CN104048664A - Autonomous orbit determination method of navigation satellite constellation - Google Patents

Abstract

The invention belongs to the field of autonomous orbit determination of satellites and relates to an autonomous orbit determination method of a navigation satellite constellation. The autonomous orbit determination method of the navigation satellite constellation comprises the following steps: (1) starting autonomous orbit determination and initializing a system; (2) acquiring an inter-satellite ranging between satellites; (3) calculating an observation matrix of the inter-satellite ranging; (4) forecasting an orbit by using an orbit dynamical model; (5) updating measurement and estimating state by using a kalman filtering algorithm; and (6) judging whether the autonomous orbit determination is ended, operating the steps (2)-(6) again if the autonomous orbit determination is not ended, and conversely, ending and exiting an autonomous orbit determination program. Compared with the conventional autonomous orbit determination of navigation satellite constellation, the autonomous orbit determination method of the navigation satellite constellation has the advantages that the method is capable of avoiding the rank defect problem of autonomous orbit determination method of the navigation satellite constellation by using the inter-satellite ranging and is high in long-term autonomous orbit determination accuracy.

Description

A kind of method of Navsat constellation autonomous orbit determination

Technical field

The invention belongs to autonomous orbit determination field, be specifically related to a kind of method of Navsat constellation autonomous orbit determination.

Background technology

Autonomous orbit determination ability will have more and more important meaning to the development of satellite navigation system.The satellite navigation system that has autonomous orbit determination ability does not need to provide support by global cloth station, can alleviate the burden of limited land station simultaneously, improves the security of satellite navigation system.

The autonomous orbit determination of satellite navigation system both can utilize single star autonomous orbit determination method, by every satellite in system independently autonomous orbit determination realize the autonomous orbit determination of whole navigational system.Also the whole net orbit determination that can utilize the relative measurement between satellite to realize satellite navigation system.Relative measurement comprises the information such as relative angle, relative distance and relative velocity between navigational system Satellite.With respect to the measurement between satellite and the celestial body of a surface imperfection, the relative accuracy between two satellites is much higher.Therefore utilizing relative measurement information between Navsat to carry out autonomous orbit determination is a feasible mode.Early stage research points out only need to utilize Angle Information between star just can carry out autonomous orbit determination, by the autonomous orbit determination precision of angle measurement, is only hundreds of rice.But combine, to use the autonomous orbit determination precision of range finding and angle measurement between star be meter level.This explanation is when utilizing between star that metrical information is carried out autonomous orbit determination, and between star, range finding is larger than the effect of angle measurement.Yet only utilize between star range finding to carry out autonomous orbit determination to near-earth satellite navigational system and have rank defect problem.

Summary of the invention

Goal of the invention: for solving the problems of the technologies described above, the invention provides a kind of method of Navsat constellation autonomous orbit determination.Need to have one at least to operate in month be the Navsat on Lagrangian track in the method.

Technical scheme: a kind of method of Navsat constellation autonomous orbit determination, comprises the steps:

(1): autonomous orbit determination starts, system initialization;

(2): obtain between the star between satellite and find range;

(3): calculate the observing matrix of finding range between star;

(4): utilize dynamics of orbits model to carry out orbit prediction;

(5): utilize Kalman filtering algorithm to measure respectively and upgrade and state estimation;

(6): judge whether autonomous orbit determination finishes, if do not finish, operating procedure (2)～step (6) again; Otherwise, finish to exit autonomous orbit determination program.

Preferred version as the method for Navsat constellation autonomous orbit determination in the present invention: range finding described in step (2) comprises range finding between Navsat and the range finding between Navsat and Lagrangian satellite.

Preferred version as the method for Navsat constellation autonomous orbit determination in the present invention: if the range finding in step (2) is the range finding matrix between Navsat, calculate the observing matrix between Navsat by (1) formula:

$H_{k+1}=\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂[{\left({\mathrm{\σ}}_i\right)}_{k+1}^T,{\left({\mathrm{\σ}}_j\right)}_{k+1}^T]}{|}_{x_{k+1}={\hat{x}}_{k+1/k}}---\left(1\right)$

ρ _ijfor finding range between star, σ _i, σ _jit is the orbital tracking of two Navsats;

(1) in formula

Wherein,

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_i}^T}=\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\\ \frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_j}^T}=-\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\end{array}\right.---\left(3\right)$

[x _eiy _eiz _ei] ^t[x _ejy _ejz _ej] ^tbe respectively near-earth satellite i and the position coordinates of near-earth satellite j under inertial system.

Preferred version as the method for Navsat constellation autonomous orbit determination in the present invention: if the range finding matrix in step (2) is the range finding between Navsat and Lagrangian satellite, calculate the observing matrix between Navsat and Lagrangian satellite by (4) formula:

Wherein,

And

${\left[\begin{array}{ccc}{x}_{{\mathrm{EL}}_k}& y_{{\mathrm{EL}}_k}& z_{{\mathrm{EL}}_k}\end{array}\right]}^T$ For the position vector of Lagrangian orbital navigation satellite under Earth central inertial system.

