CN114894199B - Space-based orbit determination method for earth-moon space spacecraft - Google Patents
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Abstract
The invention belongs to the field of spacecraft orbit judgment, and particularly relates to a space-based orbit determination method for a terrestrial-lunar space spacecraft. The method comprises the following steps: step 1, acquiring an initial state and an initial error of a spacecraft to be orbit-determined in an initial epoch; step 2, when the next epoch of the initial epoch is carried out, the distance between the low-orbit satellite and the spacecraft to be orbited is obtained, and the initial state and the initial error are subjected to extended Kalman filtering processing according to the distance to obtain the state and the error of the spacecraft to be orbited in the next epoch; and 3, taking the next epoch as an initial epoch, taking the state of the next epoch as an initial state, taking the error of the next epoch as an initial error, repeatedly executing the step 2 to obtain a plurality of groups of states and errors, and integrating the states and errors of all epochs to obtain the track of the spacecraft to be tracked. By the method, the effect of rapid and high-precision orbit determination of the Earth-moon space spacecraft can be achieved.
Description
Technical Field
The invention belongs to the field of spacecraft orbit judgment, and particularly relates to a space-based orbit determination method for a terrestrial-lunar space spacecraft.
Background
The orbit determination of the general spacecraft mainly has two ways, one is by means of a Global Navigation Satellite System (GNSS), and the other is by means of ground station measurement. In a space range within tens of thousands of kilometers away from the earth, orbit determination modes based on GNSS measurement are mature, and the method for realizing the orbit determination of a spacecraft by utilizing the GNSS is the most common method. The spacecraft running around the ground receives the measurement signals sent by the GNSS constellation through the GNSS signal receiver to obtain measurement data, then the measurement data is processed, and the position, speed and state information is calculated to further realize orbit determination. Since GNSS measurement signals are attenuated with increasing distance, and when a spacecraft is too far from the earth, orbit determination cannot be achieved by using GNSS, other methods are generally adopted for orbit determination of a distant spacecraft.
The spacecraft in the earth-moon transfer orbit, the lunar orbit and other planet transfer orbits of the solar system is far from the earth, orbit determination is realized mainly by means of measurement of a ground station, and if the requirement on the accuracy of orbit determination is not high, an astronomical navigation mode can be adopted, and autonomous orbit determination is realized by measuring the starlight angular distance between a celestial body close to the spacecraft and a distant fixed star and utilizing the relation between the change of the starlight angular distance and the change of the position of the spacecraft.
In the former lunar exploration mission and the planet exploration mission, the method of implementing orbit determination through ground station measurement is widely used, the feasibility and the reliability of the method are verified, but the method has certain limitations. The spacecraft is far away from the earth, the speed is low, the ground station rotates along with the earth rotation synchronously, the ground station is shielded by the earth and cannot be fixed when being positioned on the back of the earth relative to the spacecraft, and the duration time can reach more than ten hours. On the other hand, the low speed of the spacecraft and the low rotating speed of the earth cause that the distance and the speed of the spacecraft relative to the ground station change slowly, so the measurement sensitivity is low, a long time is needed for a real-time orbit determination method to converge, and the orbit determination precision is not high. Although these problems can be solved by increasing the number and coverage of ground stations, in order to meet the vast search mission of future earth-moon space, it is necessary to build ground stations covering the globe, which obviously has a large resistance and is expensive, so that better solutions are required.
Disclosure of Invention
The invention aims to solve the technical problem of providing a space-based orbit determination method for a terrestrial-lunar space spacecraft.
The technical scheme for solving the technical problems is as follows: a space-based orbit determination method for a Earth-moon space spacecraft comprises the following steps:
and 3, taking the next epoch as an initial epoch, taking the state of the next epoch as an initial state, taking the error of the next epoch as an initial error, repeatedly executing the step 2 to obtain a plurality of groups of states and errors, and integrating the states and errors of all epochs to obtain the track of the spacecraft to be tracked.
The beneficial effects of the invention are: the space-based measurement mode based on the low-orbit satellite is adopted, the earth-moon space spacecraft can be quickly and accurately fixed in orbit, the problems that traditional ground-based measurement signals are easy to block and slow in orbit determination convergence are solved, and the orbit determination accuracy is higher than that of a traditional orbit determination scheme.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the extended kalman filter processing specifically includes:
time updates and measurement updates.
Further, the specific process of time update is as follows:
and predicting the state of the (i + 1) th epoch according to the state of the ith epoch on the basis of the dynamic model.
Further, the specific process of the measurement update is as follows:
and correcting the state of the (i + 1) th epoch and the error of the (i + 1) th epoch by using the distance between the low-orbit satellite under the (i + 1) th epoch and the spacecraft to be orbited.
