CN103957095B - A kind of method for synchronizing time based on bidirectional ranging between star - Google Patents

Abstract

The invention discloses a kind of method for synchronizing time based on bidirectional ranging between star, is concretely comprised the following steps and clock clock correction is modeled using quadratic polynomial；Consider the impact of frequency drift change, satellite atomic clock model adopts 3 state components, sets up the state equation of filtering；Two satellites for inter-satellite link is set up in constellation, carry out pseudo range measurement using bidirectional ranging method between star, set up observational equation；According to the state equation and measurement equation of system, Kalman filter is carried out；Time synchronized is filtered using centralized Kalman filter or distributing Kalman filtering；Analysis impact of the inter-satellite link number to timing tracking accuracy, cost performance highest scheme is selected by the contrast of simulation result under different inter-satellite link numbers, synchronously estimated so as to providing reference experiment scheme and improve measurement by the contrast for concentrating the filtering accuracy under filtering and the contrast of decentralized filtering, and different inter-satellite link numbers in the present invention.

Description

A kind of method for synchronizing time based on bidirectional ranging between star

Technical field

The invention belongs to time synchronized field between star, specifically, is a kind of same to realize the time based on Kalman filtering One step process.

Background technology

The precise orbit determination of geo-synchronous orbit satellite GEO is always the Research Challenges and hot issue in precise orbit determination field. Its geostationary characteristic cause ground observation geometric configuration almost unchanged, satellite is very weak relative to the Dynamic Constraints information on ground, because This in the GEO satellite orbit determination based on pseudorange observation cannot combine clock correction to star and effectively be estimated, need the star ground time same The support of time synchronized between step and station.

So-called time synchronized, refers to that the clock jitter of each node in time synchronization network should be tried one's best unanimously.Time synchronized is to lead One of key technology of boat constellation operation, high performance atomic clock and effective time synchronous method are the effective of raising time synchronized Means.Time synchronized is the basis of navigation constellation operation, and accurate distance measurement in navigation system is actually the survey of precise time Amount.The precision of time synchronized is related to the Time synchronization technique of the performance of atomic clock and employing.

Kalman filtering algorithm is a wide variety of information fusion technology, and standard Kalman filtering algorithm is set up and is being Optimal estimation under system noise variance matrix known case, but in practical situations both, the measurement noise variance matrix of measuring system, it is known that It is significant to improving filtering accuracy how systematic survey noise variance matrix is effectively estimated.

Satellite navigation system typically all adopts high performance rubidium atomic clock or cesium-beam atomic clock now, is calculated using Kalman filtering Method is filtered to clock correction, and specific filtering method has concentration filtering and decentralized filtering, and the difference of inter-satellite link number can also reach To different filtering accuracies.

The content of the invention

For problems of the prior art, the present invention specifically demonstrates concentration filtering by emulation experiment and disperses filter Impact of the ripple to filtering accuracy, and impact of the inter-satellite link number to filtering accuracy is analyzed, consider so as to draw optimal star Between number of links.

The present invention is method for synchronizing time between a kind of star based on Kalman Filter Technology, is concretely comprised the following steps：

Step one：High-precision atomic clock is usually present clock correction.At a certain instantaneous, moment and standard that clock is given Difference between moment is referred to as clock correction x (t), typically clock clock correction is modeled using quadratic polynomial：

In formula, first three items represent the time system error parameter of clock, a₀For clock initial phase deviation, a₁For atomic clock Original frequency deviation, a₂For the linear frequency drift rate of atomic clock, ε_xT () is the clock clock jitter for causing affected by noise Random variation component.t₀For the initial time of atomic clock, the reading of t atomic clocks.Research to atomic frequency standard shows, atomic clock Change at random part is considered as the linear superposition of various independent energy spectral noises.By the instantaneous relative frequency deviation of atomic clock Y (t)=dx (t)/dt, obtains：

Y (t)=a₁+a₂t+ε_y(t) (1.2)

In formula, a₁、a₂Meaning is as above, ε_yThe random variation component of (t) for atomic clock frequency deviation of clock.To atom The research of frequency marking shows that the change at random part of atomic clock is considered as the superposition of various independent energy noises, can represent For：

