A method for measuring muzzle vibration during travel based on combination of master and inertial navigation

Abstract

The application discloses a kind of based on main sub inertial navigation combined in-transit muzzle vibration measurement method, this method is: install high-precision inertial navigation on the high overload resistance on turret, install low-precision MEMS inertial navigation at the muzzle of barrel;In initial stage, high-precision main inertial navigation at turret and MEMS sub inertial navigation at muzzle complete transfer alignment;In transfer alignment stage, according to the dynamic modeling of outer lever arm error and deflection deformation according to the characteristics of gun barrel, compensate for lever arm effect and deflection deformation;Establish the transfer alignment Kalman filter of speed and attitude matching mode;In navigation update stage, sub inertial navigation uses the alignment error at the end of transfer alignment as the initial error of navigation solution, carries out navigation state update, completes the vibration measurement of muzzle.The application has the advantages of simple installation, high stability, strong anti-interference ability and high accuracy.

Description

Technical Field

[0001] This invention relates to the field of muzzle vibration measurement technology, and in particular to a method for measuring muzzle vibration during travel based on a combination of master inertial navigation and master inertial navigation. Background Technology

[0002] During artillery operations, vibrations at the muzzle can affect firing accuracy, making muzzle vibration measurement a challenging research area. Research on muzzle vibration began abroad, with Komnkov establishing mathematical equations describing the relationship between barrel vibration and firing accuracy, proving that barrel vibration is a major factor affecting firing accuracy. In 1982, Soviet artillery design experts Orlov and Malikov, among others, provided a method for estimating the natural frequency of the barrel. Domestically, Yu Huijie, Wang Deshi, and others simplified the barrel into a beam-like structural model, and based on this, used beam vibration theory to study the barrel vibration response. Xu Da et al. used a line laser speckle field photoelectric detection method to study the mathematical relationship between the barrel vibration signal and the output current, proposing a method for measuring muzzle vibration based on the line laser speckle effect on the barrel surface, thus achieving muzzle amplitude measurement.

[0003] In most studies, non-contact measurement is used to study displacement change parameters. However, the disadvantages are that non-contact measuring instruments are inconvenient to install, data sampling is difficult, and instrument calibration is also troublesome. Summary of the Invention

[0004] The purpose of this invention is to propose a method for measuring muzzle vibration during travel based on a combination of master and slave inertial navigation systems, which is easy to install, highly stable, has strong anti-interference ability, and high accuracy.

[0005] The technical solution to achieve the purpose of this invention is: a method for measuring muzzle vibration during travel based on a combination of master inertial navigation and propulsion, comprising the following steps:

[0006] Step 1: Based on the artillery platform, design the installation positions of the main and sub-inertial navigation systems, including the main inertial navigation system and the MEMS sub-inertial navigation system;

[0007] Step 2: Based on the output of the main inertial navigation and MEMS sub-inertial navigation sensors during the artillery's movement, design an attitude update algorithm based on gyroscope angle incremental update;

[0008] Step 3: During the transfer and alignment stage, dynamic modeling of the outer rod arm error and flexural deformation is performed based on the characteristics of the gun barrel, and compensation is made for the rod arm effect and flexural deformation.

[0009] Step 4: Use the velocity and attitude calculated by the MEMS sub-inertial navigation system, and the velocity and attitude deviations calculated by the main inertial navigation system, as the measurement information of the MEMS sub-inertial navigation system, and establish a transfer alignment Kalman filter with velocity plus attitude matching.

[0010] Step 5: In the navigation update phase, the MEMS sub-inertial navigation system uses the alignment error at the end of the transmission alignment as the initial error for navigation calculation to update the navigation state and complete the vibration measurement of the gun muzzle.

[0011] Compared with the prior art, the present invention has the following significant advantages: (1) The contact measurement method of installing a high-precision main inertial navigation system at the turret and a MEMS sub-inertial navigation system at the muzzle of the gun barrel is more convenient to install and has higher stability than the traditional non-contact measurement methods such as optics. It avoids the disadvantages of traditional optical methods such as susceptibility to interference, installation difficulties, and complicated instrument calibration; (2) In the initial alignment stage, the high-precision main inertial navigation system is used to transfer and align the MEMS sub-inertial navigation system, which is within the scope of inertial navigation precision alignment. This can ensure that the MEMS sub-inertial navigation system has accurate initial inertial navigation information, thereby improving the reliability and accuracy of muzzle vibration measurement; (3) In the navigation update stage, the sub-inertial navigation system uses the alignment error at the end of the transfer alignment as the initial error for navigation calculation. The attitude update algorithm is used to continuously iterate and calculate, which can ensure the accuracy of the pose output of the MEMS sub-inertial navigation system and improve the real-time performance and reliability of the muzzle vibration measurement method. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the main inertial navigation system installation structure of the present invention.

[0013] Figure 2 This is a flowchart of the method for measuring muzzle vibration during travel based on the combination of master and slave inertial navigation, according to the present invention.

[0014] Figure 3 This is a schematic diagram of the principle of the master inertial guide arm in this invention.

[0015] Figure 4 This is a schematic diagram of the Kalman filtering process in this invention.

