CN113189619B - A method for estimating phase-keeping parameters of low-orbit constellations - Google Patents

Abstract

A low orbit constellation phase maintaining parameter estimation method belongs to the technical field of satellite orbit control. According to the invention, the orbit semi-major axis Ping Gen is indirectly estimated by using the latitude amplitude angle measured value with higher precision without directly using the orbit semi-major axis measured value output by the satellite-borne GNSS orbit determination, so that the orbit determination precision of the existing GNSS receiver is not improved, the high precision requirement of satellite constellation maintenance on the orbit semi-major axis can be met, and the configuration of a double-frequency GNSS receiver with higher price on satellites is avoided; according to the method, polynomial fitting is carried out after the relative latitude amplitude angle measured value is converted into the flat root, then the change relation between the relative latitude amplitude angle flat root and the track semi-long axis flat root is utilized, polynomial fitting is carried out on the change trend of the track semi-long axis flat root, and the fitting coefficient is calculated, so that the track semi-long axis Ping Gen at any moment is estimated indirectly, the semi-long axis flat root precision is superior to 1m, and constellation phase maintenance can be completed based on a unilateral drift ring control strategy under the condition that any semi-long axis attenuation rate is met.

Description

A method for estimating phase-keeping parameters of low-orbit constellations

Technical Field

The invention relates to a low-orbit constellation phase-keeping parameter estimation method, belonging to the technical field of satellite orbit control.

Background Art

During operation, low-orbit constellations need to maintain a stable relative configuration to prevent changes in ground coverage characteristics. Limited by the accuracy of orbit determination and orbit control, there is a deviation between the initial orbital parameters of the satellite in orbit and the design parameters, resulting in changes in the relative orbital parameters between satellites, which will gradually destroy the relative configuration of the constellation; in addition, satellites are affected by various environmental perturbations during long-term operation, such as the perturbation of the earth's gravitational field, the gravitational perturbation of the sun and the moon, the perturbation of weather resistance, and the perturbation of light pressure. These perturbations cause changes in the orbital parameters of the satellite, which will also destroy the configuration of the constellation. Therefore, during the on-orbit operation, a series of constellation phase maintenance tasks are required to ensure that the constellation configuration meets the design requirements, that is, the relative latitude arguments between satellites and the relative right ascension of the ascending nodes between different orbital planes are required to be maintained within a certain design range.

The phase holding strategy between satellites in the same orbit generally takes the constellation reference orbit as the phase holding target. By adjusting the semi-major axis root mean square of the satellite relative to the reference orbit, the relative orbital angular velocity of the satellite relative to the reference orbit is changed, and the relative latitude argument root mean square of the satellite relative to the reference orbit is indirectly controlled. The relative latitude argument root mean square is maintained within a pre-set control box, that is, at any time, the relative latitude argument root mean square does not exceed the boundary of the control box (the maximum threshold of the relative latitude argument root mean square).

The more accurately the semi-major axis root mean square of the satellite relative to the reference orbit is controlled, the longer the period of constellation phase maintenance is, the smaller the semi-major axis root mean square that needs to be adjusted is, and the less propellant is consumed.

In addition, in order to reduce the cost of transportation, low-orbit constellations generally adopt a batch launch deployment plan of multiple satellites with one rocket. Therefore, the satellite cabin layout is very compact, and the thruster can often only be installed on a certain cabin board of the satellite. Since the main task of the thruster during the long-term operation of the satellite in orbit is to maintain the phase of the constellation, under the condition of limited layout, the thruster is generally installed on the -X plane of the satellite (the +X plane of the satellite is along the flight speed direction when the three-axis orientation to the earth is specified during the orbit period), and the thrust is output along the +X direction to generate tangential thrust along the flight direction. In order not to affect the inter-satellite link and ground communication services during the constellation phase maintenance period, the co-orbit phase maintenance strategy generally adopts unilateral drift loop control. The satellite only adjusts the semi-major axis when the relative latitude angle root relative to the reference orbit reaches the right boundary of the control box. When the semi-major axis is gradually reduced under the action of atmospheric resistance, the relative latitude angle root of the satellite drifts to the left boundary of the control box to the minimum and then gradually drifts to the right boundary of the control box, forming a unilateral drift loop. Since solar activity affects the atmospheric density, the decay rate of the semi-major axis also changes accordingly. When the decay rate of the semi-major axis is small, if the mean root mean square adjustment of the semi-major axis of the satellite relative to the reference orbit is too large, the mean root mean square of the latitude argument of the satellite relative to the reference orbit will drift out of the left boundary of the control box, resulting in poor phase keeping accuracy between satellites on the same orbit.

