Calibration method of rotating bomb strapdown geomagnetic sensor and gyroscope in series

Abstract

The invention relates to a rotating missile strapdown geomagnetic sensor and gyroscope series calibration method. The method comprises the following steps: using the collected rotating missile three-axis geomagnetic sensor measurement value #imgabs0#, fitting ellipsoid parameters A and X0 according to the geomagnetic measurement principle, combining the geomagnetic field strength of the calibration point #imgabs1# to calculate the geomagnetic sensor error parameter, compensating the #imgabs2# to obtain the three-axis geomagnetic sensor theoretical output #imgabs3#, selecting the #imgabs4# as the observation variable Z(t) of the filter, selecting the rotating body attitude quaternion, the gyroscope error parameter and the zero bias error as the state variable of the system, further constructing the gyroscope error parameter filtering model, and using the EKF filtering algorithm to complete the optimal filtering estimation of the state equation X(k) #imgabs5# to calculate the gyroscope error parameter, and compensating the three-axis gyroscope measurement output ω m The present invention realizes the serial calibration and measurement data compensation of two navigation sensors, the missile-borne geomagnetic sensor and the gyroscope, and has important theoretical value and practical significance for solving the high-precision measurement problem in the guidance transformation of rotating missiles.

Description

Technical Field

[0001] The invention relates to the problem of strapdown sensor calibration in the field of rotating missile navigation and control, and in particular to a method for calibrating a strapdown geomagnetic sensor and a gyroscope in series connection of a rotating missile based on magnetic measurement information. Background Art

[0002] Due to the special application environment of high overload, high self-rotation and high speed of rotating missiles, existing missile-borne navigation sensors generally have various measurement errors such as zero bias error, scale factor error, and inter-axis non-orthogonality error. Therefore, it is necessary to calibrate the airborne sensors before launching to improve their measurement accuracy. Summary of the invention

[0003] In response to the problem of prior calibration of the above-mentioned rotating missile geomagnetic / inertial combined navigation system, the present invention provides a method for calibrating a rotating missile strapdown geomagnetic sensor and a gyroscope in series, which realizes the joint calibration and measurement output compensation of the missile-borne geomagnetic sensor and the gyroscope. It has important theoretical value and practical significance for solving the difficult problem of high-precision measurement in the guidance transformation of rotating missiles.

[0004] The method comprises the following steps:

[0005] S1 collects the geomagnetic field strength at the calibration point And collect the three-axis geomagnetic sensor measurement values ​​of the rotating missile

[0006] S2 uses the three-axis geomagnetic sensor to measure the value According to the principle of geomagnetic measurement, the ellipsoid parameters A and X0 are fitted;

[0007] S3 combined with Calculate the geomagnetic sensor error parameter matrix K m and bias error

[0008] S4 constructs a geomagnetic sensor measurement error model, Compensation to obtain the theoretical output of the three-axis geomagnetic sensor

[0009] S5 selects the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the missile attitude quaternion q, the gyro error related parameter C and the zero bias error ε are selected g The system state equation as the filter state variable;

[0010] S6 builds a gyro error parameter filtering model and uses the EKF filtering algorithm to complete the optimal filtering estimation of the state equation X(k) Calculate the inverse matrix estimate of the gyro error parameter matrix and bias error estimate

[0011] S7 builds a three-axis gyro measurement error model and calculates the three-axis gyro measurement value ω m Compensation gives the theoretical output ω′ i .

[0012] The magnetic field strength at the calibration point is a constant, which is obtained through collection and measurement.

[0013] According to the principle of geomagnetic measurement, the measurement output data of the rotating elastic geomagnetic sensor in different postures is defined. Distributed on a standard ellipsoid surface, the ellipsoid equation is:

[0014] F(η,z)=a1x 2 +a2y 2 +a3z 2 +2a4xy+2a5xz+2a6yz+2a7x+2a8y+2a9z+a0=0;

[0015] In the above formula, η=[a1,a2,a3,a4,a5,a6,a7,a8,a9] T is the ellipsoid parameter, a0 is a constant; F(η,z) is the distance from the geomagnetic sensor output data x, y, z to the ellipsoid surface F(η,z) = 0, x, y, z correspond to the output values ​​of each axis of the three-axis geomagnetic sensor

[0016] The fitting ellipsoid parameters A and X0 are:

[0017] Fitting the ellipsoid equation vector yields:

[0018]

[0019] The minimum value of the sum of squares of F(η, z) is used as the fitting criterion, that is, the fitting criterion formula is:

[0020]

[0021]

[0022] In the above formula, is the ellipsoid shape matrix; is the center point of the ellipsoid, is the inverse matrix of A.

