CN107024211B - A kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method - Google Patents

Abstract

The invention relates to a combined navigation method of angle measurement/differential velocity measurement/differential distance measurement of a deep space probe. First, the state model of the spacecraft is established according to the orbital dynamics, and then the measurement of the angular distance of starlight is obtained by using the angle sensor, the measurement of the pulse arrival time by the X-ray pulsar detector, and the measurement of the astronomical Doppler velocity by the spectrometer , and then establish the starlight angular distance measurement model, the differential pulse arrival time measurement model and the differential astronomical Doppler velocity measurement model based on these measurements. The position and velocity of the spacecraft are estimated using UKF filtering after discretization. The invention belongs to the field of autonomous navigation of spacecraft. The invention has high estimation accuracy and has important practical significance for autonomous navigation of spacecraft.

Description

A combined navigation method of angle measurement/differential velocity measurement/differential ranging measurement for deep space probes

technical field

The invention belongs to the field of autonomous navigation of spacecraft, and relates to an autonomous astronomical navigation method based on the measurement of starlight angular distance, differential pulse arrival time, and differential astronomical Doppler velocity.

Background technique

my country plans to launch a Mars probe in 2020, so Mars exploration will attract more and more attention. For deep space exploration missions, navigation accuracy has an important impact on the success or failure of the mission. At present, the navigation information is mainly provided for the spacecraft through the ground measurement and control station. As the distance between the spacecraft and the earth increases, the round-trip delay of signal transmission through the ground monitoring and control station will become larger and larger. In addition, the sun transit will cause signal interruption. Therefore, it is necessary to improve the autonomous navigation capability of the spacecraft.

The autonomous navigation methods that can be used for deep space probes mainly include astronomical angle measurement navigation method, X-ray pulsar ranging navigation method and astronomical Doppler speed measurement navigation method. The astronomical angle measurement navigation method obtains the position information of the spacecraft by measuring the angle between the spacecraft and the near celestial body and the navigation star. However, the navigation accuracy of this method decreases as the distance between the spacecraft and the near object increases. X-ray pulsar ranging navigation can provide high-precision position information, and the navigation accuracy is not affected by the position between the spacecraft and the celestial body. However, because the signals of X-ray pulsars are relatively weak, it usually needs to be folded through a long time epoch to obtain the quantity measurement. In addition, the angular position error of the pulsar and the clock error of the satellite-borne atomic clock will affect the navigation accuracy. Astro Doppler velocity measurement and navigation obtains the velocity information of the spacecraft by measuring the spectral frequency shift caused by the radial motion between the spacecraft and the star. However, this method cannot provide position information, and the dynamic change of stellar spectrum will affect its navigation accuracy.

Contents of the invention

The present invention proposes a deep-space probe angle measurement/differential speed measurement/differential ranging combination navigation method, which uses starlight angular distance measurement to provide absolute position information, and uses time difference X-ray pulsar pulse arrival time measurement to weaken the influence of system errors , provide relative position information, and use time-difference astronomical Doppler velocity measurements to weaken the influence of dynamic changes in stellar spectra and provide velocity information. Combining the three measurements through UKF filtering provides high-precision navigation information for deep space probes.

The technical solution adopted by the present invention to solve the technical problem is: establish the state model of the spacecraft according to the orbital dynamics, use the angle measuring sensor to obtain the measurement of the starlight angular distance, use the X-ray pulsar detector to obtain the measurement of the pulse arrival time, The astronomical Doppler velocity measurement is obtained by using the spectrometer, and the starlight angular distance measurement model, the differential pulse arrival time measurement model and the differential astronomical Doppler velocity measurement model are respectively established based on these measurements. The position and velocity of the spacecraft are estimated using UKF filtering after discretization.