W in formula_αT () (α=- 4, -3, -2, -1,0,1,2) represent 7 kinds of independent noise processes, to most of atomic clock ε_y(t) Can only with front 5 kinds of noise w_αT () (α=- 2, -1,0,1,2) express, successively referred to as frequency modulation random walk noise (RWFM), frequency modulation Flicker noise (FFM), frequency modulation white noise (WFM), phase modulation flicker noise (FPM), phase modulation white noise (WPM).GPS rubidium clocks are ground Study carefully and show, in addition to above-mentioned 5 kinds of noises, when smoothingtime is longer, rubidium clock is also subject to very low frequency influence of noise, such as frequency modulation flickering trip Walk noise (FWFM) w_-3(t) and frequency modulation random walk noise (RRFM) w_-4(t)。

Step 2：Set up the state equation of filtering

If considering the impact of frequency drift change, satellite atomic clock model can adopt the state equation of 3 state components Represent.It is shown below：

X_k=Φ_k-1,kX_k-1+W_k-1 (1.4)

Wherein：

a_0,k、a_1,、a_2,kRespectively t_kThe satellite clock biases (phase error) of epoch, frequency error and frequency drift rate； τ is filtering cycle；w_f,k-1、w_a,k-1Respectively t_k-1The clock phase noise of epoch, frequency noise and frequency drift rate Noise, concrete statistical property determined by the Allan variances of the clock selected, and meets following relation：

Q (t)=diag [q₁q₂q₃] it is systematic procedure noise vector, the variance intensity battle array of w (t), q₁、q₂、q₃For atomic clock Power spectral density coefficient；T is filtering interval, Q_kFor the covariance matrix that state-noise is vectorial, Φ (τ, T) is that state shifts square Battle array.

Step 3：Set up observational equation

Two satellites for inter-satellite link is set up in constellation, carry out pseudo range measurement using bidirectional ranging method between star, such as Shown in Fig. 1, a certain moment reference epoch t can be obtained_kCross-Link measurement equation：

ρ_ji=D+c δ t_i-c·δt_j+n_ji (1.7)

ρ_ij=D+c δ t_j-c·δt_i+n_ij (1.8)

In formula：ρ_jiRepresent satellite S_jTo S_iChanging pseudorange, n_jiRepresent measurement noise, δ t_jWith δ t_iSatellite S is represented respectively_j、 S_iAbsolute clock correction.D is intersatellite actual distance, and c is the light velocity.

By (1.7) and (1.8) formula, carrying out pseudo range difference can obtain：

z_k=(ρ_ij-ρ_ji)/2c=δ t_j-δt_i+n_k/2c (1.9)

Wherein, n_k=n_ij-n_ji。

Step 4：According to the state equation and measurement equation of system, Kalman filter resolving is carried out using following equations：

In formula, Q is systematic observation noise battle array, and R is system noise acoustic matrix, and its size is related to range accuracy；H is observation square Battle array, Z is observation vector, and K is gain matrix, and Φ is state-transition matrix.State variable is taken as each node and (takes and defend with datum node On the basis of star 1) timing parameter difference.

Step 5：Time synchronized is filtered using centralized Kalman filter and distributing Kalman filtering

For system, centralized and distributing Kalman filtering can be to adopting two-way satellite frequency and time transfer Star between time synchronized be filtered.

Wherein, distributing kalman filter method：Using the timing parameter of each node as state variable, using N number of filter Ripple device estimates that wherein N is the node total number of system respectively to clock correction.Comprise the following steps that：

1) ground system time synchronized is carried out by a certain outfit using two-way satellite frequency and time transfer method (TWSTFT) There is the ground=earth station of high accuracy atomic clock as system clock reference station, other earth stations synchronize.

2) system time synchronization is carried out using two-way ranging system between star.Using a certain satellite as system clock benchmark Stand, other satellites are synchronized.

