System-level calibration method for four-axis redundant gyroscope assembly based on dual-channel velocity observation

Abstract

The present invention provides a system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation, mainly addressing the high-precision calibration problem of multiple sets of four-axis redundant gyro assemblies in arbitrary configurations. The present invention adds a three-axis orthogonal accelerometer assembly as a calibration device, divides the four-axis gyro into two groups, and respectively forms an inertial navigation system with the three-axis orthogonal accelerometer, performs strapdown inertial navigation solution, calculates the dual-channel velocity error and constructs an observation value, and uses the same Kalman filter to complete the synchronous calibration of all parameter errors. The method uses the dual-channel velocity error as the observation value, has a unified calibration algorithm, and has complete error modeling, thereby improving the applicability and calibration accuracy to various redundant configuration modes.

Description

Technical Field

[0001] The invention belongs to the field of inertial navigation and mainly relates to a calibration method of a four-axis redundant gyroscope assembly. Background Art

[0002] Because space satellites operate in weightless or microgravity environments, onboard inertial measurement systems typically do not include accelerometers. Instead, gyroscopes are used in conjunction with star sensors, sun sensors, and Earth sensors to measure the satellite's attitude. Gyroscopes are required to operate year-round on satellite systems, placing extremely high demands on their lifespan and mean time between failures (MTBF). To improve the reliability and lifespan of gyroscopes, in addition to enhancing the reliability of individual gyros through raw material selection and design improvements, multi-gyroscope redundancy is also an effective approach. Component-level redundancy technology, by increasing the number of gyros to create redundant gyroscope assemblies, offers significant advantages in improving reliability, reducing size, and lowering costs. Four-axis redundant gyroscope assemblies are a commonly used component-level redundancy solution, improving the MTBF performance of three-axis gyroscope assemblies by 75% while minimizing the added size and weight. Currently, four-axis redundant gyro assemblies are commonly used in four configurations: orthogonal, oblique, pyramidal, and tetrahedral. Each gyro's installation angle varies in each configuration, making error calibration difficult. Existing discrete calibration methods require controlling the turntable to perform multiple tumbles based on the gyro's theoretical installation angle. This complex control and time-consuming calibration process require a high-precision turntable. Calibration accuracy is also affected by external factors, such as turntable foundation interference and unequal damper rigidity.

[0003] Patent CN201410599074.1 discloses a system-level calibration method for fiber optic gyroscopes in redundant inertial navigation systems based on attitude observation. This method targets redundant fiber optic gyroscope assemblies without accelerometers. The method groups three gyroscopes together, using the difference between each group's calculated attitude angle and the turntable's attitude angle as the observed quantity. Kalman filtering is then used to accurately calibrate the various errors. This method uses attitude differences as the observed quantity and the turntable's output angular position at the moment of stop as the reference. While this method does not rely on the turntable's angular rate accuracy, it does rely on its angular position accuracy. Calibration results are also affected by factors such as unequal stiffness of the shock absorbers.

[0004] Patent CN202011428886.1 discloses an error calibration method for a four-axis redundant inertial navigation system. The method targets a redundant inertial navigation system composed of a four-axis gyroscope and a four-axis accelerometer. First, the orthogonally mounted three-axis gyroscope and accelerometer assembly are calibrated, using velocity and position errors as observation values, and calibrated according to the conventional Kalman filter system-level calibration method; then, the three-axis orthogonal angular rate and specific force after calibration compensation are used as observation values, and the least squares method is used to calibrate the errors of the oblique gyroscope and accelerometer. The four-axis redundant inertial navigation system includes four common configuration schemes: orthogonal, oblique, pyramidal, and regular tetrahedron. This method is only applicable to four-axis redundant inertial navigation systems with orthogonal and oblique configurations, and has a limited scope of application. In addition, the method uses two algorithms for calibration in stages, and the process and algorithm are highly complex. The calibration accuracy of the previous stage inevitably affects the calibration results of the subsequent stage. The method does not calibrate the temporal and spatial synchronization errors between sensors, and the calibration accuracy is limited. Summary of the Invention

[0005] In order to solve the problem that the error calibration work relies on a high-precision turntable, and the calibration accuracy is affected by external factors such as turntable foundation interference and unequal stiffness of shock absorbers, the present invention provides a system-level calibration method for a four-axis redundant gyroscope assembly based on dual-channel velocity observation. The method adds a three-axis orthogonal accelerometer assembly as a calibration device, divides the four-axis gyroscope into two groups, and respectively forms an inertial navigation system with the three-axis orthogonal accelerometer and performs strapdown inertial navigation solution, calculates the dual-channel velocity error and constructs the observation value, and uses the same Kalman filter to complete the synchronous calibration of the full parameter error. The present invention uses the dual-channel velocity error as the observation value, has a unified calibration algorithm, and has complete error modeling, which can improve the applicability and calibration accuracy of various redundant configuration methods.

[0006] A system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation includes the following steps:

[0007] Step 1: Fixedly connect the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly, and install the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly on a turntable; establish a carrier coordinate system based on the installation axis direction of the three-axis orthogonal accelerometer assembly. The carrier coordinate system includes the x, y, and z axes and is defined in the right-front-up direction, that is, the coordinate axes are determined by x pointing to the right, y pointing to the front, and z pointing to the top;

[0008] Step 2: Control the turntable to rotate and stop according to a predetermined trajectory, and synchronously sample and store data; the stored data includes the original pulse number output by the four-axis redundant gyroscope assembly and the original pulse number output by the three-axis orthogonal accelerometer assembly; the data in the initial stationary stage is the data recorded when it first stops during the rotation process according to the predetermined trajectory;

[0009] Step 3: Establish a full-parameter calibration model for the four-axis redundant gyroscope assembly and a full-parameter calibration model for the three-axis orthogonal accelerometer assembly;

[0010] Step 4: Based on the stored data obtained in step 2, roughly estimate the gyro scale factor and the accelerometer scale factor, and correct the original pulse number of the four-axis redundant gyro assembly and the original pulse number of the three-axis orthogonal accelerometer assembly to obtain the compensated gyro angular rate and the compensated accelerometer specific force;

[0011] Step 5: Divide the gyros of the four-axis redundant gyro assembly into two groups, and form the first and second inertial navigation systems with the three-axis orthogonal accelerometer assembly respectively. Calculate the average of the compensated gyro angular rate and the compensated accelerometer specific force during the initial static phase. Perform coarse alignment on the first and second inertial navigation systems, respectively, to obtain the initial alignment attitude matrix of the two inertial navigation data sets.