Further, the method is based on the ith epoch t i State X of i For the (i + 1) th epoch t i+1 State X of i+1 The prediction is specifically as follows:
wherein phi i+1|i ＝Φ Y (t i+1 ,t i )，Γ i+1|i ＝Γ Y (t i+1 ,t i )，
Φ Y (t i+1 ,t i ) Is an epoch t i+1 Relative to epoch t i Of the state transition matrix, Γ Y (t i+1 ,t i ) Is an epoch t i Acceleration process noise versus epoch t i+1 Of the position velocity state of u i ＝u(t i )＝(u xi ,u yi ,u zi ) T For acceleration process noise, Y = (r) T ,v T ) T R is the position vector of the spacecraft, v is the velocity vector of the spacecraft,
as acceleration process noise u i Where ρ is the acceleration process noise standard deviation, X (t) i+1 ，X i ) Is the epoch t after numerical integration i+1 Is predicted value of the state of (1), P i Is an epoch t i The state covariance matrix of (a) is calculated,
r i is an epoch t i V position vector of the spacecraft to be tracked i Is an epoch t i The velocity vector of the spacecraft to be tracked.
Further, the (i + 1) th epoch t is utilized i+1 The distance between the low-orbit satellite and the spacecraft to be orbited is set for the (i + 1) th epoch t i+1 And the (i + 1) th epoch t i+1 The specific process for correcting the error of (2) is as follows:
X i+1 ＝X i+1|i +K i+1 (z i+1 -h(X i+1|i ))
wherein, K i+1 Is the kalman gain;
is the measurement noise standard deviation; h i+1 Is a design matrix of the state of the inter-satellite distance measurement value pair; i is the unit matrix,. Sup.>
t i Is time, z (t) i ) For inter-satellite link distance measurements, r represents the space vehicle to be orbited, s represents the low orbit satellite for measurement, and ` KQ `>
Is the geometric distance between the low-orbit satellite and the spacecraft to be orbited, epsilon (t) i ) To measure noise, h (X) i+1|i ) Express passing state prediction value X i+1|i Calculated t i+1 The predicted value of the distance between the LEO navigation satellite of the epoch and the spacecraft to be orbited,
the patent is subsidized by strategic leading scientific and technological specialization of Chinese academy of sciences, and the special serial number is as follows: XDA30010000.
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FIG. 1 is a schematic flow chart provided by an embodiment of a space-based orbit determination method for a Earth-moon space spacecraft of the present invention;
FIG. 2 is a schematic diagram of an earth-moon spacecraft orbit determination scheme for LEO satellite earth-based measurement provided by an embodiment of an earth-moon space spacecraft earth-based orbit determination method of the invention;
FIG. 3 is a schematic diagram of a DRO orbit earth-moon rotation system provided by an embodiment of the space-based orbit determination method for an earth-moon space spacecraft of the present invention;
FIG. 4 is a schematic diagram of a DRO orbit geocentric inertial system provided by an embodiment of the space-based orbit determination method for the Earth-moon space spacecraft of the present invention;
FIG. 5 is a schematic diagram of an RO orbit provided by an embodiment of the space-based orbit determination method for a Earth-moon space spacecraft of the present invention;
FIG. 6 is a schematic diagram of a DRO orbit entry transfer orbit provided by an embodiment of a space-based orbit determination method for a Earth-moon space spacecraft of the present invention;
FIG. 7 is a schematic diagram illustrating a relationship between satellite-to-satellite measurement accuracy and satellite-to-satellite distance according to an embodiment of a space-based orbit determination method for a terrestrial-lunar space spacecraft of the present invention;
FIG. 8 is a schematic diagram of the low-energy DRO orbit transfer result using only ground-based measurements provided by an embodiment of the space-based orbit determination method for Earth-moon space spacecraft of the present invention;
FIG. 9 is a schematic diagram of the orbit determination result of low-energy-consumption DRO transfer orbit using LEO measurement only provided by an embodiment of the space-based orbit determination method for Earth-moon space spacecraft of the present invention;
FIG. 10 is a schematic diagram of the orbit determination results of a DRO berthing orbit using only ground based measurements provided by an embodiment of the space-based orbit determination method of a Earth-moon space spacecraft of the present invention;
FIG. 11 is a schematic diagram of the orbit determination results of a DRO berthing orbit using LEO measurement only provided by an embodiment of the space-based orbit determination method of a Earth-moon space spacecraft of the present invention;
fig. 12 is a schematic diagram of an RO orbit and an initial phase of a spacecraft, which are used in simulation, according to an embodiment of the space-based orbit determination method for a space-based spacecraft of the present invention;
FIG. 13 is a schematic diagram of the orbit determination result of the RO orbit determination using only the ground-based survey provided by the embodiment of the method for determining the orbit of the sky-based spacecraft of the invention;
FIG. 14 is a schematic diagram of the orbit determination result of the RO orbit using only LEO measurement provided by the embodiment of the space-based orbit determination method for the Earth-moon space spacecraft of the present invention;
fig. 15 is a schematic diagram of the extended kalman filter implementation orbit determination provided by the embodiment of the space-based orbit determination method for the earth-moon space spacecraft of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with examples which are set forth to illustrate, but are not to be construed to limit the scope of the invention.
