Electric propulsion thrust on-orbit calibration simulation method based on precise orbit determination

Abstract

The invention discloses an electric propulsion thrust on-orbit calibration simulation method based on precise orbit determination. The method comprises the following steps: establishing a precise orbit model; inputting a track initial value, a thrust external control quantity and control time; track recursion is carried out; unknown measurement noise in an actual space is introduced on the basis of a recursive orbit, and orbit quantity measurement in the actual space is simulated; taking the recursive orbit with noise as a measured value, substituting the measured value into a filtering algorithm for orbit prediction, and obtaining a predicted orbit; based on the prediction orbit, the position and speed of the spacecraft under the inertial system at each moment in the control period are obtained, and the acceleration of the spacecraft at each moment can be obtained by using the integral of the speed and position quantity information; and S7, removing acceleration brought by perturbative force in the high-precision orbit recursion model to obtain thrust acceleration, and finally obtaining a curve of calibration thrust changing along with time.

Description

Technical Field

[0001] The present invention relates to the field of on-orbit calibration of thruster thrust. Specifically, it designs an on-orbit calibration and simulation method for electric propulsion thrust based on precise orbit determination. Background Art

[0002] With the development and progress of space technology, as a new type of spacecraft power system, electric thrusters have been widely studied and applied to tasks such as orbit maintenance and control of various small spacecraft due to their extremely high specific impulse and almost vibration-free working mode. However, due to the incomplete consistency between ground and space test conditions, electric thrusters need to be accurately calibrated in the initial stage of orbit injection to meet the requirements of various high-precision controls.

[0003] Currently, there are mainly two types of on-orbit calibration schemes for thrust. One is to calibrate thrust through attitude data, and the other is to calibrate thrust through orbit data. For the method of calibrating thrust through attitude data, due to the calibration of thrust in the order of dozens of millinewtons for electric propulsion, high-precision attitude sensitive devices are required, and the attitude stability of the satellite cannot be guaranteed during the thrust estimation process. Therefore, it is difficult to achieve on-orbit calibration for small thrust. And the calibration of thrust through orbit data is divided into forward and reverse types. The forward thrust calibration method mainly measures thrust through an accelerometer. However, the current most advanced accelerometer measurement accuracy is only 10 -6 ~10 -5 order of magnitude. For electric thrust in the order of dozens of millinewtons and a satellite mass of several hundred kilograms, the acceleration order of magnitude is 10 -8 m / s 2 , and it is also difficult to achieve. Summary of the Invention

[0004] The technical problem solved by the present invention is: to provide an on-orbit calibration simulation method for electric propulsion thrust based on precise orbit determination to solve the technical defects existing in the prior art.

[0005] The technical solution adopted by the present invention is: an on-orbit calibration simulation method for electric propulsion thrust based on precise orbit determination, including:

[0006] Establish an orbit model, and use the orbit model to perform orbit recursion according to the initial orbit value, thrust external control quantity, and control time;

[0007] Introduce unknown measurement noise in the actual space on the basis of the recursive orbit to simulate the orbit measurement in the real space;

[0008] Take the noisy recursive orbit as the measured value and substitute it into the filtering algorithm for orbit prediction to obtain the predicted orbit;

[0009] Based on the predicted orbit, obtain the position and velocity of the spacecraft in the inertial system at each moment within the control period, and use the integral of the velocity and the position quantity to obtain the acceleration of the spacecraft at each moment;

[0010] Remove the acceleration caused by the disturbing force in the orbit model, combine it with the acceleration of the spacecraft obtained at each moment, calculate the calibrated thrust, and finally obtain the curve of the calibrated thrust varying with time.

[0011] Preferably, verify the accuracy of thrust calibration according to the difference between the calibrated thrust and the actual thrust, that is, the calibrated thrust error.

[0012] Preferably, the orbit model needs to introduce satellite orbit disturbing forces, including the non-spherical perturbation of the Earth, solar radiation pressure, atmospheric drag, and three-body gravitational perturbation.

