A rotary modulation inertial navigation full state simulation method

Abstract

The present application belongs to the technical field of inertial navigation, and particularly relates to a rotating modulation inertial navigation full-state simulation method. The method is applied to a rotating modulation inertial navigation system and comprises the following steps: Step 1. Generating flight trajectory data under a typical flight environment; Step 2. Determining a rotation strategy of the rotating modulation inertial navigation system, and inversely calculating angular increments and velocity increments of a rotating modulation inertial navigation system sensitive system in combination with the flight trajectory data in Step 1; Step 3. Injecting inertial device errors of the rotating modulation inertial navigation system into the angular increments and velocity increments obtained in Step 2 to obtain actual output angular increments and velocity increments; Step 4. The rotating modulation inertial navigation system performs inertial calculation using the actual output angular increments and velocity increments obtained in Step 3 to generate navigation trajectory data; Step 5. Comparing and verifying the navigation trajectory data generated in Step 4 with the flight trajectory data in Step 1 for consistency, and if the consistency comparison and verification fails, returning to Step 2 to update the rotation strategy until the consistency comparison and verification passes. The method comprehensively verifies the shaft system arrangement, rotation strategy and inertial calculation process of the rotating modulation inertial navigation under any aircraft maneuver.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of inertial navigation, and particularly relates to a rotating modulation inertial navigation full-state simulation method. BACKGROUND

[0002] With the development of military equipment and the progress of national defense science and technology, new requirements such as long-time autonomous navigation and high precision are put forward in the field of airborne navigation. The rotating modulation inertial navigation system drives the inertial measurement unit (IMU) to rotate through a motor, modulates the constant and slowly changing device errors of the IMU, and can provide high-precision position and speed information to meet the requirements of autonomous navigation of the aircraft.

[0003] According to the design indexes such as precision and weight, the rotating inertial navigation system has various shaft arrangement schemes such as single-axis, double-axis and three-axis. The rotating strategies and angular motion isolation schemes used in different shaft arrangement systems are also different, but the core principles are based on the platform inertial navigation angular motion isolation and the strapdown inertial navigation error model.

[0004] At present, the verification of the rotating inertial navigation shaft arrangement and rotating strategy design mainly relies on the development experience, and lacks a comprehensive, unified and mature simulation platform, so it is difficult to carry out model-based forward design of the rotating inertial navigation, and it is difficult to guide young engineers to familiarize and master the rotating inertial navigation design process. At the same time, the existing simulation platform is mainly based on the error propagation calculation of the trajectory, lacks the forward calculation platform of the original output of the inertial navigation, and cannot comprehensively verify the inertial navigation calculation process. SUMMARY

[0005] The purpose of the application is to provide a rotating modulation inertial navigation full-state simulation method, which can verify the shaft arrangement and rotating strategy of the rotating modulation inertial navigation in the whole process by injecting flight trajectory data and inertial device original error in any flight environment. The application can be used to guide the forward design of the rotating modulation inertial navigation.

[0006] The technical scheme of the application is as follows: in order to achieve the above-mentioned application purpose, according to the first aspect of the application, a rotating modulation inertial navigation full-state simulation method is provided, which is applied to a rotating modulation inertial navigation system, and includes the following steps:

[0007] Step 1. Generating flight trajectory data in a typical flight environment;

[0008] Step 2. Determining the rotating modulation inertial navigation system's rotating strategy, and inversely calculating the angular increment and speed increment of the rotating modulation inertial navigation system's sensitive system in combination with the flight trajectory data in step 1.

[0009] Step 3. Inject the inertial device error of the rotation modulated inertial navigation system into the angular increment and velocity increment obtained in Step 2 to obtain the actual output angular increment and velocity increment;

[0010] Step 4: The rotation modulated inertial navigation system performs inertial calculation using the actual output angular increment and velocity increment obtained in Step 3 to generate navigation trajectory data;

[0011] Step 5: Perform consistency comparison verification on the navigation trajectory data generated in Step 4 and the flight trajectory data in Step 1, and if the consistency comparison verification fails, return to Step 2 to update the rotation strategy until the consistency comparison verification passes.

[0012] In one possible embodiment, in the step 1, the flight trajectory data includes attitude, velocity, position.

[0013] In one possible embodiment, in the step 1, the flight trajectory under a typical flight environment is composed of acceleration motion, roll motion, pitch motion, and azimuth motion segments.