[0023] Furthermore, let the The geomagnetic sensor error parameter matrix K m and bias error The relationship is:

[0024] Geomagnetic sensor error parameter K m and The calculation formula is:

[0025]

[0026] In the above formula, is the error parameter matrix of the three-axis geomagnetic sensor, c xx ,c yy ,c zz is the sensitivity error coefficient of each axis of the geomagnetic sensor, c xy ,c xz ,c zy K is the non-orthogonality error parameter among the three axes of the geomagnetic sensor including the installation error angle; -1 m is the geomagnetic sensor error parameter K m The inverse matrix of is the zero bias error of the geomagnetic sensor.

[0027] The geomagnetic sensor measurement error model is:

[0028] The actual measurement output of the geomagnetic sensor is defined as:

[0029]

[0030]

[0031]

[0032] In the above formula, The ideal output of the three-axis geomagnetic sensor, is the geomagnetic field component in the reference coordinate system; v(t) is the white noise measured by the magnetic sensor; q=[q0,q1,q2,q3] T is the rotational bullet attitude quaternion, is the attitude quaternion matrix.

[0033] The error compensation output of the earth axis sensor obtained by the geomagnetic sensor error model equation is:

[0034]

[0035] The observed variables are:

[0036] Select the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the formula is:

[0037]

[0038] The system state equation includes:

[0039] Select the rotating body attitude quaternion q and the gyro error related parameter C = [s′ 11 ,s′ 22 ,s′ 33 ,s′ 12 ,s′ 13 ,s′ 23 ] T and zero bias error ε g As the state variable of the system The state equation of the system is:

[0040]

[0041] Right now

[0042] In the above formula, w(t) is the system process noise, and the gyro error parameter matrix K g The inverse matrix of s′ 11 ,s′ 22 ,s′ 33 Indicates the error of the three-axis scale factor; s′ 12 ,s′ 13 ,s′ 23 represents the installation error and cross-coupling error of the gyro; ε g =[ω o,x ,ω o,y ,ω o,z ] T is the gyro bias error; ω′ i =[ω′ x ,ω′ y ,ω′ z ] T It is the output value after gyro error compensation.

[0043] The gyro error parameter filtering model is constructed by the system observation equation and the system state equation, including:

[0044] The system state equation and system observation measurement equation are simplified and discretized to obtain:

[0045]

[0046] In the above formula, Φ k,k-1 =I+F(t k-1 )T, I is the unit matrix, T = t k -t k-1 is the sampling period, F(t k-1) is the Jacobian matrix calculated by f[X(t),t] for the state variable X(t); H k is the Jacobian matrix calculated by h[X(t),t] for the state variable X(t); X(k-1) is the next state variable, w(k) is the system process noise, and v(k) is the system measurement noise.

[0047] The EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) Including time update process and measurement update process:

[0048] Time update process, the formula is:

[0049]

[0050] The measurement update process is as follows:

[0051]

[0052] In the above formula, K k is the filter gain matrix; Φ k,k-1 is the state transition matrix; H k is the measurement matrix; R k is the equivalent measurement noise matrix; P k-1 is the estimated variance matrix of the system at the previous moment; P k,k-1 is the system variance prediction matrix; P k is the system variance matrix at the current moment; Z k is the observed value; is the optimal estimate of the (k-1) sampling time, is the optimal estimate at sampling time k; Q(k-1) is the system noise variance matrix at time k-1; I is the unit matrix.

[0053] The EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) Calculate the gyro error related parameters and bias error estimate Further calculations are performed to obtain the inverse matrix estimate of the gyro error parameter matrix.

[0054] The three-axis gyro measurement error model is:

[0055] The actual measurement output of the three-axis gyroscope is defined as:

[0056] ω m =K g ω i +ε g +n g ;

[0057] Furthermore, the output value ω′ after gyro error compensation is i for:

[0058]

[0059] Gyro error parameter matrix s 11 ,s 22 ,s 33 Indicates the error of the three-axis scale factor, s 12 ,s 13 ,s 23 represents the installation error and cross-coupling error of the gyro; let the gyro error parameter matrix K g The inverse matrix of is the three-axis gyro measurement output, ω i =[ω x ,ω y ,ω z ] T is the ideal output of the three-axis gyroscope; g =[ω o,x ,ω o,y ,ω o,z ] T is the gyro bias error; n g is the gyro measurement white noise.