At present, low-orbit constellation satellites generally achieve autonomous orbit determination on board through onboard GNSS navigation receivers. The root mean square error of the semi-major axis of the orbit is generally greater than 10m. If the semi-major axis root mean square adjustment is calculated directly based on the measurement value, it is very easy for the relative latitude angle to exceed the control box boundary, resulting in the failure of the unilateral drift loop control strategy.

Summary of the invention

The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a low-orbit constellation phase holding parameter estimation method, which indirectly estimates the orbit semi-major axis through relative latitude argument measurement values, and can reduce the estimation error of the orbit semi-major axis square root to within 1m, thereby meeting the needs of the satellite for constellation phase holding based on a unilateral drift loop control strategy.

The technical solution of the present invention is: a method for estimating a phase-holding parameter of a low-orbit constellation, comprising the following steps:

Determine constellation reference orbit and constellation phase holding parameters;

Perform relative latitude argument square root polynomial fitting to obtain the relative reference orbit latitude argument square root;

Calculate the relative semi-major axis square root polynomial coefficients;

Estimate the relative RTD of the semi-major axis.

维持不变，即

Further, the constellation reference orbit is determined by: taking the semi-major axis root of the nominal orbit of the low-orbit constellation as the semi-major axis root of the reference orbit a _R , and the reference orbit is extrapolated by only considering the gravitational perturbation of the earth. When extrapolating any time t, the orbit latitude angle root is u _R (t), and the orbit semi-major axis root mean is

Remain unchanged, that is

Further, the constellation phase holding parameters are determined, specifically: for the actual orbit of the satellite subject to the perturbations of the earth's gravity, the sun-moon three-body gravity, the atmospheric drag perturbations, and the light pressure perturbations, the root mean square of the latitude argument of its orbit is u(t), and the root mean square of the latitude argument of its relative reference orbit is defined as: Δu(t)=u(t)-u _R (t); the root mean square of the semi-major axis of its orbit is a(t), and the root mean square of the semi-major axis of its relative reference orbit is defined as Δa(t)=a(t)-a _R .

Furthermore, the method for fitting the relative latitude argument square root polynomial is: in the case of no orbit control, the instantaneous orbit parameters of the satellite are obtained by GNSS orbit determination, the latitude argument square root u(t) of the satellite is calculated by conversion of the instantaneous orbit parameters and the average orbit parameters, and the latitude argument square root Δu(t) relative to the reference orbit is calculated by Δu(t)=u(t)-u _R (t); the latitude argument square root Δu(t) relative to the reference orbit is approximated by a cubic polynomial as Δu(t)≈k _u0 +k _u1 (tt ₀ )+k _u2 (tt ₀ ) ² +k _u3 (tt ₀ ) ³ ; t ₀ is the starting time of no orbit control, and k _u0 , k _u1 , k _u2 , and k _u3 are coefficients.