Specifically include the following steps:

1. Establish a system state model based on orbital dynamics

The motion of the spacecraft during the approach to Mars is described as a heliocentric three-body model, and other perturbations are considered as process noise. The dynamic model in the sun center inertial coordinate system (J2000.0) can be written as:

where ||·|| represents the 2-norm of the vector, ||·|| ³ represents the cube of ||·||, r and v are the position and velocity of the spacecraft relative to the sun. μ _s and μ _m are the gravitational constants of the sun and Mars respectively, r _m is the position vector of Mars relative to the sun, r _sm = rr _m is the position vector of the spacecraft relative to Mars. w is the process noise caused by various disturbances. The state model can be obtained from the above formula as follows:

Among them, the state quantity X=[r,v] ^T is the position and velocity of the spacecraft in the solar inertial coordinate system, is the derivative of the state quantity X, for time t f(X(t), t) is the nonlinear continuous state transfer function of the system, w is the process noise, and w(t) is w at time t.

2. Judging whether there is pulse arrival time measurement

Since the pulse signal requires a longer observation period, compared with the starlight angular distance measurement and astronomical Doppler velocity measurement, the pulse arrival time measurement has a longer sampling period. Therefore, the sampling period of starlight angular distance measurement and astronomical Doppler velocity measurement is used as the filtering period. When there is no pulse arrival time measurement at the time of filtering, the system model composed of the state model, the starlight angular distance measurement model, and the differential astronomical Doppler velocity measurement model is used to obtain the posteriori of the spacecraft in the inertial system relative to the sun through UKF filtering State estimation and posterior error covariance. When the time of arrival of the pulse is measured at the time of filtering, the system model composed of the state model, the measurement model of the starlight angular distance, the measurement model of the differential astronomical Doppler velocity, and the measurement model of the time of arrival of the differential pulse is obtained by the UKF filter. The posterior state estimation of the spacecraft relative to the sun and the posterior error covariance.

3. Establish a measurement model of starlight angular distance

Use the angular sensor to obtain the starlight angular distance between the spacecraft and Phobos, Deimos and their background stars, and use these starlight angular distances as measurements to establish a measurement model:

Among them, α _p1 and α _p2 are the starlight angular distances between the spacecraft and Phobos and the two background stars respectively, α _d1 and α _d2 are the starlight angular distances between the spacecraft and Deimos and the two background stars respectively, r _sp , rs _sd are the position vectors of Phobos and Deimos relative to the spacecraft, s ₁ , s ₂ are the direction vectors of the two stars in the inertial system, r _p , _rd are the The position vector of Pallas relative to the Sun.

Taking these starlight angular distances as quantity measurement Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T , the expression of the starlight angular distance measurement model can be established:

Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T =h ₁ [X(t),t]+v ₁ (t) (4)

where h ₁ (·) represents the nonlinear continuous measurement function of starlight angular distance, and v ₁ (t) represents the measurement noise of starlight angular distance at time t.

4. Establish a measurement model of differential astronomical Doppler velocity

Use the spectrometer to obtain the frequency shift of the solar spectrum, and obtain the radial velocity of the spacecraft relative to the sun according to the frequency shift, and use this as a quantity measurement to establish a measurement model:

where v _r represents the measurement of the radial velocity of the spacecraft relative to the sun, v _rt represents the real value of the radial velocity of the spacecraft relative to the sun, υ _p represents the disturbance term caused by the frequency fluctuation of the solar spectrum, and υ _m represents the astronomical Doppler velocity measurement noise.

Establish a measurement model of differential astronomical Doppler velocity:

where v _r (t) and v _r (t-1) are the measurements of the radial velocity of the spacecraft relative to the sun at time t and t-1 respectively, and v _rt (t) and v _rt (t-1) are t The real value of the radial velocity of the spacecraft relative to the sun at time t and t-1, υ _p (t) and υ _p (t-1) are the disturbance items caused by the frequency fluctuation of the solar spectrum at time t and t-1, respectively, υ _m (t) and υ _m (t-1) are the measurement noise at time t and time t-1 respectively, and △υ _p (t)=υ _p (t)-υ _p (t-1) is the difference between υ _p , △υ _m (t)=υ _m (t)-υ _m (t-1) is the residual of υ _m after difference.