[0012] Step 6: Based on the initial alignment attitude array obtained in step 5, the two sets of inertial navigation data are respectively subjected to conventional strapdown inertial navigation solution using the gyro angular rate and accelerometer specific force compensated during the calibration process, and the Kalman filter model parameters based on dual-channel velocity observation are established for error estimation.

[0013] Furthermore, based on the error estimation result of step 6, the compensated gyro angular rate and the compensated accelerometer specific force obtained in step 4 are corrected, and the compensated gyro angular rate is replaced by the new gyro angular rate obtained after correction, and the compensated accelerometer specific force is replaced by the new accelerometer specific force obtained after correction. Then, calculations are performed according to steps 5 and 6 to obtain a better estimation result of the error parameter to be calibrated, and the calibration is completed.

[0014] Furthermore, the configuration of the four-axis redundant gyro assembly is an orthogonal configuration, an oblique configuration, a quadrangular pyramid configuration, or a regular tetrahedron configuration.

[0015] Furthermore, the rotation rule of the predetermined trajectory is: during the rotation process, first remain stationary, and then rotate the x, y and z axes of the carrier coordinate system to the horizontal direction respectively, and use the coordinate axis rotated to the horizontal direction as the rotation axis, and rotate in the forward and reverse directions in turn; stay stationary for at least 1 minute between forward and reverse rotation, and stay stationary for at least 1 minute after reverse rotation before rotating the next coordinate axis; the forward and reverse rotation angles are not less than 90°.

[0016] Furthermore, the principle of dividing the gyroscopes into two groups is: number the four-axis gyroscopes as 1, 2, 3, and 4, and select any three of the four gyroscopes as the first group of inertial navigation systems; and the gyroscopes not selected in the first group of inertial navigation systems and any other two gyroscopes form the second group of inertial navigation systems.

[0017] Furthermore, the full parameter calibration model of the four-axis redundant gyro assembly is:

[0018]

[0019] Where, is a 4-dimensional vector, K G is the scaling factor matrix, K G The dimension is 4×3, is the 3-axis input angular rate, ε g is the 4-dimensional gyro bias; the subscript k represents the sampling period; the superscript b represents the carrier coordinate system; the superscript g represents the direction of the gyro sensitive axis;

[0020] Scaling factor matrix K G for:

[0021] K G =K G0 +δK G ;

[0022] where K G0 is the design value of the scaling factor matrix, δK G is the scale factor error matrix;

[0023] K G0 =<[K g1 K g2 K g3 K g4 ]>h G0 ;

[0024] K gi is the scale factor of the i-th gyroscope, i = 1, 2, 3, 4, symbol represents the diagonal matrix constructed based on vector u, h G0 Install the matrix for the theory;

[0025]

[0026] Among them, h i =[sinα i cosβ i sinα i sinβ i cosα i ] T , α i and β i is the theoretical installation angle between the i-th gyroscope and the carrier coordinate system, which is a known design value determined by the installation configuration;

[0027] The full parameter calibration model of the three-axis orthogonal accelerometer assembly is:

[0028]

[0029] Where, is a 3-dimensional vector, K A is the 3rd order scaling factor matrix, is the 3-axis input specific force, is the 3D accelerometer bias; represents the accelerometer inner lever arm of the x-axis, represents the accelerometer inner lever arm of the y-axis, and is the spatial non-synchronization error term; τ represents the time delay coefficient, is the time non-synchronization error term; K a2 is the coefficient of the quadratic term; W x 、W y 、M ωf is a coefficient matrix, and:

[0030]

[0031] Where W(i,:) represents the matrix The i-th row element, 0 i×j represents an i×j order zero matrix.

[0032] Furthermore, the steps of roughly estimating the gyro scale factor and the accelerometer scale factor, and correcting the original pulse number of the four-axis redundant gyro assembly and the original pulse number of the three-axis orthogonal accelerometer assembly to obtain the compensated gyro angular rate and the compensated accelerometer specific force are as follows:

[0033] Rough estimate of gyro scale factor k g and the accelerometer scale factor k a for:

[0034]

[0035] in The number of raw pulses output by the four-axis redundant gyro assembly during the initial stationary phase of the stored data The mean of Output raw pulse number of the three-axis orthogonal accelerometer component in the initial static phase of the stored data The mean of ω ie is the Earth's rotation angular rate, g is the local acceleration of gravity;

[0036] The raw pulse number of the four-axis redundant gyro component and the raw pulse number of the three-axis orthogonal accelerometer component per cycle are corrected according to the roughly estimated scale factor:

[0037]

[0038] in is the gyro angular rate after compensation, is the accelerometer specific force after compensation, I m represents the m-order unit matrix.