Further, the calculation of the relative semi-major axis flat root polynomial coefficients comprises the following steps:

其中，t₀为无轨控的起始时刻；The square root of the semi-major axis of the relative reference orbit Δa(t) is approximated by a quadratic polynomial:

Among them, t ₀ is the starting time of no track control;

计算出系数K_a；其中，μ为地心引力系数；According to the semi-major axis of the reference orbit a _R and

Calculate the coefficient _Ka ; where μ is the gravity coefficient;

计算系数Δa(t₀)、

和

use

Calculate the coefficient Δa(t ₀ ),

and

计算出无轨控的起始时刻t₀到无轨控的结束时刻t_f之间任意时刻的相对参考轨道半长轴平根Δa(t)的估计值。Furthermore, the estimated relative semi-major axis root mean square deviation is specifically:

The estimated value of the semi-major axis square root Δa(t) of the relative reference orbit at any time between the start time _t0 of no orbit control and the end time _tf of no orbit control is calculated.

A low-orbit constellation phase-holding parameter estimation system, comprising:

The first module determines the constellation reference orbit and constellation phase holding parameters;

The second module performs relative latitude argument square root polynomial fitting to obtain the relative reference orbit latitude argument square root;

The third module calculates the relative semi-major axis flat root polynomial coefficients;

The fourth module estimates the relative semi-major axis root-mean-square deviation.

维持不变，即

Further, the constellation reference orbit is determined by: taking the semi-major axis root of the low-orbit constellation nominal orbit as the semi-major axis root of the reference orbit a _R , and the reference orbit is extrapolated by only considering the earth's gravitational perturbation. When extrapolating any time t, the orbit latitude angle root is u _R (t), and the orbit semi-major axis root mean is

Remain unchanged, that is

Further, the constellation phase holding parameters are determined, specifically: for the actual orbit of the satellite perturbed by the gravity of the earth, the gravity of the sun and the moon, the atmospheric drag, and the light pressure, the root mean square of the latitude argument of the orbit is u(t), and the root mean square of the latitude argument of the orbit relative to the reference orbit is defined as: Δu(t)=u(t)-u _R (t); the root mean square of the semi-major axis of the orbit is a(t), and the root mean square of the semi-major axis of the orbit relative to the reference orbit is defined as Δa(t)=a(t)-a _R ;

Further, the method for fitting the relative latitude argument square root polynomial is as follows: in the case of no orbit control, the instantaneous orbit parameters of the satellite are obtained by GNSS orbit determination, the latitude argument square root u(t) of the satellite is calculated by conversion of the instantaneous orbit parameters and the average orbit parameters, and the latitude argument square root Δu(t) relative to the reference orbit is calculated by Δu(t)=u(t)-u _R (t); the latitude argument square root Δu(t) relative to the reference orbit is approximated by a cubic polynomial as Δu(t)≈k _u0 +k _u1 (tt ₀ )+k _u2 (tt ₀ ) ² +k _u3 (tt ₀ ) ³ ; t ₀ is the starting time of no orbit control, and k _u0 , k _u1 , k _u2 , and k _u3 are coefficients;

Further, the calculation of the relative semi-major axis flat root polynomial coefficients comprises the following steps:

其中，t₀为无轨控的起始时刻；The square root of the semi-major axis of the relative reference orbit Δa(t) is approximated by a quadratic polynomial:

Among them, t ₀ is the starting time of no track control;

计算出系数K_a；其中，μ为地心引力系数；According to the semi-major axis of the reference orbit a _R and

Calculate the coefficient _Ka ; where μ is the gravity coefficient;

计算系数Δa(t₀)、

和

use

Calculate the coefficient Δa(t ₀ ),

and

计算出无轨控的起始时刻t₀到无轨控的结束时刻t_f之间任意时刻的相对参考轨道半长轴平根Δa(t)的估计值。The estimated relative semi-major axis root mean square deviation is specifically: determined by

The estimated value of the semi-major axis square root Δa(t) of the relative reference orbit at any time between the start time _t0 of no orbit control and the end time _tf of no orbit control is calculated.

A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for estimating a phase-holding parameter of a low-orbit constellation are implemented.

A low-orbit constellation phase-holding parameter estimation device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of a low-orbit constellation phase-holding parameter estimation method when executing the computer program.

