Four-axis redundant gyro assembly system-level calibration method based on dual-channel speed observation

Abstract

The invention provides a four-axis redundant gyroscope assembly system-level calibration method based on dual-channel speed observation, and mainly aims to solve the problem of high-precision calibration of multiple sets of four-axis redundant gyroscope assemblies which are configured at will. According to the method, a three-axis orthogonal acceleration meter assembly is added to serve as calibration equipment, four-axis gyroscopes are divided into two groups to form an inertial navigation system with the three-axis orthogonal acceleration meter respectively, strapdown inertial navigation calculation is carried out, a dual-channel speed error is calculated, an observation value is constructed, and synchronous calibration of a full-parameter error is completed by adopting the same Kalman filter; according to the method, the dual-channel speed error is used as an observation value, the calibration algorithm is unified, error modeling is complete, and the applicability and calibration precision of various redundancy configuration modes can be improved.

Description

Technical Field

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

[0002] Since space satellites are in a weightless or microgravity environment, accelerometers are usually not included in the onboard inertial measurement system. Gyro components are used together with star sensors, sun sensors, and earth sensors to complete the attitude measurement of space satellites. Onboard gyro components need to be used on satellite systems all year round, which places extremely high demands on the life and mean time between failures (MTBF) of the gyro. In order to improve the reliability and life of gyro components, in addition to improving the reliability of a single gyro through raw material screening and design improvements, multi-gyro redundant design has also become an effective way. Component-level redundancy technology forms redundant gyro components by increasing the number of gyros, which has obvious advantages in improving reliability, reducing volume, and reducing costs. The four-axis redundant gyro component is a commonly used component-level redundancy solution. Under the premise of increasing less volume and weight, the MTBF performance of the three-axis gyro component can be improved by 75%. At present, the commonly used four-axis redundant gyro components include orthogonal configuration, oblique configuration, four-sided pyramid configuration and regular tetrahedron configuration. The installation angles of each gyro in different configurations are different, which brings certain difficulties to the error calibration work. In the existing discrete calibration method, it is necessary to control the turntable to roll in multiple positions according to the theoretical installation angle of the gyro. The rotation control is complex, the calibration time is long, and it is heavily dependent on the high-precision turntable. The calibration accuracy is affected by external factors such as the interference of the turntable foundation and the unequal rigidity of the shock absorber.

[0003] Patent CN201410599074.1 discloses a method for calibrating the system-level fiber optic gyroscope of a redundant inertial navigation system based on attitude observation. The method is aimed at redundant fiber optic gyroscope components without accelerometers. Every three gyroscopes are divided into a group, and the difference between the attitude angle calculated by each group and the attitude angle of the turntable is used as the observation quantity, and the various errors are accurately calibrated through Kalman filtering. This method uses the attitude difference as the observation quantity and the output angular position of the turntable at the time of stopping as the reference. Although it does not rely on the angular velocity accuracy of the turntable, it relies on the angular position accuracy of the turntable. The calibration result is also affected by factors such as the unequal stiffness of the shock absorber.

[0004] Patent CN202011428886.1 discloses an error calibration method for a four-axis redundant inertial navigation system. The method is aimed at 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 components are calibrated, and the velocity and position errors are used as observation values, and the calibration is performed 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, four-sided pyramid 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; and this 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 next stage; this method does not calibrate the time and space asynchronous 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 rigidity of shock absorbers, the present invention provides a system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation. The method adds a three-axis orthogonal accelerometer assembly as a calibration device, divides the four-axis gyro into two groups to form an inertial navigation system with the three-axis orthogonal accelerometer and perform 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 a complete error modeling, which can improve the applicability and calibration accuracy of various redundant configuration methods.

