Strapdown inertial navigation method based on north-east coordinate system

Abstract

The invention belongs to the technical field of inertial navigation, and particularly relates to a strapdown inertial navigation method based on a north-east coordinate system. On the basis of a low-cost MEMS inertial navigation system, the method is simplified on the basis of an original complete and complex strapdown inertial navigation method, a northern-east coordinate system is adopted as a navigation reference coordinate system of a near-ground medium-low speed carrier, a front-upper-right coordinate system is adopted as a carrier coordinate system, a navigation solution equation can be easily and visually established, and the navigation precision is improved. On the premise of ensuring the precision of the navigation system, complex parameter calculation is avoided, and the calculation burden of the system is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, in particular to a strapdown inertial navigation method based on a north-east coordinate system. Background Art

[0002] With the development of MEMS manufacturing technology, MEMS inertial sensors have been widely used in the military, industrial and even civilian consumer electronics fields due to their low cost, small size and low power. However, the accuracy of MEMS inertial sensors is still relatively low. In low-cost MEMS inertial navigation systems, the gyroscope accuracy (zero bias repeatability) is on the order of 0.1° / s, and the accelerometer accuracy is on the order of 5mg. For vehicles traveling at medium and low speeds, in the inertial navigation proportional equation, the magnitude of the harmful acceleration part is about 1mg, which is less than the error of the sensor itself, so the influence of the earth's rotation and the earth's curvature can be ignored.

[0003] Selecting a suitable navigation reference coordinate system is beneficial to the design and application of guidance, navigation and control systems for low-speed and medium-speed vehicles near the ground. The local horizontal coordinate system is used to describe the attitude, speed and position of the vehicle in near-ground motion, and can be divided into the northeast celestial coordinate system, the north celestial east coordinate system, the northeast earth coordinate system, etc. The z-axis of the northeast earth coordinate system points to the ground, which is the same as the direction of gravity. This makes the description of gravity acceleration simpler and more intuitive. The gravity acceleration can be associated with the z-axis, which is convenient for data processing of gyroscopes and accelerometers.

[0004] The strapdown inertial navigation method of common MEMS inertial navigation systems is complex, and the speed update method takes into account the rotation error compensation of the speed, the paddling error compensation of the speed, and the harmful acceleration caused by the rotation of the earth and the curvature of the earth. For high-precision MEMS inertial navigation systems, it is necessary to consider such errors, but the sensor errors of low-cost MEMS inertial navigation systems are large. Considering such errors will increase the amount of calculation and have little effect on reducing the inertial navigation solution error.

[0005] Existing strapdown inertial navigation system adopts northeast celestial coordinate system as navigation coordinate system, but its coordinate axis z-axis points to the opposite direction of gravity acceleration, which makes it unintuitive to describe gravity acceleration.Other types of navigation coordinate systems, such as earth-centered earth-fixed coordinate system, are applicable to positions in the global scope, but for the real-time navigation of near-earth or local motion, the amount of calculation is large, and not intuitive enough.At present, there is no perfect strapdown inertial navigation method based on northeast terrestrial coordinate system to be applied on low-cost MEMS inertial navigation system, so the present invention proposes a kind of strapdown inertial navigation method based on northeast terrestrial coordinate system for low-cost MEMS inertial navigation system. Summary of the invention

[0006] The purpose of the present invention is to provide a strapdown inertial navigation method based on a north-eastern coordinate system, based on the north-eastern navigation coordinate system and a low-cost MEMS inertial navigation system, to overcome the problems of large error and low calculation accuracy of the low-cost MEMS inertial navigation system, so as to realize strapdown inertial navigation.

[0007] The technical solution to achieve the purpose of the present invention is: a strapdown inertial navigation method based on a north-east coordinate system, wherein the strapdown inertial navigation method comprises the following specific steps:

[0008] S1: Define the coordinate system of the MEMS inertial navigation system;

[0009] S2: Construct the transformation relationship between the coordinate systems in the inertial navigation system;

[0010] S3: According to the conversion relationship between the coordinate systems of the inertial navigation system, the relationship between the rotation angular velocities of the coordinate systems is determined;

[0011] S4: Determine the relationship between Euler angles, quaternions, and direction cosines;

[0012] S5: Determine the attitude update method, velocity update method, and position update method in the north-east coordinate system, and then obtain information related to the carrier attitude, velocity, and position.

