A method and system for flight calibration of star sensor and inertial unit structure parameters

Abstract

A flight calibration method and system for the structural parameters of a star sensor and an inertial unit (IMU) includes: setting the parameters of the star sensor and IMU, and environmental parameters, and setting the initial state of the structural parameter deviation estimator; after the IMU and star sensor output data, performing time propagation on the estimated values ​​and estimated covariance of constant zero bias, zero bias drift, and structural parameter deviation; calculating the attitude increment of the IMU and star sensor using angular velocity and star observation information, and constructing the measurement equation for the structural parameter deviation; solving the corresponding regularized least squares problem using a regularized robust filtering framework to update the estimated values ​​and estimated covariance of constant zero bias, zero bias drift, and structural parameter deviation; and compensating for the structural parameters after obtaining a stable estimated value of the structural parameter deviation. This invention enables high-precision calibration of the structural parameters of the star sensor and IMU without the need for complex astronomical-ground coordinate transformations using timing and positioning information.

Description

Technical Field

[0001] This invention relates to the field of combined application technology of star sensors and inertial units, and specifically to a flight calibration method and system for the structural parameters of star sensors and inertial units. Background Technology

[0002] Inertial navigation systems (INS) are an important type of navigation system in aviation. They acquire the position, velocity, and attitude information of a vehicle in real time by integrating the measurements from the inertial unit. Due to their strong autonomy and good anti-interference capabilities, they are widely used. In real flight environments, complex factors such as overload, vibration, and temperature changes can affect the inertial unit, causing the actual performance of the INS to be inferior to its nominal performance. Therefore, it is necessary to conduct performance testing of INS in real flight environments. Star sensors are astronomical navigation devices that provide attitude information of the vehicle by observing stars. Because star sensors are highly accurate and drift-free, they can be strapped in with an INS to serve as the attitude reference for the INS, thereby enabling in-flight attitude accuracy assessment. Furthermore, star sensors and inertial units can also form a combined navigation system. However, star sensors and inertial units have independent measurement coordinate systems. Whether performing in-flight attitude accuracy assessment or combined navigation, it is necessary to first align the measurement coordinate systems, that is, to calibrate the structural parameters between the star sensor and the inertial unit.

[0003] After the strapdown system of the star sensor and inertial measurement unit is fabricated and assembled, its structural parameters can be calibrated experimentally. However, factors such as shocks during transportation, release of installation preload, and vibrations and temperature changes in the working environment can all cause structural changes between the star sensor and the inertial measurement unit. Therefore, it is necessary to perform real-time online calibration of the structural parameters. Existing online calibration methods for structural parameters use attitude data output by the inertial navigation system and pre-calibrated structural parameters in the laboratory to calculate the direction of the star observed by the star sensor. Then, the difference between the calculated direction of the star and the actual direction of the star observed by the star sensor is used to establish a measurement equation for the deviation of the structural parameters. Finally, a Kalman filter is used to calibrate the structural parameters based on this measurement equation.

[0004] Existing methods use attitude information from inertial navigation systems (INS) to establish measurement equations for structural parameter deviations. However, the cumulative errors contained in the attitude information significantly impact the calibration process. Current methods employ complex recursive calculations and compensations for cumulative attitude errors using process data from within the INS, but this process data is unavailable in applications such as INS attitude accuracy assessment. Furthermore, when observing stars within the atmosphere, atmospheric refraction deflects starlight, leading to deviations in the star sensor's observation information. However, existing methods do not provide means to overcome this problem; therefore, the results of structural parameter calibration within the atmosphere using existing methods are significantly affected by atmospheric refraction of starlight. Therefore, a more effective flight calibration method for star sensors and inertial unit structural parameters is needed to address these issues. Summary of the Invention

[0005] To address the insufficient accuracy of existing star sensor and inertial unit (IMU) structural parameter calibration, this invention aims to provide a flight calibration method and system for star sensor and IMU structural parameters. The method is a flight calibration approach for structural parameters based on attitude increment measurements. This method obtains the attitude increment of the IMU by integrating angular velocity information over a short time; it then calculates the attitude increment of the star sensor using nearby star observation information. Based on the attitude increments of the IMU and star sensor, a measurement equation for structural parameter deviation is established. Finally, a structural parameter deviation estimator is designed using a regularized robust filtering framework to calibrate the structural parameters. This invention avoids the introduction of attitude accumulation errors and atmospheric refraction of starlight, thus achieving high-precision flight calibration of structural parameters.