[0016] Figure 5 This is a flowchart illustrating the Kalman filter calculation loop and the gain calculation loop in this invention. Detailed Implementation

[0017] This invention discloses a method for measuring muzzle vibration during travel based on a combination of master and slave inertial navigation systems, comprising the following steps:

[0018] Step 1: Based on the artillery platform, design the installation positions of the main and sub-inertial navigation systems, including the main inertial navigation system and the MEMS sub-inertial navigation system;

[0019] Step 2: Based on the output of the main inertial navigation and MEMS sub-inertial navigation sensors during the artillery's movement, design an attitude update algorithm based on gyroscope angle incremental update;

[0020] Step 3: During the transfer and alignment stage, dynamic modeling of the outer rod arm error and flexural deformation is performed based on the characteristics of the gun barrel, and compensation is made for the rod arm effect and flexural deformation.

[0021] Step 4: Use the velocity and attitude calculated by the MEMS sub-inertial navigation system, and the velocity and attitude deviations calculated by the main inertial navigation system, as the measurement information of the MEMS sub-inertial navigation system, and establish a transfer alignment Kalman filter with velocity plus attitude matching.

[0022] Step 5: In the navigation update phase, the MEMS sub-inertial navigation system uses the alignment error at the end of the transmission alignment as the initial error for navigation calculation to update the navigation state and complete the vibration measurement of the gun muzzle.

[0023] Furthermore, in step 1, the installation positions of the main and sub-inertial navigation systems are designed according to the artillery platform, including the main inertial navigation system and the MEMS sub-inertial navigation system, as detailed below:

[0024] The main inertial navigation system is fixed to the turret and kept in a horizontal state. The turret's directional movement drives the main inertial navigation system to move together.

[0025] The MEMS sub-inertial navigation system is fixed to the front end of the gun barrel and is used to measure the position and attitude of the muzzle at the front end of the gun barrel.

[0026] Furthermore, in step 2, based on the outputs of the main inertial navigation system and the MEMS sub-inertial navigation system sensors during the artillery's movement, an attitude update algorithm based on gyroscope angle incremental updates is designed, as follows:

[0027] Step 2.1: Place the inertial navigation system at rest, acquire accelerometer data, obtain the pitch angle θ and roll angle γ using the gravity component relationship, and obtain the yaw angle in the navigation coordinate system using the geomagnetic sensor. Complete the initial alignment of the inertial navigation system;

[0028] Step 2.2: Set the initial zero point and update the attitude of the inertial navigation carrier using quaternions and the angular increment of the gyroscope.

[0029] Furthermore, step 2.1 is detailed as follows:

[0030] Step 2.1.1: Estimate the pitch angle θ and roll angle γ using the triaxial components of acceleration:

[0031]

[0032]

[0033] in, These are the x, y, and z axis output values ​​of the k-th accelerometer reading in the carrier coordinate system.

[0034] Step 2.1.2: Obtain the magnetic field strength in the carrier coordinate system using a geomagnetic sensor. By combining the obtained pitch angle θ and roll angle γ, the magnetic field strength in the navigation coordinate system is obtained after transformation. Further calculations yielded the yaw angle. for:

[0035]

[0036] Where, θ k γ k These represent the pitch angle and roll angle calculated in the k-th iteration, respectively.

[0037]

[0038] in, These represent the magnetic field strengths corresponding to the x, y, and z axes in the navigation coordinate system, respectively.

[0039] Step 2.1.3: Under static conditions, use three Euler angles to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system to complete the initial alignment of the inertial navigation system.

[0040] Furthermore, step 2.2 is specifically as follows:

[0041] Step 2.2.1: Calculate the angular increment Δ from the gyroscope's updated data:

[0042]

[0043] In the formula, ω x ω y ω z The scalar value of the three-axis angular velocity output by the instrument, T m Sampling time;

[0044] Step 2.2.2: Update the quaternion using angle increment:

[0045]

[0046] In the formula, q 1|k+1 q 2|k+1 q 3|k+1 q 4|k+1 Let q1, q2, q3, and q4 be the values ​​of the quaternion at time k+1, and q be the quaternion values. 1|k q 2|k q 3|k q 4|k Let q1, q2, q3, and q4 be the values ​​of the quaternion at time k, respectively.

[0047] Step 2.2.3: Normalize the quaternions:

[0048]

[0049] Where q1' |k+1 ,q' 2|k+1 ,q' 3|k+1 ,q' 4|k+1 q 1|k+1 q 2|k+1 q 3|k+1 q 4|k+1 The value after normalization; normalization transforms the quaternion into a unit quaternion, where the sum of the squares of the four values ​​is 1.

[0050] Step 2.2.4: Obtain the direction cosine matrix based on the unit quaternion, using the formula:

[0051]

[0052] Step 2.2.5: Obtain the Euler angles from the direction cosine matrix as follows:

[0053]

[0054] Step 2.2.6: Based on the direction cosine matrix information and specific force information, obtain the three-axis components of the current acceleration. Distinguishing the three-axis components can compensate for the gravity component. Removing the gravity component yields the motion acceleration in the navigation coordinate system. Performing Newtonian integration on the motion acceleration yields the velocity and position, as shown in the formula:

[0055]

[0056] in, To calculate the output value of the motion accelerometer based on the compensated gravitational component, This represents the coordinate transformation matrix from time k-1 to time k, from the vehicle coordinate system b to the navigation coordinate system n.