[0039] Furthermore, the steps of calculating the average of the compensated gyro angular rate and the compensated accelerometer specific force in the initial static phase and performing rough alignment on the first inertial navigation system and the second inertial navigation system are as follows:

[0040] Calculate the mean angular rate of the two sets of inertial navigation systems in the carrier coordinate system during the initial stationary phase and

[0041]

[0042] The average gyro angular rate in the initial stationary phase is recorded as In formula (5) for The i-th element of , i = 1, 2, 3, 4;

[0043] Calculate the initial alignment attitude matrix of the two sets of inertial navigation data:

[0044]

[0045] Where column vector N1=U×E1, N2=U×E2; is the accelerometer specific force during the initial static phase The mean of is the initial alignment attitude matrix of the first set of inertial navigation systems; is the initial alignment attitude matrix of the second inertial navigation system; the superscript n represents the navigation coordinate system, which is defined in the northeast celestial direction.

[0046] Furthermore, the steps of performing conventional strapdown inertial navigation solution on the two sets of inertial navigation data using the compensated gyro angular rate and compensated accelerometer specific force during the entire calibration process and establishing the Kalman filter model parameters based on dual-channel velocity observation for error estimation are as follows:

[0047] Establish the 47-dimensional Kalman filter error state X to be estimated:

[0048]

[0049] In the formula is the velocity error solved by the first set of inertial navigation systems, is the platform misalignment angle calculated by the first set of inertial navigation systems, is the velocity error solved by the second inertial navigation system, is the platform misalignment angle calculated by the second inertial navigation system, X p is the 35-dimensional error parameter to be calibrated:

[0050]

[0051] where δK g The 12-dimensional column vector constructed for the gyro scale factor error matrix elements, δK a 6-dimensional column vector constructed for the accelerometer scale factor error matrix;

[0052] Establish the state equation:

[0053]

[0054] In the formula represents the first-order derivative of the error state X; Q is the system noise, is the navigation system component of the Earth's rotation angular rate, g n is the navigation system component of the gravitational acceleration; The attitude matrix obtained by the first set of inertial navigation system navigation solution; The attitude matrix obtained by the second set of inertial navigation system navigation solution; Among them D f6 Indicates taking the matrix The 3×6 dimensional matrix consists of the (1st, 4th, 5th, 7th, 8th, 9th)th column elements, Accelerometer specific force The three-axis components of The angular velocity of the carrier system And there are:

[0055]

[0056] in is the gyro angular rate of the i-th axis, i=1,2,3,4; M kg1 and M kg2 is an intermediate calculation variable;

[0057] Establish the measurement equation:

[0058]

[0059] in are the velocities solved by the strapdown inertial navigation system of the first and second inertial navigation systems, respectively; V1 and V2 are the velocity measurement noises;

[0060] While performing two sets of strapdown inertial navigation solutions in each cycle, the Kalman filter is updated in time according to the state equation established by equation (9). When the turntable is stationary, sequential processing and measurement updates are performed according to equation (10) to achieve the estimation of the error state X.

[0061] Furthermore, based on the error estimation result of step 6, the compensated gyro angular rate obtained in step 4 is Compared with the compensated accelerometer The steps to make the correction are:

[0062] After correction, the new gyro angular rate is obtained Compared with accelerometer for:

[0063]

[0064] Where δK G δK is the error state estimation result g Constructed gyro scale factor error matrix, δK A δK is the error state estimation result a Constructed accelerometer scale factor error matrix;

[0065] Using the new gyro angular rate Compared with accelerometer replace and Calculate again according to steps 5 and 6 to obtain the error parameter X to be calibrated p The calibration is completed with a better estimation result.

[0066] A system using a system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation comprises a four-axis redundant gyro assembly, a three-axis orthogonal accelerometer assembly, a mounting transition plate, a turntable, and a calibration computer; the mounting transition plate is a supporting flat plate; the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly are arranged on the top surface of the mounting transition plate; the turntable is mounted on the bottom surface of the mounting transition plate; the four-axis redundant gyro assembly is connected to the three-axis orthogonal accelerometer assembly; the three-axis orthogonal accelerometer assembly is connected to the calibration computer; and the number of the four-axis redundant gyro assemblies is greater than or equal to one.

[0067] The beneficial effects of the present invention are as follows: by adding a three-axis orthogonal accelerometer, the calibration observation value is converted from angle information to velocity information, thereby getting rid of the dependence on a high-precision turntable, facilitating batch calibration, and improving calibration efficiency; the calibration method has no requirement for orthogonal installation of the gyro assembly, and is applicable to any configuration of orthogonal, oblique, quadrangular pyramid or regular tetrahedron; the observation value is constructed by dual-channel velocity error, and the same Kalman filter is used to complete the synchronous calibration of all parameter errors, and the algorithm and process are simple; the time synchronization, space synchronization and accelerometer quadratic terms are modeled, and the error modeling is complete. Compared with the prior art, the method of the present invention improves the estimation accuracy of the gyro scale factor by 97.3%, the estimation accuracy of the gyro zero bias by 89.3%, and the estimation accuracy of the gyro assembly installation deflection by 97.3%, thereby significantly improving the calibration accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of the gyro component calibration system;

[0069] Figure 2 are the gyro and accelerometer outputs in the simulation trajectory; (a) is the gyro output; (b) is the accelerometer output;

[0070] Figure 3 The gyro scale factor estimation error curves obtained by simulating the traditional method and the present method; (a) is the gyro scale factor estimation error curve of the traditional method; (b) is the gyro scale factor estimation error curve of the present method;

[0071] Figure 4 The gyro bias estimation error curves obtained by simulating the traditional method and the present method are shown in Figure 2. (a) is the gyro bias estimation error curve of the traditional method; (b) is the gyro bias estimation error curve of the present method.