[0014] In one possible embodiment, in the step 1, the generation process of the flight trajectory data includes the following steps:

[0015] Record attitude , attitude angular rate vector , body velocity , body acceleration , aircraft position .

[0016] Acceleration motion: , ;

[0017] Roll motion: , ;

[0018] Pitch motion: , ;

[0019] Azimuth motion: According to aerodynamics, when the aircraft performs azimuth motion, it will be accompanied by roll motion, and there is a formula 1 relationship between the centripetal acceleration , gravitational acceleration , heading angular rate , roll angle

[0020] Formula 1

[0021] Therefore, the azimuth motion is: , ​

[0022] The aircraft position differential equation set is:

[0023] Formula 2

[0024] The initial value is set as:

[0025]

[0026] The flight trajectory data is generated by inputting in segments and solving the time-varying state equation by differential equation integration, and the aircraft attitude , speed , and position are obtained.

[0027] In one possible embodiment, in step 2, the specific process of inversely solving the angular increment of the sensitive system includes:

[0028] The conversion matrix from the inertial sensitive system to the navigation system is calculated;

[0029] Formula 3

[0030] In the formula:

[0031] is the conversion matrix from the aircraft body b system to the navigation system n system;

[0032] is the conversion matrix from the inertial sensitive system s system to the navigation system n system;

[0033] is the conversion matrix from the inner frame dynamic coordinate system 4 system to the inertial sensitive system s system;

[0034] is the conversion matrix from the inner frame static coordinate system 3 system to the inner frame dynamic coordinate system 4 system;

[0035] is the conversion matrix from the middle frame dynamic coordinate system 2 system to the inner frame static coordinate system 3 system;

[0036] is the conversion matrix from the middle frame static coordinate system 1 system to the middle frame dynamic coordinate system 2 system;

[0037] is the conversion matrix from the aircraft body b system to the middle frame static coordinate system 1 system;

[0038] In the formula, is caused by the installation of the shaft system during assembly, which is set as a unit matrix in the present application; therefore, the above formula can be simplified as:

[0039] ​​Equation 4

[0040] The rotation matrix is a unit orthogonal matrix, so Equation 4 can be transformed as:

[0041] Equation 5

[0042] Wherein: represents the conversion matrix of s system to n system at m time; represents the conversion matrix of b system to n system at m time;

[0043] The following transformation is made to:

[0044] Equation 6

[0045] Then, combining Equation 5 and Equation 6, we can get:

[0046] Equation 7

[0047] Wherein:

[0048] represents the conversion matrix of s system at m-1 time and m time, ; in the left formula, is the equivalent rotation vector at m time, , is the angular increment at m time;

[0049] is the conversion matrix of n system to s system at m-1 time, which can be obtained by Equation 5;

[0050] represents the conversion matrix of n system at m-1 time and m time, ; is the equivalent rotation vector, let , then ; , is the angular velocity of the earth rotation, , wherein is the projection of the aircraft speed vector in the geographical system, is the radius of the earth's meridian, is the radius of the earth's prime vertical, and L is the current latitude;

[0051] From the following formula:

[0052] Equation 8

[0053] can be obtained , then the angular increment can be obtained from the following formula, let , the gyro angular increment at any time can be obtained; ​

[0054] Equation 9.

[0055] In one possible embodiment, in the step 2, the specific process of inversely solving the velocity increment of the sensitive system s includes:

[0056] The velocity update algorithm can be obtained by solving the specific process of inversely solving the velocity increment of the sensitive system s includes:

[0057] Equation 10

[0058] Wherein: denotes the projection of the aircraft velocity vector v at the moment m in the n system, denotes the projection of the aircraft velocity vector v at the moment m-1 in the n system, denotes the projection of the aircraft velocity increment at the moment m in the n system, denotes the projection of the velocity increment calculation error at the moment m in the n system;

[0059] Equation 11

[0060] , is the velocity increment at the moment m;

[0061] , is the angle increment at the moment m;

[0062]

[0063] The expression of can be written as:

[0064] Equation 12

[0065] From the above equation, we have:

[0066] Equation 13

[0067] By the relationship between the shell system b and the sensitive system s , the velocity increment of the s system is solved:

[0068] Equation 14.

[0069] In one possible embodiment, in the step 3, the inertial device error includes: acceleration, gyro scale factor error, installation bias angle error, zero error.