[0057] Furthermore, the outer lever error compensation in step 3 is as follows:

[0058] Define the inertial coordinate system as O i x i y i z i The carrier coordinate system is O b x b y b z b O b The oscillation center of the carrier is located at point p, where the sub-inertial navigation accelerometer is mounted at a fixed point p in the carrier's coordinate system. The position vector of the origin of the carrier coordinate system. Let p be the position vector of point p relative to the origin of the inertial coordinate system. Let p be the position vector relative to the origin of the carrier coordinate system. Then, the expression for the linear acceleration of p relative to the inertial coordinate system is:

[0059]

[0060] The last two terms in the above equation are the basic expressions for the lever arm acceleration sensitive to inertial navigation due to the lever arm effect;

[0061] in, This represents the angular velocity output by the gyroscope in the inertial frame of reference.

[0062] definition Let the lever arm acceleration be represented, then the basic equation for the lever arm effect error is:

[0063]

[0064] in, Indicates the acceleration of the lever arm. For tangential acceleration, This is centripetal acceleration.

[0065] Furthermore, the dynamic modeling of the flexural deformation described in step 3 is as follows:

[0066] Let the dynamic deformation angle be λ(t) and the dynamic deformation angular rate be w. f (t), that is: Expanded to:

[0067]

[0068] Among them, w fx (t), w fy (t), w fz (t) represent the dynamic deformation angular rates of the x, y, and z axes, respectively. These are the first derivatives of the dynamic deformation angles along the x, y, and z axes, respectively.

[0069] Equations of motion for dynamic deformation angular rate:

[0070]

[0071] Where, let i = x, y, z, β i =2.146 / τ i , τ i For the relevant time; W i (t) represents white noise. If it is colored noise, it needs to be whitened. White noise W i The variance of (t) satisfies Represents the three elastic deformation angles λ x,λ y ,λ z The variance.

[0072] Furthermore, the deviations between the velocity and attitude calculated by the MEMS sub-inertial navigation system in step 4 and those calculated by the main inertial navigation system are as follows:

[0073] The differential equation for the velocity difference between the master and slave inertial navigation systems is:

[0074]

[0075] In the formula, This indicates the speed difference between the master and slave inertial navigation systems. Let φ be the attitude matrix of the sub-inertial navigation system, φ× represent the antisymmetric matrix corresponding to the initial installation error angles of the main and sub-inertial navigation systems, and ξ represent the estimated installation error angles of the main and sub-inertial navigation systems. This represents the specific force felt by the main inertial navigation system in the coordinate system of the sub-inertial navigation system; This represents the Earth's rotational angular rate in the navigation coordinate system; This indicates the error of the sub-inertial accelerometer;

[0076] The attitude measurement equation is:

[0077]

[0078] In the formula, φ represents the attitude deviation calculated by the master and slave inertial navigation systems; Z φ The value represents the attitude difference between the main and sub-inertial navigation systems after removing the effects of static and dynamic deformation angles; μ represents the static deformation angle, including installation error; θ represents the dynamic deformation angle, i.e., flexural deformation.

[0079] Furthermore, the Kalman filter model for the velocity plus attitude matching method described in step 4 is as follows:

[0080] (1) One-step state prediction

[0081]

[0082] in, This is a one-step prediction of the state at time k; Φ k,k-1 This is the one-step transition matrix from time k-1 to time k; This is the optimal estimate of the state at time k-1;

[0083] (2) State one-step prediction mean square error matrix

[0084]

[0085] Among them, P k|k-1 The mean square error matrix for one-step prediction of the state; P k-1(3) Filter gain

[0086]

[0087] Wherein, coefficient matrix K k This is called the filter gain; P is the transpose of the system measurement matrix at time k; k Let be the mean square error matrix of the optimal state estimate at time k;

[0088] (4) State estimation

[0089]

[0090] in, Z is the optimal estimate of the state at time k; k Measurement at time k; H k Let k be the system measurement matrix at time k;

[0091] (5) State estimation mean square error matrix

[0092] P k =(IK k H k )P k|k-1 (twenty one)

[0093] Furthermore, step 5 is specifically as follows:

[0094] After the alignment is completed, the sub-inertial navigation system obtains the current zero drift of the gyroscope and the zero bias of the accelerometer from the state estimate, as well as the misalignment angles of the main and sub-inertial navigation systems. The sub-inertial navigation system uses the three Euler angles obtained to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system. Combined with the attitude update algorithm in step 2, the real-time position and attitude measurement of the sub-inertial navigation system is realized.

[0095] Since the sub-inertial navigation system is fixed to the muzzle, the real-time position and attitude information of the sub-inertial navigation system is the real-time vibration of the muzzle.

[0096] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0097] Example

[0098] Combination Figure 1 The present invention discloses a method for measuring muzzle vibration during travel based on a combination of master inertial navigation and conventional navigation, comprising the following steps:

[0099] Step 1: Based on the artillery platform, design the installation positions of the main and sub-inertial navigation systems, including the high-precision main inertial navigation system 1 and the MEMS sub-inertial navigation system 2;

[0100] Step 2: Based on the output of the main and sub-inertial navigation sensors during the artillery's movement, design an attitude update algorithm based on gyroscope angle incremental updates;

[0101] Step 3: During the transfer and alignment stage, dynamic modeling of the outer rod arm error and flexural deformation is performed based on the characteristics of the gun barrel, and compensation is made for the rod arm effect and flexural deformation.