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

[0007] Step 1: The four-axis redundant gyro assembly is fixedly connected to the three-axis orthogonal accelerometer assembly, and the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly are installed on a turntable; a carrier coordinate system is established according to the installation axis direction of the three-axis orthogonal accelerometer assembly, and the carrier coordinate system includes x, y and z axes, and is defined in the right front upper direction, that is, the coordinate axis is 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 gyro 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 is first stationary during the rotation according to the predetermined trajectory;

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

[0010] Step 4: Based on the stored data obtained in step 2, the gyro scale factor and the accelerometer scale factor are roughly estimated, and the original pulse number of the four-axis redundant gyro assembly and the original pulse number of the three-axis orthogonal accelerometer assembly are corrected 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 group of inertial navigation systems and the second group of 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 in the initial static stage, and perform rough alignment on the first group of inertial navigation systems and the second group of inertial navigation systems respectively to obtain the initial alignment attitude arrays of the two groups of inertial navigation data;

[0012] Step 6: Based on the initial alignment attitude array obtained in step 5, the two sets of inertial navigation data are respectively solved by conventional strapdown inertial navigation 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, according to the error estimation result of step 6, the compensated gyro angular velocity and the compensated accelerometer specific force obtained in step 4 are corrected, and the compensated gyro angular velocity is replaced by the corrected new gyro angular velocity, and the compensated accelerometer specific force is replaced by the corrected new accelerometer specific force. Then, steps 5 and 6 are followed to calculate 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 keep still, 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 still for at least 1 minute between forward and reverse rotation, and stay still for at least 1 minute after reverse rotation, and then rotate 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 combine the gyroscopes not selected in the first group of inertial navigation systems with any other two gyroscopes to form a second group of inertial navigation systems.

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

[0018]

[0019] In the formula, 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 zero 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 according to the 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 ith 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] In the formula, is a 3-dimensional vector, K A is the third-order scaling factor matrix, Input specific force for the 3 axes, is the 3D accelerometer zero 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 asynchronous error term; τ represents the time delay coefficient, is the temporal asynchronous error term; K a2 is the coefficient of the quadratic term; W x , W y 、M ωf is a coefficient matrix, and has:

[0030]

[0031] Where W(i,:) represents the matrix The i-th row element of 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 The raw pulse number output by the three-axis orthogonal accelerometer component in the initial static stage of the stored data The mean value of ie is the Earth's rotation angular rate, g is the local gravitational acceleration;

[0036] The original pulse number of the four-axis redundant gyro component and the original 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 stage and performing rough alignment on the first inertial navigation system and the second inertial navigation system are as follows:

[0040] Calculate the mean angular velocity of the two 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 using the compensated gyro angular rate and the compensated accelerometer specific force in the whole calibration process to perform conventional strapdown inertial navigation solutions on the two sets of inertial navigation data, 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 inertial navigation system, 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 from 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 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; Where D f6 Represents taking the matrix The 3×6 dimensional matrix consists of the elements in the (1st, 4th, 5th, 7th, 8th, 9th)th columns of 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 speeds solved by the strapdown inertial navigation system of the first and second inertial navigation systems, respectively; V1 and V2 are the speed 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 estimate the error state X.

[0061] Furthermore, according to 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 Comparison with accelerometer for:

[0063]

[0064] Where δK G δK is the error state estimation result g The 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 rate Comparison 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 plate; the top surface of the mounting transition plate is provided with a four-axis redundant gyro assembly and a three-axis orthogonal accelerometer assembly; the bottom surface of the mounting transition plate is provided with a turntable; 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.

[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, tetrahedral 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; 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 assembly 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; wherein (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 simulating the traditional method and the present method; wherein, (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] The system-level calibration method of 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, fix it to the three-axis orthogonal accelerometer assembly, and install the calibration transition plate on the turntable; establish the carrier coordinate system according to the installation axis direction of the three-axis orthogonal accelerometer assembly. The carrier coordinate system includes x, y and z axes, which are defined in the right front and upper direction, that is, the coordinate axis is determined by x pointing to the right, y pointing to the front, and z pointing to the top;

[0075] The turntable includes a double-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 The raw pulse count output by the three-axis orthogonal accelerometer assembly Used to complete system-level calibration offline; the data in the initial static stage 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 kept still, and then the x, y and z axes of the carrier coordinate system are rotated to the horizontal direction respectively, and the coordinate axis rotated to the horizontal direction is used as the rotation axis, and then rotated in the positive and negative directions in sequence; it is kept still for at least 1 minute between the positive and negative rotations, and after the negative rotation, it is kept still for at least 1 minute before rotating the next coordinate axis; the positive and negative rotation angles are not less than 90°;

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

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

[0082]