3) time synchronized being respectively completed between ground system and satellite system, carries out ground using radio bidirectional ranging method Time synchronized between system and satellite system.Wherein, as long as the base station in ground system and satellite system carries out the time It is synchronous.

Centralized Kalman filter method：As in system, each node (satellite and earth station) definitely clock correction can not be estimated Property, node on the basis of satellite 1 is chosen, state variable is taken as the difference of each node and the timing parameter of datum node, and dimension is (N-1) × 3 (N is system node number), carry out Kalman filtering, the relative clock correction of each node in estimating system.Wherein method for synchronizing time Selection it is consistent with decentralized filtering method.

Step 6：Analysis impact of the inter-satellite link number to timing tracking accuracy, by emulation knot under different inter-satellite link numbers Cost performance highest scheme is selected in the contrast of fruit

Impact of the inter-satellite link number to timing tracking accuracy is analyzed by taking four star seats as an example.

Three two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}

Four two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}

Five two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}{ρ₂₄ρ₄₂}

Six two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}{ρ₂₄ρ₄₂}{ρ₃₄ρ₄₃}

By the filtering essence under the concentration filtering and the contrast of decentralized filtering, and different inter-satellite link numbers in the present invention The contrast of degree is so as to providing reference experiment scheme.

It is an advantage of the current invention that：

(1) compared for concentrating the pluses and minuses of filtering and decentralized filtering.

(2) compared for the timing tracking accuracy under different inter-satellite link numbers.

Description of the drawings：

Bidirectional ranging schematic diagram between Fig. 1 stars

Tetra- star seats of Fig. 2 measure link schematic diagram

Fig. 3 concentrates the precision of the time synchronized of filtering

The precision of the time synchronized of Fig. 4 decentralized filterings

The precision of the time synchronized that can be reached during tri- inter-satellite links of Fig. 5

The precision of the time synchronized that can be reached during tetra- inter-satellite links of Fig. 6

The precision of the time synchronized that can be reached during five inter-satellite links of Fig. 7

The precision of the time synchronized that can be reached during six inter-satellite links of Fig. 8

Specific embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The present invention proposes that a kind of time synchronized based on Kalman filtering sends out method, the centralized Kalman by simulation comparison Filtering and impact of the distributing Kalman filtering to filtering accuracy, and analyze impact of the inter-satellite link number to filtering accuracy.

Step one：High-precision atomic clock is usually present clock correction.At a certain instantaneous, moment and standard that clock is given Difference between moment is referred to as clock correction x (t), typically clock clock correction is modeled using quadratic polynomial：

In formula, first three items represent the time system error parameter of clock, a₀For clock initial phase deviation, a₁For atomic clock Original frequency deviation, a₂For the linear frequency drift rate of atomic clock, ε_xT () is the clock clock jitter for causing affected by noise Random variation component.t₀For the initial time of atomic clock, the reading of t atomic clocks.Research to atomic frequency standard shows, atomic clock Change at random part is considered as the linear superposition of various independent energy spectral noises.By the instantaneous relative frequency deviation of atomic clock Y (t)=dx (t)/dt, obtains：

Y (t)=a₁+a₂t+ε_y(t) (1.11)

In formula, a₁、a₂Meaning is as above, ε_yThe random variation component of (t) for atomic clock frequency deviation of clock.To atom The research of frequency marking shows that the change at random part of atomic clock is considered as the superposition of various independent energy noises, can represent For：

W in formula_αT () (α=- 4, -3, -2, -1,0,1,2) represent 7 kinds of independent noise processes, to most of atomic clock ε_y(t) Can only with front 5 kinds of noise w_αT () (α=- 2, -1,0,1,2) express, successively referred to as frequency modulation random walk noise (RWFM), frequency modulation Flicker noise (FFM), frequency modulation white noise (WFM), phase modulation flicker noise (FPM), phase modulation white noise (WPM).GPS rubidium clocks are ground Study carefully and show, in addition to above-mentioned 5 kinds of noises, when smoothingtime is longer, rubidium clock is also subject to very low frequency influence of noise, such as frequency modulation flickering trip Walk noise (FWFM) w_-3(t) and frequency modulation random walk noise (RRFM) w_-4(t)。

