CN113074741A - Pulsar azimuth error estimation augmented state algorithm - Google Patents

Pulsar azimuth error estimation augmented state algorithm Download PDF

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CN113074741A
CN113074741A CN202110291104.2A CN202110291104A CN113074741A CN 113074741 A CN113074741 A CN 113074741A CN 202110291104 A CN202110291104 A CN 202110291104A CN 113074741 A CN113074741 A CN 113074741A
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pulsar
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CN113074741B (en
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蔡光斌
肖永强
徐刚锋
杨小冈
王宏力
杨波
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Rocket Force University of Engineering of PLA
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Abstract

The invention specifically discloses an augmentation state algorithm for pulsar azimuth error estimation, which comprises the following steps: establishing a time conversion model of the pulsar based on a solar system centroid coordinate system; selecting right ascension errors and declination errors of the pulsar azimuth information as state variables, and establishing a state equation and an observation equation of a traditional pulsar azimuth error estimation algorithm by combining a time conversion model; the satellite position error scalar, the clock error and the clock error drift rate are expanded to be new state variables, an expanded state algorithm state equation and an observation equation of pulsar azimuth error estimation are obtained, and the satellite position error and the clock error are considered in the algorithm; and processing the pulse arrival time observed quantity by using a Kalman filtering algorithm to obtain a state variable estimated value, and compensating system deviation caused by satellite position errors and clock errors in the algorithm estimation process so as to improve the estimation precision of the pulsar azimuth errors.

Description

Pulsar azimuth error estimation augmented state algorithm
Technical Field
The invention relates to the field of pulsar azimuth error estimation, in particular to an algorithm for estimating pulsar azimuth errors by using a beacon satellite.
Background
X-ray pulsar navigation is a new autonomous navigation, and mainly relies on a detector on a spacecraft to detect radiation signals of pulsars and compares the radiation signals with pulsar information obtained through long-term observation to realize positioning of the spacecraft. Because the navigation system is completely passive, the navigation system has strong anti-interference capability, is not easily interfered by human factors and the like, has high stability and strong autonomy, and navigation errors are not accumulated along with time. However, the pulsar navigation still has some problems to be solved urgently, such as weak pulse signals, long navigation filtering period, pulsar azimuth error influence and the like. The pulsar azimuth error is an important reason for influencing pulsar navigation accuracy, and is influenced by the accuracy of observation technology and equipment instruments at present, so that the pulsar azimuth information accuracy is difficult to be greatly improved only by means of observation in a short time.
Through research, the learners find that the 0.001 ″ azimuth error causes a navigation error of hundreds of meters, thereby seriously affecting the navigation accuracy. Therefore, the pulsar azimuth error is reduced, the pulsar azimuth information accuracy is improved, and the method has important theoretical significance for improving the pulsar navigation accuracy.
To reduce the influence of pulsar bearing errors to improve navigation accuracy, many scholars have conducted a great deal of research on the problem of pulsar bearing errors.
The estimation of the pulsar azimuth error by using the satellite is firstly proposed by doctor Sun Germination of the university of defense science and technology, and the inventor points out that the estimation of the pulsar azimuth error by using the beacon satellite with a known position can obtain an estimation value with higher accuracy than that of observation on the ground. However, the algorithm is accurate and error-free based on the satellite position information, but in a specific process, an error is definitely generated in the determination of the specific satellite position information, which is a satellite position error, and further, the estimation accuracy is affected. The great promise of the university of rocket military engineering and the like is that when the beacon satellite is used for estimating the azimuth error, the satellite position error scalar is expanded into a new state variable, and the satellite position error is corrected. Meanwhile, the TSKF algorithm is designed to correct the influence of the pulsar movement and the satellite position error on the estimation of the pulsar azimuth error, and the algorithm adopts a CV motion model to describe the pulsar movement. However, the algorithm does not consider the clock error problem, and in pulsar azimuth error estimation, the clock error also affects the estimation accuracy. Although Sundaming, Wanglong, etc. correct the effects of clock errors in pulsar navigation and its combined navigation with inertial navigation, Doppler navigation, etc. However, from the published literature, the clock error in the estimation process of the pulsar azimuth error has not been studied by a scholars. At present, scholars develop a series of researches on pulsar azimuth error estimation algorithms and obtain a lot of results, but the problems that clock errors and satellite position errors exist simultaneously in the estimation process are not considered, and further researches are needed.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: how to estimate and compensate the satellite position error and clock error existing at the same time in the estimation process of the pulsar azimuth error, the influence of the pulsar position error and the clock error on the estimation is reduced or even eliminated, and the estimation precision of the pulsar azimuth error is further improved.