[0006] The first aspect of the present invention provides a flight calibration method for star sensors and inertial unit structural parameters, comprising:

[0007] Step 1: Based on the datasheet and weather conditions during calibration, set the pre-calibration values ​​and uncertainties of the sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration, and set the initial state of the structural parameter deviation estimator according to the above parameters.

[0008] Step 2: After the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information, time propagation is performed on the estimated values ​​and estimated covariance of the gyroscope's constant bias, bias drift, and structural parameter deviations based on the parameter model.

[0009] Step 3: Using the angular velocity measurements and star observation information obtained in Step 2, construct the attitude increments of the inertial unit and star sensor, and then construct the measurement equations for structural parameter deviations and measurement noise covariance.

[0010] Step 4: Based on the measurement equation described in Step 3, solve the corresponding regularized least squares problem using a regularized robust filtering framework to update the estimated values ​​and covariance of constant zero bias, zero bias drift, and structural parameter deviation, thereby achieving iterative estimation.

[0011] Step 5: After obtaining the estimated stable structural parameter deviations, compensate for the structural parameters.

[0012] Furthermore, among the parameters that need to be set in step 1, the sensor accuracy includes the zero-bias repeatability σ of the three-axis gyroscope in the inertial unit. bx ,σ by ,σ bz Angle random walk N Gx N Gy N Gz Rate random walk K Gx ,K Gy ,K Gz σ, the star measurement accuracy of the star sensor w Seeing σ η The full width at half maximum (FWHM) of the visiting disk is determined by the Gaussian distribution, and is 2.355σ. η The attitude increment integration time is denoted by the symbol Δk.

[0013] Structural parameters refer to the mounting structural parameters of the star sensor and inertial unit, represented by an orthogonal matrix S, which describes the coordinate transformation from the star sensor coordinate system to the inertial unit coordinate system. The pre-calibration value of this matrix is ​​S. o The deviation between the pre-calibrated value and the actual value is represented by the structural parameter deviation matrix M, and their relationship is S = MS. o The structural parameter deviation M represents a small-angle rotation, which can be approximated by the corresponding rotation vector θ as follows:

[0014]

[0015] in,[·] × The antisymmetric matrix representing the vectors, the uncertainty of the structural parameters is the standard deviation of θ1, θ2, θ3, denoted as σ. θx ,σ θy ,σ θz .

[0016] Furthermore, in step 2, the parameter model includes models of the gyroscope's constant zero bias, zero bias drift, and structural parameter deviations, where the gyroscope's zero bias drift d... k Modeled as a first-order Markov process d k =d k-1 +ε k-1 , where ε k-1 For rate random walk noise, the constant value of zero bias bk and structural parameter deviation θ k It can be modeled as a constant to be estimated. Assuming that at time k, the inertial unit outputs a new angular velocity measurement and the star sensor outputs new stellar observation information, the estimated value and covariance of the state variables, consisting of the gyroscope's constant bias, bias drift, and structural parameter deviations, propagate from time k-1 to time k as follows:

[0017]

[0018] P x,k|k-1 =P x,k-1|k-1 +Q k-1

[0019] in, and P x,k-1|k-1 Let K and K represent the posterior estimates and posterior covariance of the state variables at time k-1, respectively. and P x,k|k-1 Let Q represent the prior estimate and prior covariance of the state variables at time k, respectively. k-1 The covariance matrix representing the process noise is: Where T s The sampling interval is denoted as .