Taking the differential astronomical Doppler velocity as the quantity measurement Z ₂ =[v _r (t)-v _r (t-1)], the expression of the differential astronomical Doppler velocity measurement model can be established:

Z ₂ =[v _r (t)-v _r (t-1)]=h ₂ [X(t),X(t-1)]+v ₂ (t) (7)

Where h ₂ (·) represents the nonlinear continuous measurement function of the differential astronomical Doppler velocity, and v ₂ (t) represents the measurement error of the differential astronomical Doppler velocity at time t. Use the posterior state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as:

Z ₂ =h ₂ [X(t),t]+v ₂ (t) (8)

5. Establish a measurement model of differential pulse arrival time

The X-ray pulsar detector is used to obtain the pulse arrival time measurement, and the pulse arrival time is used as the measurement to establish the measurement model:

Among them, t _b represents the time when the pulsar pulse reaches the barycenter of the solar system, t _SC represents the time when the pulsar pulse reaches the spacecraft, r _S represents the position vector of the spacecraft relative to the barycenter of the solar system, c represents the speed of light, and n represents the pulsar’s velocity in the inertial system Direction vector, D ₀ represents the distance from the pulsar to the barycenter of the solar system, b represents the position vector of the barycenter of the solar system relative to the sun.

Establish a measurement model for the differential pulse arrival time:

Where τ(t) represents the arrival time of the differential pulse at time t, t _b (t) and t _b (t-1) represent the time for the pulsar pulse to reach the center of mass of the solar system at time t and t-1 respectively, and t _SC (t) and t _SC (t-1) denote the arrival time of the pulsar pulse to the spacecraft at time t and time t-1 respectively.

Taking the differential pulse arrival time as the quantity measurement Z ₃ =[τ(t)], the expression of the differential pulse arrival time measurement model can be established:

Z ₃ =[τ(t)]=h ₃ [X(t),X(t-1)]+v ₃ (t) (11)

Where h ₃ (·) represents the nonlinear continuous measurement function of the differential pulse arrival time, and v ₃ (t) represents the measurement noise of the differential pulse arrival time at time t. Use the posterior state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as:

Z ₃ =h ₃ [X(t),t]+v ₃ (t) (12)

6. Perform discretization

When there is no pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z ₁₂ =[Z ₁ ,Z ₂ ] ^T , the measurement noise v ₁₂ =[v ₁ ,v ₂ ] ^T , and the navigation system model is :

where h ₁₂ (·) represents the non-linear continuous measurement function of the navigation system when there is no pulse arrival time measurement. Discretize formula (13):

Among them, X _k and Z _12k respectively represent the state quantity of the system at time k and the quantity measurement of the system when there is no pulse arrival time measurement, and F(X _k-1 ,k-1) is f(X(t),t) after the discretization The nonlinear state transfer function of , H ₁₂ (X _k ,k) is the nonlinear measurement function after discretization of h ₁₂ [X(t),t], W _k and V _12k respectively represent w(t) and v ₁₂ (t) Equivalent noise after discretization.

When there is pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z=[Z ₁ ,Z ₂ ,Z ₃ ] ^T , and the measurement noise v=[v ₁ ,v ₂ ,v ₃ ] ^T , The navigation system model is:

Where h(·) represents the nonlinear continuous measurement function of the navigation system when there is pulse arrival time measurement. Discretize formula (15):

Where Z _k represents the quantity measurement of the system at time k, H(X _k ,k) is the nonlinear measurement function after h[X(t),t] is discretized, and V _k represents the equivalent noise after v(t) is discretized .

7. Perform UKF filtering to obtain the position and velocity estimation of the spacecraft

When there is no pulse arrival time measurement at the filtering time, the discretized system model (14) is filtered by UKF to obtain the posterior state estimation of the spacecraft relative to the sun in the inertial system and the posterior error covariance in are the position and velocity posteriori estimates of the spacecraft relative to the sun at the kth moment, respectively. When the time of arrival of the pulse is measured at the time of filtering, the discretized system model (16) is filtered by UKF to obtain and Will and output, while returning these estimated values to the filter for obtaining the output at time k+1.