As shown in fig. 1, a method for determining a space-based orbit of a terrestrial-lunar space spacecraft includes:
And 3, repeating the step 2 to obtain n orbit determination results, and integrating the n orbit determination results to obtain the track of the spacecraft to be orbited.
In some possible implementation modes, a space-based measurement mode based on a low-orbit satellite is adopted, the earth-moon space spacecraft is quickly and accurately fixed in orbit, the problems that a traditional ground-based measurement signal is easy to block and the orbit determination convergence is slow are solved, and the orbit determination accuracy is higher than that of a traditional orbit determination scheme.
It should be noted that "orbit determination" refers to trajectory determination and orbit of the earth-moon space spacecraft. "space-based" refers to a ground station of known location used in ground-based tracking methods relative to "ground-based". In this patent, the orbit determination method uses low orbit (LEO) satellites with known position and velocity states, not ground stations; because the low earth orbit satellites are operational on the sky and move around the earth, they are called "space-based". The epoch mentioned in this patent is a time measurement unit in the aerospace field, and the first epoch is corresponding to the epoch t 1 In this example, the second epoch corresponds to epoch t2, and in the same way, the state of the first epoch is X 1 The state of the ith epoch is X i By analogy, the same applies to errors.
According to the technical scheme, as shown in figure 2, a GNSS receiver is configured on an LEO satellite to receive GNSS navigation satellite signals, and m-level positioning accuracy and 30 ns-level time service accuracy can be achieved in an on-orbit mode. The LEO satellite and the Earth-moon space spacecraft are both provided with radio transceiver equipment, so that the LEO satellite and the Earth-moon space spacecraft can establish a link to complete ranging and speed measurement. And after the earth-moon spacecraft receives the ranging signals and the orbit state of the LEO satellite, the orbit information can be automatically calculated in orbit.
The patent provides a method for implementing orbit determination on a lunar space spacecraft by using low-orbit satellite measurement data and an extended Kalman filtering algorithm. The method has two key points: one is the principle that when the state and orbit of the low-orbit satellite are known, the earth-moon space spacecraft is fixed by using the distance measurement data only; and the other is an extended Kalman filter orbit determination algorithm based on measurement data. The following description focuses on these two aspects:
basic principle for realizing orbit determination based on low-orbit satellite distance measurement data
The method for realizing low-orbit satellite orbit determination by utilizing GNSS measurement is mature and has higher precision, so the orbit of the low-orbit satellite is determined. A measuring link is established between a low earth orbit satellite and a Earth-moon space spacecraft (LEO spaceborne equipment sends a ranging signal which contains time information of sending time, an Earth-moon space spacecraft spaceborne receiver receives the ranging signal, extracts the sending time, calculates the time difference between sending and receiving, multiplies the time difference by the speed of light to obtain the distance, the technology is mature technology, and a sequence of the change of the distance between the two along with the time is obtained (the sequence mentioned here is a theoretical description, one distance data is arranged in each epoch, the data of different epochs are together called as a sequence. Different from the measurement of a ground station, because the low-orbit satellite has very high running speed and short earth surrounding period, the time for measuring the inter-satellite distance to be shielded by the earth is short, the change of the inter-satellite distance is relatively quick, and the measurement sensitivity is better. The orbits of the Earth-moon space spacecraft are different when the initial states of the Earth-moon space spacecraft are different, and the measurement sequences obtained by the measurement links are different, so that the orbits of the Earth-moon space spacecraft can be uniquely determined when the measurement sequences (sequences formed by distance measurement data at different times) and the initial states are known. (in the first sentence of this paragraph: "Low trackThe orbit of the satellite is determined by the GNSS ", and therefore the position and velocity state of the low orbit satellite is known and is a precondition, equivalent to a navigation satellite; what needs to be tracked is other spacecraft in earth-moon space. The text before the sentence is the description of the orbit determination principle, namely what can be realized, and the concrete implementation method is followed. ) The time series of the distance measurement data and the dynamic model (high-precision orbit dynamic model, the model used for calculation is the model of actually measured earth gravity, and the specific names are given in the table of "mechanical model and integrator setting" in the following embodiment. ) And (4) matching (the matching process is realized in the extended Kalman filtering, and the output result is an orbit formed by the positions and the speed states of the spacecraft with different epochs. A specific description of the extended Kalman Filter is shown in FIG. 15, where t i-1 Is the i-1 epoch, t i Is the ith epoch, t i+1 In the figure, time updating is carried out from the orbit determination result of the (i-1) th epoch to the predicted value of the (i) th epoch, measurement updating is carried out from the predicted value of the (i) th epoch to the orbit determination result of the (i) th epoch, time updating is carried out from the orbit determination result of the (i) th epoch to the predicted value of the (i + 1) th epoch, measurement updating is carried out from the predicted value of the (i + 1) th epoch to the orbit determination result of the (i + 1) th epoch, time updating is carried out from the orbit determination result of the (i + 1) th epoch to the predicted value of the next epoch, and the steps are repeated. ) And calculating the optimal matching orbit by using an extended Kalman filtering method, thereby realizing orbit determination of the Earth-moon space spacecraft.