[0013] Preferably, the external control quantity of the thrust is the thrust vector of the electric thruster, which is default to be arranged along the direction passing through the center of mass. The thruster is fully turned on during the thrust calibration process and is a thrust constant.

[0014] Preferably, the control time is one orbit period.

[0015] Preferably, the orbit recurrence process adopts but is not limited to the Runge-Kutta 45 algorithm.

[0016] Preferably, introduce the unknown measurement noise in the actual space by adding the on-board GNSS sensor as Gaussian noise to the simulation process, including position measurement noise, velocity measurement noise, and sampling frequency.

[0017] Preferably, select different filtering algorithms according to different requirements. When efficiency is prioritized, the KF and EKF methods are selected; when accuracy is prioritized, the UKF method is selected.

[0018] Preferably, remove the acceleration caused by the disturbing force in the orbit model and reverse-infer the thruster thrust f x 、f y 、f z The formula is:

[0019]

[0020] where a x 、a y 、a z are the accelerations of the spacecraft on the three axes in the satellite inertial system respectively; f nsphx 、f nsphy 、f nsphz are the non-spherical disturbing forces on the three axes respectively; f Dx 、f Dy 、f Dz are the atmospheric drags on the three axes respectively; f trix 、f triy 、ftriz They are respectively the three-axis three-body perturbing forces; f Sx , f Sy , f Sz They are respectively the three-axis solar radiation pressure perturbing forces; where m is the mass of the spacecraft, μ is the gravitational constant, r is the orbital altitude, and x, y, and z are respectively the three-axis positions of the spacecraft in the inertial system.

[0021] An on-orbit calibration simulation device for electric propulsion thrust based on precise orbit determination, comprising:

[0022] One or more processors;

[0023] A storage device for storing one or more programs,

[0024] When the one or more programs are executed by the one or more processors, the one or more processors implement the on-orbit calibration simulation method for electric propulsion thrust based on precise orbit determination.

[0025] The beneficial effects of the present invention compared with the prior art are:

[0026] The problem solved by the present invention is the on-orbit thrust calibration problem of the electric thruster of the space vehicle, and a simulation framework method and an evaluation method are provided for the subsequent optimization algorithm with this method as the core. This method accumulates the orbit measurement data for a certain period of time (one orbital period), reduces the influence of measurement errors on orbit identification through a filtering algorithm, and further reduces the thrust calibration error. It does not directly measure the thrust through a sensor, avoiding the limitation brought by the sensor accuracy. At the same time, a subsequent optimization framework is provided for the filtering optimization algorithm and a higher-precision perturbation model, and a simulation method is provided for evaluating the algorithm accuracy.

[0027] The present invention performs orbit maneuver by continuously applying a fixed thrust to the spacecraft, and inversely calculates the thruster thrust based on the principle of precise orbit determination. It can calibrate the on-orbit thrust of micro-thrusters similar to electric thrusters, with high thrust calibration accuracy, and solves the problem that it is difficult to directly calibrate the thrust due to the insufficient accuracy of the current satellite sensors; and a simulation method for on-orbit thrust calibration is designed for other optimization algorithms based on precise orbit determination, which can realize the accuracy evaluation of the on-orbit thrust calibration algorithm and has high practical value.. Description of the Drawings

[0028] Figure 1 It is the flow chart of the present invention;

[0029] Figure 2 It is the Kalman filter orbit simulation result;

[0030] Figure 3 It is the curve of the calibrated thrust changing with time in the thrust direction;

[0031] Figure 4 It is the curve of the mean thrust error varying with time. Detailed implementation manners

[0032] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0033] For the on-orbit calibration of micro thrust, the present invention proposes to adopt an orbit estimation method based on precise orbit determination for reverse thrust calibration. Through on-orbit measurement and filtering processing for a period of time, the thrust of the thruster is calculated reversely by using the orbit change, avoiding directly measuring the thrust with a sensor, which is more appropriate. Therefore, for the problem of on-orbit calibration of micro thrust, the present invention proposes an orbit estimation method based on precise orbit determination, and for the thrust calibration method based on precise orbit determination, a general thrust calibration simulation method is provided for subsequent optimization algorithms, which can be used to evaluate the algorithm accuracy.