[0070] In one possible embodiment, in the step 3, the specific process of injecting the inertial device error includes: gyro residual scale factor error , installation bias angle error and zero bias error The gyro angular increment output after injecting error can be expressed as:

[0071] Equation 15

[0072] Wherein:

[0073] is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system , wherein , wherein are the x, y, z axis non-orthogonal angles, respectively;

[0074] is the angular increment in the non-orthogonal coordinate system is the angular increment in the orthogonal system, obtained from equation 9;

[0075] is the gyro scale factor error;

[0076] is the zero bias error in the non-orthogonal system;

[0077] Similarly, the integrated velocity increment output after injecting error can be obtained as:

[0078] Equation 16

[0079] Wherein:

[0080] is the integrated specific force output in the non-orthogonal coordinate system is the specific force output in the orthogonal system, obtained from equation 14;

[0081] is the gyro scale factor error;

[0082] is the integrated zero bias error.

[0083] In one possible embodiment, in the step 4, the specific process of rotating the modulated inertial navigation system to generate navigation trajectory data includes:

[0084] Attitude update:

[0085] Equation 17

[0086] Equation 18

[0087] Wherein: and The calculation method is shown in equation 6; at the initial time, let I is a unit matrix; and The iterative solution can be performed through angle increment and velocity increment.

[0088] Velocity update:

[0089] Formula 19

[0090] wherein, and The calculation method is shown in formula 10; at the initial moment, let be 0, then The iterative solution can be performed through angle increment and velocity increment.

[0091] Position update:

[0092] Formula 20.

[0093] In one possible embodiment, in the step 5, the step of consistency comparison comprises: determining the accuracy indicators of position, velocity and attitude; calculating the position accuracy, velocity accuracy and attitude accuracy of the navigation result, the position accuracy is calculated by using the method two in GJB729-CEP, the velocity and attitude accuracy are calculated by using the root mean square; performing index compliance criterion according to the accuracy indicators of position, velocity and attitude, if the index requirement is not met, analyzing the error source, adjusting the injected error value or adjusting the indexing strategy to repeat the simulation.

[0094] The beneficial technical effects of the present application are:

[0095] The present application provides a full-state simulation method for rotary modulation inertial navigation, the conversion relationship between the inertial measurement coordinate system and the shell system is established through the designed complex motion profile, shaft arrangement scheme and indexing strategy, the shaft arrangement, rotation strategy and inertial calculation process of the rotary modulation inertial navigation under any aircraft maneuver are comprehensively verified through the end-to-end full-process simulation.

[0096] Before this, due to the coupling of the aircraft maneuver of the rotary modulation inertial navigation and the rotation strategy of the inertial navigation itself, it is difficult to directly calculate the original data of the gyro in the sensitive system through the flight trajectory, so that there is no feasible scheme for full-state simulation. The present application innovatively proposes a reverse calculation method, so that the end-to-end simulation verification of the rotary modulation inertial navigation becomes possible, fills the gap of the full-state simulation verification of the rotary modulation inertial navigation, and more scientifically and efficiently guides the forward design of the rotary modulation inertial navigation. BRIEF DESCRIPTION OF DRAWINGS

[0097] In order to more clearly illustrate the technical solutions of the present application, the following will briefly describe the drawings used in the present application. Obviously, the drawings described below are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained from these drawings without creative labor.

[0098] Figure 1 is a method flowchart of an embodiment of the present application;

[0099] Figure 2 is a flight trajectory combination diagram of embodiment 1 of the present application;

[0100] Figure 3 is an angular increment diagram of the rotation modulation inertial navigation of embodiment 1 of the present application;

[0101] Figure 4 is a speed increment diagram of the rotation modulation inertial navigation of embodiment 1 of the present application;

[0102] Figure 5 is a consistency comparison verification navigation error combination diagram of embodiment 1 of the present application;

[0103] Figure 6 is a flight trajectory combination diagram of embodiment 2 of the present application;

[0104] Figure 7 is an angular increment diagram of the rotation modulation inertial navigation of embodiment 2 of the present application;

[0105] Figure 8 is a speed increment diagram of the rotation modulation inertial navigation of embodiment 2 of the present application;

[0106] Figure 9 is a consistency comparison verification navigation error combination diagram of embodiment 2 of the present application. DETAILED DESCRIPTION

[0107] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0108] The features and illustrative embodiments of various aspects of the present application will be described below in detail. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one of ordinary skill in the art that the present application can be practiced without some or all of these specific details. The description of the embodiments is merely illustrative of the present application and is not intended to limit the present application to any particular setting or method. Rather, the present application covers any improvements, alternatives, and modifications of the structures, methods, devices, and the like.