In order to achieve the above object, the present invention provides an augmented state algorithm for pulsar azimuth error estimation, comprising the following steps:
step 1: establishing a time conversion model of the pulsar based on a solar system centroid coordinate system;
step 2: selecting right ascension errors and declination errors of the pulsar azimuth information as state variables, and establishing a state equation and an observation equation of a traditional pulsar azimuth error estimation algorithm by combining the time conversion model in the step 1;
and step 3: the satellite position error scalar, the clock error and the clock error drift rate are expanded to be new state variables, an expanded state algorithm state equation and an observation equation of pulsar azimuth error estimation are obtained, and the satellite position error and the clock error are considered at the same time by the expanded state algorithm;
and 4, step 4: and processing the pulse arrival time observed quantity by using a Kalman filtering algorithm to obtain a state variable estimated value, and compensating system deviation caused by satellite position error and clock error in the estimation process of the augmented state algorithm so as to improve the estimation precision of the pulsar azimuth error.
Preferably, in step 1, the time conversion model of the pulsar is established based on the solar system centroid coordinate system as follows:
Figure BDA0002982734410000031
Figure BDA0002982734410000032
c(tSSB-t'SSB)＝Δn·rsat
of formula (II) to'SSBTime, t, of arrival of pulse signal at origin of coordinate system of centroid of solar system measured by X-ray detector installed on satelliteSSBIs the time t 'when the pulse signal really reaches the origin of the solar system centroid coordinate system'satDenoted the time of arrival of the pulse obtained for the beacon satellite clock, n' denotes the unit direction vector with error obtained for the measurement, rsatIs the position vector of the satellite in BCRS, c is the speed of light, o (t) is the higher-order term caused by the annual parallax effect and the like, tsatThe real time of the pulse reaching the satellite, n is the real unit direction vector of the pulsar, and Δ n is the pulsar azimuth error.
Preferably, in step 2, the process of establishing the state equation and the observation equation of the conventional pulsar azimuth error estimation algorithm is as follows:
the pulsar unit direction vector can be expressed as:
Figure BDA0002982734410000033
in the formula, alpha and beta are the right ascension and the declination of the pulse star orientation in the solar system centroid coordinate system;
the unit direction vector with error obtained from the observation is:
Figure BDA0002982734410000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002982734410000035
and
Figure BDA0002982734410000036
the red longitude and the red latitude of the pulsar are measured; if the declination error and the declination error are Δ α and Δ β, respectively, the true declination and declination values satisfy the following relationship:
Figure BDA0002982734410000041
Figure BDA0002982734410000042
Figure BDA0002982734410000043
the pulsar azimuth error Δ n is:
Figure BDA0002982734410000044
taking the state variable as X ═ Delta alpha Delta beta]TThen, the state equation and the observation equation of the traditional pulsar azimuth error estimation algorithm are as follows:
Figure BDA0002982734410000045
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, the state transition matrix is
Figure BDA0002982734410000046
The observation matrix is
Figure BDA0002982734410000047
WkAnd ηkRepresented are system noise and measurement noise.
Preferably, in step 3, the satellite position error scalar, the clock bias and the clock bias drift rate are augmented to new state variables, and an augmented state algorithm state equation and an observation equation of the pulsar azimuth error estimation are obtained:
due to the drift of the frequency and the phase of the beacon satellite clock, the clock difference exists between the real time of the pulse reaching the satellite and the pulse reaching time measured by the satellite clock, and the clock difference is delta t, so that the following conditions are met:
tsat-δt＝t'sat
the satellite clock error model is as follows:
x1(tk+1)＝x1(tk)+τ·x2(tk)+ω(k)
in the formula, x1、x2Respectively clock error and clock error drift rate; τ is a time interval; ω is white noise with variance:
Figure BDA0002982734410000051
in the formula, q1、q2For the power spectral density of noise, the discrete process model is:
Figure BDA0002982734410000052
in the formula, the state transition matrix is
Figure BDA0002982734410000053
When the satellite position has an error delta r, the real position r is setsatFrom deviation position r'satSatisfies the following conditions:
rsat-Δr＝r′sat
when the clock error and the satellite position error are considered simultaneously, a new observation model of the system can be obtained as follows:
c(tSSB-t'SSB)＝c·δt+(n'+Δn)(r'sat+Δr)-n'·r'sat
≈c·δt+n'·Δr+Δn·r'sat＝c·δt+Δn·r'sat+Δr×cosθ
in the formula, Δ r is a satellite position error scalar quantity, and θ is an included angle between Δ r and n';
and (3) increasing the satellite position error scalar quantity, the clock error and the clock error drift rate into a new state variable, wherein the state variable after the increase is as follows:
X＝[Δα Δβ Δr x1 x2]T
obtaining an augmentation algorithm state equation of Xk+1＝AkXk+Wk
In the formula, the state transition matrix is
Figure BDA0002982734410000054
WkIs the system noise;
the observation equation is:
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, observation matrix
Figure BDA0002982734410000055
ηkTo measure noise.