[0034] As Figure 1 shown, a simulation method for on-orbit calibration of electric propulsion thrust based on precise orbit determination provided by the present invention includes:

[0035] Step S1: Establish an orbit model for simulating the real space orbit;

[0036] In a preferred embodiment provided by the present invention, an accurate orbit model is established, and satellite orbit disturbing forces including the non-spherical perturbation of the earth, solar radiation pressure, atmospheric drag, and three-body gravitational perturbation are introduced;

[0037] The non-spherical perturbation of the earth can adopt the geopotential function U of the earth's gravity field:

[0038]

[0039] where r, φ, and λ respectively correspond to the geocentric distance of the satellite and the local geographic longitude and latitude; P n (x), P nm (x) are the Legendre polynomial and the associated Legendre function respectively; some terms corresponding to J n are called zonal harmonic terms, and the terms corresponding to C nm and S nm are called tesseral harmonic terms.

[0040] The disturbing force acceleration acting on the satellite by the solar radiation pressure can be expressed as:

[0041]

[0042] Among them, k is the satellite surface reflection coefficient; s is a constant, which can be taken as 1.4×10-1 J / (cm / s) near the Earth; c is the speed of light; A / m is the area-to-mass ratio of the satellite along the direction perpendicular to the direct solar radiation direction; is the unit vector in the direction from the Earth's center to the Sun.

[0043] The atmospheric drag expression is:

[0044]

[0045] Among them, C D is the drag coefficient, which is usually taken as 2.2 in general calculations; S is the satellite windward area, m is the satellite mass, and in the analysis of atmospheric perturbation, S / m is usually called the satellite area-to-mass ratio; ρ is the local atmospheric density; V is the satellite velocity relative to the atmosphere,

[0046] Denote ε as the ratio of the three-body perturbation acceleration to the Earth's central gravitational acceleration, and there is:

[0047]

[0048] Among them, m' is the mass of the third gravitational body, M is the mass of the Earth, r is the distance between the satellite and the Earth's center, and Δ is the distance between the satellite and the third gravitational body.

[0049] Step S2: Input the initial orbit values, the external thrust control quantity, and the control time;

[0050] The external thrust control quantity is the thrust vector of the electric thruster, which is default arranged along the direction passing through the center of mass. The thruster is fully turned on during the thrust calibration process and is a thrust constant;

[0051] Theoretically, the longer the control time, the higher the orbit prediction accuracy, and thus the higher the thrust calibration accuracy. However, considering timeliness and economy, one orbital period can be taken as the control time;

[0052] Step S3: Use the precise orbit model for orbit recursion to obtain the orbit data of the spacecraft in the real space;

[0053] The recursion process can use an algorithm similar to the Runge-Kutta 45 algorithm for orbit recursion. Here, it is not limited to the Runge-Kutta 45 algorithm, and the orbit recursion algorithm can be optimized according to needs to improve the recursion accuracy, so as to more realistically simulate the satellite orbit;

[0054] Step S4: Introduce the unknown measurement noise in the actual space based on the recursive orbit to simulate the orbital measurement in the real space; the satellite orbit measurement means is the on-board GNSS sensor, which can be regarded as Gaussian noise added to the system during the simulation process, including position measurement noise, velocity measurement noise, and sampling frequency;

[0055] Step S5: Take the noisy recursive orbit as the measurement value and substitute it into the filtering algorithm for orbit prediction to obtain the predicted orbit;

[0056] The filtering algorithm can adopt classical filtering algorithms such as KF, EKF, UKF and their improved filtering algorithms. Among them, the KF and EKF methods are simple and efficient in calculation, but the accuracy is poor. The UKF method has higher accuracy but lower calculation efficiency;

[0057] Step S6: Based on the predicted orbit, obtain the position and velocity of the spacecraft in the inertial system at each moment within the control period. Using the integral of velocity and position information, the acceleration of the spacecraft at each moment can be obtained;

[0058] Step S7: Remove the acceleration caused by the perturbing force in the high-precision orbit recursive model, then the calibrated thrust can be calculated, and finally the curve of the calibrated thrust varying with time can be obtained. At the same time, the accuracy of the thrust calibration can be verified according to the calibrated thrust error.