[0020] Furthermore, in step 3, the construction of the attitude increments of the inertial unit and the star sensor includes the following steps:

[0021] (1) The starting time for calculating the attitude increment is set to The termination time is set to k;

[0022] (2) The measured angular velocity of the inertial unit at time k is ω. gm,k Then from time i-1 to time i For the interval, the rotation vector of the inertial element coordinate system can be estimated as:

[0023]

[0024] in, Let Λ be the posterior estimate of the zero-bias drift at time i, and let matrix Λ contain the scaling error λ. x , λ y , λ z Non-orthogonality error δ xy δ xz δ yz It has the following form:

[0025]

[0026] Rotation vector It can be converted into a rotation matrix form. Therefore, the attitude increment of the inertial unit It can be estimated as

[0027] (3) Let w be the direction vector of the i-th star observed by the star sensor at time k in the star sensor coordinate system. i,k At nearby times k and l, the star sensor observes several common stars; the set of these stars is denoted as . attitude increment of star sensor The following Wahba problem is solved using methods such as the QUEST algorithm or SVD decomposition:

[0028]

[0029] Furthermore, in step 4, the regularized least squares problem that needs to be solved is:

[0030]

[0031] in, H k and W k These represent the measured values, sensitivity matrix, and measurement noise covariance of the measurement equation established in step 3, respectively. W δH represents the weighted Euclidean norm of a vector. k Represents the sensitivity matrix H k The potential deviations arise from the perturbations Λ'=C that may exist in matrix Λ during operation. Λ Δ Λ E Λ , matrix δH k This can be expressed as:

[0032]

[0033] Δ Λ =diag(Rλ) x ,Rδ xy ,Rδ xz ,Rλ y ,Rδ yz ,Rλ z )

[0034]

[0035] Where λ' is used x Indicates λ x The disturbance amount, then Uλ x Indicates λ' x The boundary, Rλ x =λ' x / Uλ xOther variables are represented in the same way.

[0036] A second aspect of the present invention provides a flight calibration system for star sensors and inertial unit structural parameters, comprising:

[0037] The setting module is used to set the pre-calibration values ​​and uncertainties of sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration based on the datasheet and weather conditions during calibration, and to set the initial state of the structural parameter deviation estimator based on the above parameters.

[0038] The time propagation module is used to propagate the constant zero bias, zero bias drift, and estimated values ​​and covariance of the gyroscope based on the parameter model after the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information.

[0039] The module is used to construct the attitude increments of the inertial unit and star sensor using the obtained angular velocity measurements and star observation information, and then construct the measurement equations for structural parameter deviations and measurement noise covariance.

[0040] The iterative estimation module is used to solve the corresponding regularized least squares problem based on the measurement equation using a regularized robust filtering framework, and to update the estimated values ​​and estimated covariance of constant zero bias, zero bias drift and structural parameter deviation, thereby realizing iterative estimation.

[0041] The compensation module is used to compensate for the structural parameters after obtaining a stable estimate of the structural parameter deviation.

[0042] The technical solution of the present invention can achieve the following beneficial technical effects:

[0043] This invention establishes measurement equations for structural parameter deviations based on the attitude increments of an inertial unit and a star sensor. Due to the short integration time, the attitude increment of the inertial unit contains only a small cumulative error. Since atmospheric refraction is approximately constant in the immediate vicinity, starlight atmospheric refraction can be canceled out during the calculation of the star sensor's attitude increment. This invention avoids the introduction of attitude accumulation errors and starlight atmospheric refraction, thus enabling high-precision structural parameter calibration. Furthermore, each of the aforementioned attitude increments is based on its respective measurement coordinate system; therefore, this invention does not require complex astronomical-ground coordinate transformations using timing and positioning information. Attached Figure Description

[0044] Figure 1 This is a flowchart of the flight calibration method for the star sensor and inertial unit structural parameters of the present invention;

[0045] Figure 2 This is the curve showing the structural parameter deviation estimation result of the method of the present invention. Detailed Implementation

[0046] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0047] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0048] According to an embodiment of the present invention, an embodiment of an on-orbit multi-load reference deviation measurement method and system is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] The first aspect of the present invention provides a flight calibration method for star sensors and inertial unit structural parameters, specifically including the following steps:

[0051] Step 1: Based on the datasheet and weather conditions during calibration, set the pre-calibration values ​​and uncertainties for sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration, and set the initial state of the structural parameter deviation estimator according to the above parameters.