[0060] The inverse matrix of the gyro error parameter matrix is ​​used to estimate the value and bias error estimate Get the output value after gyro compensation:

[0061] In summary, the present invention relates to a method for calibrating a rotating missile strapdown geomagnetic sensor and a gyroscope in series, using the collected measurement values ​​of the rotating missile three-axis geomagnetic sensor. According to the principle of geomagnetic measurement, the ellipsoid parameters A and X0 are fitted, combined with the geomagnetic field strength at the calibration point Calculate the geomagnetic sensor error parameters, Compensation to obtain the theoretical output of the three-axis geomagnetic sensor Select the As the observed variable Z(t) of the filter, the rotating body attitude quaternion, gyro error parameter and zero bias error are selected as the state variables of the system, and the gyro error parameter filtering model is further constructed. The EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) The gyro error parameters are calculated and the three-axis gyro output ω is measured. mThe present invention realizes the serial calibration and measurement data compensation of two navigation sensors, the missile-borne geomagnetic sensor and the gyroscope, and has important theoretical value and practical significance for solving the high-precision measurement problem in the guidance transformation of rotating missiles. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The present invention is a schematic diagram of a method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to an embodiment.

[0063] Figure 2 A schematic diagram of the installation and coordinate system of a rotating missile navigation sensor according to an embodiment. DETAILED DESCRIPTION

[0064] The following will further describe in detail the rotating elastic strapdown geomagnetic sensor and gyroscope series calibration method of the present invention in conjunction with specific embodiments and drawings.

[0065] like Figure 1 The figure shows the principle diagram of the rotary elastic strapdown geomagnetic sensor and gyroscope series calibration method provided by the present invention, and the specific steps are as follows:

[0066] S1 collects the geomagnetic field strength at the calibration point And collect the three-axis geomagnetic sensor measurement values ​​of the rotating missile

[0067] S2 uses the three-axis geomagnetic sensor to measure the value According to the principle of geomagnetic measurement, the ellipsoid parameters A and X0 are fitted;

[0068] S3 combined with Calculate the geomagnetic sensor error parameter matrix K m and bias error

[0069] S4 constructs a geomagnetic sensor measurement error model, Compensation to obtain the theoretical output of the three-axis geomagnetic sensor

[0070] S5 selects the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the missile attitude quaternion q, the gyro error related parameter C and the zero bias error ε are selected g The system state equation as the filter state variable;

[0071] S6 builds a gyro error parameter filtering model and uses the EKF filtering algorithm to complete the optimal filtering estimation of the state equation X(k) Calculate the inverse matrix estimate of the gyro error parameter matrix and bias error estimate

[0072] S7 builds a three-axis gyro measurement error model and calculates the three-axis gyro measurement value ω m Compensation gives the theoretical output ω′ i .

[0073] like Figure 2 As shown, the navigation sensor of the rotating missile of the present invention comprises a three-axis geomagnetic sensor and a three-axis gyroscope, and each missile-borne navigation sensor is strapdown-mounted in the carrier coordinate system (OX b Y b Z b ), the three-axis sensitive directions are completely coincident with the carrier coordinate system, among which: the three-axis gyroscope is used to measure the rotational elastic X b ,Y b ,Z b The angular velocity information of each axis is divided into The geomagnetic sensor is used to measure the geomagnetic field information of each axis, and its measurement output is

[0074] When the three-axis geomagnetic sensor makes various posture changes at a fixed geographical location, that is, the calibration point, the geomagnetic field vector is regarded as a constant vector, and its magnetic field strength is a constant, which is expressed as

[0075] According to the principle of geomagnetic measurement, define the measurement output data of the geomagnetic sensor of the rotating missile in different postures Distributed on a standard ellipsoid surface, the ellipsoid equation is

[0076] F(η,z)=a1x 2 +a2y 2 +a3z 2 +2a4xy+2a5xz+2a6yz+2a7x+2a8y+2a9z+a0=0 (1)

[0077] In the above formula, η=[a1,a2,a3,a4,a5,a6,a7,a8,a9] T is the ellipsoid parameter, a0 is a constant; F(η,z) is the distance from the geomagnetic sensor output data (x, y, z) to the ellipsoid surface F(η,z) = 0, where (x, y, z) corresponds to the output of each axis of the geomagnetic sensor (H m,x ,H m,y ,H m,z ).