[0072] Figure 5 The gyro assembly installation deflection angle estimation error curves obtained by simulation of the traditional method and the present method; among them, (a) is the gyro assembly installation deflection angle estimation error curve of the traditional method; (b) is the gyro assembly installation deflection angle estimation error curve of the present method. DETAILED DESCRIPTION

[0073] A system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation includes the following steps:

[0074] Step 1: Install the four-axis redundant gyro assembly on the calibration transition plate, securely connect it to the three-axis orthogonal accelerometer assembly, and install the calibration transition plate on the turntable. Establish a carrier coordinate system based on the mounting axis orientation of the three-axis orthogonal accelerometer assembly. The carrier coordinate system includes the x, y, and z axes and is defined in the right-front-up direction, i.e., x points to the right, y points to the front, and z points to the top.

[0075] The turntable includes a two-axis turntable or a three-axis turntable;

[0076] The configuration of the four-axis redundant gyro assembly is an orthogonal configuration, an oblique configuration, a quadrangular pyramid configuration, or a regular tetrahedron configuration;

[0077] Step 2: Control the turntable to rotate and stop according to the predetermined trajectory, synchronously sample and store data; the stored data includes the original pulse number output by the four-axis redundant gyro assembly and the raw pulse count output by the tri-axis orthogonal accelerometer assembly Used to complete system-level calibration offline; the data in the initial static phase is the data recorded when it is first stationary during the rotation process according to the predetermined trajectory;

[0078] The rotation rule of the predetermined trajectory is:

[0079] During the rotation process, the carrier is first held stationary, and then the x, y, and z axes of the carrier coordinate system are rotated to the horizontal direction. The coordinate axis rotated to the horizontal direction is used as the rotation axis, and the rotation is carried out in the forward and reverse directions in sequence. The forward and reverse rotations are stopped for at least 1 minute, and after the reverse rotation, the carrier is stopped for at least 1 minute before the next coordinate axis rotation is carried out. The forward and reverse rotation angles are not less than 90 degrees.

[0080] Step 3: Establish a full-parameter calibration model for the four-axis redundant gyroscope assembly and a full-parameter calibration model for the three-axis orthogonal accelerometer assembly;

[0081] The full parameter calibration model of the four-axis redundant gyro assembly is:

[0082]

[0083] Where, is a 4-dimensional vector, K G is the scaling factor matrix, K G The dimension is 4×3, is the 3-axis input angular rate, ε g is the 4-dimensional gyro bias; the subscript k represents the sampling period; the superscript b represents the carrier coordinate system; the superscript g represents the direction of the gyro sensitive axis;

[0084] Scaling factor matrix K G for:

[0085] K G =K G0 +δK G ;

[0086] where K G0 is the design value of the scaling factor matrix, δK G is the scale factor error matrix;

[0087] K G0 =<[K g1 K g2 K g3 K g4 ]>h G0 ;

[0088] K gi is the scale factor of the i-th gyroscope, i = 1, 2, 3, 4, symbol represents the diagonal matrix constructed based on vector u, h G0 Install the matrix for the theory;

[0089]

[0090] Among them, h i =[sinα i cosβ i sinα i sinβ i cosα i ] T , α i and β i is the theoretical installation angle between the i-th gyroscope and the carrier coordinate system, which is a known design value determined by the installation configuration;

[0091] The full parameter calibration model of the three-axis orthogonal accelerometer assembly is:

[0092]

[0093] Where, is a 3-dimensional vector, K A is the 3rd order scaling factor matrix, is the 3-axis input specific force, is the 3D accelerometer bias; represents the accelerometer inner lever arm of the x-axis, represents the accelerometer inner lever arm of the y-axis, is the spatial non-synchronization error term; τ represents the time delay coefficient, is the time non-synchronization error term; K a2 is the coefficient of the quadratic term; W x 、W y 、M ωf is a coefficient matrix, and:

[0094]

[0095] Where W(i,:) represents the matrix The i-th row element, 0 i×j represents the i×j order zero matrix;

[0096] Step 4: Based on the stored data obtained in step 2, roughly estimate the gyro and accelerometer scale factors and correct the original pulse number;

[0097] Rough estimate of gyro scale factor k g and the accelerometer scale factor k a :

[0098]

[0099] in The number of raw pulses output by the four-axis redundant gyro assembly during the initial stationary phase of the stored data The mean of Output raw pulse number of the three-axis orthogonal accelerometer component in the initial static phase of the stored data The mean of ω ie is the Earth's rotation angular rate, g is the local acceleration of gravity;

[0100] The raw pulse number of the four-axis redundant gyro component and the raw pulse number of the three-axis orthogonal accelerometer component per cycle are corrected according to the roughly estimated scale factor:

[0101]

[0102] in is the compensated gyro angular rate and accelerometer ratio, I m represents the m-order unit matrix;

[0103] Step 5: Divide the gyros of the four-axis redundant gyro assembly into two groups, and form the first and second inertial navigation systems with the three-axis orthogonal accelerometers respectively, and calculate the compensated gyro angular rate Compared with the compensated accelerometer The average value in the initial static stage is used to perform rough alignment on the first and second inertial navigation systems respectively;

[0104] The principle of gyro grouping is as follows: the four-axis gyros are numbered 1, 2, 3, and 4, and three of the four gyros are randomly selected to form the first group of inertial navigation systems; the gyros not selected in the first group of inertial navigation systems are combined with any other two gyros to form the second group of inertial navigation systems;

[0105] Take the grouping method of 1-2-3 as the first group and 2-3-4 as the second group as an example to calculate the average angular rate of the two groups of inertial navigation systems in the carrier coordinate system during the initial stationary phase. and

[0106]

[0107] The average gyro angular rate in the initial stationary phase is recorded as In formula (5) for The i-th element of , i = 1, 2, 3, 4;

[0108] Calculate the initial alignment attitude matrix of the two sets of inertial navigation data:

[0109]

[0110] Where column vector N1=U×E1, N2=U×E2; is the accelerometer specific force during the initial static phase The mean of is the initial alignment attitude matrix of the first set of inertial navigation systems; is the initial alignment attitude matrix of the second inertial navigation system; the superscript n represents the navigation coordinate system, which is defined in the northeast celestial direction;

[0111] Step 6: Based on the initial alignment attitude array, use the compensated gyro angular rate during the entire calibration process Compared with the compensated accelerometer Conventional strapdown inertial navigation solutions were performed on the two sets of inertial navigation data, and the Kalman filter model parameters based on dual-channel velocity observation were established for error estimation.