[0109] It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict, and each embodiment can be referred to and cited by each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0110] Embodiment 1

[0111] A dual-axis rotation modulation inertial navigation full-state simulation method, specifically comprising:

[0112] Step 1: Typical flight trajectory generation

[0113] As shown in Figure 2 , the motion trajectory of the aircraft is composed of the following four flight maneuvers, and only one flight maneuver at the same time.

[0114] (1) Aircraft acceleration motion:

[0115] (2) Aircraft roll motion:

[0116] (3) Aircraft pitch motion:

[0117] (4) Aircraft azimuth motion:

[0118] The differential equation of the aircraft position is:

[0119] The initial value of the state variable is set as:

[0120]

[0121] By setting the aircraft to perform the above four flight maneuvers in sections, the time-varying state equation is solved by integrating the differential equation set, and the flight trajectory data is generated, and the aircraft Euler angle , speed , position are obtained as follows:

[0122] Step 2: generate angular increment and velocity increment under inertial sensitive system

[0123] The position conversion strategy of dual-axis rotation modulated inertial navigation 16 is shown as follows:

[0124]

[0125] The angular increment and velocity increment of sensitive system s are solved reversely combined with flight trajectory data in step 1;

[0126] Calculate the conversion matrix from sensitive system to navigation system;

[0127] Formula 3

[0128] In the formula:

[0129] is the conversion matrix from machine system b to navigation system n;

[0130] is the conversion matrix from inertial sensitive system s to navigation system n;

[0131] is the conversion matrix from inner frame dynamic coordinate system 4 to inertial sensitive system s;

[0132] is the conversion matrix from inner frame static coordinate system 3 to inner frame dynamic coordinate system 4;

[0133] is the conversion matrix from middle frame dynamic coordinate system 2 to inner frame static coordinate system 3;

[0134] is the conversion matrix from middle frame static coordinate system 1 to middle frame dynamic coordinate system 2;

[0135] is the conversion matrix from machine system b to middle frame static coordinate system 1;

[0136] wherein, is caused by the installation of the axis system during assembly, which is not considered here and is set to the unit matrix; then the above formula can be simplified as:

[0137] Formula 4

[0138] In the formula: It can be obtained by designing a specific rotation strategy;

[0139] The rotation matrix is a unit orthogonal matrix, so formula 4 can be transformed as:

[0140] Formula 5

[0141] Wherein: represents the conversion matrix of s system to n system at m time; represents the conversion matrix of b system to n system at m time, which can be obtained in real time from the flight trajectory.

[0142] To The following transformation is performed:

[0143] Formula 6

[0144] Then, combined with formula 5 and formula 6, we can get:

[0145] Formula 7

[0146] Wherein:

[0147] represents the conversion matrix of s system at m-1 time and m time, ; in the left formula, is the equivalent rotation vector at m time, , is the angle increment at m time (to be solved);

[0148] is the conversion matrix of n system at m-1 time and m time,

[0149] ; in the left formula, ; is the equivalent rotation vector, let , then . , is the earth rotation angular velocity, , wherein is the projection of the aircraft velocity vector in the geographical system, is the earth meridian radius, is the earth prime vertical circle radius, and L is the current latitude.

[0150] From the following formula:

[0151] Formula 8

[0152] can be obtained , then the angle increment can be obtained from the following formula, let , the gyro angle increment at any time can be solved, as shown in Figure 3 .

[0153] Formula 9

[0154] The specific process of inversely solving the velocity increment of the sensitive system s system includes:

[0155] The velocity update algorithm can be obtained by solving the specific force equation:

[0156] Equation 10

[0157] Where: represents the projection of the aircraft velocity vector v at time m in the n-frame, represents the projection of the aircraft velocity vector v at time m-1 in the n-frame, represents the projection of the actual velocity increment of the aircraft at time m in the n-frame, represents the projection of the velocity increment calculation error at time m in the n-frame.

