A method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation.

Abstract

This invention relates to a method for suppressing atmospheric density errors in spacecraft inertial and starlight refraction combined navigation. First, based on the error equations of the strapdown inertial navigation system, the atmospheric density error is extended to the system state variables, and a spacecraft state model is established. Then, the refractional apparent altitude, considering the atmospheric density error, is obtained using a star sensor as an observation, and a refractional apparent altitude measurement model considering the atmospheric density error is established. Finally, UKF filtering is used to estimate the spacecraft's position, velocity, and attitude. This invention belongs to the field of autonomous spacecraft navigation and can provide high-precision position and velocity information for spacecraft, which has significant practical implications for autonomous spacecraft navigation.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft autonomous navigation and relates to a method for suppressing atmospheric density errors in spacecraft inertial and starlight refraction combined navigation, which is applicable to high-precision autonomous positioning and attitude determination of spacecraft. Background Technology

[0002] With the development of information and science and technology, high-performance and high-precision spacecraft place higher demands on navigation systems, making research on navigation technology of great significance. Traditional radio navigation is a relatively mature method, but it requires assistance from ground control stations and is highly susceptible to electromagnetic interference, resulting in low reliability. Under targeted and strong electronic interference, it is vulnerable to enemy electronic interference, leading to navigation information failure. Therefore, research into autonomous navigation methods is urgently needed.

[0003] Inertial navigation utilizes inertial measurement units (IMUs) to measure the angular velocity and specific force changes of a vehicle in inertial space. Under conditions of known initial attitude, velocity, and position, it integrates to obtain real-time navigation information. It does not rely on external information during navigation and boasts numerous advantages, including high short-term accuracy, continuous output, strong anti-interference capability, and comprehensive navigation information. However, the navigation and positioning errors of inertial navigation systems accumulate over time and eventually diverge, making long-term independent navigation difficult. Celestial navigation systems, on the other hand, use stellar information as navigation observations. Based on the positions of stars in inertial space, they further calculate the vehicle's position and attitude information. This is a completely autonomous navigation system, independent of external electromagnetic signals, with strong anti-interference capability, and its errors do not accumulate over time, achieving accuracy down to the arcsecond level. Inertial navigation and celestial navigation are two commonly used autonomous navigation methods for spacecraft. Their advantages and disadvantages complement each other, and combining them is an important way to achieve high-precision autonomous navigation. Traditional inertial and astronomical combined navigation methods primarily correct spacecraft attitude errors, offering limited correction for position errors and failing to meet the high-precision positioning requirements of spacecraft. Since starlight refraction information contains spacecraft position information, incorporating this information is an effective means to improve the positioning accuracy of inertial and astronomical combined navigation. Therefore, inertial and starlight refraction combined navigation is a high-precision autonomous navigation method.

[0004] The accuracy of the atmospheric refraction model is a crucial factor affecting the accuracy of inertial navigation combined with starlight refraction. The atmospheric refraction model used in starlight refraction astronomical navigation is derived from the American Standard Atmosphere (ASA), which establishes an accurate mathematical relationship between the refraction angle of starlight and atmospheric altitude. The accuracy of the atmospheric refraction model directly determines the accuracy of starlight refraction measurement acquisition and the measurement model itself, thus affecting the accuracy of inertial navigation combined with starlight refraction. Research has found that the accuracy of the atmospheric refraction model is primarily affected by the accuracy of the stratospheric atmospheric density model, which is easily influenced by factors such as latitude, season, and airflow, leading to errors. Therefore, researching methods to suppress atmospheric density errors is an effective way to improve the accuracy of inertial navigation combined with starlight refraction. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of the accuracy of inertial and starlight refraction combined navigation being affected by atmospheric density error, and to provide a method for suppressing atmospheric density error for spacecraft, thereby improving the accuracy of inertial and starlight refraction combined navigation.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] A method for suppressing atmospheric density errors in spacecraft inertial and starlight refraction combined navigation includes the following steps:

[0008] Step 1: Based on the error equation of the strapdown inertial navigation system, extend the atmospheric density error to the system state variables and establish the state equation of the spacecraft;

[0009] Step 2: Use a star sensor to obtain the refractional apparent height observation considering atmospheric density error, and establish a refractional apparent height measurement model considering atmospheric density error based on the observation.