Extended Kalman filtering orbit determination method
X＝(r T ,v T ) T For the estimation, the position and velocity state of the spacecraft is represented, and the error of the position and velocity state is represented by a state covariance matrix P. The position vector r and the velocity vector v are shown as the formula, x, y and z are coordinate components of the spacecraft position under the J2000 geocentric inertia system, v x 、v y And v z Is the coordinate component of the velocity. The covariance matrix P is expressed as formula, the diagonal elements are the variance of position and velocity, and the off-diagonalThe elements are covariance.
Initialization: t is t 0 For the initial epoch, the corresponding initial state and covariance matrix are X 0 And P 0 As shown in formula (I) and (II).
X 0 ＝(x 0 y 0 z 0 v x0 v y0 v z0 ) T
Orbit determination process: using t 1 Epoch measurement data pair X 0 And P 0 Performing extended Kalman filtering to obtain t 1 Tracking result X of epoch 1 And P 1 Then using t 2 Epoch measurement data pair X 1 And P 1 Performing extended Kalman filtering again to obtain t 2 Orbit determination result X of epoch 2 And P 2 Repeating the above process to calculate X 3 And P 3 、X 4 And P 4 、X 5 And P 5 Etc. X 1 、X 2 、X 3 The equal state constitutes the final orbit determination result.
The orbit determination method based on the extended Kalman filtering is a real-time orbit determination method, so theoretically, the process can be continued as long as measurement data exist. In the engineering task, the ending condition is selected according to the actual situation.
Each extended kalman filter process has two steps: the first step is called "time update", that is, the next epoch state is predicted using a high-precision dynamical model using the previous epoch state (the state and the state covariance matrix are used together); the second step is 'measurement update', which uses the measurement data of the next epoch to correct the obtained prediction state and calculate the state orbit determination result of the next epoch. In the "time update" stage, the orbit dynamics model is needed, and in the "measurement update" stage, the partial derivative of the measurement data to be estimated is needed, so the linearization of the orbit dynamics model, the measurement model, and the measurement model is described first in detail.
1. Orbit dynamics model
The motion rule of the spacecraft which does not have dynamic free navigation in the earth-moon system can be expressed by a first-order ordinary differential equation as shown in the formula:
wherein r is the position vector of the spacecraft, v is the velocity vector of the spacecraft, r m Is the position vector of the moon, r s The lunar and solar position vectors are determined from ephemeris as the position vector of the sun. Mu.s e Is the constant of the earth's gravity, mu m Is the moon gravitational constant; mu.s s Is the solar gravitational constant; a is a a Atmospheric resistance acceleration; a is s Is solar radiation pressure acceleration; a is e And a m The earth and moon, respectively. The vectors in the formula are all represented in the J2000 geocentric inertial coordinate system. Let the state vector be Y = (r) T ,v T ) T Then the above formula can be abbreviated as:
in combination with a mechanical model, the orbital state can be calculated using numerical integration. The state of any epoch t relative to the initial epoch t 0 The state transition matrix of (a) is defined as:
the linearized mathematical expression of the state prediction process using the high-precision orbit dynamics model represents the process of transition from the state of the previous epoch to the state of the next epoch, the state of the state transition matrix multiplied by the previous epoch being equal to the state of the next epoch, i.e. Y (t) = Φ Y (t,t 0 )Y(t 0 )。
Due to errors of the dynamic model, acceleration process noise u (t) = (u) is introduced x u y u z ) T Modeling unmodeled kinetic model errors. U (t) is different for each epoch, but follows a normal distribution with a mean of zero. t is t 0 The effect of the acceleration process noise of an epoch on the state of the t epoch is represented by the transfer matrix Γ Y ：
Further unfolding it can yield:
where Δ t is the numerical integration step, I 3×3 Is an identity matrix.