[0083] In the formula, 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 zero 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 according to the 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 ith 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] In the formula, is a 3-dimensional vector, K A is the third-order scaling factor matrix, Input specific force for the 3 axes, is the 3D accelerometer zero bias; represents the accelerometer inner lever arm of the x-axis, represents the accelerometer inner lever arm of the y-axis, is the spatial asynchronous error term; τ represents the time delay coefficient, is the temporal asynchronous error term; K a2 is the coefficient of the quadratic term; W x , W y 、M ωf is a coefficient matrix, and has:

[0094]

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

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

[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 The raw pulse number output by the three-axis orthogonal accelerometer component in the initial static stage of the stored data The mean value of ie is the Earth's rotation angular rate, g is the local gravitational acceleration;

[0100] The original pulse number of the four-axis redundant gyro component and the original 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 specific force, 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 group of inertial navigation systems and the second group of 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 stationary stage, and the first set of inertial navigation systems and the second set of inertial navigation systems are roughly aligned respectively;

[0104] The principle of gyro grouping is: number the four-axis gyros as 1, 2, 3, and 4, and select any three of the four gyros as 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 in the initial stationary stage. 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 It is the initial alignment attitude array of the first set of inertial navigation systems; is the initial alignment attitude array 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 are performed on the two sets of inertial navigation data respectively, and the Kalman filter model parameters based on dual-channel velocity observation are 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 from 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 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; Where D f6 Represents taking the matrix The 3×6 dimensional matrix consists of the elements in the (1st, 4th, 5th, 7th, 8th, 9th)th columns of 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 speeds solved by the strapdown inertial navigation system of the first and second inertial navigation systems, respectively; V1 and V2 are the speed 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 Comparison with accelerometer Make corrections to obtain a new gyro angular rate Comparison with accelerometer

[0127]

[0128] Where δK G δK is the error state estimation result g The 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 rate Comparison with accelerometer replace and Calculate again according to steps 5 and 6 to obtain the error parameter X to be calibrated p A better estimation result is obtained to reduce the nonlinear error and the calibration is completed.

[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 installed 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 is further described below in conjunction with the accompanying drawings and embodiments.

[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 In the process, multiple sets of gyro components can be installed on the same mounting plate, and batch calibration can be performed using the same set of three-axis speedometer components to improve calibration efficiency. The function of the synchronous acquisition unit is to synchronously sample the gyro component and the speedometer component and send the sampled data to the calibration computer.

[0135] Step 2: Refer to Table 1 to control the turntable to rotate in sequence according to the predetermined trajectory, and stay still 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 gyro assembly and the three-axis orthogonal accelerometer assembly is established;

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

[0141]

[0142] In the formula, is the number of 4-dimensional raw pulses output by the gyro component, K G is a 4×3 dimensional scaling factor matrix, is the 3-axis input angular rate, ε g is the 4-dimensional gyro zero 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. The scaling factor matrix K 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 according to the 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 system, which is a known design value determined by the installation configuration.

[0145] The implementation process takes the non-orthogonal installation of the regular tetrahedron configuration as an example. The design installation angle of the four-axis gyroscope in the regular tetrahedron configuration is α1 = -180°, α2 = α3 = α4 = 70.53°, β1 = 0, β2 = 0, β3 = 120°, β4 = 240°. The specific value of the theoretical installation matrix is:

[0146]

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

[0148]

[0149] In the formula, K is the number of 3D raw pulses output by the accelerometer component. A is the third-order scaling factor matrix, Enter the specific force values ​​for the 3 axes, is the 3D accelerometer zero 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 has:

[0150]

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

[0152] Step 4: Use the data of 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 of ie is the Earth's rotation angular rate, and g is the local gravitational acceleration.

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

[0157]

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

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

[0160] Every three gyros are grouped into one group, and there are four possible combinations: 1-2-3, 1-2-4, 1-3-4, and 2-3-4. This solution uses the two groupings of 1-2-3 and 2-3-4 as examples for calibration, and the 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 gyro in the initial static stage The mean of In formula (5) for The ith 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 Comparison with accelerometer Conventional strapdown inertial navigation solutions are performed on the two sets of inertial navigation data respectively, and the Kalman filter model parameters based on dual-channel velocity observation are 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 The 12-dimensional column vector constructed by the 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; Where D f6 Represents taking the matrix The 3×6 dimensional matrix consists of the elements in the (1st, 4th, 5th, 7th, 8th, 9th)th columns of 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 time is updated according to the state equation established by equation (9). When the turntable is stationary, sequential processing 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, the data is reused to 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 by simulation experiments below.