The advantages of the present invention compared with the prior art are:

(1) The present invention does not directly use the orbit semi-major axis measurement value output by the satellite-borne GNSS orbit determination, but uses the higher-precision latitude argument measurement value to indirectly estimate the orbit semi-major axis flat root, thereby achieving the goal of not improving the orbit determination accuracy of the existing GNSS receiver (typical value is 10m), and can meet the high-precision requirements of the satellite constellation for the orbit semi-major axis, thus avoiding the configuration of a more expensive dual-frequency GNSS receiver on the satellite;

(2) The present invention converts the relative latitude argument measurement value into a square root and then performs polynomial fitting. Then, using the change relationship between the relative latitude argument square root and the orbit semi-major axis square root, the present invention performs polynomial fitting on the change trend of the orbit semi-major axis square root and calculates the fitting coefficient, thereby indirectly estimating the orbit semi-major axis square root at any time, and obtains a semi-major axis square root accuracy better than 1m. Under any semi-major axis attenuation rate, the constellation phase can be maintained based on the unilateral drift loop control strategy;

(3) The present invention performs polynomial fitting on the relative latitude argument measurement value and the semi-major axis square root, thereby achieving autonomous in-orbit semi-major axis square root estimation, realizing fully autonomous constellation phase maintenance of the satellite, and reducing ground operation control operations.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the method of the present invention;

FIG2 is a relative reference orbit semi-major axis root mean square variation curve using a unilateral drift loop control strategy of the present invention;

FIG3 is a curve showing the relative reference orbit latitude argument root mean square change using the unilateral drift loop control strategy of the present invention;

FIG4 is a curve showing the root mean square change of the latitude argument of the trackless control section relative to the reference track (GNSS output and theoretical value);

FIG5 is a plot of the semi-major axis root mean square variation curve of the trackless control section relative to the reference track (GNSS output and theoretical value);

FIG6 is a semi-major axis root mean square variation curve (theoretical value and estimated value) of the trackless control section of the present invention relative to the reference track;

FIG. 7 is a relative error curve of the semi-major axis RPM estimation value of the trackless control section relative to the reference track relative to the theoretical value of the present invention.

DETAILED DESCRIPTION

In order to better understand the above technical scheme, the technical scheme of the present application is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical scheme of the present application, rather than limitations on the technical scheme of the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

The following is a further detailed description of a low-orbit constellation phase-keeping parameter estimation method provided by an embodiment of the present application in conjunction with the accompanying drawings of the specification. The specific implementation method may include (as shown in Figures 1 to 7):

In the solution provided in the embodiment of the present application, the relative semi-major axis root is expressed as a quadratic polynomial according to the perturbation characteristics of the semi-major axis root relative to the reference orbit, the relative latitude argument root is fitted with a cubic polynomial using the high-precision relative latitude argument measurement value obtained by GNSS, the quadratic polynomial coefficients of the relative semi-major axis root are determined using the equivalent relationship between the latitude argument root and the relative semi-major axis root relative to the reference orbit, and finally the relative semi-major axis root at different times is estimated using the quadratic polynomial. The specific steps are as follows:

1) Define the constellation reference orbit

维持不变，即

The semi-major axis root mean square of the nominal orbit of the low-orbit constellation is taken as the semi-major axis root mean square of the reference orbit, which is defined as a _R . The reference orbit is extrapolated by only considering the Earth's gravitational perturbation. Then, when extrapolating any time t, the orbit latitude angle root mean square is u _R (t). The orbit semi-major axis root mean square is

Remain unchanged, that is

2) Define constellation phase holding parameters

For the actual orbit of the satellite, which is perturbed by the gravity of the earth, the gravity of the sun and the moon, the atmospheric drag, and the light pressure, the root mean square of the latitude argument of the orbit is u(t). The root mean square of the latitude argument of the satellite relative to the reference orbit is defined as:

Δu(t)＝u(t)-u _R (t) (1)

The mean root of the semi-major axis of its orbit is a(t), and the mean root of the semi-major axis of its relative reference orbit is defined as:

Δa(t)＝a(t)-a _R (2)

3) Relative latitude angle square root polynomial fitting

In the absence of orbit control, the instantaneous orbit parameters of the satellite can be obtained through GNSS orbit determination. The satellite's latitude argument root mean square u(t) can be calculated using the conversion formula between the instantaneous orbit parameters and the average orbit parameters. The latitude argument root mean square Δu(t) relative to the reference orbit can be calculated using formula (1).