[0010] Step 3: Based on the state equation in Step 1 and the measurement model in Step 2, the position, velocity and attitude of the spacecraft are estimated using UKF (Unscented Kalman Filter) filtering to complete the spacecraft's inertial and starlight refraction combined navigation.

[0011] The specific steps are as follows:

[0012] 1. Based on the error equations of the strapdown inertial navigation system, the atmospheric density error is extended to the system state variables, and the system state equations are established:

[0013] use As state variables, the state equation is:

[0014] (1)

[0015] In the formula, It's a platform misalignment angle. These represent the azimuth angles of east and north, respectively. It is the spacecraft's velocity error. These are the speed errors in the east, north, and sky directions, respectively. It is the spacecraft's position error. These are the longitude, latitude, and altitude errors, respectively. Gyroscope constant drift, These are the constant drift values ​​of the gyroscopes in the x, y, and z directions of the inertial navigation system. It is the constant bias of the accelerometer. These are the constant biases of the accelerometers in the x, y, and z directions of the inertial navigation system. It is an error in atmospheric density; and These represent the commanded angular velocity and its error, respectively. , ; and It is the projection of the Earth's rotational angular velocity and its error onto the navigation coordinate system. , ; and δ It is the angular velocity of the navigation coordinate system relative to the Earth-fixed coordinate system, and its error is projected onto the navigation system. , and These are the principal radii of curvature of the Mao-You circle and the Zi-Wu circle, respectively. , It is the projection of the accelerometer output onto the navigation system. It is the attitude matrix:

[0016] (2)

[0017] In the formula, These are the heading angle, pitch angle, and roll angle;

[0018] The above state equation can be written as:

[0019] (3)

[0020] In the formula, yes The derivative of It is the system state transition matrix. It is system process noise.

[0021] 2. Acquisition of refractional apparent height observations and establishment of a measurement model considering atmospheric density error:

[0022] (1) Obtaining the refracted apparent height observation considering atmospheric density error:

[0023] By using a star sensor to capture star images, and through star image recognition and centroid extraction methods, combined with a standard navigation star catalog, the pixel coordinates of star points before and after refraction of the refracted star can be obtained. , The starlight vectors before and after refraction are obtained through the imaging principle of star sensors. , :

[0024] (4)

[0025] In the formula, It's the focal length. , , It's the number of pixels. It is the field of view of the star sensor;

[0026] Calculate the starlight refraction angle using the starlight vectors before and after refraction:

[0027] (5)

[0028] An empirical formula for the apparent height of refraction is derived from a starlight atmospheric refraction model without atmospheric density error:

[0029] (6)

[0030] Based on the starlight atmospheric refraction model with atmospheric density errors, the refraction apparent altitude observation considering atmospheric density errors is obtained as follows:

[0031] (7)

[0032] (2) Establishment of a refractional apparent height measurement model considering atmospheric density error:

[0033] Based on the geometric relationship of starlight refraction, the apparent height of refraction can be expressed as:

[0034] (8)

[0035] In the formula, , It is the spacecraft's position vector. , It is the starlight vector of the refracted star before refraction in the geocentric inertial coordinate system. It is the Earth's radius;

[0036] Based on formulas (6) and (7), the refraction apparent height error is obtained:

[0037] (9)

[0038] Based on formulas (8) and (9), the apparent height of refraction considering atmospheric density error is obtained:

[0039] (10)

[0040] The model for measuring apparent height by refraction, taking into account atmospheric density error, can be expressed as:

[0041] (11)

[0042] In the formula, This represents the refractional apparent height observation that takes into account atmospheric density errors. Represents a nonlinear measurement function. It measures noise.

[0043] 3. Perform UKF filtering to obtain spacecraft position, velocity, and attitude estimates:

[0044] The discretized state model and measurement model of the spacecraft inertial and starlight refraction combined navigation system, which suppresses atmospheric density errors, are as follows:

[0045] (12)

[0046] In the formula, For the nonlinear transfer function of the integrated navigation system, It is a nonlinear measurement function. and Representing process and measurement noise respectively, UKF filtering estimation is used to obtain the posterior state estimate of the spacecraft. X k For the posterior state estimation, the components correspond in order to: platform misalignment angle, velocity error, position error, gyroscope constant drift, accelerometer constant bias, atmospheric density error, and posterior error covariance. ,Will and The output is then returned to the UKF filter, along with the estimated values ​​of the state variables and error covariance at time k, to obtain the output at time k+1.