[0158] Equation 11

[0159] Where:

[0160] , is the velocity increment at time m;

[0161] , is the angle increment at time m;

[0162]

[0163] The expression for can be written as:

[0164] Equation 12

[0165] From the above equation, we have:

[0166] Equation 13

[0167] By solving the relationship between the shell system b-frame and the sensitive system s-frame , the s-frame velocity increment can be calculated, as shown in Figure 4 :

[0168] Equation 14

[0169] Step 3: Angle increment, velocity increment injection, inertial device error

[0170] Gyroscope residual scale factor error

[0171] Gyroscope installation angle error

[0172] Gyroscope zero drift error Therefore, the gyroscope angle increment output after injecting the error can be represented as:

[0173] Equation 15

[0174] wherein:

[0175] is the angular increment in the non-orthogonal coordinate system, is the angular increment in the orthogonal coordinate system, obtained from Equation 9;

[0176] is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system , wherein ;

[0177] is the gyro scale factor error, wherein ;

[0178] is the non-orthogonal coordinate system zero drift, .

[0179] Similarly, the integrated velocity increment output after injecting errors can be obtained as:

[0180] Equation 16

[0181] wherein:

[0182] is the integrated specific force output in the non-orthogonal coordinate system, is the specific force output in the orthogonal coordinate system, obtained from Equation 13;

[0183] is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system , wherein ;

[0184] is the gyro scale factor error, wherein ;

[0185] is the integrated zero bias, .

[0186] Step 4: Perform forward resolution using the inertial data with injected errors

[0187] The specific process of performing inertial resolution using the rotation modulation inertial navigation system to generate navigation trajectory data includes:

[0188] Attitude update:

[0189] Equation 17

[0190] Equation 18

[0191] Where: and The calculation method is shown in Equation 6; at the initial moment, let be the unit matrix; then The angle increment and velocity increment can be used for iterative solution.

[0192] Velocity update:

[0193] Equation 19

[0194] Where, and The calculation method is shown in Equation 10; at the initial moment, let be 0, then The angle increment and velocity increment can be used for iterative solution.

[0195] Position update:

[0196] Equation 20

[0197] Step 5: Consistency comparison between navigation data and flight trajectory data

[0198] Index requirements:

[0199] Attitude: 0.01° (RMS)

[0200] Velocity: 0.8 m / s (RMS)

[0201] Position: 500 m (MAX)

[0202] Calculate the error between navigation data and simulation trajectory, adjust the indexing strategy or device error according to the error, so that the navigation result is closest to the simulation trajectory. As shown in Figure 5 the navigation result error:

[0203] Velocity RMS index calculation:

[0204] Where, represents the velocity value (east or north) of each sampling point;

[0205] Attitude RMS index calculation:

[0206] Where, represents the angle value (pitch, roll, heading) of each sampling point;

[0207] Position maximum value index calculation:

[0208]

[0209] From the above formula, we have:

[0210] RMS θ : 0.002 RMS γ : 0.005 RMS ψ : 0.004

[0211] RMS ve : 0.3 RMS vn : 0.33

[0212] POS max : 775

[0213] The position error is greater than the index requirement, and the indexing scheme does not meet the requirements, and the indexing strategy needs to be adjusted.

[0214] Example 2

[0215] A dual-axis rotation modulation inertial navigation full-state simulation method, specifically comprising:

[0216] Step 1: Typical flight trajectory generation

[0217] As shown in Figure 6 , the motion trajectory of the aircraft is composed of the following four flight maneuvers, and only one flight maneuver at the same time.

[0218] (1) Aircraft acceleration motion:

[0219] (2) Aircraft roll motion:

[0220] (3) Aircraft pitch motion:

[0221] (4) Aircraft azimuth motion:

[0222] The differential equation of the aircraft position is:

[0223] The initial value of the state variable is set as:

[0224]

[0225] By setting the aircraft to perform the above four flight maneuvers in sections, the time-varying state equation is solved by integrating the differential equation set, and the flight trajectory data is generated, and the aircraft Euler angle , speed , position are obtained as follows:

[0226] Step 2: generate angular increment and velocity increment under inertial sensitive system

[0227] The position conversion strategy of dual-axis rotation modulated inertial navigation 32 is as follows:

[0228]

[0229] The angular increment and velocity increment of the sensitive system s system are inversely calculated combined with the flight trajectory data in step 1;

[0230] Calculate the conversion matrix from the sensitive system to the navigation system;

[0231] Formula 3

[0232] In the formula:

[0233] is the conversion matrix from the aircraft system b system to the navigation system n system;

[0234] is the conversion matrix from the inertial sensitive system s system to the navigation system n system;

[0235] is the conversion matrix from the inner frame dynamic coordinate system 4 system to the inertial sensitive system s system;

[0236] is the conversion matrix from the inner frame static coordinate system 3 system to the inner frame dynamic coordinate system 4 system;

[0237] is the conversion matrix from the middle frame dynamic coordinate system 2 system to the inner frame static coordinate system 3 system;

[0238] is the conversion matrix from the middle frame static coordinate system 1 system to the middle frame dynamic coordinate system 2 system;

[0239] is the conversion matrix from the aircraft system b system to the middle frame static coordinate system 1 system;

[0240] wherein, is caused by the installation of the axis system during assembly, which is not considered here, and is set to the unit matrix; then the above formula can be simplified as:

[0241] Formula 4

[0242] In the formula: It can be obtained by designing a specific rotation strategy;

[0243] The rotation matrix is a unit orthogonal matrix, so formula 4 can be transformed as:

[0244] Formula 5

[0245] wherein: is the conversion matrix from s-frame to n-frame at time m; is the conversion matrix from b-frame to n-frame at time m, which can be obtained in real time from the flight trajectory.

[0246] is transformed as follows:

[0247] Equation 6

[0248] Then, combining Equation 5 and Equation 6, we have:

[0249] Equation 7

[0250] wherein:

[0251] is the conversion matrix from s-frame at time m-1 to s-frame at time m, ; in the left equation, is the equivalent rotation vector at time m, , is the angular increment at time m (to be solved);

[0252] is the conversion matrix from n-frame at time m-1 to s-frame at time m-1, which can be obtained from Equation 5;

[0253] is the conversion matrix from n-frame at time m-1 to n-frame at time m, ; is the equivalent rotation vector, let , then . , is the angular velocity of the earth rotation, wherein is the projection of the aircraft velocity vector in the geographical frame, is the radius of the earth's meridian, is the radius of the earth's prime vertical, and L is the current latitude.

[0254] From the following equation:

[0255] Equation 8

[0256] we can obtain , then from the following equation we can obtain the angular increment, let , we can obtain the gyroscopic angular increment at any time, as shown in Figure 7 ;

[0257] Equation 9

[0258] ​The specific process of inversely calculating the velocity increment of the sensitive system s includes:

[0259] The velocity update algorithm can be obtained by solving the specific process of inversely calculating the velocity increment of the sensitive system s includes:

[0260] Formula 10

[0261] Wherein: represents the projection of the aircraft velocity vector v at time m in the n system, represents the projection of the aircraft velocity vector v at time m-1 in the n system, represents the projection of the actual velocity increment of the aircraft at time m in the n system, represents the projection of the velocity increment calculation error at time m in the n system.

[0262] Formula 11

[0263] Wherein:

[0264] , is the velocity increment at time m;

[0265] , is the angular increment at time m;

[0266]

[0267] The expression of can be written as:

[0268] Formula 12

[0269] From the above formula, we can get:

[0270] Formula 13

[0271] By the relationship between the shell system b and the sensitive system s , the velocity increment of s is calculated, as shown in Figure 8 :

[0272] Formula 14

[0273] Step 3: Angular increment, velocity increment, and inertial device error injection

[0274] Gyroscope residual scale factor error

[0275] Gyroscope installation angle error

[0276] Gyroscope zero drift error The gyro angular increment output after injecting the error can be expressed as:

[0277] Equation 15

[0278] Wherein:

[0279] is the angular increment in the non-orthogonal coordinate system, is the angular increment in the orthogonal system, which is obtained from Equation 9;

[0280] is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system , wherein ;

[0281] is the gyro scale factor error, wherein ;

[0282] is the non-orthogonal system zero drift, .

[0283] Similarly, the integrated velocity increment output after injecting the error can be obtained as:

[0284] Equation 16

[0285] Wherein:

[0286] is the integrated specific force output in the non-orthogonal coordinate system, is the specific force output in the orthogonal system, which is obtained from Equation 13;

[0287] is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system , wherein ;

[0288] is the gyro scale factor error, wherein ;

[0289] is the integrated zero bias, .