[0102] Step 4: Use the velocity and attitude deviations calculated by the MEMS sub-inertial navigation system relative to the velocity and attitude deviations calculated by the high-precision main inertial navigation system as the measurement information of the sub-inertial navigation system, and establish a transfer alignment Kalman filter with velocity plus attitude matching.

[0103] Step 5: In the navigation update phase, the sub-inertial navigation system uses the alignment error at the end of the transmission alignment as the initial error for navigation calculation to update the navigation state and complete the vibration measurement of the gun muzzle.

[0104] Furthermore, step 1 involves designing the installation positions of the main and sub-inertial navigation systems based on the artillery platform, including a high-precision main inertial navigation system 1 and a MEMS sub-inertial navigation system 2, as detailed below:

[0105] The high-precision anti-high overload inertial navigation system 1 is fixedly connected to the turret 4 and kept in a horizontal state. The turret 4 moves in a directional motion, which drives the high-precision anti-high overload inertial navigation system 1 to move together.

[0106] The MEMS sub-inertial navigation system 2 is fixed to the front end of the gun barrel 3 and is used to measure the position and attitude of the muzzle at the front end of the gun barrel 3.

[0107] Furthermore, the attitude update algorithm based on gyroscope angle increment updates, as described in step 2, based on the outputs of the main and sub-inertial navigation sensors during the artillery's movement, is as follows:

[0108] Different navigation systems use different coordinate systems, especially for navigation coordinate systems. The default is OX. n Y n Z n Used as a navigation coordinate system.

[0109] (1) Geographic coordinate system

[0110] The geographic coordinate system has its origin at the center of mass of the carrier. One coordinate axis is aligned with the local geographic vertical, and the other two axes lie in the local horizontal plane along the tangents of the local meridians and parallels of latitude, respectively. The Northeast-Eastern Sky (ENU) geographic coordinate system is chosen, where the x-axis points east, the y-axis points north, and the z-axis is perpendicular to the local horizontal plane and points upwards along the local vertical.

[0111] (2) Carrier coordinate system

[0112] Carrier coordinate system Ox b y b zb The origin point coincides with the centroid of the carrier. b To the right along the transverse axis of the carrier, y b Forward along the longitudinal axis of the carrier, z b The coordinate system is located upwards along the vertical axis of the carrier and is also known as the "right front upper" coordinate system.

[0113] (3) Navigation coordinate system

[0114] Since multiple coordinate systems are involved, it is necessary to transform these coordinate systems to the same coordinate system for solving the problem, using Ox n y n z n express.

[0115] (4) Main inertial navigation coordinate system

[0116] The main inertial navigation coordinate system is chosen to be consistent with the carrier coordinate system, using Ox m y m z m express.

[0117] (5) Sub-inertial navigation coordinate system

[0118] Sub-inertial navigation coordinate system using Ox s y s z s This indicates that the inertial navigation system is installed at the muzzle.

[0119] Step 2.1: First, initial alignment of the main and sub-inertial navigation systems (INS) is required. The INS is placed at rest, and accelerometer data is acquired. The pitch angle θ and roll angle γ are obtained using the gravity component relationship, and the yaw angle in the navigation coordinate system is obtained using a geomagnetic sensor. Complete the initial alignment of the inertial navigation system.

[0120] Step 2.1.1: Estimate the pitch angle θ and roll angle γ using the triaxial components of acceleration:

[0121]

[0122] in, The x, y, and z axis output values ​​of the accelerometer at the kth time in the carrier coordinate system.

[0123] Step 2.1.2: Combining the obtained pitch angle θ and roll angle γ, determine the magnetic field strength in the carrier coordinate system. Transform to navigation coordinate system

[0124]

[0125] The calculated yaw angle is:

[0126]

[0127] Step 2.1.3: Under static conditions, the three Euler angles can be used to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system, thus completing the initial alignment of the inertial navigation system.

[0128] Step 2.2 describes setting the initial zero point and using quaternions and the angular increment of the gyroscope to update the attitude of the inertial navigation carrier;

[0129] Step 2.2.1: Calculate the angular increment Δ from the gyroscope's updated data:

[0130]

[0131] ω x ω y ω z The scalar value of the three-axis angular velocity output by the instrument, T m Sampling time;

[0132] Step 2.2.2: Update the quaternion using angle increment:

[0133]

[0134] In the formula, q 1|k+1 Let q1 be the value of the quaternion at time k+1, and q 1|k Let q1 be the quaternion value at time k, and so on; Step 2.2.3: Normalize the quaternion:

[0135]

[0136] Normalization transforms a quaternion into a unit quaternion, where the sum of the squares of its four values ​​is 1.

[0137] Step 2.2.4: Obtain the direction cosine matrix based on the unit quaternion, using the formula:

[0138]

[0139] Step 2.2.5: Obtain the Euler angles from the direction cosine matrix as follows:

[0140]

[0141] Step 2.2.6: Based on the matrix information above and the force information, the components of the current acceleration along the three axes can be obtained. Distinguishing the three-axis components allows for compensation of the gravity component. Removing the gravity component yields the acceleration in the navigation coordinate system. Integrating the acceleration using Newtonian mechanics yields the velocity and position, as shown in the formula:

[0142]

[0143] in, The output value of the motion accelerometer is based on the compensation for the gravity component.