2. Measurement model and linearization thereof
For a single inter-satellite link (two satellites), the distance between the low-orbit satellite and the spacecraft is obtained by measurement, and the model thereof is expressed as follows:
wherein, t for time, z (t) is the inter-satellite link distance measurement, r represents the spacecraft, s represents the low earth orbit satellite for the measurement,
is the geometric distance between the low-orbit satellite and the spacecraft, and epsilon (t) is the measurement noise。
In the "measurement update" orbit determination process of the extended kalman filter, a partial derivative of a distance to a state is needed, so that the measurement needs to be linearized, and a partial derivative of a measurement model is obtained:
wherein r (t) is the spacecraft centroid position;
is a unit vector (LoS) for the spacecraft to point to the low orbit satellite.
3. Extended Kalman Filter "time update"
The "time update" step is carried out from the previous epoch t i State X of i Sum covariance matrix P i Calculating and deducing the next epoch t by using a numerical integration method through a high-precision orbit dynamics model i+1 Is predicted value X of i+1|i And its corresponding covariance matrix P i+1|i The calculation method is as follows:
X i+1|i ＝X(t i+1 ,X(t i )＝X i )+Γ i+1|i u i
the orbit dynamics model is shown as the formula, and the unmodeled orbit dynamics error is formed by the acceleration process noise u i And (4) showing. The state transition matrix is calculated as follows:
Φ i+1|i ＝Φ Y (t i+1 ,t i )
the process noise transfer matrix is represented as:
Γ i+1|i ＝Γ Y (t i+1 ,t i )
in the formula, Q c Is the acceleration process noise u i The covariance matrix of (A) is as followsIt is a three by three diagonal matrix. The values on the diagonal represent the standard deviation of the acceleration noise, which is a fixed value, set according to the unmodeled dynamic model error. The acceleration process noise is increased, so that the situation that the state covariance matrix is converged too fast to cause the orbit determination result to be deteriorated can be prevented, and meanwhile, the subsequent measurement data are allowed to continuously influence the filtering estimation. In the orbit determination simulation test, a trial and error method is adopted for selection to obtain an optimal orbit determination result.
4. Measurement update for extended Kalman filtering "
The second step of extended Kalman Filtering is "measurement update", using t i+1 Epoch distance measurement data z i+1 For state prediction value X from time update i+1|i And its corresponding covariance matrix P i+1|i Performing state correction processing to calculate t i+1 Orbit determination result X of epoch i+1 Sum co-defense difference matrix P i+1 ：
X i+1 ＝X i+1|i +K i+1 (z i+1 -h(X i+1|i ))
In the formula K i+1 Is the kalman gain;
is the measurement noise standard deviation; h i+1 Is a design matrix (partial derivative) of inter-satellite distance measurements versus state; i is the identity matrix. Design matrix H i+1 The calculation method of (2) is as follows:
state covariance matrix P i+1 Indicating the accuracy of the estimated state, may also be used to evaluate the convergence of the tracking process.
Example 1, three typical orbits of earth-moon space are taken as an example, orbit determination calculation is carried out on the spacecraft on the orbits by using the method of the patent, and the result is evaluated.
1. Basic introduction to three tracks
The first type of track is a DRO track. The spacecraft is located near the moon and is located tens of thousands kilometers away from the earth, and moves around the moon under the earth-moon rotation system, the rotation direction around the moon is opposite to the revolution direction of the moon, the rotation direction around the earth under the earth-center inertia system is the same as the revolution direction of the moon, and the revolution period of the moon and the period of the spacecraft around the moon are in integral ratio, and the ratio is the resonance ratio. The orbit in which the spacecraft is located is a long-range retrograde orbit (DRO), and the typical resonance ratio is 2. The simulation of the patent uses a DRO with a period ratio of 2, the representation of the DRO under the earth-moon rotation system and the earth-center inertia system is shown in fig. 1, DU in the figure represents the earth-moon average distance, fig. 3 is the representation of the DRO (2). Fig. 4 is a representation of the DRO (2.
The second is the RO track. The large elliptical orbit refers to an elliptical orbit which has large eccentricity, low perigee and high apogee. The number of such orbits is numerous, and one of them has special properties, i.e., the ratio of the revolution period of the moon to the period of its orbit is an integer, which makes this type of orbit interesting. Fig. 5 shows a stable large elliptical orbit, the left diagram is a lunar rotation system, the right diagram is a geocentric inertia system, the resonance ratio is 3. DU in the figure represents the earth-moon average distance.