[0013] Compared with the prior art, the present invention has the following significant advantages:

[0014] The present invention is based on a low-cost MEMS inertial navigation system, adopts a "north-east-ground" coordinate system as a navigation reference coordinate system for a medium- and low-speed carrier near the ground, and adopts a "front-up-right" coordinate system as a carrier coordinate system, which makes it simpler and more intuitive to describe the acceleration of gravity. The acceleration of gravity can be associated with the z-axis, which is convenient for data processing of a gyroscope and an accelerometer on the carrier, and is conducive to simply and intuitively establishing a navigation solution equation. Under the premise of ensuring the accuracy of the navigation system, complex parameter calculations are avoided, thereby reducing the calculation burden of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 :North-east coordinate system strapdown inertial navigation system mechanical arrangement block diagram;

[0016] Figure 2 : Simulation diagram of attitude error of strapdown inertial navigation method provided by the present invention;

[0017] Figure 3 : Velocity error simulation diagram of the strapdown inertial navigation method provided by the present invention;

[0018] Figure 4 : Position error simulation diagram of the strapdown inertial navigation method provided by the present invention. DETAILED DESCRIPTION

[0019] The following will be combined with the attached embodiment of the present invention Figure 1-4 , the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] S1: Define the coordinate system of the MEMS inertial navigation system;

[0021] S1.1: Define the geocentric inertial coordinate system: This coordinate system does not rotate with the Earth, its origin is at the center of the Earth, and x i The axis points to the vernal equinox within the equator, z i The axis is along the Earth's rotation axis, y i Axis and x i Axis, z i The axes form a right-hand system, denoted as the i system;

[0022] S1.2: Define the Earth coordinate system: This coordinate system is fixed to the Earth, with its origin at the center of the Earth, and x e Axis, y e The axis lies in the equatorial plane, x e The axis points to the prime meridian, z e The axis is the earth's rotation axis, denoted as e-system;

[0023] S1.3: Define the carrier coordinate system:

[0024] Define the b system, the origin of the coordinate system is the center of mass of the aircraft, x b The axis is along the carrier's horizontal axis to the right, y b The axis moves forward along the longitudinal axis of the carrier, z b The axis is upward along the vertical axis of the carrier, which is the "right front upper" system, recorded as system b;

[0025] Define b1 system, the origin of coordinates is the center of mass of the aircraft, x b1 The y axis is the symmetry axis of the aircraft shell, pointing to the head. b1 The axis is in the main symmetry plane of the aircraft and is perpendicular to the x b1 Axis, upward is positive, z b1 Axis and x b1 Axis, y b1 The axes form a right-hand system, which is the "front-up-right" system, recorded as b1 system.

[0026] Define the b2 system, the origin of the coordinate system is the center of mass of the aircraft, x b2 The y axis is the symmetry axis of the aircraft shell, pointing to the head. b2 The axis is to the right of the aircraft's horizontal axis and perpendicular to the x b2 Axis, z b2 Axis and x b2 Axis, yb2 The axes form a right-hand system, which is the "front right lower" system, recorded as b2 system.

[0027] S1.4: Define the navigation coordinate system:

[0028] Define n system, the origin is at the center of mass of the carrier, x n The axis points eastward along the reference circle, y n The axis points north along the meridian of the reference ellipsoid, z n The axis points in the opposite direction of the center of the earth along the outer normal of the reference ellipsoid, which is the "northeast sky"

[0029] System, recorded as n system.

[0030] Define the n1 system, with the origin at the center of mass of the carrier, x n1 The axis points north along the meridian of the reference ellipsoid, y n1 The axis points eastward along the reference circle, z n1 The axis points to the center of the earth along the outer normal of the reference ellipsoid. This is the "northeast earth".

[0031] System, denoted as n1 system.

[0032] S2: Construct the conversion relationship between the coordinate systems in the inertial navigation system.

[0033] The specific steps are as follows:

[0034] S2.1: According to the definition of the navigation coordinate system, determine the direction cosine matrix from the "northeast sky" coordinate system (n system) to the "northeast earth" coordinate system (n1 system) for:

[0035]

[0036] Wherein, M1 represents the basic rotation matrix with the coordinate axis x-axis as the rotation axis; M3 represents the basic rotation matrix with the coordinate axis z-axis as the rotation axis;

[0037] S2.2: Determine the direction cosine matrix from the Earth coordinate system (e system) to the "Northeast Sky" coordinate system (n system) for:

[0038]

[0039] Where L represents the latitude of the carrier at any time; λ represents the longitude of the carrier at any time;

[0040] S2.3: According to the chain rule, the direction cosine matrix from the earth coordinate system (e system) to the "northeast" coordinate system (n1 system) can be determined from equations (1) and (2): for:

[0041]

[0042] S2.4: Attitude transformation matrix from the "northeast" coordinate system (n1 system) to the "front right lower" coordinate system (b2 system) for:

[0043]

[0044] Wherein, M2 represents the basic rotation matrix with the y-axis as the rotation axis; θ is the pitch angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system; γ is the roll angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system; ψ is the yaw angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system, and north-east is positive.