[0112] Establish the 47-dimensional Kalman filter error state X to be estimated:

[0113]

[0114] In the formula They represent the velocity error and platform misalignment angle solved by the first and second inertial navigation systems, respectively. p is the 35-dimensional error parameter to be calibrated:

[0115]

[0116] where δK g The 12-dimensional column vector constructed for the gyro scale factor error matrix elements, δK a 6-dimensional column vector constructed for the accelerometer scale factor error matrix;

[0117] Establish the state equation:

[0118]

[0119] In the formula represents the first-order derivative of the error state X; Q is the system noise, is the navigation system component of the Earth's rotation angular rate, g n is the navigation system component of the gravitational acceleration; The attitude matrix obtained by the first set of inertial navigation system navigation solution; The attitude matrix obtained by the second set of inertial navigation system navigation solution; Among them D f6 Indicates taking the matrix The 3×6 dimensional matrix consists of the (1st, 4th, 5th, 7th, 8th, 9th)th column elements, Accelerometer specific force The three-axis components of The angular velocity of the carrier system And there are:

[0120]

[0121] in is the gyro angular rate of the i-th axis, i=1,2,3,4; M kg1 and M kg2 is an intermediate calculation variable;

[0122] Establish the measurement equation:

[0123]

[0124] in are the velocities solved by the strapdown inertial navigation system of the first and second inertial navigation systems, respectively; V1 and V2 are the velocity measurement noises;

[0125] While performing two sets of strapdown inertial navigation solutions in each cycle, the Kalman filter time is updated according to the state equation established by formula (9). When the turntable is stationary, the sequential processing measurement update is performed according to formula (10) to achieve the estimation of the error state X.

[0126] Step 7: Based on the error state estimation result, the gyro angular rate obtained in step 4 is Compared with accelerometer Make corrections to obtain a new gyro angular rate Compared with accelerometer

[0127]

[0128] Where δK G δK is the error state estimation result g Constructed gyro scale factor error matrix, δK A δK is the error state estimation result a Constructed accelerometer scale factor error matrix;

[0129] Using the new gyro angular rate Compared with accelerometer replace and Calculate again according to steps 5 and 6 to obtain the error parameter X to be calibrated p The calibration is completed by obtaining a better estimation result to reduce the nonlinear error.

[0130] A system using a system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation comprises a four-axis redundant gyro assembly, a three-axis orthogonal accelerometer assembly, a mounting transition plate, a turntable, and a calibration computer; the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly are arranged on the top surface of the mounting transition plate; the turntable is mounted on the bottom surface of the mounting transition plate; the four-axis redundant gyro assembly is connected to the three-axis orthogonal accelerometer assembly; and the three-axis orthogonal accelerometer assembly is connected to the calibration computer.

[0131] The configuration of the four-axis redundant gyro assembly is an orthogonal configuration, an oblique configuration, a quadrangular pyramid configuration, or a regular tetrahedron configuration.

[0132] The number of the four-axis redundant gyro components is greater than or equal to 1.

[0133] The present invention will be further described below with reference to the accompanying drawings and examples.

[0134] Step 1: Reference Figure 1 , install the four-axis redundant gyro assembly on the calibration transition plate, connect it with the three-axis orthogonal accelerometer assembly, and install them together on a two-axis or three-axis turntable. Figure 1 Multiple gyro assemblies can be mounted on the same mounting plate, and batch calibration can be performed using the same triaxial speedometer assembly, improving calibration efficiency. The synchronous acquisition unit is responsible for synchronously sampling the gyro and speedometer assemblies and sending the sampled data to the calibration computer.

[0135] Step 2: Refer to Table 1 to control the turntable to rotate in sequence along the predetermined trajectory and remain stationary for 3 minutes at each position. During this period, the data of the four-axis gyroscope component and the three-axis orthogonal accelerometer component are sampled and stored for offline system-level calibration.

[0136] Table 1 System-level calibration turntable motion trajectory

[0137]

[0138]

[0139] Step 3: After data collection is completed, a full parameter calibration model of the four-axis gyroscope component and the three-axis orthogonal accelerometer component is established;

[0140] Establish a calibration model for the four-axis gyroscope assembly:

[0141]

[0142] Where, K is the number of 4-dimensional raw pulses output by the gyro component. G is a 4×3 dimensional scaling factor matrix, is the 3-axis input angular rate, ε g is the 4D gyro bias; the subscript k represents the sampling period; the superscript b represents the three-axis orthogonal carrier coordinate system, defined as the right front upper direction; the superscript g represents the direction of the gyro sensitive axis. G =K G0 +δK G , where K G0 =<[K g1 K g2 K g3 K g4 ]>h G0 is the design value of the scaling factor matrix, δK G is the scale factor error matrix, K gi is the scale factor of the i-th (i=1,2,3,4) gyroscope, symbol represents the diagonal matrix constructed based on vector u, h G0 Fit the matrix for theory:

[0143]

[0144] Among them, h i =[sinα i cosβ i sinα i sinβ i cosα i ] T , α i and β i is the theoretical installation angle between the ith gyroscope and the b-frame, which is a known design value determined by the installation configuration.