The third is a DRO in-track transfer track. The transfer of spacecraft from the vicinity of the earth to a DRO does not take the form of direct transfer, but rather uses low energy transfer orbits, which do not consume too much fuel, but at the expense of long transfer times. The low energy consumption transfer orbit is shown in fig. 6, the spacecraft on the orbit gradually runs to a DRO orbit insertion point under the action of the earth, the sun and the moon, and enters the DRO orbit through maneuvering, and in the process, the spacecraft is farthest from the earth by more than one million kilometers.
2. Link and track setup.
The inter-satellite measurement noise was set to 0.5m and the system difference was 5m. The ground station is located in Beijing dense cloud, and the variation relation of the ranging error along with the station satellite distance is shown in figure 7. Fitting into a function of the satellite-ground distance, wherein y is measurement noise (in m), x is station satellite distance (in km), the visible satellite-ground distance is 50 km, the distance measurement precision is better than 1m, the satellite-ground distance is 100 km, the distance measurement precision is better than 3m, the satellite-ground distance is 150 km, and the distance measurement precision is 5m. The satellite-to-ground measurement system difference is set to 5m.
The initial time of the DRO and RO tracks was set to 1 month, 1 day zero (UTC time) 2023, the initial state is shown in table 1 (expressed in the J2000 coordinate system), and the mechanical model is shown in table 2. The LEO orbit is a sun-synchronous orbit with a height of 500km, the initial orbit state is shown in table 3 (expressed in the J2000 coordinate system), and the mechanical model is shown in table 2.
TABLE 1 initial time states (J2000 coordinate system) for DRO and RO orbits
TABLE 2 mechanics model and integrator setup
TABLE 3 initial time state of LEO orbit (J2000 coordinate system)
| Parameter(s) | LEO |
| Semi-major axis/km | 6878.137 |
| |
0 |
| Orbital inclination angle/° | 97.4065 |
| Amplitude/degree of |
0 |
| Ascending crossing point Chin Jing/° | 10.3886 |
| True angle/degree of |
0 |
| Ground/month cycle | 1.5 hours |
Assuming that the low energy consumption DRO is transferred to the in-orbit (as shown in fig. 3) at the launch (star-arrow separation) time 10Feb 202315. The mechanical model setting of the low-energy consumption DRO transfer orbit is shown in Table 5, and the actual positions of the sun and the planet are obtained by interpolation according to an ephemeris file DE430 of JPL.
TABLE 4 Low energy DRO transfer orbital maneuver
TABLE 5 mechanics model for Low energy DRO transfer into orbit
The low-orbit satellite realizes orbit determination by receiving the GNSS satellite, the position precision is better than 1m, the speed precision reaches sub mm/s, and the precision setting of the simulation low-orbit satellite is shown in a table 6.
TABLE 6 accuracy of low orbit satellites
The space-based orbit determination parameter settings based on the low orbit satellite are shown in table 7, and the mechanical model is shown in table 2.
TABLE 7 space-based orbital parameters settings based on low-earth satellites
The ground station is assumed to be located in the dense cloud of Beijing, and the location is precisely known. The ground orbit determination parameter settings are shown in table 8, and the mechanical model still adopts the model listed in table 2.
TABLE 8 Foundation-based tracksetting parameters settings
And (5) determining a track simulation result.
The following simulation compares the low-earth orbit satellite-based orbit determination result with the ground-based orbit determination result. The results for each measurement mode are divided into two cases, assuming that the measurements are continuous (earth occlusion is a consideration) and assuming that every 8 hour arc segment contains 2 hours of measurements.
Orbit determination result of low-energy-consumption DRO transfer orbit
The spacecraft on the low-energy-consumption DRO transfer orbit implements 3 maneuvers in the transfer process, and the orbit determination process simulates pulses with errors, wherein the errors are 20% of the actual pulse size.
When only the ground based measurement is used, the convergence criterion is that the position residual is less than 10km, and the orbit determination result is shown in fig. 8.
When only LEO measurement is used, the decision criterion for convergence is that the position residual is less than 1km, and the tracking result is shown in fig. 9.
The tracking statistics are shown in table 9. (MC)
TABLE 9 Low energy DRO transfer orbital tracking results
Orbit determination result of DRO orbit
The decision criterion of the DRO track orbit determination convergence is that the position residual error is less than 100m.
The results of the orbit determination using only the ground based measurements are shown in fig. 10.
The results of the tracking using LEO measurements only are shown in fig. 11.
The tracking statistics are shown in table 10. (MC)
TABLE 10 DRO parking track tracking results
Orbit determination result of RO orbit
The determination criterion of the convergence of the RO orbit is that the position residual error is less than 100m.