[0052] Specifically, among the parameters that need to be set, sensor accuracy includes the zero-bias repeatability σ of the three-axis gyroscope in the inertial unit. bx ,σ by ,σ bz Angle random walk N Gx N Gy NGz Rate random walk K Gx ,K Gy ,K Gz σ, the star measurement accuracy of the star sensor w Seeing σ η The full width at half maximum (FWHM) of the visiting disk is determined by the Gaussian distribution, and is 2.355σ. η The attitude increment integration time is represented by the symbol Δk.

[0053] Specifically, the structural parameters refer to the mounting structural parameters of the star sensor and the inertial unit, represented by an orthogonal matrix S, which describes the coordinate transformation from the star sensor coordinate system to the inertial unit coordinate system. The pre-calibration value of this matrix is ​​S. o The deviation between the pre-calibrated value and the actual value is represented by the structural parameter deviation matrix M, and their relationship is S = MS. o The structural parameter deviation M typically represents a small angle rotation, and therefore can be approximated by the corresponding rotation vector θ:

[0054]

[0055] in,[·] × This represents the antisymmetric matrix of the vectors. The uncertainty of the structural parameters is the standard deviation of θ1, θ2, θ3, denoted as σ. θx ,σ θy ,σ θz .

[0056] Specifically, the state variables of the structural parameter deviation estimator consist of three parts: the constant zero bias b of the gyroscope output. k Zero bias drift d k The structural parameter deviation vector θ between the star sensor and the inertial measurement unit k Where the subscript k is the time variable, i.e., the state vector is The initial state of the structural parameter deviation estimator needs to be set as the posterior estimate of the state variables at time 0. and posterior covariance

[0057] Step 2: After the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information, time propagation is performed on the estimated values ​​and covariance of the gyroscope's constant bias, bias drift, and structural parameter deviations based on the parameter model.

[0058] Specifically, the parameter model includes models of the gyroscope's constant zero bias, zero bias drift, and structural parameter deviations, with the gyroscope's zero bias drift d... k It can be modeled as a first-order Markov process d k =d k-1 +εk-1 , where ε k-1 For rate random walk noise, the constant value of zero bias b k and structural parameter deviation θ k It can be modeled as a constant to be estimated. Assuming that at time k, the inertial unit outputs a new angular velocity measurement and the star sensor outputs new stellar observation information, the process of the estimated values ​​and covariance of the state variables, consisting of the gyroscope's constant bias, bias drift, and structural parameter deviations, propagating from time k-1 to time k is as follows:

[0059]

[0060] P x,k|k-1 =P x,k-1|k-1 +Q k-1

[0061] in, and P x,k-1|k-1 Let K and K represent the posterior estimates and posterior covariance of the state variables at time k-1, respectively. and P x,k|k-1 Let Q represent the prior estimate and prior covariance of the state variables at time k, respectively. k-1 The covariance matrix representing the process noise is: Where T s The sampling interval is denoted as .

[0062] Step 3: Using the angular velocity measurements and star observation information obtained in Step 2, construct the attitude increments of the inertial unit and star sensor, and then construct the measurement equations for structural parameter deviations and measurement noise covariance.

[0063] Specifically, the construction of attitude increments for the inertial unit and star sensor includes the following steps:

[0064] (1) The starting time for calculating the attitude increment is set to The termination time is set to k.

[0065] (2) The measured angular velocity of the inertial unit at time k is ω. gm,k Then from time i-1 to time i For the interval, the rotation vector of the inertial element coordinate system can be estimated as:

[0066]

[0067] in, Let Λ be the posterior estimate of the zero-bias drift at time i, and let matrix Λ contain the scaling error λ. x , λ y , λ z Non-orthogonality error δ xy δ xzδ yz It has the following form:

[0068]

[0069] Rotation vector It can be converted into a rotation matrix form. Therefore, the attitude increment of the inertial unit It can be estimated as

[0070] (3) Let w be the direction vector of the i-th star observed by the star sensor at time k in the star sensor coordinate system. i,k At the nearest k-time and At any given time, a star sensor can often observe several common stars; the set of these stars is denoted as _____. Therefore, the attitude increment of the star sensor The following Wahba problem can be solved using methods such as the QUEST algorithm or SVD decomposition.