Preferred version as the method for Navsat constellation autonomous orbit determination in the present invention: utilize dynamics of orbits model to carry out orbit prediction described in step (4) and comprise the following steps:

(41) initial value using the orbit determination result of previous moment as orbit prediction;

(42) initial value is brought into the dynamics of orbits model of satellite, wherein dynamics of orbits model has been considered the impact of atmospherical drag, sun optical pressure, the earth non-spherical gravitation, trisome gravitation, tidal force;

(43) utilize RKF78 numerical integration method to obtain the result of orbit prediction.

Preferred version as the method for Navsat constellation autonomous orbit determination in the present invention: utilize Kalman filtering algorithm to measure respectively in step (5) and upgrade and state estimation, comprise the steps:

(51) by (7) formula and (8) formula, to being estimated state, carry out one-step prediction

${\hat{X}}_{k+1/k}={\mathrm{\Φ}}_{k+1/k}{X}_{k/k}+U_k=f({\hat{X}}_k,k)---\left(7\right)$

$P_{k+1/k}={\mathrm{\Φ}}_{k+1/k}{P}_{k/k}{\mathrm{\Φ}}_{k+1/k}^T+{\mathrm{\Γ}}_k{Q}_k{\mathrm{\Γ}}_k^T---\left(8\right)$

(52) using the result of step (1) as prior imformation, by (9) formula calculated gains matrix K _k+1

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T{(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R_{k+1})}^{-1}---\left(9\right)$

(53) utilize K _k+1, by (10) formula, obtain new state estimation value

${\hat{X}}_{k+1/k+1}={\hat{X}}_{k+1/k}+K_{k+1}(Z_{k+1}-Z^{*})---\left(10\right)$

(54) by (11) formula, calculate new covariance matrix, for next step filtering is prepared

$\begin{array}{c}{P}_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T\\ +K_{k+1}{R}_{k+1}{K}_{k+1}^T\end{array}---\left(11\right).$

Beneficial effect: the present invention, with respect to the method for traditional Navsat constellation autonomous orbit determination, has the following advantages:

1, can solve navigation constellation and only utilize the rank defect problem of finding range while carrying out autonomous orbit determination between star;

2, long-term autonomous orbit determination accuracy is higher.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of circular re stricted three body problem

Fig. 2 is five Lagrangian points position views in circular re stricted three body problem

Fig. 3 is method flow diagram of the present invention

Fig. 4 carries out simulating, verifying schematic diagram to the present invention

Fig. 5 is site error and the user's pseudorange error of GPS navigation satellite PRN9 in emulation experiment

Fig. 6 is site error and the user's pseudorange error of GPS navigation satellite PRN30 in emulation experiment

Fig. 7 is site error and the user's pseudorange error of GPS navigation satellite PRN31 in emulation experiment

Embodiment:

The improvement of having done with respect to prior art in order to understand better the present invention, before the specific embodiment of the present invention is elaborated, is first that Lagrangian track further supplements to the ground moon in summary of the invention.

For the Navsat operating on Lagrangian track, the simplest model that can describe its dynamic characteristic is circular re stricted three body problem model as shown in Figure 1---establish two large celestial body m ₁and m ₂only under attractive interaction effect, move, and the track mutually detouring between them is that radius is r ₁₂circle.If a noninertial system of coordinates xyz (junction coordinate system), true origin is the barycenter of two large celestial bodies, and x axle is by m ₁point to m ₂, z axle is perpendicular to m ₂around m ₁orbit plane, y axle and x, z axle meet the right-hand rule.In this coordinate system, m ₁and m ₂seem transfixion, introducing now quality is the 3rd object of m, its quality and m ₁and m ₂compare negligiblely, m is at m ₁and m ₂motion under gravitational field effect is exactly so-called circular re stricted three body problem.

In junction coordinate system, there are five Lagrangian points, as shown in Figure 2, wherein three conllinear Lagrangian points are unsettled, two triangle Lagrangian points are stable, no matter be stable Lagrangian points or unsettled Lagrangian points, near it, all have periodic orbit, the Navsat constellation in present specification is distributed on Lagrangian points periodic orbit just.

As shown in Figure 3, a kind of method of Navsat constellation autonomous orbit determination, comprises the steps:

(1): autonomous orbit determination starts, system initialization;

(2): obtain between the star between satellite and find range;

(3): calculate the observing matrix of finding range between star;

(4): utilize dynamics of orbits model to carry out orbit prediction;

(5): utilize Kalman filtering algorithm to measure respectively and upgrade and state estimation;

(6): judge whether autonomous orbit determination finishes, if do not finish, operating procedure (2)～step (6) again; Otherwise, finish to exit autonomous orbit determination program.