[0144] At this point, the instantaneous attitude, velocity, and position information of the turret and muzzle can be obtained.

[0145] Furthermore, in step 3, during the transfer alignment stage, dynamic modeling of the outer rod arm error and deflection deformation is performed based on the characteristics of the gun barrel, and compensation is made for the rod arm effect and deflection deformation, as detailed below:

[0146] Because the main and sub-inertial navigation systems are installed in different locations, their sensitive information differs to some extent. To improve the performance of the transmission alignment, certain measures need to be taken to compensate for errors caused by lever effects and deflection during information matching, so as to reflect the relationship between each error state and the observed quantity as accurately as possible. In the lever effect, the outer lever error has a much greater impact than the inner lever error, so the inner lever error is ignored for now, and only the outer lever error is considered.

[0147] (1) External arm error compensation

[0148] In practical applications, it is assumed that neither the main nor the sub-inertial navigation system (INS) may be installed at the center of the vehicle's oscillation, or even at a considerable distance. Therefore, the accelerometers of the main and sub-INS will have different sensitivities to acceleration. Errors caused by the lever arm need to be compensated for in real time during the transmission matching process.

[0149] like Figure 3 As shown, the inertial coordinate system is defined as O. i x i y i z i The carrier coordinate system is O b x b y b z b And believe O b It is the center of sway of the carrier, and in most studies it is considered to be the center of gravity of the carrier. Generally, the position of the center of gravity is determined based on the designed load distribution, and it is assumed that the center of gravity is fixed. It is also often assumed that the main inertial navigation system is installed at O. b The accelerometers of the sub-inertial navigation system are installed at a fixed point p in the carrier coordinate system.

[0150] Figure 4 middle, The position vector of the origin of the carrier coordinate system. Let p be the position vector of point p relative to the origin of the inertial coordinate system. Let p be the position vector of point p relative to the origin of the carrier coordinate system.

[0151] They are clearly related as follows:

[0152]

[0153] Differentiating both sides of the above equation with respect to time yields:

[0154]

[0155] Taking the differential of the above equation with respect to time, we can obtain:

[0156]

[0157] According to the principle of relative differentiation of vector differentials, we can obtain:

[0158]

[0159] in, This represents the linear acceleration of point p relative to the carrier coordinate system.

[0160] Similarly, we can obtain:

[0161]

[0162] Combining the above equations, we can obtain the expression for the linear acceleration of point p relative to the inertial coordinate system:

[0163]

[0164] When studying the lever effect, the carrier is generally considered to be a rigid structure. When flexible deformation exists, other methods are needed to compensate for the errors caused by the flexible deformation. We assume that point p is fixed relative to the carrier coordinate system, therefore:

[0165]

[0166]

[0167] The expression for linear acceleration can be further simplified to:

[0168]

[0169] Ideally, the installation point should be at the center of the carrier's sway, i.e. rp =0, thus eliminating the lever arm effect. In practice, during the transmission matching process, neither the master nor the slave inertial navigation system is installed at the center of the vehicle's sway, and the error caused by the lever arm effect is usually not negligible. The last two terms of the above equation are the basic expressions for the lever arm acceleration sensitive to the inertial navigation system due to the lever arm effect. Definition Let the lever arm acceleration be represented, then the basic equation for the lever arm effect error is:

[0170]

[0171] because:

[0172]

[0173] Therefore, further organization yields:

[0174]

[0175] in, For tangential acceleration, This is centripetal acceleration.

[0176] (2) Dynamic modeling of flexural deformation

[0177] Carrier deformation can be divided into two categories: one is static deformation, which is not absolutely constant, but only has a relatively long change cycle, hence it is also called quasi-static deformation; the other is dynamic flexible deformation, which changes faster in terms of detection.

[0178] In recent studies on organisms, the dynamic structural deformation of the corresponding carrier is usually regarded as a Markov process because the dynamic deformation of the carrier is a random variable caused by random disturbances. This invention proposes to use a second-order Markov process as the model for the dynamic deformation of the carrier, and assumes that the dynamic deformation processes of each axis are independent; that is, the pitch noise and roll noise caused by disturbances are independent of each other. The second-order Markov process of dynamic deformation is as follows:

[0179] Let the dynamic deformation angle be λ(t), which is a second-order Markov process excited by white noise, and let the dynamic deformation angular rate be... wf(t) That is: Expanded to:

[0180]

[0181] Equations of motion for dynamic deformation angular rate:

[0182]

[0183] Where, β x =2.146 / τ i (i = x, y, z), τ i The relevant timeframe can be determined depending on the specific carrier. i (t) is generally considered to be white noise with a certain variance. If it is colored noise, it needs to be whitened. Its variance satisfies: Represents the three elastic deformation angles λ x ,λ y ,λ z The variance.

[0184] Furthermore, step 4 involves using the velocity and attitude deviations calculated by the MEMS sub-inertial navigation system relative to the velocity and attitude deviations calculated by the high-precision main inertial navigation system as the measurement information of the sub-inertial navigation system, and establishing a transfer-aligned Kalman filter with velocity plus attitude matching, as detailed below:

[0185] (1) Error model of velocity plus attitude matching

[0186] The velocity vector relationships in the sub-inertial navigation system are as follows:

[0187]

[0188] From the fundamental equations of inertial navigation, we know that:

[0189]

[0190] Taking the derivative of both sides of the velocity vector formula with respect to time, substituting them into the above equation, and projecting them onto the navigation coordinate system, we can see that:

[0191]

[0192] in: Let be the attitude matrix of the sub-inertial navigation system.

