, the interval parameter ( ψ n1 + ψ m1 ) / 2=0 、( ψ n2 + ψ m2 ) / 2=180 ;when γ n >0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=90 ;when γ m <0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=-90 ; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

6. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Set up a "+" shaped activity area γ n γ γ m or ψ n ψ ψ m ,in, γ n This is the lower limit value of the "+" shaped vertical activity area. γ m This represents the upper limit of the "+" shaped vertical activity area; ψ n This is the lower limit value of the "+" shaped horizontal activity area. ψ m The upper limit of the "+" shaped horizontal movement area; given compliant variable structure parameters. K The value is -4 10 -3 Determine the angular velocity correction value for the compliant structure: Among them, when γ n >0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=90 ;when γ m <0 hour, γ n and γ m satisfy( γ n + γ m ) / 2=-90 ;when ψ m <90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=0 ;when ψ n >90 hour, ψ n and ψ m satisfy( ψ n + ψ m ) / 2=180 ; according to k , ψ k , γ k , ξ k Δ ω k and ,Sure k+1 , ψ k+1 , γ k+1 and ξ k+1 The specific calculation formula is as follows: based on k+1 , ψ k+1 , γ k+1 and ξ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; After performing an integration operation based on the apparent acceleration, gravitational acceleration and the coordinate transformation matrix, velocity update calculation is completed.

7. A method for calculating inertial navigation attitude angles based on extended Krylov angles, characterized in that, Comprising: In strapdown inertial navigation, the relationship between the navigation coordinate system and the body coordinate system is described by four extended Krylov angles, including the yaw angle. Pitch angle ψ Roll angle γ and extended pitch angle ξ ; During the navigation recursive solution process, determine the relative... t At time 0, the k Time series t k Attitude angles at any given moment, including yaw angles k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k ,in, t k = t 0+ k Δ T Δ T Sampling time; Based on the angular velocity output by the gyroscope mounted on the strapdown inertial system, the following is obtained: t k angular velocity of the body relative to the navigation frame at any moment ; Based on yaw angle k Pitch angle ψ k Roll angle γ k and extended pitch angle ξ k and angular velocity Solution t k The next moment after the moment t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 ; Solve the next time step t k+1 = t k +Δ T The four attitude angles k+1 , ψ k+1 , γ k+1 and ξ k+1 The methods include: Set the activity area in the shape of "#". γ n1 γ γ m1 or γ n2 γ γ m2 or ψ n1 ψ ψ m1 or ψ n2 ψ ψ m2 ,in, ψ n1 This is the lower limit value of the horizontal left-hand active area of ​​the "#" shape. ψ m1 This is the upper limit of the horizontal active area to the left of the "#" shape; ψ n2 This is the lower limit value of the horizontal right-hand active area of ​​the "#" shape. ψ m2 This is the upper limit of the horizontal active area to the right of the "#" shape; γ n1 This is the lower limit value of the upper vertical active area of ​​the "#" shape. [[ID=3 m1 This represents the upper limit of the vertically oriented upper area of ​​the "#" shape. ​ n2 This is the lower limit value of the vertical lower part of the "#" shaped active area. ​ m2 The upper limit of the vertical lower part of the "#" shaped active area; given the compliant variable structure parameters. K The value is -4 10 -3 Determine the angular velocity correction value for the compliant structure: Wherein, interval parameter ​ n2 < ​ m2 < ​ n1 < ​ m1 , ​ n1 < ​ m1 < ​ n2 < ​ m2 ,and( ​ n1 + ​ m1 ) / 2=90 and( ​ n2 + ​ m2 ) / 2=-90 and( ​ n1 + ​ m1 ) / 2=0 and( ​ n2 + ​ m2 ) / 2=180 ; according to k , ​ k , ​ k , ​ k Δ ​ k and ,Sure k+1 , ​ k+1 , ​ k+1 and ​ k+1 The specific calculation formula is as follows: based on k+1 , ​ k+1 , ​ k+1 and ​ k+1 Solve t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles at each moment; ​ 8. The inertial navigation attitude angle calculation method according to any one of claims 1 to 7, characterized in that, ​ 9. The inertial navigation attitude angle calculation method according to any one of claims 1 to 7, characterized in that, This solution method is based on a strapdown inertial system fixed to the carrier, and the body coordinate system corresponding to the strapdown inertial system is: ​ y z The navigation coordinate system corresponding to the carrier's motion attitude angle is described as follows: ​ The origins of the two coordinate systems coincide, and the relationship between them is described using four Krylov angles. The navigation coordinate system reaches the body coordinate system after four rotations. The specific rotation process is as follows: Navigation coordinate system ​ Around ​ Shaft rotation Angle, arrive ​ ; ​ Go around again ​ Shaft rotation ​ Angle, arrive ​ ; ​ Around ​ Shaft rotation ​ Angle, arrive ​ P ;at last, ​ P Around ​ Rotation ​ Angle, arrive ​ y z .

10. The inertial navigation attitude angle calculation method according to claim 9, characterized in that, ​ 11. The inertial navigation attitude angle calculation method according to any one of claims 1 to 7, characterized in that, t k+1 The coordinate transformation matrix from the navigation coordinate system to the body coordinate system, expressed in terms of four Krylov angles, at time t is: in, p Indicates the navigation coordinate system. b Indicates the body coordinate system.

12. The inertial navigation attitude angle calculation method according to any one of claims 1 to 7, characterized in that, ​

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