Step 2：Set up the state equation of filtering

If considering the impact of frequency drift change, satellite atomic clock model can adopt the state equation of 3 state components Represent.It is shown below：

X_k=Φ_k-1,kX_k-1+W_k-1 (1.13)

Wherein：

a_0,k、a_1,k、a_2,kRespectively t_kThe satellite clock biases (phase error) of epoch, frequency error and frequency drift rate； τ is filtering cycle；w_f,k-1、w_a,k-1Respectively t_k-1The clock phase noise of epoch, frequency noise and frequency drift rate Noise, concrete statistical property determined by the Allan variances of the clock selected, and meets following relation：

Q (t)=diag [q₁q₂q₃] it is systematic procedure noise vector, the variance intensity battle array of w (t), q₁、q₂、q₃For atomic clock Power spectral density coefficient；T is filtering interval, Q_kFor the covariance matrix that state-noise is vectorial, Φ (τ, T) is that state shifts square Battle array.

Step 3：Set up observational equation

Two satellites for inter-satellite link is set up in constellation, carry out pseudo range measurement using bidirectional ranging method between star, such as Shown in Fig. 1, a certain moment reference epoch t can be obtained_kCross-Link measurement equation：

ρ_ji=D+c δ t_i-c·δt_j+n_ji (1.16)

ρ_ij=D+c δ t_j-c·δt_i+n_ij (1.17)

In formula：ρ_jiRepresent satellite S_jTo S_iChanging pseudorange, n_jiRepresent measurement noise, δ t_jWith δ t_iSatellite S is represented respectively_j、 S_iAbsolute clock correction.D is intersatellite actual distance, and c is the light velocity.

By (1.8) and (1.9) formula, carrying out pseudo range difference can obtain：

z_k=(ρ_ij-ρ_ji)/2c=δ t_j-δt_i+n_k/2c (1.18)

Wherein, n_k=n_ij-n_ji。

Step 4：According to the state equation and measurement equation of system, Kalman filter resolving is carried out using following equations：

In formula, Q is systematic observation noise battle array, and R is system noise acoustic matrix, and its size is related to range accuracy；H is observation square Battle array, Z is observation vector, and K is gain matrix, and Φ is state-transition matrix.State variable is taken as each node and (takes and defend with datum node On the basis of star 1) timing parameter difference.

Step 5：Time synchronized is filtered using centralized Kalman filter and distributing Kalman filtering

For system, centralized and distributing Kalman filtering can be to adopting two-way satellite frequency and time transfer Star between time synchronized be filtered.

Wherein, distributing kalman filter method：Using the timing parameter of each node as state variable, using N number of filter Ripple device estimates that wherein N is the node total number of system respectively to clock correction.Comprise the following steps that：

1) ground system time synchronized is carried out by a certain outfit using two-way satellite frequency and time transfer method (TWSTFT) There is the ground=earth station of high accuracy atomic clock as system clock reference station, other earth stations synchronize.

2) system time synchronization is carried out using two-way ranging system between star.Using a certain satellite as system clock benchmark Stand, other satellites are synchronized.

3) time synchronized being respectively completed between ground system and satellite system, carries out ground using radio bidirectional ranging method Time synchronized between system and satellite system.Wherein, as long as the base station in ground system and satellite system carries out the time It is synchronous.

Centralized Kalman filter method：As in system, each node (satellite and earth station) definitely clock correction can not be estimated Property, node on the basis of satellite 1 is chosen, state variable is taken as the difference of each node and the timing parameter of datum node, and dimension is (N-1) × 3 (N is system node number), carry out Kalman filtering, the relative clock correction of each node in estimating system.Wherein method for synchronizing time Selection it is consistent with decentralized filtering method.

Step 6：Analysis impact of the inter-satellite link number to timing tracking accuracy, by emulation knot under different inter-satellite link numbers Cost performance highest scheme is selected in the contrast of fruit

Impact of the inter-satellite link number to timing tracking accuracy is analyzed by taking four star seats as an example, using the method for concentration filtering, Clock correction using satellite 1 is used as standard.