[0290] Step 4: Perform forward resolution using the inertial data after injecting the error

[0291] The specific process of performing inertial resolution by the rotation modulation inertial navigation system to generate navigation trajectory data includes:

[0292] Attitude update:

[0293] Equation 17

[0294] Equation 18

[0295] Where: and The calculation method is shown in Equation 6; at the initial moment, let be the unit matrix; then can be solved iteratively through angular increments and velocity increments.

[0296] Velocity update:

[0297] Equation 19

[0298] Where, and The calculation method is shown in Equation 10; at the initial moment, let be 0, then can be solved iteratively through angular increments and velocity increments.

[0299] Position update:

[0300] Equation 20

[0301] Step 5: Consistency comparison between navigation data and flight trajectory data

[0302] Index requirements:

[0303] Attitude: 0.01° (RMS)

[0304] Velocity: 0.8 m / s (RMS)

[0305] Position: 500 m (MAX)

[0306] Calculate the error between navigation data and simulation trajectory, adjust the indexing strategy or device error according to the error, so that the navigation result is closest to the simulation trajectory. As shown in Figure 9 the navigation result error:

[0307] Velocity RMS index calculation:

[0308] Where, represents the velocity value (east or north) of each sampling point;

[0309] Attitude RMS index calculation:

[0310] Where, represents the angle value (pitch, roll, heading) of each sampling point;

[0311] Position maximum index calculation:

[0312]

[0313] From the above formula, we have:

[0314] RMS θ : 0.0014 RMS γ : 0.0012 RMS ψ : 0.003

[0315] RMS ve : 0.15 RMS vn : 0.16

[0316] POS max : 247

[0317] This rotation scheme meets the index requirements.

[0318] Although the embodiments of the present application are disclosed as above, the content described is only the embodiments adopted for facilitating the understanding of the present application, and is not intended to limit the present application. Any person skilled in the art of the present application can make any modification and change in the implementation form and details without departing from the spirit and scope of the present application disclosed, but the patent protection scope of the present application shall be subject to the scope defined by the appended claims.

Claims

1. A rotary modulated inertial navigation full state simulation method, characterized in that, The application is applied to a rotary modulation inertial navigation system, and comprises the following steps: step 1, generating flight trajectory data under a typical flight environment; the generation process of the flight trajectory data comprises the following steps: pose , angular rate vector , body velocity , body acceleration , aircraft position accelerated motion: , ; Rolling movement: , ; Pitching movement: , ; Azimuth motion: According to aerodynamics, the aircraft azimuth motion will be accompanied by roll motion, then there is a formula 1 relationship between the centripetal acceleration , the gravitational acceleration , the heading angle rate , the roll angle ​ Equation 1 From this the azimuthal motion is derived: , Then, the aircraft position differential equation set is: Equation 2 Wherein, the initial value is set as: By piecewise input And , the generation of flight trajectory data can be completed by solving the time-varying state equation with differential equation set integration, and the attitude , speed , position of the aircraft are obtained; Step 2, determining the rotation strategy of the rotary modulation inertial navigation system, and inversely solving the angular increment and the velocity increment of the rotary modulation inertial navigation system sensitive system in combination with the flight trajectory data in step 1; Step 3, injecting the inertial device error of the rotary modulation inertial navigation system into the angular increment and the velocity increment obtained in step 2 to obtain the actual output angular increment and the actual output velocity increment; Step 4, the rotary modulation inertial navigation system performs inertial calculation by using the actual output angular increment and the actual output velocity increment obtained in step 3 to generate navigation trajectory data; Step 5, comparing and verifying the navigation trajectory data generated in step 4 with the flight trajectory data in step 1 for consistency, and if the consistency comparison and verification fails, returning to step 2 to update the rotation strategy until the consistency comparison and verification passes.

2. The method of claim 1, wherein, In the step 1, the flight trajectory data comprises attitude, velocity and position.

3. The method of claim 1, wherein, In the step 1, the flight trajectory under the typical flight environment is composed of acceleration motion, roll motion, pitch motion and azimuth motion.