[0045] S2.5: The direction cosine matrix from the "front lower right" coordinate system (b2 system) to the "front upper right" coordinate system (b1 system) is:

[0046]

[0047] S2.6; According to the chain rule, the attitude transformation matrix from the "front-up-right" system (b1 system) to the "north-east-ground" system (n1 system) represented by the Euler angle can be determined by equations (4) and (5): for:

[0048]

[0049] S3: According to the conversion relationship between the coordinate systems of the inertial navigation system, the relationship between the rotation angular velocities of the coordinate systems is determined;

[0050] The specific steps are as follows:

[0051] S3.1: According to the chain rule, the projection of the rotational angular velocity of the Earth coordinate system (e system) relative to the Earth-centered inertial coordinate system (i system) in the “north-east” coordinate system (n1 system) can be determined from equation (3): for:

[0052]

[0053] In the formula, ω ie is the angular velocity of the Earth's rotation; is the projection of the Earth's rotation angular velocity in the Earth coordinate system;

[0054] S3.2: Projection of the rotational angular velocity of the Northeast Sky coordinate system (n system) relative to the Earth coordinate system (e system) in the Northeast Sky coordinate system (n system) for:

[0055]

[0056] In the formula, v N 、vE are the north and east velocities of the carrier respectively; h is the height of the carrier; R M , R N They are respectively the principal curvature radius of the earth's meridian circle at the carrier and the principal curvature radius of the earth's meridian circle at the carrier, and the specific formula is:

[0057]

[0058] In the formula, R e represents the length of the earth's semi-major axis; f represents the earth's elliptical flattening;

[0059] S3.3: According to the chain rule, the projection of the rotation angular velocity of the “northeast” coordinate system (n1 system) relative to the earth coordinate system (e system) in the “northeast” coordinate system (n1 system) can be determined from equations (1) and (8):

[0060]

[0061] S3.4: From equations (7) and (9), the projection of the rotational angular velocity of the “northeast” coordinate system (n1 system) relative to the geocentric inertial coordinate system (i system) in the “northeast” coordinate system (n1 system) can be determined as:

[0062]

[0063] S4: Determine the relationship between Euler angles, quaternions, and direction cosines. The specific steps are as follows:

[0064] S4.1: Coordinate transformation matrix from the "front-up-right" coordinate system (b1 system) to the "north-east-ground" coordinate system (n1 system) represented by quaternions for:

[0065]

[0066] In the formula, q0 represents the real part of the quaternion, q1, q2, q3 represent the imaginary part of the quaternion respectively;

[0067] S4.2: From the "front-up-right" coordinate system (b1 system) to the "north-east-ground" coordinate system (n1 system) represented by the direction cosine matrix

[0068] Coordinate transformation matrix for:

[0069]

[0070] In the formula, C 11 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 12 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 13 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 21 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 22 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 23 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 31 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 32 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 33 Indicates b1 series Axis and n1 system Cosine of the axis angle;

[0071] S4.3: Quaternions (q0 q1 q2 q3) and direction cosines are equivalent. Let the coordinate transformation matrix represented by the quaternion be Each element in is transformed into the coordinate matrix represented by the direction cosine matrix If the corresponding elements in are equal, then

[0072] The relationship between quaternion and direction cosine matrix is:

[0073]

[0074] S4.4: According to equations (6), (12) and (13), the quaternion represented by the Euler angle can be determined as:

[0075]

[0076] S4.5: Similarly, the Euler angle represented by the quaternion can be determined as

[0077]

[0078] S5: Determine the attitude update method, speed update method, and position update method of the carrier in the north-east coordinate system, and then obtain information related to the attitude, speed, and position of the carrier; the specific steps are as follows:

[0079] S5.1: carrier posture update method;

[0080] The attitude update method uses quaternions for solution. According to the matrix chain rule, we have

[0081]

[0082] In the formula, t m The quaternion of attitude transformation at the moment; It means that the i system is used as the reference coordinate system, and the n1 system is from t m Time to t m-1 The quaternion of rotation change at the moment; Indicates that the i system is used as the reference coordinate system, and the b1 system is from t m-1 Time to t m The quaternion of rotation change at the moment; t m-1 The quaternion of attitude transformation at the moment;