[0071]

[0072] Specifically, the construction of the measurement equations for structural parameter deviations and the measurement noise covariance includes the following steps:

[0073] (1) The attitude increment of the inertial unit mentioned above attitude increment of star sensor and the pre-calibration value S of structural parameters o A quantity that can form an identity matrix. Its deviation from the identity matrix can be used to establish the measurement quantity. The relationship is

[0074] (2) Measurement quantity With state variable x k The relationship is the measurement equation, which is... in, H represents the measurement noise. k The sensitivity matrix is ​​expressed as follows:

[0075]

[0076] Among them, J i The left-multiplied Baker-Campbell-Hausdorff approximation Jacobian matrix at time i is given by the following equation:

[0077]

[0078] (3) Noise measurement The covariance matrix is ​​Wk , expressed as:

[0079]

[0080] Among them, P d,i|i Let be the posterior estimate covariance of the zero-bias drift at time i, and be the covariance matrix of the star sensor attitude increment. and the angle random walk noise covariance P of the three-axis gyroscope Δω They are expressed as follows:

[0081]

[0082] Step 4: Based on the measurement equations in Step 3, the corresponding regularized least squares problem is solved using a regularized robust filtering framework. This completes the update of the estimated values ​​and covariance of constant zero bias, zero bias drift, and structural parameter deviations, thus achieving iterative estimation.

[0083] Specifically, the regularized least squares problem that needs to be solved is:

[0084]

[0085] in, H k and W k These represent the measured values, sensitivity matrix, and measurement noise covariance of the measurement equation established in step 3, respectively. W δH represents the weighted Euclidean norm of a vector. k Represents the sensitivity matrix H k The potential deviations arise from the perturbations Λ'=C that may exist in matrix Λ during operation. Λ Δ Λ E Λ , matrix δH k It can be expressed as

[0086]

[0087] Δ Λ =diag(Rλ) x ,Rδ xy ,Rδ xz ,Rλ y ,Rδ yz ,Rλ z )

[0088]

[0089] Where λ' is used x Indicates λ x The disturbance amount, then Uλ x Indicates λ'x The boundary, Rλ x =λ' x / Uλ x Other variables are represented in the same way.

[0090] Specifically, suppose a robust version of the regularized least squares problem can be described as:

[0091]

[0092] Where x is the value to be estimated, A and y are the known matrix and vector parameters, respectively, Q and W are both symmetric and positive semi-definite weight matrices, and δA and δy represent the uncertainties of parameters A and y, having the same dimensions as A and y and can be decomposed as follows:

[0093] [δAδy]=CΔ[E a E y ]

[0094] Among them, C, E a E y All are predefined quantities with appropriate dimensions, and Δ is an arbitrary contraction matrix satisfying ||Δ||≤1. For the matrix, ||·|| represents the 2-induced norm. Then the unique solution to this problem can be expressed as:

[0095]

[0096] Among them, the new weight matrix The original weight matrix {Q,W} is corrected as follows:

[0097]

[0098] mark Represents the pseudo-inverse of a matrix, and non-negative scalar parameters. The following optimization problem was identified.

[0099]

[0100] The function G(β) is defined as

[0101]

[0102] There is here

[0103]

[0104] Specifically, by making the following substitution to solve the regularized least squares problem, the posterior estimate of the state variables at time k can be obtained using the above solution method.

[0105]

[0106] Meanwhile, the posterior estimate covariance of the state variables at time k can be updated as follows:

[0107]

[0108] Step 5: After obtaining the estimated stable structural parameter deviations, compensate for the structural parameters.