[0047] The advantages of this invention compared to the prior art are:

[0048] (1) A single navigation method cannot meet the requirements of high-precision autonomous navigation for spacecraft. Therefore, inertial navigation and celestial navigation are combined to complement each other's advantages and disadvantages and achieve high-precision autonomous navigation. In addition, in view of the problem that the traditional inertial and celestial navigation combination method mainly corrects the attitude error of the spacecraft and has a low effect on the correction of position error, which cannot meet the high-precision positioning requirements of the spacecraft, starlight refraction information containing the spacecraft's position information is introduced to improve the positioning accuracy of the inertial and celestial navigation combination.

[0049] (2) The accuracy of the atmospheric refraction model directly determines the accuracy of starlight refraction measurement acquisition and the measurement model, which in turn affects the accuracy of inertial and starlight refraction combined navigation. The accuracy of the atmospheric refraction model is mainly affected by the accuracy of the stratospheric atmospheric density model, and the stratospheric atmospheric density is easily affected by various factors such as latitude, season, and airflow, resulting in errors. This invention proposes to use the state dimension expansion method to suppress atmospheric density errors, taking atmospheric density errors as new state variables, establishing a system dimension expansion state model and a measurement model that considers atmospheric density errors, and suppressing atmospheric density errors by filtering and estimating atmospheric density errors, thereby improving the accuracy of inertial and starlight refraction combined navigation. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for suppressing atmospheric density error in the combined navigation of spacecraft inertia and starlight refraction in this invention. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] like Figure 1 The flowchart shown is a method for suppressing atmospheric density errors in spacecraft inertial and starlight refraction combined navigation according to the present invention. Specific implementation process:

[0053] 1. Based on the error equations of the strapdown inertial navigation system, the atmospheric density error is extended to the system state variables, and the system state equations are established:

[0054] use As state variables, the state equation is:

[0055] (1)

[0056] In the formula, It's a platform misalignment angle. These represent the azimuth angles of east and north, respectively. It is the spacecraft's velocity error. These are the speed errors in the east, north, and sky directions, respectively. It is the spacecraft's position error. These are the longitude, latitude, and altitude errors, respectively. Gyroscope constant drift, These are the constant drift values ​​of the gyroscopes in the x, y, and z directions of the inertial navigation system. It is the constant bias of the accelerometer. These are the constant biases of the accelerometers in the x, y, and z directions of the inertial navigation system. It is an error in atmospheric density; and These represent the commanded angular velocity and its error, respectively. , ; and It is the projection of the Earth's rotational angular velocity and its error onto the navigation coordinate system. , ; and δ It is the angular velocity of the navigation coordinate system relative to the Earth-fixed coordinate system, and its error is projected onto the navigation system. , and These are the principal radii of curvature of the Mao-You circle and the Zi-Wu circle, respectively. , It is the projection of the accelerometer output onto the navigation system. It is the attitude matrix:

[0057] (2)

[0058] In the formula These are the heading angle, pitch angle, and roll angle.

[0059] The above state equation can be written as:

[0060] (3)

[0061] In the formula, yes The derivative of It is the system state transition matrix. It is system process noise.

[0062] 2. Acquisition of refractional apparent height observations and establishment of a measurement model considering atmospheric density error:

[0063] (1) Obtaining the refracted apparent height observation considering atmospheric density error:

[0064] By using a star sensor to capture star images, and through star image recognition and centroid extraction methods, combined with a standard navigation star catalog, the pixel coordinates of star points before and after refraction of the refracted star can be obtained. , The starlight vectors before and after refraction are obtained through the imaging principle of star sensors. , :

[0065] (4)

[0066] Substituting the star pixel coordinates (x0, y0) before refraction into formula (4) yields S0, and substituting the star pixel coordinates (x1, y1) after refraction into formula (4) yields S1.