Range finding described in step (2) comprises range finding between Navsat and the range finding between Navsat and Lagrangian satellite.

If the range finding in step (2) is the range finding between Navsat, by (1) formula, calculate the observing matrix between Navsat:

$H_{k+1}=\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂[{\left({\mathrm{\σ}}_i\right)}_{k+1}^T,{\left({\mathrm{\σ}}_j\right)}_{k+1}^T]}{|}_{x_{k+1}={\hat{x}}_{k+1/k}}---\left(1\right)$

ρ _ijfor finding range between star, σ _i, σ _jit is the orbital tracking of two Navsats;

(1) in formula

Wherein,

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_i}^T}=\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\\ \frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_j}^T}=-\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\end{array}\right.---\left(3\right)$

[x _eiy _eiz _ei] ^t[x _ejy _ejz _ej] ^tbe respectively near-earth satellite i and the position coordinates of near-earth satellite j under inertial system.

If the range finding in step (2) is the range finding between Navsat and Lagrangian satellite,

By (4) formula, calculate the observing matrix between Navsat and Lagrangian satellite:

Wherein,

And

${\left[\begin{array}{ccc}{x}_{{\mathrm{EL}}_k}& y_{{\mathrm{EL}}_k}& z_{{\mathrm{EL}}_k}\end{array}\right]}^T$ For the position vector of Lagrangian orbital navigation satellite under Earth central inertial system.

Described in step (4), utilizing dynamics of orbits model to carry out orbit prediction comprises the following steps:

(41) initial value using the orbit determination result of previous moment as orbit prediction;

(42) initial value is brought into the dynamics of orbits model of satellite, wherein dynamics of orbits model has been considered the impact of atmospherical drag, sun optical pressure, the earth non-spherical gravitation, trisome gravitation, tidal force;

(43) utilize RKF78 numerical integration method to obtain the result of orbit prediction.

In step (5), utilize Kalman filtering algorithm to measure respectively and upgrade and state estimation, comprise the steps:

(51) by (7) formula and (8) formula, to being estimated state, carry out one-step prediction

${\hat{X}}_{k+1/k}={\mathrm{\Φ}}_{k+1/k}{X}_{k/k}+U_k=f({\hat{X}}_k,k)---\left(7\right)$

(52) using the result of step (1) as prior imformation, by (9) formula calculated gains matrix K _k+1

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T{(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R_{k+1})}^{-1}---\left(9\right)$

(53) utilize K _k+1, by (10) formula, obtain new state estimation value

${\hat{X}}_{k+1/k+1}={\hat{X}}_{k+1/k}+K_{k+1}(Z_{k+1}-Z^{*})---\left(10\right)$

(54) by (11) formula, calculate new covariance matrix, for next step filtering is prepared

$\begin{array}{c}{P}_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T\\ +K_{k+1}{R}_{k+1}{K}_{k+1}^T\end{array}---\left(11\right).$

Simulating, verifying scheme

As shown in Figure 4, in order to verify the correctness of method of the present invention, adopt the method for simulating, verifying to verify, step is as follows:

(1), utilizing the precise ephemeris of gps satellite to produce between the star between Navsat finds range;

(2), the precise ephemeris that utilizes Lagrangian satellite produces between the star between Lagrangian satellite and gps satellite and finds range in conjunction with the precise ephemeris of gps satellite, will in two classes range findings, add suitable range error;

(3), utilize kalman filter method to carry out autonomous orbit determination in conjunction with two class range findings;

(4), by orbit determination result and precise ephemeris comparison, orbit determination accuracy is assessed.

Emulation initial time elects 2000/4/13 as, 23:59:47 (UTC), emulation duration 180 days, terrestrial gravitation field model adopts 10 * 10 rank WGS-84 models, trisome (life) Gravitational perturbation adopts DE200 to calculate life ephemeris, and solar radiation pressure perturbation adopts new RPR model.The observation interval of finding range between star is made as 1 hour, supposes that the systematic error of finding range between near-earth Navsat is 0.1m, random difference 0.1m, errors of the distance measurement system 0.5m between near-earth Navsat and Lagrangian Navsat, random difference 0.5m; Draw the poor 1m of range measurement system between a bright day Navsat, random difference 1m.LU is ground month distance.