[0083] Taking the geocentric inertial coordinate system (i system) as the reference coordinate system, the "northeast" system (n1 system) is from t m Time to t m-1 The quaternion of rotation change at the moment is:

[0084]

[0085] In the formula, is the angular velocity of the Earth's rotation in the time period [t m-1 ,t m ] is the negative of the corresponding angular increment, for The modulus value is:

[0086]

[0087] In the formula, Indicates t m The projection of the rotational angular velocity of system n1 relative to system i on system n1 at time t, ΔT is m-1 Time and t m The time difference between moments.

[0088] Taking the geocentric inertial coordinate system (i system) as the reference coordinate system, the “front-up-right” system (b1 system) is calculated from t m-1 Time to t m The quaternion of rotation change at the moment is:

[0089]

[0090] In the formula, is the time period [t m-1 ,t m ] corresponds to the angular increment, for The modulus value is:

[0091]

[0092] In the formula, Indicates t m The angular velocity output by the gyroscope on the carrier at this moment.

[0093] S5.2: carrier speed update method;

[0094] The simplified specific force equation is:

[0095]

[0096] In the formula, Indicates the velocity of the carrier in the "northeast" coordinate system The first derivative with respect to time t, where v D is the ground velocity of the carrier; is the specific force in the “front, top, right” coordinate system, where for Specific force in the axial direction, for Specific force in the axial direction, for Specific force in the axial direction; is the gravity vector in the “north-east” coordinate system, where And let g0=9.7803m / s 2 ;

[0097] By integrating and discretizing the above equation, we get the velocity equation of the carrier in the “north-east” coordinate system:

[0098]

[0099] In the formula, t m ,t m-1 The velocity of the carrier at the moment in the "north-east" coordinate system; is the time period [t m-1 ,t m ], the specific formula is as follows:

[0100]

[0101] In the formula, is with The corresponding attitude matrix; Δθ m is the accelerometer in the time period [t m-1 ,t m ] The angular increment of the output; Δvm is the accelerometer in the time period [t m-1 ,t m ]Specific force increment of internal output;

[0102] S5.3 Carrier location update method:

[0103] The differential equation for determining latitude is:

[0104]

[0105] In the formula, represents the first derivative of latitude L with respect to time t;

[0106] The differential equation for determining longitude is:

[0107]

[0108] In the formula, represents the first derivative of longitude λ with respect to time t;

[0109] Determine the highly differential equation as:

[0110]

[0111] In the formula, represents the first derivative of height h with respect to time t;

[0112] Combining formulas (24), (25) and (26), the position differential equation of the carrier is obtained as follows:

[0113]

[0114] In the formula, represents the first-order derivative of the position matrix p with respect to time t, M pv express The coefficient matrix of is expressed as:

[0115]

[0116] Example

[0117] Assuming that the carrier is a low-speed, short-distance UAV equipped with a low-cost MEMS inertial navigation system, some typical flight motion features are combined and spliced ​​to simulate a relatively simple carrier motion trajectory. The strapdown inertial navigation method of the present invention is used to calculate the attitude, speed, and position information. The navigation data calculated by the inertial navigation is compared with the original trajectory data to obtain Figure 2 , Figure 3 and Figure 4 The inertial navigation error curve. The simulation time is 42.2s. Given the initial inertial navigation error, Figure 2It can be seen that the maximum value of the attitude error is 1.3°; Figure 3 It can be seen that the maximum absolute value of the velocity error is 4.5m / s; Figure 4 It can be seen that the maximum absolute value of the position error is 79.3m. Therefore, the above error values ​​are all within the error range of the low-cost MEMS inertial navigation system, proving that the strapdown inertial navigation method based on the north-east coordinate system of the present invention is effective and can be used in low-cost MEMS inertial navigation systems.

Claims

1. A strapdown inertial navigation method based on a north-east coordinate system, characterized in that: The specific steps of the linked inertial navigation method are as follows: S1: Define the coordinate system of the MEMS inertial navigation system; S2: Construct the transformation relationship between the coordinate systems in the inertial navigation system; S3: According to the conversion relationship between the coordinate systems of the inertial navigation system, the relationship between the rotation angular velocities of the coordinate systems is determined; S4: Determine the relationship between Euler angles, quaternions, and direction cosines; S5: Determine the attitude update method, velocity update method, and position update method in the north-east coordinate system, and then obtain information related to the carrier attitude, velocity, and position.