[0067] In the formula, It's the focal length. , , It's the number of pixels. It is the field of view of the star sensor.

[0068] Calculate the starlight refraction angle using the starlight vectors before and after refraction:

[0069] (5)

[0070] An empirical formula for the apparent height of refraction is derived from a starlight atmospheric refraction model without atmospheric density error:

[0071] (6)

[0072] Based on the starlight atmospheric refraction model with atmospheric density errors, the refraction apparent altitude observation considering atmospheric density errors is obtained as follows:

[0073] (7)

[0074] (2) Establishment of a refractional apparent height measurement model considering atmospheric density error:

[0075] Based on the geometric relationship of starlight refraction, the apparent height of refraction can be expressed as:

[0076] (8)

[0077] In the formula, , It is the spacecraft's position vector. , It is the starlight vector of the refracted star before refraction in the geocentric inertial coordinate system. It is the Earth's radius.

[0078] Based on formulas (6) and (7), the refraction apparent height error is obtained:

[0079] (9)

[0080] Based on formulas (8) and (9), the apparent height of refraction considering atmospheric density error is obtained:

[0081] (10)

[0082] The model for measuring apparent height by refraction, taking into account atmospheric density error, can be expressed as:

[0083] (11)

[0084] In the formula, This represents the refractional apparent height observation that takes into account atmospheric density errors. Represents a nonlinear measurement function. It measures noise.

[0085] 3. Perform UKF filtering to obtain spacecraft position, velocity, and attitude estimates:

[0086] The discretized state model and measurement model of the spacecraft inertial and starlight refraction combined navigation system, which suppresses atmospheric density errors, are as follows:

[0087] (12)

[0088] In the formula, For the nonlinear transfer function of the integrated navigation system, It is a nonlinear measurement function. and Representing process and measurement noise respectively, UKF filtering estimation is used to obtain the posterior state estimate of the spacecraft. X k For the posterior state estimation, the components correspond in order to: platform misalignment angle, velocity error, position error, gyroscope constant drift, accelerometer constant bias, atmospheric density error, and posterior error covariance. ,Will and The output is then returned to the UKF filter, along with the estimated values ​​of the state variables and error covariance at time k, to obtain the output at time k+1.

[0089] The specific process of UKF filtering is as follows:

[0090] UKF filtering obtains sampling points based on the U-Transform, and the standard UKF filtering algorithm... A series of sample points were selected from the vicinity, and the mean and covariance of the sample points were respectively... and Let the state variable be... Wei, then The sample points and their weights are as follows:

[0091] (13)

[0092] In the formula, ;when , Pick The Okay; when , Pick The The specific process of UKF filtering in this invention is as follows:

[0093] ① Initialization:

[0094] (14)

[0095] (15)

[0096] In the formula, These are the actual values ​​of the spacecraft's state variables at the initial moment. These are estimates of the spacecraft's state variables at the initial moment. It is the initial state error variance matrix.

[0097] ② Sigma sampling points and their weights calculation:

[0098] (16)

[0099] ③Time update:

[0100] Perform one-step state prediction for each sampling point:

[0101] (17)

[0102] Prior state estimates are obtained through weight calculation:

[0103] (18)

[0104] Prior estimation error covariance matrix:

[0105] (19)

[0106] In the formula, It is the process noise covariance matrix.

[0107] Observational predictions are made for each sampling point:

[0108] (20)

[0109] Measurement prediction is obtained through weight calculation.

[0110] (twenty one)

[0111] ④ Measurement Update:

[0112] Measurement prediction covariance calculation:

[0113] (twenty two)

[0114] In the formula, It is the measurement noise covariance matrix.

[0115] Calculation of cross-covariance matrix:

[0116] (twenty three)

[0117] Filter gain calculation:

[0118] (twenty four)

[0119] State estimation calculation:

[0120] (25)

[0121] Calculation of the estimation error covariance matrix:

[0122] (26)

[0123] Will and The output is then returned to the UKF filter, along with the estimated values ​​of the state variables and error covariance at time k, to obtain the output at time k+1.