The principle of the invention is: using starlight angular distance to obtain fully observable spacecraft position information, but the accuracy is not high. The differential pulse arrival time is obtained by using the measurement of the pulse arrival time obtained at the front and rear times, and the influence of the pulsar angular position error and the satellite-borne atomic clock difference on the navigation accuracy is weakened, and high-precision position information is obtained. The differential astronomical Doppler velocity is obtained by using the astronomical Doppler velocity measurement obtained at the front and rear moments, and the influence of the dynamic change of the stellar spectrum on the navigation accuracy is weakened, and high-precision velocity information is obtained. Establish the state model of the spacecraft according to the orbital dynamics, establish the starlight angular distance measurement model, the differential pulse arrival time measurement model and the differential astronomical Doppler velocity measurement model, and use the UKF filter after discretization to obtain high-precision spacecraft position and velocity.

Compared with the prior art, the present invention has the following advantages: (1) realizing high-precision autonomous navigation of spacecraft. (2) Using the differential pulse arrival time to obtain high-precision position information. (3) Using differential astronomical Doppler velocity to obtain high-precision velocity information.

Description of drawings

Fig. 1 is a flow chart of the combined navigation method of angle measurement/differential speed measurement/differential distance measurement of the deep space probe in the present invention.

FIG. 2 is a schematic diagram of a starlight angular distance measurement model in the present invention.

Fig. 3 is a schematic diagram of the principle of X-ray pulsar ranging and navigation in the present invention.

Detailed ways

Figure 1 shows the system flow chart of the combined navigation method of angle measurement/differential speed measurement/differential distance measurement of deep space probes. Here, taking the approaching section of Mars exploration as an example, the specific implementation process of the present invention is described in detail:

1. Establish a system state model based on orbital dynamics

The motion of the spacecraft during the approach to Mars is described as a heliocentric three-body model, and other perturbations are considered as process noise. The dynamic model in the sun center inertial coordinate system (J2000.0) can be written as:

where ||·|| represents the 2-norm of the vector, ||·|| ³ represents the cube of ||·||, r and v are the position and velocity of the spacecraft relative to the sun. μ _s and μ _m are the gravitational constants of the sun and Mars respectively, r _m is the position vector of Mars relative to the sun, r _sm = rr _m is the position vector of the spacecraft relative to Mars. w is the process noise caused by various disturbances. The state model can be obtained from the above formula as follows:

Among them, the state quantity X=[r,v] ^T is the position and velocity of the spacecraft in the solar inertial coordinate system, is the derivative of the state quantity X, for time t f(X(t), t) is the nonlinear continuous state transfer function of the system, w is the process noise, and w(t) is w at time t.

2. Judging whether there is pulse arrival time measurement

Since the pulse signal requires a longer observation period, compared with the starlight angular distance measurement and astronomical Doppler velocity measurement, the pulse arrival time measurement has a longer sampling period. Therefore, the sampling period of starlight angular distance measurement and astronomical Doppler velocity measurement is used as the filtering period. When there is no pulse arrival time measurement at the time of filtering, the system model composed of the state model, the starlight angular distance measurement model, and the differential astronomical Doppler velocity measurement model is used to obtain the posteriori of the spacecraft in the inertial system relative to the sun through UKF filtering State estimation and posterior error covariance. When the time of arrival of the pulse is measured at the time of filtering, the system model composed of the state model, the measurement model of the starlight angular distance, the measurement model of the differential astronomical Doppler velocity, and the measurement model of the time of arrival of the differential pulse is obtained by the UKF filter. The posterior state estimation of the spacecraft relative to the sun and the posterior error covariance.

3. Establish a measurement model of starlight angular distance

The angular distance between the spacecraft and Phobos, Deimos and their background stars is obtained by using the angle sensor, and the measurement model is established by using these angular distances as measurements. Figure 2 shows the schematic diagram of the starlight angular distance measurement model. Among them, r _sp , _rsd are the position vectors of Phobos and Deimos relative to the spacecraft, s ₁ , s ₂ are the direction vectors of the two stars in the inertial system, r _p , _rd are Phobos , the position vector of Deimos relative to the sun. The starlight angular distance measurement model can be written as:

Among them, α _p1 and α _p2 are the starlight angular distances between the spacecraft and Phobos and the two background stars, respectively, and α _d1 and α _d2 are the starlight angular distances between the spacecraft and Deimos and the two background stars, respectively. Taking these starlight angular distances as quantity measurement Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T , the expression of the starlight angular distance measurement model can be established:

Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T =h ₁ [X(t),t]+v ₁ (t) (4)

where h ₁ (·) represents the nonlinear continuous measurement function of starlight angular distance, and v ₁ (t) represents the measurement noise of starlight angular distance at time t.