4. The method of claim 1, wherein, In the step 2, the specific process of inversely solving the angular increment of the sensitive system comprises: calculating the conversion matrix from the inertial sensitive system s to the navigation system n; Equation 3 In the formula 4, the rotation matrix is a unit orthogonal matrix, so the formula 4 can be transformed into: Conversion matrix from the machine system b to the navigation system n; is the transformation matrix from the inertial frame s to the navigation frame n. is the transformation matrix of the inner frame moving coordinate system 4 to the inertial sensitive system s; is the transformation matrix of the inner frame static coordinate system 3 to the inner frame dynamic coordinate system 4; is the transformation matrix from the middle frame moving coordinate system 2 to the inner frame static coordinate system 3; is the transformation matrix of the middle frame static coordinate system 1 to the middle frame dynamic coordinate system 2; is the conversion matrix from the machine coordinate system b to the middle frame coordinate system 1. wherein is the shafting installation caused by the assembly, set to the unit matrix; then the formula can be simplified as: Formula 4 Then, the formula 5 and the formula 6 can be combined to obtain: Equation 5 wherein: represents a conversion matrix from the s system to the n system at the m time; represents a conversion matrix from the b system to the n system at the m time; To the following transformation is made: Formula 6 In the formula 7, the angular increment of the sensitive system s is obtained by the following formula: Equation 7 In the step 2, the specific process of inversely solving the velocity increment of the sensitive system s comprises: denotes the transition matrix from the inertial frame s to the body frame m at time instant m-1 to m, ; in the left equation, is the equivalent rotation vector at time instant m, , is the angular increment at time instant m; The transformation matrix of the navigation system n to the inertial sensitive system s at time m-1 can be obtained by formula 5. denotes the transition matrix of the navigation system n to the system at time m-1 and m, ; is the equivalent rotation vector, let then ; , is the earth rotation angular velocity, where is the projection of the aircraft velocity vector in the geographical system, is the earth meridian radius, is the earth prime vertical radius, L is the current latitude; The velocity update algorithm can be obtained by solving the specific force equation: Equation 8 The angular increment can be obtained from The angular increment can be obtained from The angular increment of the gyroscope at any time can be obtained Equation 9.

5. The method of claim 4, wherein, In the formula 8, the velocity increment of the sensitive system s is obtained by the following formula: In the formula 9, the velocity increment of the sensitive system s is obtained by the following formula: Formula 10 wherein: denotes the projection of the aircraft velocity vector v at time m in the n-frame, denotes the projection of the aircraft velocity vector v at time m-1 in the n-frame, denotes the projection of the aircraft velocity increment at time m in the n-frame, denotes the projection of the velocity increment calculation error at time m in the n-frame; ; Equation 11 , is the speed increment at time m. , is the angular increment for the moment m; The expression of the above can be written as: Formula 12 In the step 4, the specific process of the rotary modulation inertial navigation system performing inertial calculation to generate the navigation trajectory data comprises: Equation 13 By shell system b system and sensitive system s system relationship , the sensitive system s system velocity increment is calculated: Equation 14.

6. The method of claim 5, wherein, In the step 3, the specific process of injecting inertial device errors includes: gyro residual scale factor error , installation angle error , and zero drift error , then the gyro angular increment output after injecting errors can be expressed as: Equation 15 attitude update: is the coordinate transformation matrix from the orthogonal coordinate system to the non-orthogonal coordinate system wherein wherein are the x, y, z axis non-orthogonality angles, respectively For the angular increment in non-orthogonal coordinates, For the angular increment in orthogonal coordinates, obtained from equation 9; Gyro scale factor error; zero drift error for non-orthogonal systems; velocity update: Equation 16 position update: For non-orthogonal coordinate system under the plus ratio force output, For orthogonal system under the ratio force output, by formula 14; Gyro scale factor error; To add zero bias error.

7. The method of claim 6, wherein, The step of performing consistency comparison comprises: determining the accuracy indexes of the position, the velocity and the attitude; calculating the position accuracy, the velocity accuracy and the attitude accuracy of the navigation result, the position accuracy is calculated by using the method two in the GJB729-CEP, the velocity and the attitude accuracy are calculated by using the root mean square; performing index compliance criterion according to the accuracy indexes of the position, the velocity and the attitude, if the index requirement is not met, analyzing the error source, adjusting the injected error value or adjusting the rotation strategy to repeat the simulation. ​ Formula 17 Official 18 Wherein: With The calculation method is shown in formula 6; at the initial moment, let Be a unit matrix; then Can be solved by iteration of angular increment, velocity increment; ​ Formula 19 wherein, with The calculation method is shown in formula 10; at the initial moment, let be 0, then The angle increment and the speed increment can be used for iterative solution. ​ Equation 20.

8. The method of claim 1, wherein, ​

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