Three two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}

Corresponding observing matrix can be obtained is：

Four two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}

Corresponding observing matrix can be obtained is：

Five two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}{ρ₂₄ρ₄₂}

Corresponding observing matrix can be obtained is：

Six two-way links：{ρ₁₂ρ₂₁}{ρ₁₃ρ₃₁}{ρ₁₄ρ₄₁}{ρ₂₃ρ₃₂}{ρ₂₄ρ₄₂}{ρ₃₄ρ₄₃}

Embodiment：

Still by taking the time synchronized between four stars as an example, it is 0m in the average of H_2O maser error, when standard deviation is 2m, adopts respectively With concentrating the method for filtering and decentralized filtering to be emulated, a length of 86400s during emulation concentrates the time synchronized of filtering gained The average of error be -0.12ns, standard deviation is 0.5ns, and the average of the error of the time synchronized obtained by decentralized filtering for - 0.09ns, standard deviation are -0.39ns.

When inter-satellite link number is three, the average -0.12ns of the error of gained time synchronized, standard deviation is 0.34ns.

When inter-satellite link number for four is, the average -0.12ns of the error of gained time synchronized, standard deviation is 0.31ns.

When inter-satellite link number for five is, the average -0.11ns of the error of gained time synchronized, standard deviation is 0.28ns.

When inter-satellite link number for six is, the average -0.10ns of the error of gained time synchronized, standard deviation is 0.26ns.

It can be seen that the precision of decentralized filtering is better than the precision for concentrating filtering from simulation result, but advantage is nor very Substantially.Increase inter-satellite link number, filtering accuracy increased, but increased effect is not it is obvious that but being to increase inter-satellite link Cost can be accordingly increased.Consider or select three inter-satellite links to be advisable.

Claims (4)

1. it is a kind of based on bidirectional ranging method for synchronizing time between star, it is characterised in that to specifically include following steps：

Step one：Difference between a certain moment that instantaneously, clock is given and etalon time is referred to as clock correction x (t), using secondary Multinomial is modeled to clock clock correction；

Step 2：Consider the impact of frequency drift change, satellite atomic clock model adopts 3 state components, sets up the shape of filtering State equation；

Step 3：Two satellites for inter-satellite link is set up in constellation, carry out pseudo range measurement using bidirectional ranging method between star, Set up observational equation；

Step 4：According to the state equation and measurement equation of system, Kalman filter is carried out；

Step 5：Time synchronized is filtered using centralized Kalman filter or distributing Kalman filtering：

Wherein, distributing kalman filter method：Using the timing parameter of each node as state variable, using N number of wave filter Respectively clock correction is estimated, wherein N is the node total number of system, comprises the following steps that：

1) ground system time synchronized is carried out using two-way satellite frequency and time transfer method TWSTFT, by a certain equipped with high-precision Used as system clock reference station, other earth stations synchronize for the earth station of degree atomic clock；

2) system time synchronization is carried out using two-way ranging system between star, using a certain satellite as system clock base station, its He synchronizes satellite；

3) time synchronized being respectively completed between ground system and satellite system, carries out ground system using radio bidirectional ranging method Time synchronized and between satellite system, wherein, as long as carrying out time synchronized i.e. to the base station in ground system and satellite system Can；

Centralized Kalman filter method：Due to the not estimability of the absolute clock correction of each node in system, on the basis of choosing satellite 1 Node, state variable are taken as the difference of each node and the timing parameter of datum node, and it is system node number that dimension is (N-1) × 3, N, Kalman filtering is carried out, the relative clock correction of each node in estimating system, the wherein selection of method for synchronizing time and distributing karr Graceful filtering method is consistent；

Step 6：Analysis impact of the inter-satellite link number to timing tracking accuracy, by simulation result under different inter-satellite link numbers Cost performance highest scheme is selected in contrast；

Wherein in above-mentioned steps one, the difference between a certain moment that instantaneously, clock is given and etalon time is referred to as clock correction x (t), using quadratic polynomial to concretely comprising the following steps that clock clock correction is modeled：