[0193] Further analysis reveals:

[0194]

[0195] The acceleration of the sub-inertial navigation system relative to the i-frame is:

[0196]

[0197] Furthermore, it can be seen that:

[0198]

[0199] Similarly, in the main inertial navigation:

[0200]

[0201] Both of the above formulas contain The terms are obtained in different master and slave inertial navigation systems, and each represents different acceleration information:

[0202] In the sub-inertial navigation:

[0203]

[0204] In the main inertial navigation system:

[0205]

[0206] Combining the above equations, we can see that:

[0207]

[0208]

[0209] Subtract the two equations above and let It can be known that:

[0210]

[0211] and:

[0212]

[0213]

[0214] Furthermore, we can obtain:

[0215]

[0216] in: Is it a sub-inertial navigation system? s The comparison felt in

[0217]

[0218] in:

[0219] The acceleration caused by the rigid rotation of the main inertial navigation system, which is sensed by the sub-inertial navigation system;

[0220] The flexural acceleration sensed by the sub-inertial navigation system;

[0221] Sub-inertial accelerometer error.

[0222] Further results were obtained:

[0223]

[0224] Ignore higher-order small quantities And consider The results were:

[0225]

[0226] Assuming that the error terms caused by lever effect and flexible motion have been compensated, we can simplify to obtain:

[0227]

[0228] Attitude matrix using sub-inertial navigation Attitude matrix replacing the main inertial navigation system Finally, the differential equation for the velocity difference between the master and slave inertial navigation systems is obtained:

[0229]

[0230] Set the static deformation angle (including installation error) to (abbreviated as μ), the dynamic deformation angle (i.e., flexural deformation) is... (abbreviated as θ), at this time, due to the existence of static deformation angle and dynamic deformation angle, It should be changed to:

[0231]

[0232] In the formula, [μ×] and [θ×] represent the antisymmetric matrices of the static deformation angle and the dynamic deformation angle, respectively. Ignoring second-order minterms, the above formula can be approximated as:

[0233]

[0234] Further considering the attitude difference equation when considering the static deformation angle and the dynamic deformation angle, we have:

[0235]

[0236] After processing, the attitude measurement equation is obtained as follows:

[0237]

[0238] In the formula, φ represents the attitude deviation calculated by the master and slave inertial navigation systems, and Z... φ This represents the attitude difference between the master and slave inertial navigation systems after removing the effects of static and dynamic deformation angles.

[0239] (2) Kalman filter model for velocity plus attitude matching

[0240] The Kalman filter algorithm essentially utilizes all measurement information from the initial time to the current time, employing an iterative method that does not require storing previous measurements. It leverages both state and measurement equations. Building upon the measurement equations, the state equation is also incorporated into the filtering algorithm, utilizing both the inherent changes in the state and the measured quantities to maximize the accuracy of muzzle inertial navigation estimation.

[0241] Kalman filtering primarily employs a discrete recursive expression, and its state-space model is as follows:

[0242]

[0243] Among them, X k Let φ be the state vector of the system at time k, which is the state variable to be estimated; k,k-1 Γ is the state transition matrix from time k-1 to time k; k-1The system noise assignment matrix represents the degree to which each system noise from time k-1 to time k affects each state variable at time k; W k-1 Z represents the system noise vector at time k-1; k H represents the measurement vector of the system at time k; k V is the system measurement matrix at time k; k This represents the measurement noise vector at time k. Meanwhile, according to the requirements of Kalman filtering, W... k and V k Given mutually independent zero-mean Gaussian white noise vector sequences, satisfying:

[0244]

[0245] The above equation represents the condition that noise must satisfy during the Kalman filtering process, and also because Q k Let Q be the noise variance matrix of the system, while a certain state variable of the system may not have noise, therefore Q k R is a non-negative definite matrix; k To measure the noise variance matrix, and since each measurement contains noise, therefore R k It is a positive definite matrix.

[0246] The Kalman filter algorithm can be represented by the following equations:

[0247] (1) One-step state prediction

[0248]

[0249] (2) State one-step prediction mean square error matrix

[0250]

[0251] (3) Filtering gain

[0252]

[0253] (4) State estimation

[0254]

[0255] (5) State estimation mean square error matrix

[0256] P k =(IK k H k )P k|k-1 (75)

[0257] Set the static deformation angle (including installation error) to (abbreviated as μ), the dynamic deformation angle (i.e., flexural deformation) is... (abbreviated as θ), dynamic deformation angular rate (abbreviated as ω). The dynamic deformation angle θ adopts a second-order Markov model:

[0258]

[0259] Right now:

[0260]

[0261] in, Var(w) = Q = 4β 3 σ 2 σ is the variance of the dynamic deformation angle θ, τ is the correlation time, and w and Q are the excitation noise and their variances.

[0262] Select state variables Where ε represents the zero drift of the gyroscope. For accelerometer zero bias, the state equation Expand as

[0263]

[0264] The measurement equation z=Hx+v expands to

[0265]

[0266] Therefore, the system transformation matrix is

[0267]

[0268] The observation matrix is

[0269]

[0270] in, The attitude array established for the sub-inertial navigation.