[0059] The formula for back-calculating the thruster thrust by removing the acceleration caused by the perturbing force in the high-precision orbit recursive model is:

[0060]

[0061] where a x 、a y 、a z are the three-axis accelerations in the satellite inertial system respectively, which can be calculated by the difference of the filtered orbit position and velocity; f nsphx 、f nsphy 、f nsphz are the three-axis non-spherical perturbing forces respectively; f Dx 、f Dy 、f Dz are the three-axis atmospheric drags respectively; f trix 、f triy 、f triz are the three-axis three-body perturbing forces respectively; f Sx 、f Sy 、f Sz are the three-axis solar radiation pressure perturbing forces respectively; m is the mass of the spacecraft, μ is the gravitational constant, r is the orbital altitude, and xyz are the three-axis positions in the inertial system..

[0062] Embodiment

[0063] In one embodiment, a method for on-orbit calibration and simulation of the thrust of an electric propulsion based on precise orbit determination is as follows:

[0064] Step 1: Establish an accurate orbit model:

[0065] The non-spherical perturbation of the Earth can be introduced by using the Earth's gravitational potential function U:

[0066]

[0067] where J2 = 1.082630×10 -3 , J3 = 2.565×10 -6 , J4 = 1.608×10 -6

[0068] Introduce solar radiation pressure:

[0069]

[0070] where k is taken as 1.2, s is taken as 1.4×10 -1 J / (cm / s), A is taken as 1.5 m 2

[0071] Introduce atmospheric drag:

[0072]

[0073] Introduce the ratio of the three-body perturbation acceleration to the Earth-centered gravitational acceleration for solving the three-body gravitational perturbation acceleration:

[0074]

[0075] Step 2: Input the orbit initial value, the external control quantity of the thrust, and the control time, where:

[0076] The orbital elements are: circular orbit, orbital altitude 500 km, semi-major axis 6978.14 km, orbital inclination 35°, eccentricity 0, right ascension of the ascending node 110°, argument of perigee 30°, true anomaly 60°, the control force is set to 15 mN, the satellite mass is 300 kg, and the control time is 14000 s.

[0077] Step 3: Use the accurate orbit model for orbit recursion, and the orbit recursion algorithm is RK45;

[0078] Step 4: Introduce the unknown measurement noise in the actual space on the basis of the recursive orbit. The introduced measurement quantity is the GNSS navigation error, where the position measurement error is 7 m, the velocity measurement error is 0.1 m / s, and the measurement frequency is 10 Hz;

[0079] Step 5: Take the noisy recursive orbit as the measurement value and substitute it into the filtering algorithm for orbit prediction. Here, the basic Kalman filter is used for filtering, and its filtering formula is as follows:

[0080] X p ' = AX p + Bu

[0081] P' = APA T + Q

[0082] K = PF T (FPF T + R) -1

[0083] X pk = X p + K([r0, v0] T - FX p ')

[0084] P = (I - KF)P'

[0085] Among them, X p is the state quantity, A is the state transition matrix, B is the control transfer matrix, P is the covariance matrix, Q is the estimated error noise matrix, R is the measurement error matrix, K is the Kalman gain, and F is the identity matrix for the directly measured system.

[0086] Through filtering simulation, the Kalman filter orbit simulation results can be obtained as Figure 2 shown.

[0087] Step 6: Based on the predicted orbit, obtain the position and velocity of the spacecraft in the inertial system at each moment within the control period. Using the integral of velocity and the position information, the acceleration at each moment in the thrust direction of the spacecraft can be obtained;

[0088] Step 7: Remove the acceleration caused by the perturbing force in the high-precision orbit recursive model, and the calibrated thrust curve varying with time in the thrust direction can be obtained as Figure 3 shown.