[0078] The minimum value of the sum of squares of F(η, z) is used as the fitting criterion, that is, the fitting criterion formula is:

[0079]

[0080] In the above formula (2),

[0081] Arrange the fitted ellipsoid equation into vector form (X-X0) T A(X-X0)=1, further expansion gives:

[0082]

[0083] In the above formula, is the ellipsoid shape matrix; is the center point of the ellipsoid, is the inverse matrix of A.

[0084] Furthermore, let the and The relationship is:

[0085]

[0086] After sorting, the measurement output of the three-axis geomagnetic sensor satisfies the quadratic standard equation:

[0087]

[0088] In the above formula, is the error parameter matrix of the three-axis geomagnetic sensor, c xx ,c yy ,c zz is the sensitivity error coefficient of each axis of the geomagnetic sensor, c xy ,c xz ,c zy K is the non-orthogonality error parameter among the three axes of the geomagnetic sensor including the installation error angle; -1 m is the geomagnetic sensor error parameter K m The inverse matrix of is the zero bias error of the geomagnetic sensor.

[0089] Comparing formula (3) and formula (5), the sensor error parameter matrix K is obtained m and bias error The calculation formula is:

[0090]

[0091] Construct a geomagnetic sensor measurement error model. The ideal measurement output of the geomagnetic sensor is:

[0092]

[0093] Due to various measurement errors of the geomagnetic sensor, the actual measurement output of the magnetic sensor is:

[0094]

[0095] In the above formula, The ideal output of the three-axis geomagnetic sensor, is the geomagnetic field component in the reference coordinate system; v(t) is the white noise measured by the magnetic sensor; q=[q0,q1,q2,q3] T is the rotational bullet attitude quaternion, is the attitude quaternion matrix:

[0096]

[0097] The error compensation formula obtained from the three-axis geomagnetic sensor error model equation (8) is:

[0098]

[0099] The observed variables are:

[0100] Select the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the formula is:

[0101]

[0102] The system state equation includes:

[0103] Select the rotating body attitude quaternion q and the gyro error related parameter C = [s′ 11 ,s′ 22 ,s′ 33 ,s′ 12 ,s′ 13 ,s′ 23 ] T and zero bias error ε g As the state variable of the system The state equation of the system is:

[0104]

[0105] Right now

[0106] In the above formula, w(t) is the system process noise, and the gyro error parameter matrix K g The inverse matrix of s′ 11 ,s′ 22 ,s′ 33 Indicates the error of the three-axis scale factor; s′ 12 ,s′ 13 ,s′ 23 represents the installation error and cross-coupling error of the gyro; εg =[ω o,x ,ω o,y ,ω o,z ] T is the gyro bias error; ω′ i =[ω′ x ,ω′ y ,ω′ z ] T It is the output value after gyro error compensation.

[0107] The system observation equation (10) and state equation (11) together constitute the gyro error parameter filtering model:

[0108]

[0109] Linearize it:

[0110]

[0111] After discretization:

[0112]

[0113] In the above formula, Φ k,k-1 =I+F(t k-1 )T, I is the unit matrix, T = t k -t k-1 is the sampling period, is the optimal estimate of the (k-1) sampling time, is the one-step prediction value of the state; F(t k-1 ) is the Jacobian matrix calculated by f[X(t),t] for the state variable X(t):

[0114]

[0115] The observation matrix H k The Jacobian matrix calculated for the state variable X(t) is h[X(t),t]:

[0116]

[0117] The EKF filtering algorithm is used to filter the state parameters To estimate, the algorithm includes two processes: time update and measurement update: Time update process, the formula is:

[0118]

[0119] The measurement update process is as follows:

[0120]

[0121] In the above formula, K k is the filter gain matrix; Φ k,k-1 is the state transition matrix; H k is the measurement matrix; R k is the equivalent measurement noise matrix; P k-1 is the estimated variance matrix of the system at the previous moment; P k,k-1 is the system variance prediction matrix; P k is the system variance matrix at the current moment; Z k is the observed value; is the optimal estimate of the (k-1) sampling time, is the optimal estimate at sampling time k; Q(k-1) is the system noise variance matrix at time k-1; I is the unit matrix.