[0145] The implementation process takes the non-orthogonal installation of a regular tetrahedron configuration as an example. The design installation angles of the four-axis gyroscope in the regular tetrahedron configuration are α1 = -180°, α2 = α3 = α4 = 70.53°, β1 = 0, β2 = 0, β3 = 120°, and β4 = 240°. Substituting these values ​​into the theoretical installation matrix, the specific values ​​are:

[0146]

[0147] Build a complete calibration model for a three-axis orthogonal accelerometer assembly:

[0148]

[0149] Where, K is the number of 3D raw pulses output by the accelerometer component. A is the 3rd order scaling factor matrix, Enter the specific force values ​​for the 3 axes, is the 3D accelerometer bias; represents the inner arm of the x-axis and y-axis accelerometers, which is the spatial non-synchronization error term; τ represents the time delay coefficient, which is the time non-synchronization error term; K a2 is the quadratic coefficient of the accelerometer; W x 、W y 、M ωf is a coefficient matrix, and:

[0150]

[0151] Where W(i,:) represents the matrix The i-th row element, 0 i×j represents an i×j order zero matrix.

[0152] Step 4: Use the data from the initial static phase in the stored data to roughly estimate the gyro and accelerometer scale factors and correct the original pulse number;

[0153] Rough estimate of gyro and accelerometer scale factors:

[0154]

[0155] in The number of pulses output by the gyro and accelerometer components in the initial static phase The mean value, ω ie is the Earth's rotation angular rate, and g is the local acceleration of gravity.

[0156] The gyro and accelerometer outputs are corrected each cycle by a rough estimate of the scale factor:

[0157]

[0158] in is the compensated gyro angular rate and accelerometer ratio, I m represents the m-order unit matrix.

[0159] Step 5: Divide the four-axis gyroscope into two groups, and form two inertial navigation systems with the three-axis orthogonal accelerometer to calculate the angular rate. and Competitive The average value in the initial static stage is obtained, and the two sets of inertial navigation data are roughly aligned;

[0160] Each group of three gyros can be divided into four groups: 1-2-3, 1-2-4, 1-3-4, and 2-3-4. This solution uses the 1-2-3 and 2-3-4 groupings as examples for calibration. Other groupings are similar. The average gyro data in the initial static stage is calculated based on the two groups:

[0161]

[0162] The angular rate of the four-axis gyroscope in the initial static stage The mean of In formula (5) for The i-th element of .

[0163] Calculate the initial attitude matrix of two sets of inertial navigation data:

[0164]

[0165] Where column vector N1=U×E1, N2=U×E2; is the accelerometer specific force during the initial static phase The mean of is the initial attitude matrix of the first and second groups of inertial navigation systems; the superscript n represents the navigation coordinate system, which is defined in the northeast celestial direction.

[0166] Step 6: Based on the initial alignment attitude array, use the gyro angular rate Compared with accelerometer Conventional strapdown inertial navigation solutions were performed on the two sets of inertial navigation data, and the Kalman filter model parameters based on dual-channel velocity observation were established for error estimation.

[0167] Establish the 47-dimensional Kalman filter error state to be estimated:

[0168]

[0169] In the formula They represent the velocity error and platform misalignment angle calculated by the first and second strapdown inertial navigation systems, respectively. p is the 35-dimensional error parameter to be calibrated:

[0170]

[0171] where δK g is the gyro scale factor error matrix δK G 12-dimensional column vector constructed by elements, δK a is the accelerometer scale factor error matrix δK A Constructed 6-dimensional column vector.

[0172] Establish the state equation:

[0173]

[0174] Where Q is the system noise, g n are the navigation system components of the Earth's rotation angular rate and gravitational acceleration; The attitude matrix obtained by the navigation solution of the first and second groups of inertial navigation systems; Among them D f6 Indicates taking the matrix The 3×6 dimensional matrix consists of the (1st, 4th, 5th, 7th, 8th, 9th)th column elements, The accelerometer outputs specific force The three-axis components of The angular velocity of the carrier system And there are:

[0175]

[0176] in is the angular velocity of the carrier system The three-axis components.

[0177] Establish the measurement equation:

[0178]

[0179] in are the speeds solved by the strapdown inertial navigation systems of the two inertial navigation systems, and V1 and V2 are the speed measurement noises.

[0180] While performing two sets of strapdown inertial navigation solutions in each cycle, the Kalman filter is updated in time according to the state equation established by equation (9). When the turntable is stationary, sequential processing and measurement updates are performed according to equation (10), thereby realizing the estimation of the error state X.

[0181] Step 7: After the stored data processing is completed, repeat the data and perform steps 5 and 6 again to reduce the nonlinear error and obtain the estimated results of the model parameters. Calibration is complete.

[0182] The implementation effect of the present invention is further illustrated below through simulation experiments.

[0183] The simulation trajectory is set as follows: the system-level calibration simulation trajectory is generated according to the turntable motion shown in Table 1. The total time is 3600s, the sensor sampling period is 10ms, and the angular rate and specific force output by the four-axis gyroscope and accelerometer components are obtained as follows: Figure 2 As shown, the maximum angular rate is greater than 40° / s.

[0184] The sensor error RMSD is set as follows: gyro bias is 0.05° / h, random walk coefficient is 0.001° / √h, scale factor error is 100ppm, and the installation angle is 30". Accelerometer bias is 100μg, random noise is 2μg / √Hz, scale factor error is 100ppm, the installation angle is 30", and the quadratic coefficient is 100μg / g. 2 , the inner arm error is 1cm and the time delay is 1ms.

[0185] Figure 3 This is the gyro scale factor estimation error curve obtained by simulation using the traditional method and the technology of the present invention. Figure 3 The scale factor estimation error of the traditional method in (a) fluctuates violently, with the maximum value reaching 1×10 4 ppm; and Figure 3 In (b), the fluctuations during the estimation process using the present invention are significantly reduced, reaching a maximum value of 500 ppm. Statistics on the accuracy of the scale factor estimation at the end of calibration show that the traditional method achieved 32.93 ppm, while the present invention achieved 0.88 ppm, resulting in a 97.3% improvement in estimation accuracy.