2. The strapdown inertial navigation method based on the north-east coordinate system according to claim 1, characterized in that: In S1, the specific steps for defining the coordinate system of the MEMS inertial navigation system are as follows: S1.1: Define the geocentric inertial coordinate system: This coordinate system does not rotate with the Earth, its origin is at the center of the Earth, and x i The axis points to the vernal equinox within the equator, z i The axis is along the Earth's rotation axis, y i Axis and x i Axis, z i The axes form a right-hand system, denoted as the i system; S1.2: Define the Earth coordinate system: This coordinate system is fixed to the Earth, with its origin at the center of the Earth, and x e Axis, y e The axis lies in the equatorial plane, x e The axis points to the prime meridian, z e The axis is the earth's rotation axis, denoted as e-system; S1.3: Define the carrier coordinate system: including the definition of the "front right upper" system, the "front upper right" system, and the "front right lower" system; S1.4: Define navigation coordinate systems: This includes defining the "northeast celestial" system and the "northeast terrestrial" system.

3. The strapdown inertial navigation method based on the north-east coordinate system according to claim 2, characterized in that: In S1.3, the specific method for defining the carrier coordinate system is: Define the b system, the origin of the coordinate system is the center of mass of the aircraft, x b The axis is along the carrier's horizontal axis to the right, y b The axis moves forward along the longitudinal axis of the carrier, z b The axis is upward along the vertical axis of the carrier, which is the "right front upper" system, recorded as system b; Define b1 system, the origin of coordinates is the center of mass of the aircraft, x b1 The axis is the symmetry axis of the aircraft shell, pointing to the head. y b1 The axis is in the main symmetry plane of the aircraft and is perpendicular to the x b1 Axis, upward is positive, z b1 Axis and x b1 Axis, y b1 The axes form a right-hand system, which is the "front-up-right" system, denoted as b1 system; Define the b2 system, the origin of the coordinate system is the center of mass of the aircraft, x b2 The axis is the symmetry axis of the aircraft shell, pointing to the head. y b2 The axis is to the right of the aircraft's horizontal axis and perpendicular to the x b2 Axis, z b2 Axis and x b2 Axis, y b2 The axes form a right-hand system, which is the "front right lower" system, recorded as b2 system.

4. The strapdown inertial navigation method based on the north-east coordinate system according to claim 3, characterized in that: In S1.4, the specific method for defining the navigation coordinate system is: Define n system, the origin is at the center of mass of the carrier, x n The axis points eastward along the reference circle, y n The axis points north along the meridian of the reference ellipsoid, z n The axis points in the opposite direction of the center of the earth along the outer normal of the reference ellipsoid. This is the "northeastern" system, recorded as n system; Define the n1 system, with the origin at the center of mass of the carrier, The axis points north along the meridian of the reference ellipsoid. The axis points eastward along the reference circle. The axis points toward the center of the earth along the outer normal of the reference ellipsoid. This is the "northeast" system, denoted as the n1 system.

5. The strapdown inertial navigation method based on the north-east coordinate system according to claim 4, characterized in that: In S2, the conversion relationship between the coordinate systems is as follows: S2.1: According to the definition of the navigation coordinate system, determine the direction cosine matrix from the "northeast sky" coordinate system to the "northeast earth" coordinate system: S2.2: Determine the direction cosine matrix from the Earth coordinate system to the "Northeast Sky" coordinate system: S2.3: According to the chain rule, the direction cosine matrix from the earth coordinate system to the "north-east" coordinate system is determined as: In the formula, Direction cosine matrix from Earth coordinate system to "North-East" coordinate system is the direction cosine matrix from the "northeast sky" coordinate system to the "northeast earth" coordinate system, is the direction cosine matrix from the earth coordinate system to the "northeast sky" coordinate system, where L represents the latitude of the carrier at any time; λ represents the longitude of the carrier at any time; S2.4: Determine the attitude transformation matrix from the "northeast ground" coordinate system to the "front right bottom" coordinate system: S2.5: Direction cosine matrix from the "front lower right" coordinate system to the "front upper right" coordinate system; S2.6; According to the chain rule, the attitude transformation matrix from the "front-up-right" system to the "north-east-ground" system represented by the Euler angle is determined as: In the formula, is the attitude transformation matrix from the "front-up-right" system to the "north-east-ground" system, is the attitude transformation matrix from the "northeast ground" coordinate system to the "front right bottom" coordinate system, is the direction cosine matrix from the "front lower right" coordinate system to the "front upper right" coordinate system, is the pitch angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system; γ is the roll angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system; ψ is the yaw angle of the "front lower right" coordinate system relative to the "northeast ground" coordinate system, and north-east is positive.