Preferably, in step 4, the observed quantity of the pulse arrival time is processed by using a kalman filter algorithm to obtain a state variable estimated value, and the system deviation caused by the satellite position error and the clock error is compensated in the algorithm estimation process:
Figure BDA0002982734410000061
Figure BDA0002982734410000062
Figure BDA0002982734410000063
Figure BDA0002982734410000064
Pk＝(I-KkHk)Pk|k-1
in the formula (I), the compound is shown in the specification,
Figure BDA0002982734410000065
denoted as the a priori state estimate at the time k,
Figure BDA0002982734410000066
and
Figure BDA0002982734410000067
expressed as k-1 and the a posteriori state estimate at time k, Pk|k-1Represented by a prior estimated covariance matrix, Pk-1And PkExpressed as the K-1 and a posteriori estimated covariance matrix at time K, KkRepresented is a gain matrix.
The invention has the beneficial effects that:
the method is based on a solar system centroid coordinate system, and a pulsar time conversion model is established; selecting right ascension errors and declination errors of the pulsar azimuth information as state variables, and establishing a state equation and an observation equation of a traditional pulsar azimuth error estimation algorithm by combining a time conversion model; the satellite position error scalar, the clock error and the clock error drift rate are expanded to be new state variables, an expanded state algorithm state equation and an observation equation of pulsar azimuth error estimation are obtained, and the satellite position error and the clock error are considered in the algorithm; and processing the pulse arrival time observed quantity by using a Kalman filtering algorithm to obtain a state variable estimated value, and compensating system deviation caused by satellite position errors and clock errors in the algorithm estimation process so as to improve the estimation precision of the pulsar azimuth errors. According to the method, the traditional pulsar azimuth error estimation algorithm is improved, the improved extended state algorithm can effectively overcome the influence of satellite position errors and clock errors on pulsar azimuth error estimation, and the pulsar azimuth error estimation precision is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is an augmented state algorithm estimation; (a) right ascension error; (b) declination error.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an augmentation state algorithm for pulsar azimuth error estimation, which is used for estimating and compensating a satellite position error and a clock error which exist at the same time, reducing or even eliminating the influence of the estimation on the pulsar azimuth error, and further improving the estimation precision of the pulsar azimuth error.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, an intelligent hypersonic aircraft reentry maneuver guidance method comprises the following steps:
step 101: and establishing a pulsar time conversion model based on a solar system centroid coordinate system.
The reentry dynamic model of the hypersonic gliding aircraft is as follows:
Figure BDA0002982734410000071
Figure BDA0002982734410000081
c(tSSB-t'SSB)＝Δn·rsat
of formula (II) to'SSBTime, t, of arrival of pulse signal at origin of coordinate system of centroid of solar system measured by X-ray detector installed on satelliteSSBIs the time t 'when the pulse signal really reaches the origin of the solar system centroid coordinate system'satDenoted the time of arrival of the pulse obtained for the beacon satellite clock, n' denotes the unit direction vector with error obtained for the measurement, rsatIs the position vector of the satellite in BCRS, c is the speed of light, o (t) is the higher-order term caused by the annual parallax effect and the like, tsatThe real time of the pulse reaching the satellite, n is the real unit direction vector of the pulsar, and Δ n is the pulsar azimuth error.
Step 102: selecting the right ascension error and the declination error of the pulsar azimuth information as state variables, and establishing a state equation and an observation equation of a traditional pulsar azimuth error estimation algorithm by combining the time conversion model in the step one.