[0186] Figure 4 This is the gyro bias estimation error curve obtained by simulation using the traditional method and the technology of the present invention. Figure 4 The gyro bias estimation error of the traditional method in (a) fluctuates violently, with the maximum value exceeding 0.2° / h; Figure 4 In (b), the estimation error fluctuation of the present invention's technique is significantly reduced, with a maximum value of 0.05° / h. Statistics on the gyro bias estimation accuracy at the end of calibration show that the traditional method is 0.022° / h, while the present invention's technique is 0.0024° / h, improving the estimation accuracy by 89.3%.

[0187] Figure 5 The gyro assembly installation deflection estimation error curve obtained by simulation using the traditional method and the technology of the present invention. Figure 5 The error of the installation deflection estimation of the traditional method in (a) fluctuates violently, with a maximum value of 6000″; Figure 5 The estimation error fluctuation of the technology of the present invention in (b) is significantly reduced, with the maximum value being on the order of 200". The estimation accuracy of the installation deflection angle at the end of calibration is statistically analyzed. The traditional method is 16.22", while the technology of the present invention is 0.43", and the estimation accuracy is improved by 97.3%.

[0188] The effects of the embodiments show that the technology of the present invention is applicable to the regular tetrahedron configuration and does not require orthogonal installation of redundant gyro components. The observation value is constructed by dual-channel velocity error, which is not affected by the turntable accuracy, and the time synchronization, space synchronization and accelerometer quadratic terms are fully modeled, thereby greatly improving the estimation accuracy of the redundant gyro component scale factor, zero bias and installation deflection angle.

Claims

1. A system-level calibration method for a four-axis redundant gyroscope assembly based on dual-channel velocity observation, characterized in that: The steps include: Step 1: Fix the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly together, and install the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly on a turntable; establish a carrier coordinate system according to the installation axis direction of the three-axis orthogonal accelerometer assembly, and the carrier coordinate system includes 、 and Axis, defined by the right front upper direction, that is, Point to the right, Point forward, Point upward to determine the coordinate axis; Step 2: Control the turntable to rotate and stop according to a predetermined trajectory, and synchronously sample and store data; the stored data includes the raw pulse counts output by the four-axis redundant gyroscope assembly and the raw pulse counts output by the three-axis orthogonal accelerometer assembly; the data during the initial stationary phase is recorded when the device first stops during the rotation process according to the predetermined trajectory; Step 3: Establish a full-parameter calibration model for the four-axis redundant gyroscope assembly and a full-parameter calibration model for the three-axis orthogonal accelerometer assembly; The full parameter calibration model of the four-axis redundant gyro assembly is: （1） Where, is a 4-dimensional vector, is the scaling factor matrix, The dimension is 4×3, Input angular rate for the 3 axes, is the 4-dimensional gyro bias; Indicates the sampling period; superscript Indicates the carrier coordinate system; superscript Indicates the direction of the gyro's sensitive axis; Scale factor matrix for: ； in is the design value of the scale factor matrix, is the scale factor error matrix; ； For the The scale factor of the gyroscope, ,symbol Indicates that according to the vector The constructed diagonal matrix, Install the matrix for the theory; in, , and For the The theoretical installation angle between each gyroscope and the carrier coordinate system is a known design value determined by the installation configuration; The full parameter calibration model of the three-axis orthogonal accelerometer assembly is: （2） Where, is a 3-dimensional vector, is the 3rd order scaling factor matrix, is the 3-axis input specific force, is the 3D accelerometer bias; express axis of the accelerometer inner lever arm, express axis of the accelerometer inner lever arm, and is the spatial asynchronous error term; represents the time delay coefficient, which is the time synchronization error term; is the coefficient of the quadratic term; 、 、 is a coefficient matrix, and: ， ， ； in Indicates taking the matrix No. row elements, express rank zero matrix; Step 4: Based on the stored data obtained in step 2, roughly estimate the gyro scale factor and the accelerometer scale factor, and correct the original pulse number of the four-axis redundant gyro assembly and the original pulse number of the three-axis orthogonal accelerometer assembly to obtain the compensated gyro angular rate and the compensated accelerometer specific force; Step 5: Divide the gyros of the four-axis redundant gyro assembly into two groups, and form the first and second inertial navigation systems with the three-axis orthogonal accelerometer assembly respectively. Calculate the average of the compensated gyro angular rate and the compensated accelerometer specific force during the initial static phase. Perform coarse alignment on the first and second inertial navigation systems, respectively, to obtain the initial alignment attitude matrix of the two inertial navigation data sets. Step 6: Based on the initial alignment attitude array obtained in step 5, the two sets of inertial navigation data are respectively subjected to conventional strapdown inertial navigation solution using the gyro angular rate and accelerometer specific force compensated during the calibration process, and the Kalman filter model parameters based on dual-channel velocity observation are established for error estimation.

2. A system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: According to the error estimation result of step 6, the compensated gyro angular rate and compensated accelerometer specific force obtained in step 4 are corrected, and the new gyro angular rate obtained after correction replaces the compensated gyro angular rate, and the new accelerometer specific force obtained after correction replaces the compensated accelerometer specific force. Then calculate according to steps 5 and 6 to obtain a better estimation result of the error parameter to be calibrated, and the calibration is completed.

3. The system-level calibration method of a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The configuration of the four-axis redundant gyro assembly is an orthogonal configuration, an oblique configuration, a quadrangular pyramid configuration, or a regular tetrahedron configuration.