[0271] Furthermore, in step 5, during the navigation update phase, the sub-inertial navigation system uses the alignment error at the end of the transmission alignment as the initial error for navigation calculation to update the navigation state and complete the muzzle vibration measurement, as detailed below:

[0272] After the alignment is completed, the sub-INS can obtain the current zero drift of the gyroscope and the zero bias of the accelerometer from the state estimate, as well as the misalignment angles of the master and sub-INS. The sub-INS uses the three Euler angles obtained to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system. Combined with the attitude update algorithm in step 2, the real-time position and attitude measurement of the sub-INS can be realized.

[0273] Since the sub-inertial navigation system is fixed to the muzzle, the real-time position and attitude information of the sub-inertial navigation system is the real-time vibration of the muzzle, thus completing the vibration measurement of the muzzle.

[0274] In summary, this invention employs a contact measurement method—installing a high-precision main inertial navigation system (INS) at the turret and a MEMS sub-INS at the muzzle—which, compared to traditional non-contact measurement methods such as optical methods, offers greater ease of installation and stability, avoiding the drawbacks of traditional optical methods such as susceptibility to interference, installation difficulties, and cumbersome instrument calibration. During the initial alignment phase, the high-precision main INS is used to transfer and align the MEMS sub-INS, falling within the scope of precise INS alignment. This ensures the MEMS sub-INS has accurate initial INS information, improving the reliability and accuracy of muzzle vibration measurement. In the navigation update phase, the sub-INS utilizes the alignment error at the end of the transfer alignment as the initial error for navigation calculation. Iterative calculation using an attitude update algorithm ensures the accuracy of the MEMS sub-INS's pose output, improving the real-time performance and reliability of the muzzle vibration measurement method.

Claims

1. A method for measuring muzzle vibration during travel based on a combination of master and slave inertial navigation systems, characterized in that, Includes the following steps: Step 1: Based on the artillery platform, design the installation positions of the main and sub-inertial navigation systems, including the main inertial navigation system and the MEMS sub-inertial navigation system; Step 2: Based on the output of the main inertial navigation and MEMS sub-inertial navigation sensors during the artillery's movement, design an attitude update algorithm based on gyroscope angle incremental update; Step 3: During the transfer and alignment stage, dynamic modeling of the outer rod arm error and flexural deformation is performed based on the characteristics of the gun barrel, and compensation is made for the rod arm effect and flexural deformation. Step 4: Use the velocity and attitude calculated by the MEMS sub-inertial navigation system, and the velocity and attitude deviations calculated by the main inertial navigation system, as the measurement information of the MEMS sub-inertial navigation system, and establish a transfer alignment Kalman filter with velocity plus attitude matching. Step 5: During the navigation update phase, the MEMS sub-inertial navigation system uses the alignment error at the end of the transmission alignment as the initial error for navigation calculation to update the navigation state and complete the muzzle vibration measurement. In step 1, the installation positions of the main and sub-inertial navigation systems are designed according to the artillery platform, including the main inertial navigation system and the MEMS sub-inertial navigation system, as detailed below: The main inertial navigation system is fixed to the turret and kept in a horizontal state. The turret's directional movement drives the main inertial navigation system to move together. The MEMS sub-inertial navigation system is fixed to the front end of the gun barrel and is used to measure the position and attitude of the muzzle at the front end of the gun barrel. In step 2, based on the outputs of the main inertial navigation system and the MEMS sub-inertial navigation system sensors during the artillery's movement, an attitude update algorithm based on gyroscope angle incremental updates is designed, as follows: Step 2.1: Place the inertial navigation system at rest, acquire accelerometer data, and obtain the pitch angle using the relationship between gravity components. and roll angle The yaw angle in the navigation coordinate system is obtained using a geomagnetic sensor. Complete the initial alignment of the inertial navigation system; Step 2.2: Set the initial zero point and update the attitude of the inertial navigation carrier using quaternions and the angular increment of the gyroscope. The outer boom error compensation in step 3 is as follows: Define the inertial coordinate system as O i x i y i z i The carrier coordinate system is O b x b y b z b O b The oscillation center of the carrier is located at point p, where the sub-inertial navigation accelerometer is mounted at a fixed point p in the carrier's coordinate system. The position vector of the origin of the carrier coordinate system. Let p be the position vector of point p relative to the origin of the inertial coordinate system. Let p be the position vector of point p relative to the origin of the carrier coordinate system. Then, the expression for the linear acceleration of point p relative to the inertial coordinate system is: (11) The last two terms in the above equation are the basic expressions for the lever arm acceleration sensitive to inertial navigation due to the lever arm effect; in, This represents the angular velocity output by the gyroscope in the inertial frame of reference. definition Let the lever arm acceleration be an expression. Then the basic equation for the lever arm effect error is: (12) in, Indicates the acceleration of the lever arm. For tangential acceleration, Centripetal acceleration; The dynamic modeling of the flexural deformation described in step 3 is as follows: Set the dynamic deformation angle to The dynamic deformation angular rate is That is: Expanded as: (13) in, , , These represent the dynamic deformation angular rates along the x, y, and z axes, respectively. , , These are the first derivatives of the dynamic deformation angles along the x, y, and z axes, respectively. Equations of motion for dynamic deformation angular rate: (14) Among them, let , , For the relevant time; It's white noise. If it were colored noise, it would need to be whitened. The variance satisfies , Represents the three elastic deformation angles The variance.