[0122] In summary, the EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) Calculate the gyro error related parameters and bias error estimate Further calculations are performed to obtain the inverse matrix estimate of the gyro error parameter matrix.

[0123] Construct a three-axis gyro measurement error model, specifically:

[0124] The actual measurement output of the three-axis gyroscope is defined as:

[0125] ω m =K g ω i +ε g +n g ; (20)

[0126] Furthermore, the output value ω′ after gyro error compensation is i for:

[0127]

[0128] Gyro error parameter matrix s 11 ,s 22 ,s 33 Indicates the error of the three-axis scale factor, s 12 ,s 13 ,s 23 represents the installation error and cross-coupling error term of the gyro; is the three-axis gyro measurement output, ω i =[ω x ,ω y ,ω z ] T is the ideal output of the three-axis gyroscope; g =[ωo,x ,ω o,y ,ω o,z ] T is the gyro bias error; n g is the gyro measurement white noise.

[0129] The inverse matrix of the gyro error parameter matrix is ​​used to estimate the value and bias error estimate Get the output value after gyro compensation:

[0130]

[0131] The present invention relates to a method for calibrating a rotating missile strapdown geomagnetic sensor and a gyroscope in series, using the collected measurement values ​​of the rotating missile three-axis geomagnetic sensor According to the principle of geomagnetic measurement, the ellipsoid parameters A and X0 are fitted, combined with the geomagnetic field strength at the calibration point Calculate the geomagnetic sensor error parameters, Compensation to obtain the theoretical output of the three-axis geomagnetic sensor Select the As the observed variable Z(t) of the filter, the rotating body attitude quaternion, gyro error parameter and zero bias error are selected as the state variables of the system, and the gyro error parameter filtering model is further constructed. The EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) The gyro error parameters are calculated and the three-axis gyro output ω is measured. m The present invention realizes the serial calibration and measurement data compensation of two navigation sensors, the missile-borne geomagnetic sensor and the gyroscope, and has important theoretical value and practical significance for solving the high-precision measurement problem in the guidance transformation of rotating missiles.

[0132] Although the present invention is described in conjunction with the above specific embodiments, it is obvious that those skilled in the art can make many substitutions, modifications and changes according to the above content. Therefore, all such substitutions, improvements and changes are included in the spirit and scope of the appended claims.

Claims

1. A method for calibrating a rotating strapdown geomagnetic sensor and a gyroscope in series, characterized in that: include: S1 collects the geomagnetic field strength at the calibration point And collect the three-axis geomagnetic sensor measurement values ​​of the rotating missile S2 uses the three-axis geomagnetic sensor to measure the value According to the principle of geomagnetic measurement, the ellipsoid parameters A and X0 are fitted; S3 combined with Calculate the geomagnetic sensor error parameter matrix K m and bias error S4 constructs a geomagnetic sensor measurement error model, Compensation to obtain the theoretical output of the three-axis geomagnetic sensor S5 selects the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the missile attitude quaternion q, the gyro error related parameter C and the zero bias error ε are selected g The system state equation as the filter state variable; S6 builds a gyro error parameter filtering model and uses the EKF filtering algorithm to complete the optimal filtering estimation of the state equation X(k) Calculate the inverse matrix estimate of the gyro error parameter matrix and bias error estimate S7 builds a three-axis gyro measurement error model and calculates the three-axis gyro measurement value ω m Compensation to get the theoretical output ω i ′.

2. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The geomagnetic measurement principle is specifically as follows: Definition: The measurement output data of the geomagnetic sensor in different postures are distributed on a standard ellipsoid surface, and the ellipsoid equation is: <h2 style=";text-align:left;direction:ltr">F(η,z) = a1x<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a2y<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a3z<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2a4xy+2a5xz+2a6yz+2a7x+2a8y+2a9z+a0=0; In the above formula, η=[a1,a2,a3,a4,a5,a6,a7,a8,a9] T is the ellipsoid parameter, a0 is a constant; F(η,z) is the distance from the geomagnetic sensor output data x, y, z to the ellipsoid surface F(η,z) = 0, x, y, z correspond to the output values ​​of each axis of the three-axis geomagnetic sensor 3. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 2, characterized in that: The fitting ellipsoid parameters A and X0 are specifically: Fitting ellipsoid equation, the formula is: The minimum value of the sum of squares of F(η,z) is selected as the fitting criterion, and the fitting criterion formula is: In the above formula, is the ellipsoid shape matrix; is the center point of the ellipsoid, is the inverse matrix of A.

4. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The S3 further includes: Order The geomagnetic sensor error parameter matrix K m and bias error The relationship is: Geomagnetic sensor error parameter K m and The calculation formula is: In the above formula, is the error parameter matrix of the three-axis geomagnetic sensor, c xx ,c yy ,c zz is the sensitivity error coefficient of each axis of the geomagnetic sensor, c xy ,c xz ,c zy K is the non-orthogonality error parameter among the three axes of the geomagnetic sensor including the installation error angle; -1 m is the geomagnetic sensor error parameter K m The inverse matrix of is the zero bias error of the geomagnetic sensor.

5. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The geomagnetic sensor measurement error model is specifically: The actual measurement output of the geomagnetic sensor is defined as: In the above formula, The ideal output of the three-axis geomagnetic sensor, is the geomagnetic field component in the reference coordinate system; v(t) is the white noise measured by the magnetic sensor; q=[q0,q1,q2,q3] T is the rotational bullet attitude quaternion, is the attitude quaternion matrix.

6. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The observed variables are specifically: Select the theoretical output of the three-axis geomagnetic sensor As the observed variable Z(t) of the filter, the formula is:

7. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The system state equation includes: Select the rotating body attitude quaternion q and the gyro error related parameter C = [s′ 11 ,s′ 22 ,s′ 33 ,s′ 12 ,s′ 13 ,s′ 23 ] T and zero bias error ε g As the state variable of the system The state equation of the system is: Right now In the above formula, w(t) is the system process noise, and the gyro error parameter matrix K g The inverse matrix of s′ 11 ,s′ 22 ,s′ 33 Indicates the error of the three-axis scale factor; s′ 12 ,s′ 13 ,s′ 23 represents the installation error and cross-coupling error of the gyro; ε g =[ω o,x ,ω o,y ,ω o,z ] T is the gyro bias error; ω i ′=[ω′ x ,ω′′,ω′ z ] T It is the output value after gyro error compensation.

8. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The construction of the gyro error parameter filtering model is specifically as follows: The system state equation and system observation measurement equation are simplified and discretized to obtain: In the above formula, Φ k,k-1 =I+F(t k-1 )T, I is the unit matrix, T = t k -t k-1 is the sampling period, F(t k-1 ) is the Jacobian matrix calculated by f[X(t),t] for the state variable X(t); H k is the Jacobian matrix calculated by h[X(t),t] for the state variable X(t); X(k-1) is the next state variable, w(k) is the system process noise, and v(k) is the system measurement noise.

9. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The EKF filtering algorithm is used to complete the optimal filtering estimation of the state equation X(k) Including time update process and measurement update process: Time update process, the formula is: The measurement update process is as follows: In the above formula, K k is the filter gain matrix; Φ k,k-1 is the state transition matrix; H k is the measurement matrix; R k is the equivalent measurement noise matrix; P k-1 is the estimated variance matrix of the system at the previous moment; P k,k-1 is the system variance prediction matrix; P k is the system variance matrix at the current moment; Z k is the observed value; is the optimal estimate of the (k-1) sampling time, is the optimal estimate at sampling time k; Q(k-1) is the system noise variance matrix at time k-1; I is the unit matrix.

10. The method for calibrating a rotating elastic strapdown geomagnetic sensor and a gyroscope in series according to claim 1, characterized in that: The three-axis gyro measurement error model is specifically: The actual measurement output of the three-axis gyroscope is defined as: oh m =K g oh i +e g +n g ; Output value after gyro error compensation ω i 'for: Gyro error parameter matrix s 11 ,s 22 ,s 33 Indicates the error of the three-axis scale factor, s 12 ,s 13 ,s 23 represents the installation error and cross-coupling error of the gyro; let the gyro error parameter matrix K g The inverse matrix of is the three-axis gyro measurement output, ω i =[ω x ,ω y ,ω z ] T is the ideal output of the three-axis gyroscope; g =[ω o,x ,ω o,y ,ω o,z ] T is the gyro bias error; n g is the gyro measurement white noise.

Images