The square root of the latitude argument Δu(t) relative to the reference orbit can be approximated by a cubic polynomial:

Δu(t)≈k _u0 +k _u1 (tt ₀ )+k _u2 (tt ₀ ) ² +k _u3 (tt ₀ ) ³ (3)

4) Calculation of relative semi-major axis flat root polynomial coefficients

For low-orbit constellations, the semi-major axis root relative to the reference orbit is mainly affected by atmospheric drag. In the absence of orbit control, it can be approximated by a Taylor expansion quadratic polynomial:

为Δa(t)在t₀时刻的一阶导数，

为Δa(t)在t₀时刻的二阶导数。Where: Δa(t ₀ ) is the value of Δa(t) at time t ₀ ,

is the first-order derivative of Δa(t) at time t ₀ ,

is the second-order derivative of Δa(t) at time _t0 .

The rate of change of the mean square root of the latitude argument Δu(t) relative to the reference orbit can be approximately expressed as:

Since the difference between a(t) and a _R is very small, the above formula can be expanded using Taylor series to:

in

Substituting (4) into (6) we can obtain:

The derivative of (3) is:

Comparing equation (8) and equation (9), we can obtain:

From the above, we can know that the calculation steps of the relative semi-major axis flat root polynomial coefficients are as follows:

a) Assuming that the satellite is in an unchanged orbit from time _t0 to time _tf , the instantaneous orbit parameters of the satellite can be obtained through GNSS orbit determination. The conversion formula between the instantaneous orbit parameters and the average orbit parameters can be used to calculate the satellite's orbital latitude argument u(t). Formula (1) can be used to calculate the relative reference orbital latitude argument Δu(t).

b) Using equation (3) and the Δu(t) values from time t ₀ to time t _f , a cubic polynomial fit can be performed to obtain the polynomial coefficients _ku0 , _ku1 , _ku2 and _ku3 .

c) Calculate the coefficient _Ka based on the semi-major axis square root of the reference orbit _aR and equation (7).

和

d) Use equation (10) to calculate the coefficients Δa(t ₀ ) and

and

5) Relative semi-major axis root mean square deviation DA estimation

Using equation (4), calculate the approximate value of the semi-major axis square root Δa(t) relative to the reference orbit at any time between _t0 and _tf .

The specific implementation process of the present invention is as follows:

1) Define the constellation reference orbit

The semi-major axis root mean square of the nominal orbit of the low-orbit constellation is taken as the semi-major axis root mean square of the reference orbit, which is defined as a _R . The reference orbit is extrapolated by only considering the Earth's gravitational perturbation. Then, for any extrapolated time t, the orbit latitude angle root mean square is u _R (t), and the orbit semi-major axis root mean square a _R remains unchanged, that is, a _R = a _R .

2) Define constellation phase holding parameters

For the actual orbit of the satellite, which is perturbed by the gravity of the earth, the gravity of the sun and the moon, the atmospheric drag, and the light pressure, the root mean square of the latitude argument of the orbit is u(t). The root mean square of the latitude argument of the satellite relative to the reference orbit is defined as:

Δu(t)＝u(t)-u _R (t) (1)

The mean root of the semi-major axis of its orbit is a(t), and the mean root of the semi-major axis of its relative reference orbit is defined as:

Δa(t)＝a(t)-a _R (2)

3) Relative latitude angle square root polynomial fitting

In the absence of orbit control, the instantaneous orbit parameters of the satellite can be obtained through GNSS orbit determination. The conversion formula between the instantaneous orbit parameters and the average orbit parameters can be used to calculate the satellite's latitude argument u(t). Formula (1) can be used to calculate the latitude argument Δu(t) relative to the reference orbit.