$x\left(t\right)=a_0+a_1(t-t_0)+\frac{1}{2}{a}_2{(t-t_0)}^2+{\mathrm{\ϵ}}_x\left(t\right)$

In formula, first three items represent the time system error parameter of clock, a₀For clock initial phase deviation, a₁For the initial of atomic clock Frequency departure, a₂For the linear frequency drift rate of atomic clock, ε_xT () is random for the clock clock jitter for causing affected by noise Change component, t₀For the initial time of atomic clock, the reading of t atomic clocks；

Wherein in above-mentioned steps two, it is considered to which the impact of frequency drift change, satellite atomic clock model adopt 3 state components, build The state equation of vertical filtering is concretely comprised the following steps：

X_k=Φ_k-1,kX_k-1+W_k-1

Wherein：

a_0,k、a_1,k、a_2,kRespectively t_kThe satellite clock biases of epoch, frequency error and frequency drift rate；τ is filtering cycle；w_f,k-1、w_a,k-1Respectively t_k-1The clock phase noise of epoch, frequency noise and frequency drift rate noise, it is concrete to count Characteristic determined by the Allan variances of the clock selected, and meets following relation：

$Q_k=\underset{0}{\overset{\mathrm{\τ}}{\∫}}\mathrm{\Φ}(\mathrm{\τ},T){\mathrm{Q\Φ}}^T(\mathrm{\τ},T)dT=\left[\begin{array}{ccc}{q}_{1}T+q_2\frac{T^3}{3}+q_3\frac{T^5}{20}& q_2\frac{T^2}{2}+q_3\frac{T^4}{3}& q_3\frac{T^3}{6}\\ q_2\frac{T^2}{2}+q_3\frac{T^4}{3}& q_{2}T+q_3\frac{T^3}{3}& q_3\frac{T^2}{2}\\ q_3\frac{T^3}{6}& q_3\frac{T^2}{2}& q_{3}T\end{array}\right]$

Wherein,

Q (t) δ (τ)=E { w (t+ τ) w (t)^T}

Q (t)=diag [q₁q₂q₃] it is systematic procedure noise vector, the variance intensity battle array of w (t), q₁、q₂、q₃For the work(of atomic clock Rate spectrum density coefficient；T is filtering interval, Q_kFor the covariance matrix of state-noise vector, Φ (τ, T) is state-transition matrix；

Wherein in above-mentioned steps three, two satellites for inter-satellite link is set up in constellation are entered using bidirectional ranging method between star Row pseudo range measurement, sets up observational equation and concretely comprises the following steps：

A certain moment reference epoch t_kCross-Link measurement equation be：

ρ_ji=D+c δ t_i-c·δt_j+n_ji (1.7)

ρ_ij=D+c δ t_j-c·δt_i+n_ij (1.8)

In formula：ρ_jiRepresent satellite S_jTo S_iChanging pseudorange, n_jiRepresent measurement noise, δ t_jWith δ t_iSatellite S is represented respectively_j、S_i's Absolute clock correction, D is intersatellite actual distance, and c is the light velocity；

By (1.7) and (1.8) formula, carrying out pseudo range difference can obtain：

z_k=(ρ_ij-ρ_ji)/2c=δ t_j-δt_i+n_k/2c (1.9)

Wherein, n_k=n_ij-n_ji；

Wherein in above-mentioned steps four, according to the state equation and measurement equation of system, carry out Kalman filter and concretely comprise the following steps, adopt Kalman filter resolving is carried out with following equations：

$\left\{\begin{array}{c}{X}_{k/k-1}={\mathrm{\φ}}_{k-1,k}{X}_{k-1}\\ P_{k/k-1}={\mathrm{\φ}}_{k-1,k}{P}_{k-1}{\mathrm{\φ}}_{k-1,k}^T+Q_{k-1}\\ K_k=P_{k/k-1}{H}_k^T{\left(H_k{P}_{k/k-1}{H}_k^T+R_k\right)}^{-1}\\ X_k=X_{k/k-1}+K_k\left(Z_k-H_k{X}_{k/k-1}\right)\\ P_k=\left(I-K_k{H}_k\right)P_{k/k-1}{\left(I-K_k{H}_k\right)}^T+K_k{R}_k{K}_k^T\end{array}\right.$