4. Establish a measurement model of differential astronomical Doppler velocity

Use the spectrometer to obtain the frequency shift of the solar spectrum, and obtain the radial velocity of the spacecraft relative to the sun according to the frequency shift, and use this as a quantity measurement to establish a measurement model:

where v _r represents the measurement of the radial velocity of the spacecraft relative to the sun, v _rt represents the real value of the radial velocity of the spacecraft relative to the sun, υ _p represents the disturbance term caused by the frequency fluctuation of the solar spectrum, and υ _m represents the astronomical Doppler velocity measurement noise.

Establish a measurement model of differential astronomical Doppler velocity:

where v _r (t) and v _r (t-1) are the measurements of the radial velocity of the spacecraft relative to the sun at time t and t-1 respectively, and v _rt (t) and v _rt (t-1) are t The real value of the radial velocity of the spacecraft relative to the sun at time t and t-1, υ _p (t) and υ _p (t-1) are the disturbance items caused by the frequency fluctuation of the solar spectrum at time t and t-1, respectively, υ _m (t) and υ _m (t-1) are the measurement noise at time t and time t-1 respectively, and △υ _p (t)=υ _p (t)-υ _p (t-1) is the difference between υ _p , △υ _m (t)=υ _m (t)-υ _m (t-1) is the residual of υ _m after difference.

Taking the differential astronomical Doppler velocity as the quantity measurement Z ₂ =[v _r (t)-v _r (t-1)], the expression of the differential astronomical Doppler velocity measurement model can be established:

Z ₂ =[v _r (t)-v _r (t-1)]=h ₂ [X(t),X(t-1)]+v ₂ (t) (7)

Where h ₂ (·) represents the nonlinear continuous measurement function of the differential astronomical Doppler velocity, and v ₂ (t) represents the measurement error of the differential astronomical Doppler velocity at time t. Use the posterior state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as:

Z ₂ =h ₂ [X(t),t]+v ₂ (t) (8)

5. Establish a measurement model of differential pulse arrival time

Figure 3 shows a schematic diagram of the principle of X-ray pulsar ranging and navigation. where t _SC and t _b represent the time when the i-th pulsar pulse reaches the spacecraft and the solar system barycenter (SSB), respectively, n is the direction vector of the i-th pulsar in the heliocentric inertial system, and r _S is the detector relative to the solar system barycenter The position vector of , can be expressed as r _S =rb, b is the position vector of SSB relative to the sun, and c represents the speed of light. It can be seen from the figure that c·(t _b -t _SC ) can be regarded as the projection of r _S on n. Considering the relativistic and geometric effects, the time transition model can be expressed as:

Among them, D ₀ represents the distance from the pulsar to the barycenter of the solar system, the first term on the right side of the equation is the Doppler delay caused by the geometric distance, and the second term represents the time delay caused by the X-rays reaching the solar system in parallel, and the first two items are usually collectively called the Roemer delay, The third term represents the time delay caused by the bending of light rays under the action of the sun's gravitational field, called the Shapiro delay.

Establish a measurement model for the differential pulse arrival time:

Where τ(t) represents the arrival time of the differential pulse at time t, t _b (t) and t _b (t-1) represent the time for the pulsar pulse to reach the center of mass of the solar system at time t and t-1 respectively, and t _SC (t) and t _SC (t-1) denote the arrival time of the pulsar pulse to the spacecraft at time t and time t-1 respectively.