The pulsar unit direction vector can be expressed as:
Figure BDA0002982734410000082
in the formula, alpha and beta are the right ascension and the declination of the pulse star orientation in the solar system centroid coordinate system.
The unit direction vector with error obtained from the observation is:
Figure BDA0002982734410000083
in the formula (I), the compound is shown in the specification,
Figure BDA0002982734410000084
and
Figure BDA0002982734410000085
the obtained red meridians and declination of the pulsar were measured. If the declination error and the declination error are Δ α and Δ β, respectively, the true declination and declination values satisfy the following relationship:
Figure BDA0002982734410000086
Figure BDA0002982734410000087
Figure BDA0002982734410000091
the pulsar azimuth error Δ n is:
Figure BDA0002982734410000092
taking the state variable as X ═ Delta alpha Delta beta]TThen, the state equation and the observation equation of the traditional pulsar azimuth error estimation algorithm are as follows:
Figure BDA0002982734410000093
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, the state transition matrix is
Figure BDA0002982734410000094
The observation matrix is
Figure BDA0002982734410000095
WkAnd ηkRepresented are system noise and measurement noise.
Step 103: and (3) the satellite position error scalar quantity, the clock error and the clock error drift rate are expanded to be new state variables, and an expanded state algorithm state equation and an observation equation of the pulsar azimuth error estimation are obtained.
Due to the drift of the frequency and the phase of the beacon satellite clock, the clock difference exists between the real time of the pulse reaching the satellite and the pulse reaching time measured by the satellite clock, and the clock difference is delta t, so that the following conditions are met:
tsat-δt＝t'sat
the satellite clock error model is as follows:
x1(tk+1)＝x1(tk)+τ·x2(tk)+ω(k)
in the formula, x1、x2Respectively clock error and clock error drift rate; τ is a time interval; ω is white noise with variance:
Figure BDA0002982734410000101
in the formula, q1、q2Is the power spectral density of the noise. The discrete process model is as follows:
Figure BDA0002982734410000102
in the formula, the state transition matrix is
Figure BDA0002982734410000103
When the satellite position has an error delta r, the real position r is setsatFrom deviation position r'satSatisfies the following conditions:
rsat-Δr＝r′sat
when the clock error and the satellite position error are considered simultaneously, a new observation model of the system can be obtained as follows:
c(tSSB-t'SSB)＝c·δt+(n'+Δn)(r'sat+Δr)-n'·r'sat
≈c·δt+n'·Δr+Δn·r'sat＝c·δt+Δn·r'sat+Δr×cosθ
in the formula, Δ r is a scalar quantity of satellite position errors, and θ is an included angle between Δ r and n'.
And (3) increasing the satellite position error scalar quantity, the clock error and the clock error drift rate into a new state variable, wherein the state variable after the increase is as follows:
X＝[Δα Δβ Δr x1 x2]T
obtaining an augmentation algorithm state equation of Xk+1＝AkXk+Wk。
In the formula, the state transition matrix is
Figure BDA0002982734410000104
WkIs the system noise.
The observation equation is:
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, observation matrix
Figure BDA0002982734410000111
ηkTo measure noise.
Step 104: and processing the pulse arrival time observed quantity by using a Kalman filtering algorithm to obtain a state variable estimated value, and compensating system deviation caused by satellite position errors and clock errors in the algorithm estimation process so as to improve the estimation precision of the pulsar azimuth errors.
The Kalman filtering process comprises the following steps:
Figure BDA0002982734410000112
Figure BDA0002982734410000113
Figure BDA0002982734410000114
Figure BDA0002982734410000115
Pk＝(I-KkHk)Pk|k-1
in the formula (I), the compound is shown in the specification,
Figure BDA0002982734410000116
denoted as the a priori state estimate at the time k,
Figure BDA0002982734410000117
and
Figure BDA0002982734410000118
expressed as k-1 and the a posteriori state estimate at time k, Pk|k-1Represented by a prior estimated covariance matrix, Pk-1And PkExpressed as the K-1 and a posteriori estimated covariance matrix at time K, KkRepresented is a gain matrix.