In formula, Q be systematic observation noise battle array, P_kObtain error covariance matrix for state variable, R is system noise acoustic matrix, its size with Range accuracy is related, and H is observing matrix, and Z is observation vector, and K is gain matrix, and Φ is state-transition matrix, and state variable takes For the difference of each node and the timing parameter of datum node, wherein on the basis of taking satellite 1.

2. according to claim 1 based on bidirectional ranging method for synchronizing time between star, wherein during analysis inter-satellite link number pair Between synchronization accuracy impact, cost performance highest scheme is selected by the contrast of simulation result under different inter-satellite link numbers concrete Step is：

With impact of the four star constellation analysis inter-satellite link numbers to timing tracking accuracy, using the method for centralized Kalman filter, Clock correction using satellite 1 as standard,

Three two-way links：{ρ₁₂ ρ₂₁}{ρ₁₃ ρ₃₁}{ρ₁₄ ρ₄₁}

Corresponding observing matrix can be obtained is：

$H=\left[\begin{array}{ccccccccc}-1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0& 0\end{array}\right]$

Four two-way links：{ρ₁₂ ρ₂₁}{ρ₁₃ ρ₃₁}{ρ₁₄ ρ₄₁}{ρ₂₃ ρ₃₂}

Corresponding observing matrix can be obtained is：

$H=\left[\begin{array}{ccccccccc}-1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0& 0\\ 1& 0& 0& -1& 0& 0& 0& 0& 0\end{array}\right]$

Five two-way links：{ρ₁₂ ρ₂₁}{ρ₁₃ ρ₃₁}{ρ₁₄ ρ₄₁}{ρ₂₃ ρ₃₂}{ρ₂₄ ρ₄₂}

Corresponding observing matrix can be obtained is：

$H=\left[\begin{array}{ccccccccc}-1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0& 0\\ 1& 0& 0& -1& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& -1& 0& 0\end{array}\right]$

Six two-way links：{ρ₁₂ ρ₂₁}{ρ₁₃ ρ₃₁}{ρ₁₄ ρ₄₁}{ρ₂₃ ρ₃₂}{ρ₂₄ ρ₄₂}{ρ₃₄ ρ₄₃}

$H=\left[\begin{array}{ccccccccc}-1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0& 0\\ 1& 0& 0& -1& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& -1& 0& 0\\ 0& 0& 0& 1& 0& 0& -1& 0& 0\end{array}\right].$

3. according to claim 1 based on bidirectional ranging method for synchronizing time between star, wherein during analysis inter-satellite link number pair Between synchronization accuracy impact, cost performance highest scheme is selected by the contrast of simulation result under different inter-satellite link numbers concrete Step is：

With impact of the four star constellation analysis inter-satellite link numbers to timing tracking accuracy, it is 0m in the average of H_2O maser error, marks When quasi- difference is 2m, emulated using the method for centralized Kalman filter or distributing Kalman filtering, it is a length of during emulation 86400s, the average of the error of the time synchronized obtained by centralized Kalman filter is -0.12ns, and standard deviation is 0.5ns, and is divided The average of the error of the time synchronized obtained by scattered formula Kalman filtering is -0.09ns, and standard deviation is -0.39ns；

When inter-satellite link number is three, the average -0.12ns of the error of gained time synchronized, standard deviation is 0.34ns；

When inter-satellite link number is four, the average -0.12ns of the error of gained time synchronized, standard deviation is 0.31ns；

When inter-satellite link number is five, the average -0.11ns of the error of gained time synchronized, standard deviation is 0.28ns；

When inter-satellite link number is six, the average -0.10ns of the error of gained time synchronized, standard deviation is 0.26ns.

4. according to claim 3 based on bidirectional ranging method for synchronizing time between star, its Intersatellite Link number is only selected as three.