[0089] It can be seen from the simulation results that the thrust magnitude finally converges to around 15 mN, and at the same time, the curve of the mean value of the thrust error varying with time can be obtained as Figure 4 shown.

[0090] From the simulation results shown above, it can be seen that the thrust calibration error reaches 1.652 mN at the simulation time of 1047 s. Relative to the thrust magnitude of 15 mN, the accuracy reaches 88.99%, which is relatively high. Since the filtering algorithms used in this implementation case are all of the lowest accuracy, their accuracy, stability and convergence speed all need to be improved. For other improved filtering algorithms, orbit recurrence algorithms and higher-precision orbit models, the simulation method provided by the present invention can also be used to simulate and evaluate the algorithm accuracy.

[0091] It should be noted that in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A simulation method for on-orbit calibration of the thrust of an electric propulsion based on precise orbit determination, characterized in that Including: Establish an orbit model, and perform orbit recursion using the orbit model based on the initial orbit values, external thrust control quantities, and control time; Introduce unknown measurement noise in the actual space on the basis of the recursive orbit to simulate the orbit measurement values in the real space; Take the recursive orbit with noise as the measurement value, substitute it into the filtering algorithm for orbit prediction, and obtain the predicted orbit; Based on the predicted orbit, obtain the position and velocity of the spacecraft in the inertial system at each moment within the control period, and use the integral of the velocity and the position quantity to obtain the acceleration of the spacecraft at each moment; Remove the acceleration caused by the perturbing force in the orbit model, combine with the acceleration of the spacecraft obtained at each moment, calculate the calibrated thrust, and finally obtain the curve of the calibrated thrust varying with time.

2. The method according to claim 1, wherein: Verify the accuracy of thrust calibration according to the difference between the calibrated thrust and the actual thrust, i.e., the calibrated thrust error.

3. The method according to claim 1, wherein: The orbit model needs to introduce satellite orbit perturbing forces, including the non-spherical perturbation of the earth, solar radiation pressure, atmospheric drag, and three-body gravitational perturbation.

4. The method according to claim 1, characterized in that: The external thrust control quantity is the thrust vector of the electric thruster, which is default arranged along the direction passing through the center of mass, and the thruster is fully turned on during the thrust calibration process and is a thrust constant.

5. The method according to claim 1, wherein: The control time is one orbit period.

6. The method according to claim 1, characterized in that: The orbit recursion process adopts but is not limited to the Runge-Kutta 45 algorithm.

7. The method according to claim 1, wherein: The unknown measurement noise introduced in the actual space is added by regarding the on-board GNSS sensor as Gaussian noise during the simulation process, including position measurement noise, velocity measurement noise, and sampling frequency.

8. The method according to claim 1, wherein: Select different filtering algorithms according to different requirements. When efficiency is prioritized, the KF and EKF methods are selected; when accuracy is prioritized, the UKF method is selected.

9. The method according to claim 1, wherein: Remove the acceleration caused by the perturbation force in the orbital model and reverse the thrust of the thruster f x 、f y 、f z The formula is: where a x , a y , a z are the three-axis accelerations of the spacecraft in the satellite inertial system; f nsphx , f nsphy , f nsphz are the three-axis non-spherical perturbing forces; f Dx , f Dy , f Dz are the three-axis atmospheric drag forces; f trix , f triy , f triz are the three-axis three-body perturbing forces; f Sx , f Sy , f Sz are the three-axis solar radiation pressure perturbing forces; where m is the mass of the spacecraft, μ is the gravitational constant, r is the orbital altitude, and x, y, and z are the three-axis positions of the spacecraft in the inertial system.

10. An on-orbit calibration simulation device for electric propulsion thrust based on precise orbit determination, characterized in that Including: One or more processors; A storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement an on-orbit calibration simulation method for electric propulsion thrust based on precise orbit determination according to one of claims 1 to 9.

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