As an augmented state algorithm, in step 3, on the basis of a traditional pulsar azimuth error estimation model, the influence of a satellite position error and a clock bias is considered at the same time, a satellite position error scalar, a clock bias and a clock bias drift rate are augmented into a new state variable, and the pulsar azimuth error estimation augmented state algorithm model is obtained again. When a beacon satellite is used for estimating the pulsar azimuth error, the satellite position information has errors, and meanwhile, due to the influence of factors such as clock drift, clock error also exists, and the influence of the two errors is not considered in the traditional pulsar azimuth error estimation model, so that the estimation precision is influenced, the accuracy of the pulsar azimuth information is reduced, and the pulsar navigation precision is influenced.
As an optimal estimation method, in the step 3, the pulse arrival time observed quantity is processed by Kalman filtering to obtain a state variable estimation value, and system deviation caused by satellite position error and clock error is compensated in the algorithm estimation process, so that the estimation precision of the pulsar azimuth error is improved.
The simulation experiment is described below.
Step 1: experiments were performed with B0531+21 pulsar, with parameters as in table 1.
TABLE 1 pulsar parameters
Figure BDA0002982734410000121
In the table, the letter P indicates a pulse period, the letter W indicates a pulse width, and the letter F indicates a pulse periodxThe photon flux, denoted by the letter p, brought about by the pulsed radiationfRepresenting the ratio between the pulsed radiation flux generated by different pulse periods and the average radiation flux. The variance of the observed noise generated by the pulsar can be calculated by:
Figure BDA0002982734410000131
in the formula, A is the effective area of the detector, and is set to be 1m in the simulation2；Bx＝0.005ph·cm-2·s-1Cosmic background noise; the letter d indicates the ratio between different pulse widths W and different pulse periods P; symbol tobsThe observation time is shown, which takes one kilosecond.
Step 2: the pulsar azimuth error is set to (2mas ).
And step 3: the satellite orbit used for the simulation was an HPOP orbit generated using STK software, and the parameters thereof are shown in table 2.
TABLE 2 satellite orbital parameters
Figure BDA0002982734410000132
In simulation, the solar quality is set as Msun＝1.9891×1030kg, G is 6.67 × 10, which is a common value of gravitational force-11m3kg-1s-2。
And 4, step 4: setting the clock error drift rate to 3.637979 × 10 according to rubidium atomic clock model-12Setting the noise spectral density of the clock as q1＝1.11×10-22s and q2＝2.22×10-32And/s, setting the clock difference of the initial time of the clock to be 0s and setting the time interval to be 1 s. Let the projection of the satellite position error in three coordinate directions be 100 m.
According to simulation experiments, the pulsar azimuth error estimation augmentation state algorithm provided by the invention can effectively overcome the influences of satellite position errors and clock errors, and remarkably improve the pulsar azimuth error estimation precision.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (5)

1. An augmented state algorithm for pulsar bearing error estimation, comprising the steps of:
step 1: establishing a time conversion model of the pulsar based on a solar system centroid coordinate system;
step 2: selecting right ascension errors and declination errors of the pulsar azimuth information as state variables, and establishing a state equation and an observation equation of a traditional pulsar azimuth error estimation algorithm by combining the time conversion model in the step 1;
and step 3: the satellite position error scalar, the clock error and the clock error drift rate are expanded to be new state variables, an expanded state algorithm state equation and an observation equation of pulsar azimuth error estimation are obtained, and the satellite position error and the clock error are considered at the same time by the expanded state algorithm;
and 4, step 4: and processing the pulse arrival time observed quantity by using a Kalman filtering algorithm to obtain a state variable estimated value, and compensating system deviation caused by satellite position error and clock error in the estimation process of the augmented state algorithm so as to improve the estimation precision of the pulsar azimuth error.
2. The augmented state algorithm for pulsar azimuth error estimation according to claim 1, wherein in the step 1, the time transformation model of pulsar is established based on a solar system centroid coordinate system as follows:
Figure FDA0002982734400000011
Figure FDA0002982734400000012
c(tSSB-t'SSB)＝Δn·rsat
of formula (II) to'SSBTime, t, of arrival of pulse signal at origin of coordinate system of centroid of solar system measured by X-ray detector installed on satelliteSSBIs the time t 'when the pulse signal really reaches the origin of the solar system centroid coordinate system'satDenoted the time of arrival of the pulse obtained for the beacon satellite clock, n' denotes the unit direction vector with error obtained for the measurement, rsatIs a satelliteA position vector in BCRS, c is the speed of light, o (t) is a higher-order term caused by the annual parallax effect and the like, tsatThe real time of the pulse reaching the satellite, n is the real unit direction vector of the pulsar, and Δ n is the pulsar azimuth error.