Taking the differential pulse arrival time as the quantity measurement Z ₃ =[τ(t)], the expression of the differential pulse arrival time measurement model can be established:

Z ₃ =[τ(t)]=h ₃ [X(t),X(t-1)]+v ₃ (t) (11)

Where h ₃ (·) represents the nonlinear continuous measurement function of the differential pulse arrival time, and v ₃ (t) represents the measurement noise of the differential pulse arrival time at time t. Use the posterior state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as:

Z ₃ =h ₃ [X(t),t]+v ₃ (t) (12)

6. Perform discretization

When there is no pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z ₁₂ =[Z ₁ ,Z ₂ ] ^T , the measurement noise v ₁₂ =[v ₁ ,v ₂ ] ^T , and the navigation system model is :

where h ₁₂ (·) represents the non-linear continuous measurement function of the navigation system when there is no pulse arrival time measurement. Discretize formula (13):

Among them, X _k and Z _12k respectively represent the state quantity of the system at time k and the quantity measurement of the system when there is no pulse arrival time measurement, and F(X _k-1 ,k-1) is f(X(t),t) after the discretization The nonlinear state transfer function of , H ₁₂ (X _k ,k) is the nonlinear measurement function after discretization of h ₁₂ [X(t),t], W _k and V _12k respectively represent w(t) and v ₁₂ (t) Equivalent noise after discretization.

When there is pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z=[Z ₁ ,Z ₂ ,Z ₃ ] ^T , and the measurement noise v=[v ₁ ,v ₂ ,v ₃ ] ^T , The navigation system model is:

Where h(·) represents the nonlinear continuous measurement function of the navigation system when there is pulse arrival time measurement. Discretize formula (15):

Where Z _k represents the quantity measurement of the system at time k, H(X _k ,k) is the nonlinear measurement function after h[X(t),t] is discretized, and V _k represents the equivalent noise after v(t) is discretized .

7. Perform UKF filtering to obtain the position and velocity estimation of the spacecraft

The discretized system model is filtered by UKF, and the specific steps are as follows.

A. Initialize the state quantity and state error variance matrix P ₀

In the formula, is the estimated value of the position and velocity of the spacecraft at the 0th moment (initial moment), and X ₀ is the real value of the position and velocity of the spacecraft at the 0th moment.

B. Select sigma sampling point

exist A series of sampling points are selected nearby, and the mean and covariance of these sample points are respectively and The state variable is 6×1 dimension, then select 13 sample points And their weights w ₀ , w ₁ ..., w ₁₂ are as follows:

where τ represents the scaling parameter, Indicates taking the i-th row or column of the square root matrix.

C. Transfer sigma sampling points and obtain prior estimates and prior error covariance

One-step forecast for each sample point for:

merge all Get a prior state estimate for:

prior error covariance for:

In the formula, Q _k is the noise covariance matrix of the state model at time k.

D. Measurement update

According to the measurement equation, calculate each sampling point The pre-measurement of the When there is no time-of-arrival measurement of pulses at the filtering instant:

When there is a time-of-arrival measurement of pulses at the filtering instant:

merge all Obtain the predicted measurement Y _k as:

Calculate the predicted measurement covariance P _yy,k and the cross-covariance P _xy,k :

where R _k is the measurement noise covariance matrix of the system at time k. Calculate the filter gain K _k as:

Computing the posterior state estimate

Calculate the posterior error covariance

Will and output, while returning these estimated values to the filter for obtaining the output at time k+1.

The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims (1)