Table 1: the original state of Lagrangian Navsat

Fig. 5～Fig. 7 has provided range error 1m between Lagrangian Satellite, under initial position error 0.1m condition, utilize expansion kalman filtering algorithm only to utilize between star and find range and carry out the simulation result of autonomous orbit determination the navigation constellation of the satellite on Lagrangian points track and gps satellite composition.Maximum error in three coordinate axis sees the following form:

Table 2: the maximum Orbit Error of RNT coordinate of near-earth Navsat

Table 3: the maximum Orbit Error of Lagrangian Navsat

Claims (6)

1. a method for Navsat constellation autonomous orbit determination, comprises the steps:

(1), autonomous orbit determination starts, system initialization;

(2), obtain between the star between satellite and find range;

(3), calculate the observing matrix of finding range between star;

(4), utilize dynamics of orbits model to carry out orbit prediction;

(5), utilizing Kalman filtering algorithm to measure respectively upgrades and state estimation;

(6), judge whether autonomous orbit determination finishes, if do not finish, operating procedure (2)～step (6) again; Otherwise, finish to exit autonomous orbit determination program.

2. the method for the autonomous set pattern of Navsat constellation as described in claim 1, is characterized in that, range finding described in step (2) comprises range finding between Navsat and the range finding between Navsat and Lagrangian satellite.

3. the method for Navsat constellation autonomous orbit determination as described in claim 1, is characterized in that, if the range finding in step (2) is the range finding between Navsat, by (1) formula, calculates the observing matrix between Navsat:

$H_{k+1}=\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂[{\left({\mathrm{\σ}}_i\right)}_{k+1}^T,{\left({\mathrm{\σ}}_j\right)}_{k+1}^T]}{|}_{x_{k+1}={\hat{x}}_{k+1/k}}---\left(1\right)$

ρ _ijfor finding range between star, σ _i, σ _jit is the orbital tracking of two Navsats;

(1) in formula

Wherein,

$\left\{\begin{array}{c}\frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_i}^T}=\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\\ \frac{\∂{\mathrm{\ρ}}_{\mathrm{ij}}}{\∂{r_j}^T}=-\frac{1}{{\mathrm{\ρ}}_{\mathrm{ij}}}\left[\begin{array}{ccc}{x}_{\mathrm{Ei}}-x_{\mathrm{Ej}}& y_{\mathrm{Ei}}-y_{\mathrm{Ej}}& z_{\mathrm{Ei}}-z_{\mathrm{Ej}}\end{array}\right]\end{array}\right.---\left(3\right)$ [x _eiy _eiz _ei] ^t[x _ejy _ejz _ej] ^tbe respectively near-earth satellite i and the position coordinates of near-earth satellite j under inertial system.

4. the method for Navsat constellation autonomous orbit determination as described in claim 1, it is characterized in that, if the range finding in step (2) is the range finding between Navsat and Lagrangian satellite, by (4) formula, calculate the observing matrix between Navsat and Lagrangian satellite:

wherein,

and

${\left[\begin{array}{ccc}{x}_{{\mathrm{EL}}_k}& y_{{\mathrm{EL}}_k}& z_{{\mathrm{EL}}_k}\end{array}\right]}^T$ For the position vector of Lagrangian orbital navigation satellite under Earth central inertial system.

5. the method for Navsat constellation autonomous orbit determination as described in claim 1, is characterized in that, utilizes dynamics of orbits model to carry out orbit prediction and comprise the following steps described in step (4):

(41) initial value using the orbit determination result of previous moment as orbit prediction;

(42) initial value is brought into the kinetic model of satellite, the wherein consideration of the kinetic model impact of atmospherical drag, sun optical pressure, the non-spherical gravitation of the earth, trisome gravitation, tidal force of knowing clearly;

(43) utilize RKF78 numerical integration method to obtain the result of orbit prediction.

6. the method for Navsat constellation autonomous orbit determination as described in claim 1, is characterized in that, utilizes Kalman filtering algorithm to measure respectively and upgrade and state estimation in step (5), comprises the steps:

(51) by (7) formula and (8) formula, to being estimated state, carry out one-step prediction

${\hat{X}}_{k+1/k}={\mathrm{\Φ}}_{k+1/k}{X}_{k/k}+U_k=f({\hat{X}}_k,k)---\left(7\right)$

$P_{k+1/k}={\mathrm{\Φ}}_{k+1/k}{P}_{k/k}{\mathrm{\Φ}}_{k+1/k}^T+{\mathrm{\Γ}}_k{Q}_k{\mathrm{\Γ}}_k^T---\left(8\right)$

(52) using the result of step (1) as prior imformation, by (9) formula calculated gains matrix K _k+1

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T{(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R_{k+1})}^{-1}---\left(9\right)$

(53) utilize K _k+1, by (10) formula, obtain new state estimation value

${\hat{X}}_{k+1/k+1}={\hat{X}}_{k+1/k}+K_{k+1}(Z_{k+1}-Z^{*})---\left(10\right)$

(54) by (11) formula, calculate new covariance matrix, for next step filtering is prepared

$\begin{array}{c}{P}_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T\\ +K_{k+1}{R}_{k+1}{K}_{k+1}^T\end{array}---\left(11\right).$