[0109] Specifically, after obtaining the estimated stable structural parameter deviation, the stable value is denoted as [value]. Then the calibration value S of the structural parameter * as follows

[0110]

[0111] Using the method described in this invention, various performance parameters, ideal structural parameters, and structural parameter deviations of the star sensor and inertial unit were set, and the calibration accuracy of the method was verified through simulation. The set triaxial structural parameter deviations were -30.60″, 19.76″, and 40.85″, respectively. The estimated results of the structural parameter deviations are as follows: Figure 2 As shown in the figure, the estimated structural parameter deviations, after experiencing initial fluctuations, quickly converge to the true values ​​of the structural parameter deviations. The root mean square error of the converged estimation results is less than 1″, which meets the high-precision structural parameter calibration requirements of the combined application of star sensors and inertial units.

[0112] A second aspect of the present invention provides a flight calibration system for star sensors and inertial unit structural parameters, comprising:

[0113] The setting module is used to set the pre-calibration values ​​and uncertainties of sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration based on the datasheet and weather conditions during calibration, and to set the initial state of the structural parameter deviation estimator based on the above parameters.

[0114] The time propagation module is used to propagate the constant zero bias, zero bias drift, and estimated values ​​and covariance of the gyroscope based on the parameter model after the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information.

[0115] The module is used to construct the attitude increments of the inertial unit and star sensor using the obtained angular velocity measurements and star observation information, and then construct the measurement equations for structural parameter deviations and measurement noise covariance.

[0116] The iterative estimation module is used to solve the corresponding regularized least squares problem based on the measurement equation using a regularized robust filtering framework, and to update the estimated values ​​and estimated covariance of constant zero bias, zero bias drift and structural parameter deviation, thereby realizing iterative estimation.

[0117] The compensation module is used to compensate for the structural parameters after obtaining a stable estimate of the structural parameter deviation.

[0118] In summary, this invention relates to a flight calibration method and system for the structural parameters of a star sensor and an inertial unit. The calibration method includes the following steps: setting the parameters of the star sensor and the inertial unit, and environmental parameters, and setting the initial state of the structural parameter deviation estimator; after the inertial unit and the star sensor output data, performing time propagation on the estimated values ​​and estimated covariance of constant zero bias, zero bias drift, and structural parameter deviation; calculating the attitude increments of the inertial unit and the star sensor using angular velocity and star observation information, and then constructing the measurement equation for the structural parameter deviation; solving the corresponding regularized least squares problem using a regularized robust filtering framework to update the estimated values ​​and estimated covariance of constant zero bias, zero bias drift, and structural parameter deviation; and compensating for the structural parameters after obtaining stable estimates of the structural parameter deviation. This invention's method avoids the introduction of attitude accumulation errors and atmospheric refraction of starlight, thus enabling high-precision calibration of the structural parameters of the star sensor and the inertial unit. Furthermore, since each attitude increment is based on its respective measurement coordinate system, this invention's method does not require complex astronomical-ground coordinate transformation using timing and positioning information.