6. The strapdown inertial navigation method based on the north-east coordinate system according to claim 4, characterized in that: In step S3, the specific steps are as follows: S3.1: Determine the projection of the rotational velocity of the Earth coordinate system relative to the Earth-centered inertial coordinate system in the "North-East" coordinate system according to the chain rule for: In the formula, ω ie is the angular velocity of the Earth's rotation; is the projection of the Earth's rotation angular velocity in the Earth coordinate system, and L represents the latitude of the carrier at any time; S3.2: Determine the projection of the rotational angular velocity of the "Northeast Sky" coordinate system relative to the Earth coordinate system in the "Northeast Sky" coordinate system for: In the formula, v N 、v E are the north and east velocities of the carrier respectively; h is the height of the carrier; R M , R N are respectively the principal curvature radius of the earth's meridian circle at the carrier and the principal curvature radius of the earth's meridiem circle at the carrier; S3.3: According to the chain rule, the projection of the rotational angular velocity of the "northeast" coordinate system relative to the earth coordinate system in the "northeast" coordinate system is determined as: S3.4: Determine the projection of the angular velocity of the "northeast" coordinate system relative to the geocentric inertial coordinate system in the "northeast" coordinate system for:

7. The strapdown inertial navigation method based on the north-east coordinate system according to claim 4, characterized in that: In step S4, the specific steps are as follows: S4.1: Coordinate transformation matrix from the "front-up-right" coordinate system to the "north-east-ground" coordinate system represented by quaternions for: In the formula, q0 represents the real part of the quaternion, q1, q2, q3 represent the imaginary part of the quaternion respectively; S4.2: Coordinate transformation matrix from the "front-up-right" coordinate system to the "north-east-ground" coordinate system represented by the direction cosine matrix for: In the formula, C 11 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 12 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 13 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 21 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 22 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 23 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 31 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 32 Indicates b1 series Axis and n1 system Cosine of the axis angle; C 33 Indicates b1 series Axis and n1 system Cosine of the axis angle; S4.3: Quaternions (q0 q1 q2 q3) and direction cosines are equivalent. Let the coordinate transformation matrix represented by the quaternion be Each element in is transformed into the coordinate matrix represented by the direction cosine matrix If the corresponding elements in are equal, the relationship between the quaternion and the direction cosine matrix is: S4.4: Determine the quaternion represented by the Euler angles: S4.5: Determine the Euler angles represented by the quaternion:

8. The strapdown inertial navigation method based on the north-east coordinate system according to claim 4, characterized in that: In step S5, the specific steps are as follows: S5.1: Carrier posture update method; The attitude update method uses quaternions for solution. According to the matrix chain rule, we have In the formula, t m The quaternion of attitude transformation at the moment; It means that the i system is used as the reference coordinate system, and the n1 system is from t m Time to t m-1 The quaternion of rotation change at the moment; Indicates that the i system is used as the reference coordinate system, and the b1 system is from t m-1 Time to t m The quaternion of rotation change at the moment; t m-1 The quaternion of the attitude transformation at the moment; S5.2: carrier speed update method; The velocity equation of the carrier in the "north-east" coordinate system is: In the formula, t m ,t m-1 The velocity of the carrier in the "north-east" coordinate system at the moment; is the time period [t m-1 ,t m ] within the specific velocity increment, is the gravity vector in the "northeast" coordinate system; S5.3 Carrier location update method: The position differential equation of the carrier is: In the formula, represents the first-order derivative of the position matrix p with respect to time t, M pv express The coefficient matrix of is expressed as:

9. The strapdown inertial navigation method based on the north-east coordinate system according to claim 8, characterized in that: In S5.1, the Earth-centered inertial coordinate system is used as the reference coordinate system, and the "North-East Earth" system is from t m Time to t m-1 The quaternion of rotation change at the moment for: In the formula, is the angular velocity of the Earth's rotation in the time period [t m-1 ,t m ] is the negative of the corresponding angular increment, for The modulus value of Taking the geocentric inertial coordinate system as the reference coordinate system, the "front, top, right" system is from t m-1 Time to t m The quaternion of rotation change at the moment is: In the formula, is the carrier in the time period [t m-1 ,t m ] corresponds to the angular increment in for The modulus value of .

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