4. The system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The rotation rule of the predetermined trajectory is: first keep still during the rotation process, and then respectively 、 and The axis is rotated to the horizontal direction, and the coordinate axis rotated to the horizontal direction is used as the rotation axis, and rotates in the forward and reverse directions in sequence; stand still for at least 1 minute between forward and reverse rotation, and stand still for at least 1 minute after reverse rotation before rotating the next coordinate axis; the forward and reverse rotation angles are not less than 90°.

5. The system-level calibration method of a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The principle of dividing the gyros into two groups is as follows: the four-axis gyros are numbered 1, 2, 3 and 4, and three of the four gyros are randomly selected as the first group of inertial navigation systems; the gyros not selected in the first group of inertial navigation systems and any other two gyros are combined into the second group of inertial navigation systems.

6. The system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The steps for roughly estimating the gyro scale factor and the accelerometer scale factor, and correcting the raw pulse count of the four-axis redundant gyro assembly and the raw pulse count of the three-axis orthogonal accelerometer assembly to obtain the compensated gyro angular rate and the compensated accelerometer specific force are as follows: Rough estimate of gyro scale factor and accelerometer scale factor for: （3） in The number of raw pulses output by the four-axis redundant gyro assembly during the initial stationary phase of the stored data The mean of Output raw pulse number of the three-axis orthogonal accelerometer component in the initial static phase of the stored data The mean of is the Earth's rotation angular rate, is the local gravitational acceleration; The raw pulse number of the four-axis redundant gyro component and the raw pulse number of the three-axis orthogonal accelerometer component per cycle are corrected according to the roughly estimated scale factor: （4） in is the gyro angular rate after compensation, To compensate for the accelerometer specific force, express Level unit array.

7. The system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The steps of calculating the average of the compensated gyro angular rate and the compensated accelerometer specific force in the initial static phase and performing coarse alignment on the first and second inertial navigation systems are as follows: Calculate the mean angular rate of the two sets of inertial navigation systems in the carrier coordinate system during the initial stationary phase and ; （5） The average gyro angular rate in the initial stationary phase is recorded as , in formula (5) for No. elements, ; Calculate the initial alignment attitude matrix of the two sets of inertial navigation data: （6） Where column vector , , , , ; is the accelerometer specific force during the initial static phase The mean of is the initial alignment attitude matrix of the first set of inertial navigation systems; is the initial alignment attitude matrix of the second inertial navigation system; Represents the navigation coordinate system, defined according to the northeast celestial direction.

8. The system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: The steps of performing conventional strapdown inertial navigation solution on the two sets of inertial navigation data using the compensated gyro angular rate and compensated accelerometer specific force during the entire calibration process and establishing the Kalman filter model parameters based on dual-channel velocity observation for error estimation are as follows: Establish the 47-dimensional Kalman filter error state to be estimated : （7） In the formula is the velocity error solved by the first set of inertial navigation systems, is the platform misalignment angle calculated by the first set of inertial navigation systems, is the velocity error solved by the second inertial navigation system, is the platform misalignment angle calculated by the second inertial navigation system, is the 35-dimensional error parameter to be calibrated: （8） in A 12-dimensional column vector constructed as the elements of the gyro scale factor error matrix, 6-dimensional column vector constructed for the accelerometer scale factor error matrix; is the 4D gyro bias; is the 3D accelerometer bias; express axis accelerometer inner lever arm; express axis accelerometer inner lever arm; represents the time delay coefficient; is the coefficient of the quadratic term; Establish the state equation: （9） In the formula Indicates error status The first derivative of ; is the system noise, is the navigation system component of the Earth's rotation angular rate, is the navigation system component of the gravitational acceleration; The attitude matrix obtained by the first set of inertial navigation system navigation solution; The attitude matrix obtained by the second set of inertial navigation system navigation solution; , ; , ,in Indicates taking the matrix The 3×6 dimensional matrix consists of the (1st, 4th, 5th, 7th, 8th, 9th)th column elements, 、 、 Accelerometer specific force The three-axis components of , ; , ; , , where the angular velocity of the carrier system is ; and there is: ； ； in For the axis gyro angular rate, ; and is an intermediate calculation variable; Establish the measurement equation: （10） in 、 are the speeds of the strapdown inertial navigation solutions of the first and second inertial navigation systems, 、 is the speed measurement noise; While performing two sets of strapdown inertial navigation solutions in each cycle, the Kalman filter time is updated according to the state equation established by formula (9). When the turntable is stationary, the measurement update is performed sequentially according to formula (10) to achieve the error state Estimates.

9. The system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1, characterized in that: According to the error estimation result of step 6, the compensated gyro angular rate obtained in step 4 is calculated. Compared with the compensated accelerometer The steps to make the correction are: Get the new gyro angular rate after correction Compared with accelerometer for: ； In the formula The error state estimation result The constructed gyro scale factor error matrix, The error state estimation result Constructed accelerometer scale factor error matrix; is the 4D gyro bias; is the 3D accelerometer bias; express axis accelerometer inner lever arm; express axis accelerometer inner lever arm; 、 and is the coefficient matrix; is the coefficient of the quadratic term; represents the time delay coefficient; Using the new gyro angular rate Compared with accelerometer replace and , calculate again according to steps 5 and 6 to obtain the error parameters to be calibrated The calibration is completed with a better estimation result.

10. A system using the system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation according to any one of claims 1 to 9, characterized in that: The invention comprises a four-axis redundant gyro assembly, a three-axis orthogonal accelerometer assembly, a mounting transition plate, a turntable and a calibration computer; the mounting transition plate is a supporting plate; the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly are arranged on the top surface of the mounting transition plate; the turntable is mounted on the bottom surface of the mounting transition plate; the four-axis redundant gyro assembly is connected to the three-axis orthogonal accelerometer assembly; the three-axis orthogonal accelerometer assembly is connected to the calibration computer; the number of the four-axis redundant gyro assemblies is greater than or equal to 1.

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