[0119] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A flight calibration method for star sensor and inertial unit structural parameters, characterized in that, Includes the following steps: Step 1: Based on the datasheet and weather conditions during calibration, set the pre-calibration values ​​and uncertainties of the sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration, and set the initial state of the structural parameter deviation estimator according to the above parameters. Step 2: After the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information, time propagation is performed on the estimated values ​​and estimated covariance of the gyroscope's constant bias, bias drift, and structural parameter deviations based on the parameter model. Step 3: Using the angular velocity measurements and star observation information obtained in Step 2, construct the attitude increments of the inertial unit and star sensor, and then construct the measurement equations for structural parameter deviations and measurement noise covariance. The construction of attitude increments for inertial cells and star sensors involves the following steps: (1) The starting time for calculating the attitude increment is set to The termination time is set to , Indicates the attitude increment integration time; (2) Remember the inertial unit in The measured angular velocity at time t is ,but Time to time For the interval, the rotation vector of the inertial element coordinate system is estimated as follows: ； in, for The posterior estimate of the zero-bias drift at time step zero, matrix Includes scaling error , , Non-orthogonality error , , It has the following form: ； Rotation vector Transform into rotation matrix form Therefore, the attitude increment of the inertial unit Estimated as ; (3) The star sensor is located at The first time observed The direction vector of the star in the star sensor coordinate system is ; in the vicinity Time and At a certain moment, the star sensor observes several common stars; the set of these stars is denoted as _____. Therefore, the attitude increment of the star sensor The following Wahba problem can be solved using the QUEST algorithm or SVD decomposition method. ； The construction of the measurement equations for structural parameter deviations and the measurement noise covariance includes the following steps: (1) The attitude increment of the inertial unit mentioned above attitude increment of star sensor and pre-calibration values ​​of structural parameters The quantities that form an identity matrix. Its deviation from the identity matrix is ​​used to establish the measurement quantity. The relationship is ; (2) Measurement quantity With state quantity The relationship is the measurement equation, which is... ,in, Indicates measurement noise. The sensitivity matrix is ​​expressed as follows: ； in, for The left-multiplied Baker-Campbell-Hausdorff approximation Jacobian matrix at time t is given by the following equation: ； (3) Noise measurement The covariance matrix is , expressed as: ； in, for The posterior estimate covariance of the zero-bias drift at time intervals, and the covariance matrix of the star sensor attitude increment. and the angle random walk noise covariance of the three-axis gyroscope They are expressed as follows: ； ； in, The accuracy of star measurement in star sensors Seeing of star sensors The angle of the three-axis gyroscope wanders randomly. The sampling interval; Step 4: Based on the measurement equation described in Step 3, solve the corresponding regularized least squares problem using a regularized robust filtering framework to update the estimated values ​​and covariance of constant zero bias, zero bias drift, and structural parameter deviation, thereby achieving iterative estimation. Step 5: After obtaining the estimated stable structural parameter deviations, compensate for the structural parameters.

2. The flight calibration method for star sensor and inertial unit structural parameters as described in claim 1, characterized in that, Among the parameters that need to be set in step 1, the sensor accuracy includes the zero-bias repeatability of the three-axis gyroscope in the inertial unit. Angle random walk Rate random walk Star measurement accuracy of star sensors Seeing The full width at half maximum (FWHM) of the Shining disk is determined by the full width at half maximum (FWHM) of the Shining disk under a Gaussian distribution. ; Attitude increment integral time using symbols express; Structural parameters refer to the installation structural parameters of the star sensor and inertial unit, represented by an orthogonal matrix. This indicates that it describes the coordinate transformation from the star sensor coordinate system to the inertial unit coordinate system, and the pre-calibration value of this matrix is... The deviation between the pre-calibrated value and the actual value is the structural parameter deviation matrix. Their relationship is Structural parameter deviation To represent a small angle of rotation, use the corresponding rotation vector. Approximately: ； in, Let represent the antisymmetric matrix of the vector, and the uncertainty of the structural parameters be . The standard deviation of is expressed as .

3. The flight calibration method for the structural parameters of a star sensor and inertial unit as described in claim 2, characterized in that: In step 2, the parameter model includes models of the gyroscope's constant bias, bias drift, and structural parameter deviations. The gyroscope's bias drift... Modeled as a first-order Markov process ,in For rate random walk noise, constant with zero bias and structural parameter deviation It can be modeled as a constant estimator, assuming that in At any given moment, the inertial unit outputs a new angular velocity measurement and the star sensor outputs new stellar observation information. Then, the estimated values ​​and covariance of the state variables, composed of the gyroscope's constant bias, bias drift, and structural parameter deviations, are derived from... Spreading to the moment The process of time is as follows: ； ； in, and They represent The posterior estimates and posterior covariance of the state variables at time step [time]. and They represent Prior estimates and prior covariance of the state variables at time step The covariance matrix representing the process noise is: ,in The sampling interval is denoted as .