The distance between different positions of the RO orbit and the earth is very different, the selection of the initial position may affect the convergence time of orbit determination, and the RO orbit used in the simulation process is shown in fig. 12.
The results of the orbit determination using only the ground based measurements are shown in fig. 13.
The results of the tracking using LEO measurements only are shown in fig. 14.
The tracking statistics are shown in table 11.
TABLE 11 RO orbit determination results
And (6) analyzing the result.
The orbit determination result shows that the time required by the convergence of the orbit determination process is dozens of hours or even hundreds of hours when the measurement is carried out only by the ground station, the orbit determination process is very sensitive to the velocity pulse error, and the convergence of the orbit determination process is difficult when the velocity pulse error is large and the measurement is carried out only by the ground station. When orbit determination is carried out based on continuous measurement of low-orbit satellites, convergence time required by orbit determination of spacecrafts on three different orbits is about two hours and three hours, and the method is greatly improved compared with a ground station. In the aspect of orbit determination precision, for spacecrafts with three different orbits, orbit determination results of two arc length measurement strategies show that the orbit determination precision based on low-orbit satellite measurement is better than that based on ground station measurement, which is particularly obvious in the aspect of transferring non-periodic DRO into orbit, and the difference of the orbit determination precision is about one order of magnitude. From the orbit determination result, the orbit determination method based on the low-orbit satellite measurement successfully solves the problems of long convergence time and poor precision caused by the fact that the ground station is shielded for a long time and the measurement sensitivity is low when the orbit determination is carried out based on the ground station measurement, the deployment of the low-orbit satellite is more convenient to realize than the construction of a large number of ground stations in the global scope, and the large number of low-orbit satellites are likely to form a GPS-like space-based measurement and control network in the future to meet more earth-moon space exploration tasks.
Preferably, in any of the above embodiments, the extended kalman filtering process specifically includes:
time updates and measurement updates.
Preferably, in any embodiment described above, the specific process of time updating is:
based on a kinetic model, according to epoch t i State X of i For epoch t i+1 State X of i+1 And performing prediction, wherein i is a natural number not greater than n.
Preferably, in any of the above embodiments, the specific process of the measurement update is:
using epoch t i+1 The distance between the low-orbit satellite and the spacecraft to be orbited is in a state X i+1 And an error P i+1 And (6) carrying out correction.
Preferably, in any of the above embodiments, the time-dependent epoch t is a time-dependent epoch i State X of i For epoch t i+1 State X of i+1 The prediction is specifically as follows:
wherein phi i+1|i ＝Φ Y (t i+1 ,t i )，Γ i+1|i ＝Γ Y (t i+1 ,t i )，
Φ Y (t i+1 ,t i ) Is an epoch t i+1 Relative to epoch t i Of the state transition matrix, Γ Y (t i+1 ,t i ) Is an epoch t i Acceleration process noise versus epoch t i+1 Of the position velocity state of u i ＝u(t i )＝(u xi ,u yi ,u zi ) T For acceleration process noise, Y = (r) T ,v T ) T R is the position vector of the spacecraft, v is the velocity vector of the spacecraft,
for acceleration process noise u i Where ρ is the acceleration process noise standard deviation.
Preferably, in any embodiment above, the epoch t is used i+1 The distance between the low-orbit satellite and the spacecraft to be orbited is in a state X i+1 And an error P i+1 The specific process of correcting is as follows:
X i+1 ＝X i+1|i +K i+1 (z i+1 -h(X i+1|i ))
wherein, K i+1 Is the Kalman gain;
is the measurement noise standard deviation; h i+1 Is the distance between starsA design matrix of the state from the measurement value; i is a unit matrix, in>
t i Is time, z (t) i ) For inter-satellite link distance measurements, r represents the space vehicle to be orbited, s represents the low orbit satellite for measurement, and ` KQ `>
Is the geometric distance between the low-orbit satellite and the spacecraft to be orbited, epsilon (t) i ) In order to measure the noise of the sound,
H i+1 to design a matrix.
The reader should understand that in the description of the specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of various embodiments or examples described in this specification can be combined and combined by one skilled in the art without being mutually inconsistent.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described method embodiments are merely illustrative, and for example, the division of steps into only one type of logical functional division may be implemented in practice in other ways, for example, multiple steps may be combined or integrated into another step, or some features may be omitted, or not implemented.