3. The augmented state algorithm for pulsar azimuth error estimation according to claim 1, wherein in the step 2, the process of establishing the state equation and the observation equation of the conventional pulsar azimuth error estimation algorithm is as follows:
the pulsar unit direction vector can be expressed as:
Figure FDA0002982734400000021
in the formula, alpha and beta are the right ascension and the declination of the pulse star orientation in the solar system centroid coordinate system;
the unit direction vector with error obtained from the observation is:
Figure FDA0002982734400000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002982734400000023
and
Figure FDA0002982734400000024
the red longitude and the red latitude of the pulsar are measured; if the declination error and the declination error are Δ α and Δ β, respectively, the true declination and declination values satisfy the following relationship:
Figure FDA0002982734400000025
Figure FDA0002982734400000026
Figure FDA0002982734400000027
the pulsar azimuth error Δ n is:
Figure FDA0002982734400000028
taking the state variable as X ═ Delta alpha Delta beta]TThen, the state equation and the observation equation of the traditional pulsar azimuth error estimation algorithm are as follows:
Figure FDA0002982734400000031
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, the state transition matrix is
Figure FDA0002982734400000032
The observation matrix is
Figure FDA0002982734400000033
WkAnd ηkRepresented are system noise and measurement noise.
4. The augmented state algorithm for pulsar azimuth error estimation according to claim 1, wherein in the step 3, the satellite position error scalar, the clock bias and the clock bias drift rate are augmented to new state variables, and an augmented state algorithm state equation and an observation equation for pulsar azimuth error estimation are obtained:
due to the drift of the frequency and the phase of the beacon satellite clock, the clock difference exists between the real time of the pulse reaching the satellite and the pulse reaching time measured by the satellite clock, and the clock difference is delta t, so that the following conditions are met:
tsat-δt＝t'sat
the satellite clock error model is as follows:
x1(tk+1)＝x1(tk)+τ·x2(tk)+ω(k)
in the formula, x1、x2Respectively clock error and clock error drift rate; τ is a time interval; ω is white noise with variance:
Figure FDA0002982734400000034
in the formula, q1、q2For the power spectral density of noise, the discrete process model is:
Figure FDA0002982734400000035
in the formula, the state transition matrix is
Figure FDA0002982734400000041
When the satellite position has an error delta r, the real position r is setsatFrom deviation position r'satSatisfies the following conditions:
rsat-Δr＝r′sat
when the clock error and the satellite position error are considered simultaneously, a new observation model of the system can be obtained as follows:
c(tSSB-t'SSB)＝c·δt+(n'+Δn)(r'sat+Δr)-n'·r'sat≈c·δt+n'·Δr+Δn·r'sat＝c·δt+Δn·r'sat+Δr×cosθ
in the formula, Δ r is a satellite position error scalar quantity, and θ is an included angle between Δ r and n';
and (3) increasing the satellite position error scalar quantity, the clock error and the clock error drift rate into a new state variable, wherein the state variable after the increase is as follows:
X＝[Δα Δβ Δr x1 x2]T
obtaining an augmentation algorithm state equation of Xk+1＝AkXk+Wk
In the formula, the state transition matrix is
Figure FDA0002982734400000042
WkIs the system noise;
the observation equation is:
Zk＝c(tSSB-t'SSB)＝HkXk+ηk
in the formula, observation matrix
Figure FDA0002982734400000043
ηkTo measure noise.
5. The augmented state algorithm of pulsar azimuth error estimation according to claim 1, wherein in the step 4, the observed quantity of pulse arrival time is processed by using a kalman filter algorithm to obtain a state variable estimation value, and a system deviation caused by a satellite position error and a clock error is compensated in an algorithm estimation process:
Figure FDA0002982734400000051
Figure FDA0002982734400000052
Figure FDA0002982734400000053
Figure FDA0002982734400000054
Pk＝(I-KkHk)Pk|k-1
in the formula (I), the compound is shown in the specification,
Figure FDA0002982734400000055
denoted as the a priori state estimate at the time k,
Figure FDA0002982734400000056
and
Figure FDA0002982734400000057
expressed as k-1 and the a posteriori state estimate at time k, Pk|k-1Represented by a prior estimated covariance matrix, Pk-1And PkExpressed as the K-1 and a posteriori estimated covariance matrix at time K, KkRepresented is a gain matrix.
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