1. A deep-space probe angle measurement/differential speed measurement/differential ranging combined navigation method, characterized in that: the state model of the spacecraft is established according to orbital dynamics, the angle measurement sensor is used to obtain the starlight angular distance measurement, and the X The ray pulsar detector obtains the pulse arrival time measurement, and the spectrometer obtains the astronomical Doppler velocity measurement. Based on these measurements, the starlight angular distance measurement model, the differential pulse arrival time measurement model and the differential astronomical Doppler velocity are respectively established. Measurement model; use UKF filter to estimate the position and velocity of the spacecraft after discretization; specifically include the following steps: ①Establish a system state model based on orbital dynamics The motion of the spacecraft in the Mars approach segment is described as a three-body model with the sun as the center of the celestial body, and other disturbances are regarded as process noise; the dynamic model in the sun-centered inertial coordinate system can be written as: Where ||·|| represents the 2-norm of the vector, ||·|| ³ represents the cube of ||·||, r and v are the position and velocity of the spacecraft relative to the sun; μ _s and μ _m are the sun and The gravitational constant of Mars, r _m is the position vector of Mars relative to the sun, r _sm = rr _m is the position vector of the spacecraft relative to Mars; w is the process noise caused by various disturbances; the state model can be obtained from the above formula as follows: Among them, the state quantity X=[r,v] ^T is the position and velocity of the spacecraft in the solar inertial coordinate system, is the derivative of the state quantity X, for time t f(X(t),t) is the nonlinear continuous state transfer function of the system, w is the process noise, and w(t) is w at time t; ②Judge whether there is pulse arrival time measurement Due to the longer observation period required by the pulse signal, compared with the measurement of starlight angular distance and astronomical Doppler velocity measurement, the sampling period of pulse arrival time measurement is longer; therefore, the measurement of starlight angular distance and astronomical multi- The sampling period of the Doppler velocity measurement is used as the filtering period; when there is no pulse arrival time measurement at the time of filtering, the system model composed of the state model, the starlight angular distance measurement model, and the differential astronomical Doppler velocity measurement model is passed through the UKF Filter to obtain the posterior state estimation and posterior error covariance of the spacecraft relative to the sun in the inertial system; The system model composed of the measurement model and the differential pulse arrival time measurement model obtains the posterior state estimation and posterior error covariance of the spacecraft relative to the sun in the inertial system through UKF filtering; ③Establish the measurement model of starlight angular distance Use the angular sensor to obtain the starlight angular distance between the spacecraft and Phobos, Deimos and their background stars, and use these starlight angular distances as measurements to establish a measurement model: Among them, α _p1 and α _p2 are the starlight angular distances between the spacecraft and Phobos and the two background stars respectively, α _d1 and α _d2 are the starlight angular distances between the spacecraft and Deimos and the two background stars respectively, r _sp and r _sd are respectively the position vectors of Phobos and Deimos relative to the spacecraft, s ₁ and s ₂ are respectively the direction vectors of the two stars in the inertial system, r _p and r _d are respectively the position vectors of Phobos and Mars The position vector of Saturn relative to the sun; Taking these starlight angular distances as quantity measurement Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T , the expression of the starlight angular distance measurement model can be established: Z ₁ =[α _p1 ,α _p2 ,α _d1 ,α _d2 ] ^T =h ₁ [X(t),t]+v ₁ (t) (4) where h ₁ (·) represents the nonlinear continuous measurement function of starlight angular distance, v ₁ (t) represents the measurement noise of starlight angular distance at time t; ④Establish the measurement model of differential astronomical Doppler velocity Use the spectrometer to obtain the frequency shift of the solar spectrum, and obtain the radial velocity of the spacecraft relative to the sun according to the frequency shift, and use this as a quantity measurement to establish a measurement model: where v _r represents the measurement of the radial velocity of the spacecraft relative to the sun, v _rt represents the real value of the radial velocity of the spacecraft relative to the sun, υ _p represents the disturbance term caused by the frequency fluctuation of the solar spectrum, and υ _m represents the astronomical Doppler velocity measurement noise; Establish a measurement model of differential astronomical Doppler velocity: where v _r (t) and v _r (t-1) are