[0183] The simulation trajectory is set as follows: The system-level calibration simulation trajectory is generated according to the turntable motion mode 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 mean square error is set as follows: gyro bias is 0.05° / h, random walk coefficient is 0.001° / √h, scale factor error is 100ppm, installation deflection angle is 30″; accelerometer bias is 100μg, random noise is 2μg / √Hz, scale factor error is 100ppm, installation deflection angle is 30″, quadratic coefficient is 100μg / g 2 , the inner arm error is 1cm and the time delay is 1ms.

[0185] Figure 3 The figure is the gyro scale factor estimation error curve obtained by simulating the traditional method and the technology of the present invention. Figure 3 The error of the scale factor estimation of the traditional method in (a) fluctuates violently, with the maximum value reaching 1×10 4 ppm; and Figure 3 (b) The fluctuation in the estimation process of the present invention is significantly reduced, with the maximum value being at the order of 500ppm. The estimation accuracy of the scale factor at the end of the calibration is statistically analyzed. The traditional method is 32.93ppm, while the present invention is 0.88ppm. The estimation accuracy of the present invention is improved by 97.3%.

[0186] Figure 4 This is the gyro bias estimation error curve obtained by simulating 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 (b) The estimation error fluctuation of the present invention is significantly reduced, with the maximum value at the order of 0.05° / h. The gyro bias estimation accuracy at the end of calibration is statistically analyzed. The traditional method is 0.022° / h, while the present invention is 0.0024° / h. The estimation accuracy of the present invention is improved by 89.3%.

[0187] Figure 5 The gyro assembly installation deflection angle estimation error curve obtained by simulation of 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, and the maximum value is at 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", and 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 assemblies. The observation values ​​are constructed by dual-channel velocity errors, which are not affected by the turntable accuracy, and the time synchronization, space synchronization and accelerometer quadratic terms are completely modeled, thereby greatly improving the estimation accuracy of the redundant gyro assembly scale factor, zero bias and installation deflection angle.

Claims

1. A system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation, characterized in that: The steps include: Step 1: The four-axis redundant gyro assembly is fixedly connected to the three-axis orthogonal accelerometer assembly, and the four-axis redundant gyro assembly and the three-axis orthogonal accelerometer assembly are installed on a turntable; a carrier coordinate system is established according to the installation axis direction of the three-axis orthogonal accelerometer assembly, and the carrier coordinate system includes x, y and z axes, and is defined in the right front upper direction, that is, the coordinate axis is determined by x pointing to the right, y pointing to the front, and z pointing to the top; 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 gyro 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 is first stationary during the rotation according to the predetermined trajectory; Step 3: Establish a full parameter calibration model of the four-axis redundant gyro assembly and a full parameter calibration model of the three-axis orthogonal accelerometer assembly; Step 4: Based on the stored data obtained in step 2, the gyro scale factor and the accelerometer scale factor are roughly estimated, and the original pulse number of the four-axis redundant gyro assembly and the original pulse number of the three-axis orthogonal accelerometer assembly are corrected 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 group of inertial navigation systems and the second group of 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 in the initial static stage, and perform rough alignment on the first group of inertial navigation systems and the second group of inertial navigation systems respectively to obtain the initial alignment attitude arrays of the two groups of inertial navigation data; Step 6: Based on the initial alignment attitude array obtained in step 5, the two sets of inertial navigation data are respectively solved by conventional strapdown inertial navigation 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. According to claim 1, a system-level calibration method for a four-axis redundant gyro assembly based on dual-channel velocity observation is 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 compensated gyro angular rate is replaced by the corrected new gyro angular rate, and the compensated accelerometer specific force is replaced by the corrected new accelerometer specific force. Then, according to steps 5 and 6, a better estimation result of the error parameter to be calibrated is obtained, 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 is 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 of a four-axis redundant gyro assembly based on dual-channel velocity observation according to claim 1 is characterized in that: The rotation rule of the predetermined trajectory is: first keep still during the rotation process, 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; keep still for at least 1 minute between forward and reverse rotation, and keep 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 is characterized in that: The principle of dividing the gyroscopes into two groups is: the four-axis gyroscopes are numbered as 1, 2, 3 and 4, and three of the four gyroscopes are randomly selected as the first group of inertial navigation systems; the gyroscopes not selected in the first group of inertial navigation systems are combined with any other two gyroscopes to form the second group of inertial navigation systems.