2. The method for measuring muzzle vibration during travel based on master-slave inertial navigation as described in claim 1, characterized in that, Step 2.1 is as follows: Step 2.1.1: Estimate the pitch angle using the triaxial components of acceleration. and roll angle : (1) (2) in, These are the x, y, and z axis output values ​​of the k-th accelerometer reading in the carrier coordinate system. Step 2.1.2: Obtain the magnetic field strength in the carrier coordinate system using a geomagnetic sensor. Combined with the obtained pitch angle and roll angle The magnetic field strength in the navigation coordinate system after transformation is obtained. The yaw angle was further calculated. for: (3) in, , These represent the pitch angle and roll angle calculated in the k-th iteration, respectively. (4) in, , , These represent the magnetic field strengths corresponding to the x, y, and z axes in the navigation coordinate system, respectively. Step 2.1.3: Under static conditions, use three Euler angles to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system to complete the initial alignment of the inertial navigation system.

3. The method for measuring muzzle vibration during travel based on master-slave inertial navigation as described in claim 1, characterized in that, Step 2.2 is as follows: Step 2.2.1: Calculate the angle increment from the gyroscope's updated data. : (5) In the formula, The scalar values ​​of the three-axis angular velocity output by the instrument. Sampling time; Step 2.2.2: Update the quaternion using angle increment: (6) In the formula, , , , The quaternions at time k+1 are respectively , , , value, , , , The quaternions at time k are respectively , , , value; Step 2.2.3: Normalize the quaternions: (7) in, , , , They are respectively , , , The value after normalization; normalization transforms the quaternion into a unit quaternion, where the sum of the squares of the four values ​​is 1. Step 2.2.4: Obtain the direction cosine matrix based on the unit quaternion, using the formula: (8) Step 2.2.5: Obtain the Euler angles from the direction cosine matrix as follows: (9) Step 2.2.6: Based on the direction cosine matrix information and specific force information, obtain the three-axis components of the current acceleration. Distinguishing the three-axis components can compensate for the gravity component. Removing the gravity component yields the motion acceleration in the navigation coordinate system. Performing Newtonian integration on the motion acceleration yields the velocity and position, as shown in the formula: (10) in, To calculate the output value of the motion accelerometer based on the compensated gravitational component, This represents the coordinate transformation matrix from time k-1 to time k, from the vehicle coordinate system b to the navigation coordinate system n.

4. The method for measuring muzzle vibration during travel based on master-slave inertial navigation as described in claim 1, characterized in that, The deviations between the velocity and attitude calculated by the MEMS sub-inertial navigation system in step 4 and those calculated by the main inertial navigation system are as follows: The differential equation for the velocity difference between the master and slave inertial navigation systems is: (15) In the formula, This indicates the speed difference between the master and slave inertial navigation systems. Let be the attitude matrix of the sub-inertial navigation system. This represents the antisymmetric matrix corresponding to the initial installation error angles of the master and slave inertial navigation systems. This represents the estimated installation error angle values ​​for the main and sub-inertial navigation systems; This represents the specific force felt by the main inertial navigation system in the coordinate system of the sub-inertial navigation system; This represents the Earth's rotational angular rate in the navigation coordinate system; This indicates the error of the sub-inertial accelerometer; The attitude measurement equation is: (16) In the formula, This represents the attitude deviation calculated by the master and slave inertial navigation systems. This represents the attitude difference between the main and sub-inertial navigation systems after removing the effects of static and dynamic deformation angles. Indicates the static deformation angle, including installation error; This represents the dynamic deformation angle, i.e., flexural deformation.

5. The method for measuring muzzle vibration during travel based on master-slave inertial navigation as described in claim 1, characterized in that, The Kalman filter model for velocity plus attitude matching described in step 4 is as follows: (1) One-step state prediction (17) in, for One-step prediction of the state at any given moment; for Time's up The one-step transition matrix for each time step; for Optimal estimation of the state at time step; (2) State one-step prediction mean square error matrix (18) in, The mean square error matrix for one-step prediction of the state; for The mean square error matrix of the optimal state estimate at time step; (3) Filtering gain (19) Wherein, the coefficient matrix This is called the filter gain; for The transpose of the system measurement matrix at time t; for The mean square error matrix of the optimal state estimate at time step; (4) State estimation (20) in, for Optimal estimation of the state at time step; for Measurement of time; for The system measurement matrix at time t; (5) State estimation mean square error matrix (21)。 6. The method for measuring muzzle vibration during travel based on master-slave inertial navigation as described in claim 1, characterized in that, Step 5 is described in detail below: After the alignment is completed, the sub-inertial navigation system obtains the current zero drift of the gyroscope and the zero bias of the accelerometer from the state estimate, as well as the misalignment angles of the main and sub-inertial navigation systems. The sub-inertial navigation system uses the three Euler angles obtained to obtain the direction cosine matrix from the carrier coordinate system to the navigation coordinate system. Combined with the attitude update algorithm in step 2, the real-time position and attitude measurement of the sub-inertial navigation system is realized. Since the sub-inertial navigation system is fixed to the muzzle, the real-time position and attitude information of the sub-inertial navigation system is the real-time vibration of the muzzle.

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