The above method, if implemented in the form of software functional units and sold or used as a stand-alone product, can be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention essentially or partially contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A space-based orbit determination method for a Earth-moon space spacecraft is characterized by comprising the following steps:
step 1, acquiring an initial state and an initial error of a spacecraft to be tracked in an initial epoch;
step 2, when the next epoch of the initial epoch is carried out, the position and the speed of the low-orbit satellite determined by the GNSS are obtained, the distance between the low-orbit satellite determined by the on-satellite measuring equipment and the spacecraft to be orbited is obtained, and the initial state and the initial error are subjected to extended Kalman filtering processing according to the position, the speed and the distance of the low-orbit satellite to obtain the state and the error of the spacecraft to be orbited in the next epoch;
step 3, taking the next epoch as an initial epoch, taking the state of the next epoch as an initial state, taking the error of the next epoch as an initial error, repeatedly executing the step 2 to obtain a plurality of groups of states and errors, and integrating the states and errors of all epochs to obtain the track of the spacecraft to be tracked;
the extended kalman filtering process specifically includes:
time updates and measurement updates;
the specific process of time update is as follows:
based on the kinetic model, according to the ith epoch t i State X of i For the (i + 1) th epoch t i+1 State X of i+1 Carrying out prediction;
the specific process of the measurement update is as follows:
using the i +1 th epoch t i+1 The distance between the low-orbit satellite and the spacecraft to be orbited and the position and the speed of the low-orbit satellite corresponding to the epoch and determined by the GNSS for the (i + 1) th epoch t i+1 And the (i + 1) th epoch t i+1 Correcting the error of (2);
the method is based on the ith epoch t i State X of i For the (i + 1) th epoch t i+1 State X of i+1 The prediction is specifically as follows:
wherein phi is i+1|i ＝Φ Y (t i+1 ,t i )，Γ i+1|i ＝Γ Y (t i+1 ,t i )，
Φ Y (t i+1 ,t i ) Is epoch t i+1 Relative to epoch t i Of the state transition matrix, Γ Y (t i+1 ,t i ) Is epoch t i Acceleration process noise versus epocht i+1 Of the position velocity state of (a), u i ＝u(t i )＝(u xi ,u yi ,u zi ) T For acceleration process noise, Y = (r) T ,v T ) T R is the position vector of the spacecraft, v is the velocity vector of the spacecraft,
for acceleration process noise u i The covariance matrix of (a) is determined, therein->
And ρ uz Respectively the acceleration process noise standard deviation in the directions of X, y and z coordinate axes of the geocentric inertial system, X (t) i+1 ，X i ) Is the epoch t after numerical integration i+1 Without increasing the state prediction value of the process noise influence, P i Is epoch t i Is greater than or equal to the state covariance matrix, < >, is selected>
r i Is an epoch t i V position vector of the spacecraft to be tracked i Is an epoch t i Of the spacecraft to be orbited, X i+1|i Is according to t i Orbit determination result X corresponding to epoch i Calculated t i+1 State prediction value, P, corresponding to epoch i+1|i Is t i+1 State prediction value X of epoch i+1|i The corresponding covariance matrix, Y (t) i ) Is from t i Epoch to t i+1 T in the course of orbit prediction of epoch i Corresponding position velocity state vector, Y (t) i+1 ) Is from t i Epoch to t i+1 T in the course of orbit prediction of epoch i+1 A position speed state vector corresponding to the epoch; />
The utilization of the (i + 1) th epoch t i+1 The distance between the low-orbit satellite and the spacecraft to be orbited is set for the (i + 1) th epoch t i+1 And the (i + 1) th epoch t i+1 The specific process for correcting the error of (2) is as follows:
X i+1 ＝X i+1|i +K i+1 (z i+1 -h(X i+1|i ))
wherein, P i+1 Is t i+1 Epoch track fix result state X i+1 The covariance matrix of (a); k is i+1 Is the kalman gain; p i+1|i Is t i+1 State prediction value X of epoch i+1|i A corresponding covariance matrix;
is the measurement noise standard deviation; h i+1 Is a design matrix of the state of the inter-satellite distance measurement value pair; i is a unit matrix of the image data,
t i+1 is time, z i+1 For on-board measuring devices at t i+1 A distance measurement taken by an epoch, r represents the space vehicle to be orbited, s represents the low-orbit satellite for measurement, and/or>
Is the geometric distance between the low-orbit satellite and the spacecraft to be orbited, epsilon (t) i+1 ) To measure noise, h (X) i+1|i ) Express passing state prediction value X i+1|i T calculated from the position and velocity of the GNSS determined low-earth satellites i+1 Predicted value of distance between low-orbit satellite of epoch and spacecraft to be orbited, h (X (t) i+1 ),t i+1 ) Denotes the passage through t i+1 Epoch State X (t) i+1 ) Calculating a function expression of the distance between the low-orbit satellite and the spacecraft to be estimated;
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