the measurements of the radial velocity of the spacecraft relative to the sun at time t and t-1 respectively, and v _rt (t) and v _rt (t-1) are t The real value of the radial velocity of the spacecraft relative to the sun at time t and t-1, υ _p (t) and υ _p (t-1) are the disturbance items caused by the frequency fluctuation of the solar spectrum at time t and t-1 respectively, υ _m (t) and υ _m (t-1) are the measurement noise at time t and t-1 respectively, and Δυ _p (t)=υ _p (t)-υ _p (t-1) is the difference of υ _p Residual error, Δυ _m (t)=υ _m (t)-υ _m (t-1) is the residual error of υ _m after difference; Taking the differential astronomical Doppler velocity as the quantity measurement Z ₂ =[v _r (t)-v _r (t-1)], the expression of the differential astronomical Doppler velocity measurement model can be established: Z ₂ =[v _r (t)-v _r (t-1)]=h ₂ [X(t),X(t-1)]+v ₂ (t) (7) where h ₂ (·) represents the nonlinear continuous measurement function of the differential astronomical Doppler velocity, v ₂ (t) represents the measurement error of the differential astronomical Doppler velocity at time t; the posteriori state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as: Z ₂ =h ₂ [X(t),t]+v ₂ (t) (8) ⑤Establish the measurement model of differential pulse arrival time The X-ray pulsar detector is used to obtain the pulse arrival time measurement, and the pulse arrival time is used as the measurement to establish the measurement model: Among them, t _b represents the time when the pulsar pulse reaches the barycenter of the solar system, t _SC represents the time when the pulsar pulse reaches the spacecraft, _rS represents the position vector of the spacecraft relative to the barycenter of the solar system, c represents the speed of light, and n represents the velocity of the pulsar in the inertial system Direction vector, D ₀ represents the distance from the pulsar to the barycenter of the solar system, b represents the position vector of the barycenter of the solar system relative to the sun; Establish a measurement model for the differential pulse arrival time: Among them, τ(t) represents the differential pulse arrival time at time t, t _b (t) and t _b (t-1) respectively represent the time for the pulsar pulse to reach the center of mass of the solar system at time t and t-1, and t _SC (t) and t _SC (t-1) represent the arrival time of the pulsar pulse to the spacecraft at time t and time t-1 respectively; Taking the differential pulse arrival time as the quantity measurement Z ₃ =[τ(t)], the expression of the differential pulse arrival time measurement model can be established: Z ₃ =[τ(t)]=h ₃ [X(t),X(t-1)]+v ₃ (t) (11) where h ₃ (·) represents the nonlinear continuous measurement function of the differential pulse arrival time, v ₃ (t) represents the measurement noise of the differential pulse arrival time at time t; the posterior state estimation at time t-1 Instead of X(t-1), the expression of the differential pulse arrival time measurement model can be written as: Z ₃ =h ₃ [X(t),t]+v ₃ (t) (12) ⑥ Discretization When there is no pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z ₁₂ =[Z ₁ ,Z ₂ ] ^T , the measurement noise v ₁₂ =[v ₁ ,v ₂ ] ^T , and the navigation system model is : Among them, h ₁₂ (·) represents the nonlinear continuous measurement function of the navigation system when there is no pulse arrival time measurement; the formula is discretized: Among them, X _k and Z _12k represent the state quantity of the system at time k and the quantity measurement of the system when there is no pulse arrival time measurement, and F(X _k-1 ,k-1) is f(X(t),t) after the discretization The nonlinear state transfer function of , H ₁₂ (X _k ,k) is the nonlinear measurement function after discretization of h ₁₂ [X(t),t], W _k and V _12k respectively represent w(t) and v ₁₂ (t) The equivalent noise after discretization; When there is pulse arrival time measurement at the time of filtering, it is assumed that the navigation system measurement Z=[Z ₁ ,Z ₂ ,Z ₃ ] ^T , and the measurement noise v=[v ₁ ,v ₂ ,v ₃ ] ^T , The navigation system model is: Among them, h( ) represents the nonlinear continuous measurement function of the navigation system when the pulse arrival time is measured; the formula is discretized: Where Z _k represents the quantity measurement of the system at time k, H(X _k ,k) is the nonlinear measurement function after h[X(t),t] is discretized, and V _k represents the equivalent noise after v(t) is discretized ; ⑦ Perform UKF filtering to obtain the position and velocity estimation of the spacecraft When there is no pulse arrival time measurement at the time of filtering, filter the discretized system model formula through UKF to obtain the posterior state estimation of the spacecraft relative to the sun in the inertial system and the posterior error covariance in are the position and velocity posteriori estimates of the spacecraft relative to the sun at the k-th moment; when the time of arrival of the pulse is measured at the filtering time, the discretized system model can be obtained by filtering the UKF and Will and output, while returning these estimated values to the filter for obtaining the output at time k+1.