The square root of the latitude argument Δu(t) relative to the reference orbit can be approximated by a cubic polynomial:

Δu(t)≈k _u0 +k _u1 (tt ₀ )+k _u2 (tt ₀ ) ² +k _u3 (tt ₀ ) ³ (3)

4) Calculation of relative semi-major axis flat root polynomial coefficients

For low-orbit constellations, the semi-major axis root relative to the reference orbit is mainly affected by atmospheric drag. In the absence of orbit control, it can be approximated by a Taylor expansion quadratic polynomial:

为Δa(t)在t₀时刻的一阶导数，

为Δa(t)在t₀时刻的二阶导数。Where: Δa(t ₀ ) is the value of Δa(t) at time t ₀ ,

is the first-order derivative of Δa(t) at time t ₀ ,

is the second-order derivative of Δa(t) at time _t0 .

The rate of change of the mean square root of the latitude argument Δu(t) relative to the reference orbit can be approximately expressed as:

Since the difference between a(t) and a _R is very small, the above formula can be expanded using Taylor series to:

in

Substituting (4) into (6) we can obtain:

The derivative of (3) is:

Comparing equation (8) and equation (9), we can obtain:

From the above, we can know that the calculation steps of the relative semi-major axis flat root polynomial coefficients are as follows:

a) Using equation (3) and the Δu(t) values from time _t0 to time _tf , a cubic polynomial fit can be performed to obtain the polynomial coefficients _ku0 , _ku1 , _ku2 and _ku3 .

b) Calculate the coefficient _Ka based on the semi-major axis root mean square of the reference orbit _aR and equation (7).

和

c) Using equation (10), calculate the coefficients Δa(t ₀ ) and

and

5) Relative semi-major axis root mean square deviation DA estimation

Using equation (4), calculate the approximate value of the semi-major axis square root Δa(t) relative to the reference orbit at any time between _t0 and _tf .

Example:

Assume that the semi-major axis of the nominal orbit of the low-orbit constellation is 7578.137km, the eccentricity is 0.001562, the inclination is 60°, the perigee argument is 90°, and the true perigee is 270°. The phase keeping accuracy of the satellite on the same track is required to be ±0.1°, the latitude argument control box boundary relative to the reference orbit is ±0.1°, the GNSS orbit determination semi-major axis measurement error is 10m, and the corresponding relative latitude argument measurement error is 0.0001°.

Using the unilateral drift loop control strategy, within 280 days, the relative reference orbit semi-major axis root mean square change curve is shown in Figure 2, and the relative reference orbit latitude argument root mean square change curve is shown in Figure 3. When the relative reference orbit latitude argument root mean square is close to the right boundary of the control box, through orbit maneuvers, the relative reference orbit semi-major axis root mean square needs to be controlled near the target value, which is in the range of 10m to 14m. Since the orbit semi-major axis root mean square error output by the onboard GNSS orbit determination is 10m, the relative reference orbit semi-major axis root mean square error is also 10m, which will make the actual relative reference orbit semi-major axis root mean square control result between 0 and 24m. When the relative semi-major axis root mean square control value exceeds 14m, the relative latitude argument will drift out of the left boundary of the control box, eventually leading to the failure of the unilateral drift loop control strategy.

Using the method proposed in this paper, taking the first uncontrolled orbit as an example, from the 0th day to the 50th day, the measured value and theoretical value change curve of the relative reference orbit latitude argument Δu(t) obtained according to GNSS orbit determination are shown in Figure 4, and the measured value and theoretical value change curve of the relative reference orbit semi-major axis Δa(t) obtained according to GNSS orbit determination are shown in Figure 5. It can be seen that the difference between the GNSS output and the theoretical value of Δu(t) is very small, and the difference between the GNSS output and the theoretical value of Δa(t) is large.