[0124] After establishing the system state equations, to further improve the accuracy and stability of the integrated navigation system, the specific implementation of this invention may also include the following optimization steps:

[0125] When establishing a model for measuring refracted apparent height, atmospheric density error can be used as a calibrable parameter. Through subsequent filtering processes, atmospheric density error can be estimated and compensated in real time, effectively reducing the error caused by inaccuracies in the atmospheric refraction model in calculating refracted apparent height.

[0126] Before obtaining the refracted apparent altitude observation using a star sensor, the captured star image must first undergo optical distortion correction. Specifically, this involves correcting the pixel coordinates of the identified navigation stars based on pre-calibrated distortion parameters of the star sensor's optical system to eliminate the influence of lens distortion on the accuracy of starlight vector pointing. Then, by comparing with a standard navigation star catalog, the refracted navigation stars are identified for subsequent refracted apparent altitude calculations.

[0127] In the subsequent unscented Kalman filter (UKF) calculation, a symmetric sampling strategy is used to select the Sigma sampling points. The total number of sampling points is twice the dimension of the system state variables plus one, and all points are symmetrically distributed around the current state estimate. By adjusting a scaling parameter, the distribution range of these sampling points can be controlled, thereby achieving a balance between accuracy and stability in nonlinear propagation.

[0128] In the time update step of UKF filtering, based on the linearized error state equation, a high-order Taylor expansion is used to calculate the state transition matrix, which is then used for the propagation of Sigma points. This avoids the computational burden of numerical integration for each Sigma point in traditional UKF, while ensuring prediction accuracy.

[0129] The measurement update step of the UKF filter includes a state constraint mechanism. When the estimated value of the atmospheric density error state exceeds its physically reasonable range, the filtering algorithm will constrain it within a preset range to ensure the stability and physical meaning of the system state estimate.

[0130] Finally, this method also includes an open-loop correction step for the navigation results. The high-precision position, velocity, and attitude error information finally estimated by UKF filtering is used to directly compensate for the navigation parameters, without feeding the estimated position, velocity, and attitude errors back to the inertial navigation system's calculation loop.

Claims

1. A method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation, characterized in that, Includes the following steps: Step 1: Based on the error equation of the strapdown inertial navigation system, extend the atmospheric density error to the system state variables and establish the state equation of the spacecraft; Step 2: Use a star sensor to obtain the refractional apparent height observation considering atmospheric density error, and establish a refractional apparent height measurement model considering atmospheric density error based on the observation. Step 3: Based on the state equation in Step 1 and the measurement model in Step 2, UKF filtering is used to estimate the spacecraft's position, velocity, and attitude, thus completing the spacecraft's inertial and starlight refraction combined navigation.

2. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 1, characterized in that, The state equation in step 1 is as follows: (using...) As state variables, the state equation is: （1） In the formula, It's a platform misalignment angle. These represent the azimuth angles for east and north, respectively. It is the spacecraft's velocity error. These are the speed errors in the east, north, and sky directions, respectively. It is the spacecraft's position error. These are the longitude, latitude, and altitude errors, respectively. gyroscope constant drift, These are the constant drift values ​​of the gyroscopes in the x, y, and z directions of the inertial navigation system. It is the constant bias of the accelerometer. These are the constant biases of the accelerometers in the x, y, and z directions of the inertial navigation system. It is an error in atmospheric density; and These represent the commanded angular velocity and its error, respectively. , ; and It is the projection of the Earth's rotational angular velocity and its error onto the navigation coordinate system. , ω ie L is the Earth's rotational angular velocity, and L is the geographic latitude. and δ It is the angular velocity of the navigation coordinate system relative to the Earth-fixed coordinate system, and the projection of its error onto the navigation coordinate system. ,ν E ν N These represent the eastward and northward velocities, respectively, and h is the spacecraft's altitude. and These are the principal radii of curvature of the Mao-You circle and the Zi-Wu circle, respectively. , , It is the Earth's radius. It is the Earth's oblateness; , , , It is the projection of the accelerometer output onto the navigation coordinate system. It is the attitude matrix: （2） In the formula, These are the heading angle, pitch angle, and roll angle; The above state equation can be written as: （3） In the formula, yes The derivative of It is the system state transition matrix. It is system process noise.

3. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 1, characterized in that, Step 2 includes: (1) Obtaining the refracted apparent height observation considering atmospheric density error: By using a star sensor to capture star images, and through star image recognition and centroid extraction methods, combined with a standard navigation star catalog, the pixel coordinates of star points before and after refraction of the refracted star can be obtained. , The starlight vectors before and after refraction are obtained through the imaging principle of star sensors. , : （4） In the formula, It's the focal length. , , It's the number of pixels. It is the field of view of the star sensor; Calculate the starlight refraction angle using the starlight vectors before and after refraction: （5） An empirical formula for the apparent height of refraction is derived from a starlight atmospheric refraction model without atmospheric density error: （6） Based on the starlight atmospheric refraction model with atmospheric density errors, the refraction apparent altitude observation considering atmospheric density errors is obtained as follows: （7） (2) Establishment of a refractional apparent height measurement model considering atmospheric density error: Based on the geometric relationship of starlight refraction, the apparent height of refraction can be expressed as: （8） In the formula, , It is the spacecraft's position vector. , It is the starlight vector of the refracted star before refraction in the geocentric inertial coordinate system. It is the Earth's radius; Based on formulas (6) and (7), the refraction apparent height error is obtained: （9） Based on formulas (8) and (9), the refraction apparent height observation considering atmospheric density error is obtained. : （10） The model for measuring apparent height by refraction, taking into account atmospheric density error, can be expressed as: （11） In the formula, This represents the refractional apparent height observation that takes into account atmospheric density errors. Represents a nonlinear measurement function. It measures noise.

4. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 1, characterized in that, In step 3, UKF filtering is performed to obtain the spacecraft's position, velocity, and attitude estimates as follows: The discretized state model and measurement model of the spacecraft inertial and starlight refraction combined navigation system, which suppresses atmospheric density errors, are as follows: （12） In the formula, For the nonlinear transfer function of the integrated navigation system, It is a nonlinear measurement function. and Representing process and measurement noise respectively, UKF filtering estimation is used to obtain the posterior state estimate of the spacecraft. X k For the posterior state estimation, the components correspond in order to: platform misalignment angle, velocity error, position error, gyroscope constant drift, accelerometer constant bias, atmospheric density error, and posterior error covariance. ,Will and The output is then returned to the UKF filter, along with the estimated values ​​of the state variables and error covariance at time k, to obtain the output at time k+1.

5. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 1, characterized in that, When establishing the refractive apparent height measurement model, atmospheric density error is used as a calibrable parameter. The atmospheric density error is compensated through a filtering process to reduce the impact of atmospheric refraction model error on the calculation of refractive apparent height.

6. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 3, characterized in that, Before obtaining the refracted apparent altitude observation, the process also includes an optical distortion correction step for the star map captured by the star sensor. By calibrating the distortion parameters of the star sensor's optical system, the pixel coordinates of the navigation star are corrected. Then, by comparing with a standard navigation star catalog, the navigation star that is refracted is determined for subsequent refracted apparent altitude calculation.

7. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 4, characterized in that, In UKF filtering, the selection of Sigma sampling points adopts a symmetric sampling strategy. The number of sampling points is twice the dimension of the state variables plus one. The sampling points are symmetrically distributed around the state estimates, and the distribution range of the sampling points is controlled by adjusting the scaling parameter.

8. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 4, characterized in that, In the time update step of UKF filtering, based on the linearized error state equation, a high-order Taylor expansion is used to calculate the state transition matrix, which is then used for the propagation of Sigma points. This avoids the computational burden of numerical integration for each Sigma point in traditional UKF, while ensuring prediction accuracy.

9. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 4, characterized in that, In the measurement update step of UKF filtering, when the estimated value of atmospheric density error state exceeds the preset physical reasonable range, it is constrained within that range to maintain the stability of the system estimate.

10. The method for suppressing atmospheric density error in spacecraft inertial and starlight refraction combined navigation according to claim 1, characterized in that, The integrated navigation filter adopts an open-loop correction method, using the position, velocity, and attitude errors estimated by the UKF filter to directly compensate for the navigation parameters, without feeding the estimated position, velocity, and attitude errors back to the inertial navigation system's calculation loop.

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