6. 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: The full parameter calibration model of the four-axis redundant gyro assembly is: In the formula, is a 4-dimensional vector, K G is the scaling factor matrix, K G The dimension is 4×3, is the angular rate of the three axes input, ε g is the 4-dimensional gyro zero 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; Scaling factor matrix K G for: K G =K G0 +δK G ; Where K G0 is the design value of the scaling factor matrix, δK G is the scale factor error matrix; K G0 =<[K g1 K g2 K g3 K g4 ]>h G0 ; K gi is the scale factor of the i-th gyroscope, i = 1, 2, 3, 4, symbol represents the diagonal matrix constructed according to the vector u, h G0 Install the matrix for the theory; 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 carrier coordinate system, which is a known design value determined by the installation configuration; The full parameter calibration model of the three-axis orthogonal accelerometer assembly is: In the formula, is a 3-dimensional vector, K A is the third-order scaling factor matrix, Input specific force for the 3 axes, is the 3D accelerometer zero 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 asynchronous error term; τ represents the time delay coefficient, is the temporal asynchronous error term; K a2 is the coefficient of the quadratic term; W x , W y 、M ωf is a coefficient matrix, and has: Where W(i,:) represents the matrix The i-th row element of i×j represents an i×j-order zero matrix.

7. 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: 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: Rough estimate of gyro scale factor k g and the accelerometer scale factor k a for: 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 The raw pulse number output by the three-axis orthogonal accelerometer component in the initial static stage of the stored data The mean value of ie is the Earth's rotation angular rate, g is the local gravitational acceleration; The original pulse number of the four-axis redundant gyro component and the original pulse number of the three-axis orthogonal accelerometer component per cycle are corrected according to the roughly estimated scale factor: in is the gyro angular rate after compensation, is the accelerometer specific force after compensation, I m represents the m-order unit matrix.

8. 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 steps of calculating the mean of the compensated gyro angular rate and the compensated accelerometer specific force in the initial static stage and performing rough alignment on the first inertial navigation system and the second inertial navigation system are as follows: Calculate the mean angular velocity of the two inertial navigation systems in the carrier coordinate system during the initial stationary phase and 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; Calculate the initial alignment attitude matrix of the two sets of inertial navigation data: 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.

9. 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 steps of using the compensated gyro angular rate and compensated accelerometer specific force in the whole calibration process to perform conventional strapdown inertial navigation solution on the two sets of inertial navigation data, 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 X to be estimated: 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: where δK g The 12-dimensional column vector constructed from the gyro scale factor error matrix elements, δK a 6-dimensional column vector constructed for the accelerometer scale factor error matrix; Establish the state equation: 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 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; Where D f6 Represents taking the matrix The 3×6 dimensional matrix consists of the elements in the (1st, 4th, 5th, 7th, 8th, 9th)th columns of Accelerometer specific force The three-axis components of The angular velocity of the carrier system And there are: 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; Establish the measurement equation: in are the speeds solved by the strapdown inertial navigation system of the first and second inertial navigation systems, respectively; V1 and V2 are the speed measurement noises; 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 estimate the error state X.

10. 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: According to 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: After correction, the new gyro angular rate is obtained Comparison with accelerometer for: Where δK G δK is the error state estimation result g The constructed gyro scale factor error matrix, δK A δK is the error state estimation result a Constructed accelerometer scale factor error matrix; Using the new gyro rate Comparison 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.

11. A system using the system-level calibration method of a four-axis redundant gyro assembly based on dual-channel velocity observation according to any one of claims 1 to 10, characterized in that: It includes 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 top surface of the mounting transition plate is provided with a four-axis redundant gyro assembly and a three-axis orthogonal accelerometer assembly; the bottom surface of the mounting transition plate is provided with a turntable; the four-axis redundant gyro assembly is connected with the three-axis orthogonal accelerometer assembly; the three-axis orthogonal accelerometer assembly is connected with the calibration computer; the number of the four-axis redundant gyro assemblies is greater than or equal to 1.

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