According to formula (7), the coefficient _Ka = 0.0009455°/day/m can be calculated.

Using equation (4) to fit a cubic polynomial, we can obtain _ku0 = 0.0622°, _ku1 = -0.0094°/day, _ku2 = 1.3793×10 ^-4 °/ ^day2 and _ku3 = 3.1113×10 ^-7 °/ ^day3 , that is:

Δu(t)≈0.0622 ⁰ -0.0094(tt ₀ )+1.3793×10 ^-4 (tt ₀ ) ² +3.1113×10 ^-7 (tt ₀ ) ³ (11)

天和

即：Using formula (10), we can calculate the coefficient of formula (3) Δa(t ₀ ) = 9.9002m,

Tianhe

Right now:

Δa(t)≈9.9002m-0.2918(tt ₀ )-0.0010(tt ₀ ) ² (12)

From day 0 to day 50, the variation curves of the approximate value and the theoretical value of the semi-major axis root mean square error Δa(t) relative to the reference orbit calculated according to formula (12) are shown in Figure 6, and the variation curve of the error of the approximate value of the semi-major axis root mean square error Δa(t) relative to the reference orbit compared with the theoretical value is shown in Figure 7. It can be seen from the figure that the error of the approximate value of the semi-major axis root mean square error Δa(t) relative to the reference orbit using the method proposed in this paper is better than ±0.7m, which meets the on-orbit implementation of the unilateral drift loop control strategy.

Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims (7)

1. The low-orbit constellation phase maintaining parameter estimation method is characterized by comprising the following steps of:

determining a constellation reference orbit and a constellation phase maintaining parameter;

performing relative latitude amplitude angle flat root polynomial fitting to obtain a relative reference orbit latitude amplitude angle Ping Gen;

calculating the coefficients of the opposite semi-major axis flat root polynomials;

estimating a relative semi-major axis Ping Gen deviation;

the determining constellation reference track specifically comprises the following steps: the low-orbit constellation nominal orbit semi-long axis flat root is taken as a reference orbit semi-long axis Ping Gen a _R The reference orbit extrapolation only considers the gravitational perturbation, extrapolates any time t, and the orbit latitude amplitude root is u _R (t) track semi-major axis Ping Gen mean

Is kept unchanged, i.e.)>

The constellation phase maintaining parameter is determined, specifically: for the actual running orbit of satellite affected by earth attraction perturbation, solar-lunar three-body attraction perturbation, atmospheric resistance perturbation and light pressure perturbation, the orbit latitude amplitude angle flat root is u (t), and the relative reference orbit latitude amplitude angle flat root is defined as: Δu (t) =u (t) -u _R (t); the semi-long axis flat root of the track is a (t), and the semi-long axis flat root of the track relative to the reference track is defined as delta a (t) =a (t) -a _R ；

The method for carrying out the relative latitude amplitude angle flat root polynomial fitting comprises the following steps: under the condition of no orbit control, obtaining instantaneous orbit parameters of a satellite by GNSS orbit determination, calculating latitude argument Ping Gen u (t) of the satellite by using conversion of the instantaneous orbit parameters and the average orbit parameters, and using Deltau (t) =u (t) -u _R (t) calculating a relative reference orbit latitude argument Ping Gen u (t); approximating the relative reference orbit latitude argument Ping Gen u (t) to Deltau (t) ≡k with a cubic polynomial _u0 +k _u1 (t-t ₀ )+k _u2 (t-t ₀ ) ² +k _u3 (t-t ₀ ) ³ ；t ₀ Start time of trackless control, k _u0 、k _u1 、k _u2 、k _u3 Is a coefficient.