4. The flight calibration method for star sensor and inertial unit structural parameters as described in claim 3, characterized in that: Step 3, the construction of the attitude increments of the inertial unit and the star sensor, includes the following steps: (1) The starting time for calculating the attitude increment is set to The termination time is set to ; (2) Remember the inertial unit in The measured angular velocity at time t is ,but Time to time For the interval, the rotation vector of the inertial element coordinate system is estimated as follows: ； in, for The posterior estimate of the zero-bias drift at time step zero, matrix Includes scaling error , , Non-orthogonality error , , It has the following form: ； Rotation vector Transform into rotation matrix form Therefore, the attitude increment of the inertial unit Estimated as ; (3) The star sensor is located at The first time observed The direction vector of the star in the star sensor coordinate system is In the vicinity Time and At a certain moment, the star sensor observes several common stars; the set of these stars is denoted as _____. attitude increment of star sensor The following Wahba problem is solved using the QUEST algorithm or SVD decomposition method: 。 5. The flight calibration method for the structural parameters of a star sensor and inertial unit as described in claim 4, characterized in that: In step 4, the regularized least squares problem that needs to be solved is: ； in, , and These are the measured values, sensitivity matrix, and measurement noise covariance of the measurement equation established in step 3. The weighted Euclidean norm of a vector. Represents the sensitivity matrix The potential deviations arise from the matrix during the working process. Potential disturbances ,matrix Expressed as: ； ； ； ； Among them, if using express The amount of disturbance, then express The boundary, Other variables are represented in the same way.

6. A flight calibration system for star sensor and inertial unit structural parameters, characterized in that, include: The setting module is used to set the pre-calibration values ​​and uncertainties of sensor accuracy, seeing, attitude increment integration time, and structural parameters during calibration based on the datasheet and weather conditions during calibration, and to set the initial state of the structural parameter deviation estimator based on the above parameters. The time propagation module is used to propagate the constant zero bias, zero bias drift, and estimated values ​​and covariance of the gyroscope based on the parameter model after the inertial unit outputs new angular velocity measurements and the star sensor outputs new stellar observation information. The module is used to construct the attitude increments of the inertial unit and star sensor using the obtained angular velocity measurements and star observation information, and then construct the measurement equations for structural parameter deviations and measurement noise covariance. The construction of attitude increments for inertial cells and star sensors involves the following steps: (1) The starting time for calculating the attitude increment is set to The termination time is set to , Indicates the attitude increment integration time; (2) Remember the inertial unit in The measured angular velocity at time t is ,but Time to time For the interval, the rotation vector of the inertial element coordinate system is estimated as follows: ； in, for The posterior estimate of the zero-bias drift at time step zero, matrix Includes scaling error , , Non-orthogonality error , , It has the following form: ； Rotation vector Transform into rotation matrix form Therefore, the attitude increment of the inertial unit Estimated as ; (3) The star sensor is located at The first time observed The direction vector of the star in the star sensor coordinate system is ; in the vicinity Time and At a certain moment, the star sensor observes several common stars; the set of these stars is denoted as _____. Therefore, the attitude increment of the star sensor The following Wahba problem can be solved using the QUEST algorithm or SVD decomposition method. ； The construction of the measurement equations for structural parameter deviations and the measurement noise covariance includes the following steps: (1) The attitude increment of the inertial unit mentioned above attitude increment of star sensor and pre-calibration values ​​of structural parameters The quantities that form an identity matrix. Its deviation from the identity matrix is ​​used to establish the measurement quantity. The relationship is ; (2) Measurement quantity With state quantity The relationship is the measurement equation, which is... ,in, Indicates measurement noise. The sensitivity matrix is ​​expressed as follows: ； in, for The left-multiplied Baker-Campbell-Hausdorff approximation Jacobian matrix at time t is given by the following equation: ； (3) Noise measurement The covariance matrix is , expressed as: ； in, for The posterior estimate covariance of the zero-bias drift at time intervals, and the covariance matrix of the star sensor attitude increment. and the angle random walk noise covariance of the three-axis gyroscope They are expressed as follows: ； ； in, The accuracy of star measurement in star sensors Seeing of star sensors The angle of the three-axis gyroscope wanders randomly. The sampling interval; The iterative estimation module is used to solve the corresponding regularized least squares problem based on the measurement equation using a regularized robust filtering framework, and to update the estimated values ​​and estimated covariance of constant zero bias, zero bias drift and structural parameter deviation, thereby realizing iterative estimation. The compensation module is used to compensate for the structural parameters after obtaining a stable estimate of the structural parameter deviation.

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