2. A method of estimating phase-preserving parameters of a low-rail constellation according to claim 1, wherein said calculating coefficients of a parallel root polynomial with respect to a major axis comprises the steps of:

approximating the relative reference orbit semi-major axis Ping Gen a (t) to a quadratic polynomial

Wherein t is ₀ Is the starting moment of trackless control;

according to the reference orbit semi-major axis Ping Gen a _R And

calculating coefficient K _a The method comprises the steps of carrying out a first treatment on the surface of the Wherein,,μ is the gravitational coefficient;

by means of

Calculating the coefficient Δa (t ₀ )、

And->

3. The method according to claim 1, wherein the estimation is biased with respect to a semi-major axis Ping Gen, specifically: from the determination of

Calculating the starting time t of the trackless control ₀ To the end time t of the trackless control _f An estimate of the relative reference orbit semi-major axis Ping Gen a (t) at any time in between.

4. A low-rail constellation phase-preserving parameter estimation system, comprising:

a first module for determining a constellation reference orbit and a constellation phase maintaining parameter;

the second module is used for carrying out relative latitude amplitude angle flat root polynomial fitting to obtain a relative reference orbit latitude amplitude angle Ping Gen;

the third module is used for calculating the polynomial coefficient of the flat root relative to the semi-major axis;

a fourth module that estimates a deviation from the median axis Ping Gen;

the determining constellation reference track specifically comprises the following steps: the low-orbit constellation nominal orbit semi-long axis flat root is taken as a reference orbit semi-long axis Ping Gen a _R The reference orbit extrapolation only considers the gravitational perturbation, extrapolates any time t, and the orbit latitude amplitude root is u _R (t) track semi-major axis Ping Gen mean

Is kept unchanged, i.e.)>

The constellation phase maintaining parameter is determined, specifically: for the actual running orbit of satellite affected by earth attraction perturbation, solar-lunar three-body attraction perturbation, atmospheric resistance perturbation and light pressure perturbation, the orbit latitude amplitude angle flat root is u (t), and the relative reference orbit latitude amplitude angle flat root is defined as: Δu (t) =u (t) -u _R (t); the semi-long axis flat root of the track is a (t), and the semi-long axis flat root of the track relative to the reference track is defined as delta a (t) =a (t) -a _R ；

The method for carrying out the relative latitude amplitude angle flat root polynomial fitting comprises the following steps: under the condition of no orbit control, obtaining instantaneous orbit parameters of a satellite by GNSS orbit determination, calculating latitude argument Ping Gen u (t) of the satellite by using conversion of the instantaneous orbit parameters and the average orbit parameters, and using Deltau (t) =u (t) -u _R (t) calculating a relative reference orbit latitude argument Ping Gen u (t); approximating the relative reference orbit latitude argument Ping Gen u (t) to Deltau (t) ≡k with a cubic polynomial _u0 +k _u1 (t-t ₀ )+k _u2 (t-t ₀ ) ² +k _u3 (t-t ₀ ) ³ ；t ₀ Start time of trackless control, k _u0 、k _u1 、k _u2 、k _u3 Is a coefficient.

5. The low-rail constellation phase preserving parameter estimation system of claim 4, wherein said calculating relative semi-major axis flat root polynomial coefficients comprises the steps of:

approximating the relative reference orbit semi-major axis Ping Gen a (t) to a quadratic polynomial

Wherein t is ₀ Is the starting moment of trackless control;

according to the reference orbit semi-major axis Ping Gen a _R And

calculating coefficient K _a The method comprises the steps of carrying out a first treatment on the surface of the Wherein μ is a gravitational coefficient;

by means of

Calculating the coefficient Δa (t ₀ )、

And->

The estimation is biased with respect to the semi-major axis Ping Gen, specifically: from the determination of

Calculating the starting time t of the trackless control ₀ To the end time t of the trackless control _f An estimate of the relative reference orbit semi-major axis Ping Gen a (t) at any time in between.

6. A computer readable storage medium storing a computer program, which when executed by a processor performs the steps of the method according to any one of claims 1 to 3.

7. A low-rail constellation phase-preserving parameter estimation device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized by: the processor, when executing the computer program, performs the steps of the method of any one of claims 1 to 3.

Images