A time difference navigation method based on pulsar binary system

Abstract

The present invention provides a time differential navigation method based on a pulsar binary system, and belongs to the field of aerospace navigation technology. Since isolated millisecond pulsars are scarce and unevenly distributed in space, the present invention adopts a pulsar binary system with a specific time propagation delay, and establishes an observation pulse phase model on a spacecraft according to the inherent spin phase and time propagation delay of the pulsar binary system, and linearizes to obtain a navigation measurement model based on the binary system. In order to suppress system errors such as pulsar direction error and linearization error in the measurement model, a time differential model based on the binary system is used, that is, differentials are performed between adjacent filtering periods. Isolated pulsars can be regarded as a special case of the present invention. The present invention can use isolated pulsars and pulsar binary systems for navigation at the same time, expand the range of navigation stars, solve the problem of the small number of currently available pulsars, effectively suppress the influence of system errors, and improve the accuracy of the navigation system.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace navigation, and in particular relates to a time difference navigation method based on a pulsar binary star system. Background Art

[0002] Deep space exploration is an important direction of human space activities in the new era and is the only way for humans to explore the unknown universe. With the expansion of deep space exploration in space missions in recent years, deep space probe navigation technology plays an increasingly important role in deep space exploration missions. It is a vital technology for spacecraft to use navigation systems to determine their own position, speed and attitude. Due to the many limitations of ground-based navigation methods in deep space exploration, the autonomous navigation technology of deep space probes has become the key to the success of deep space exploration missions. The celestial navigation system (CNS) is a commonly used autonomous navigation method for deep space probes, which can provide the position, speed and attitude information of the probe completely independently.

[0003] Pulsars are a special type of neutron star, the product of a supernova explosion at the end of a massive star's life. According to general relativity and stellar structure theory, neutron stars are one of several types of ultra-dense stars formed by the collapse of stars that are not massive enough to form a black hole. Since the collapse phase complies with the law of conservation of angular momentum, neutron stars will have extremely fast spin speeds, and their poles will emit extremely high-intensity pulses. This type of neutron star with an extremely fast spin speed is called a pulsar. Pulsars have a stable rotation period and can continuously emit periodic pulse signals into the universe. Since 1967, when the team of Antony Hewish, a radio astronomer at the University of Cambridge, discovered pulsars using a huge new radio telescope, pulsars have become a very important research object in the field of astrophysics and astronomy. Observations of pulsars have rapidly expanded to visible light, infrared, ultraviolet, X-ray, gamma-ray and other frequency bands, and they are still active at the forefront of science. Pulsar signals have extremely high periodic stability, so that their characteristic signals can be used to achieve high-precision deep space exploration navigation and positioning. Since even smaller spacecraft can easily capture X-ray signals, X-ray signals from pulsars can be used for autonomous navigation of spacecraft. This navigation method is called X-ray pulsar-based navigation (XPNAV). XPNAV is an autonomous navigation method that uses X-ray pulse radiation signals emitted by pulsars and uses related signal processing algorithms to calculate the navigation parameters of spacecraft. XPNAV has the characteristics of strong autonomy, strong anti-interference ability, synchronous positioning and attitude determination, and no accumulation of navigation errors over time.

[0004] Pulsars can be divided into ordinary pulsars and millisecond pulsars. Generally speaking, pulsars with a period of less than 10ms are called millisecond pulsars, and their period is much smaller than that of ordinary pulsars. Millisecond pulsars are mostly old pulsars with more stable rotation periods, making them the first choice for pulsar navigation. However, 80% of millisecond pulsars belong to binary star systems, and isolated millisecond pulsars are rare. Using a limited number of isolated millisecond pulsars for navigation makes pulsar navigation difficult in the star selection stage. Therefore, it is necessary to incorporate pulsar binary star systems that also have stable periods and can achieve precise timing into the navigation system.

[0005] It is generally believed in the physics community that ordinary pulsars are formed by supernova explosions of stars, while pulsars are formed by supernova explosions of binary star systems with companion stars, and under harsh conditions, the companion star does not escape, thus forming a pulsar binary system. At this time, the pulsar in the binary system undergoes spin acceleration due to the accretion of the companion star, forming a millisecond pulsar binary system, which is composed of a white dwarf-neutron star binary system with a millisecond pulsar and a white dwarf. If the pulsar binary system undergoes a supernova explosion again and the binary system survives the process, a millisecond pulsar and a pulsar binary neutron star binary system will be formed. If the pulsar binary system is destroyed in the complex environment afterwards, an isolated millisecond pulsar will be formed, which also explains the scarcity of isolated millisecond pulsars.

[0006] Since the first binary pulsar PSR B1913 + 16 was discovered by Hulse and Taylor in 1974, a large number of relativistic phenomena have been observed. With the completion of long-term, precise pulsar timing experimental tests, increasingly accurate and applicable binary star timing and motion models have been established, making it possible to incorporate binary pulsar systems into pulsar navigation.

[0007] At present, there are few studies on using binary pulsar systems for pulsar navigation. In order to solve the problem of insufficient number of isolated millisecond pulsars, single pulsars in binary pulsar systems are usually used directly as isolated pulsars for research. In 2018, NASA released the SEXTANT project on its official website, the first fully autonomous X-ray pulsar navigation experiment in orbit. Among the four millisecond pulsars used in the experiment, PSR J0218+4232 and PSR J0437-4715 are binary pulsar systems. In 2012, Huang Liangwei and others proposed using binary pulsar systems for navigation, demonstrated the inclusion of binary star motion effects in navigation measurement equations, and established a timing model that includes solar system delay, interstellar delay, and binary system delay, but did not analyze in detail the navigation system errors caused by binary pulsar systems. Summary of the invention

[0008] The present invention uses a pulsar binary system for X-ray pulsar navigation and establishes a time differential navigation model that includes solar system delay, interstellar delay and binary system delay to expand the range of navigation stars and suppress navigation system errors, thereby improving the accuracy of navigation position positioning.

[0009] In order to solve the problem that there are few isolated millisecond pulsars in the universe, few pulsars that can be used for navigation, and large navigation errors in binary star systems, the present invention uses a pulsar binary star system for navigation. First, based on the inherent spin phase and space-time propagation delay of the pulsar binary star system, a pulse phase model at the spacecraft is established; secondly, a linear position estimation model of the spacecraft under the pulsar binary star system is established; then, a linear velocity estimation model of the spacecraft based on the Doppler frequency shift of the pulsar binary star system is established. For Martian spacecraft, the system errors of the position estimation model and velocity estimation model based on the pulsar binary star system change slowly over time.

[0010] Finally, a time difference navigation method in a pulsar system is proposed to eliminate the influence of system errors. The position estimation of the time difference measurement model is based on the difference between the position measurement model of the phase model of the pulsar system between adjacent filtering periods, and the velocity estimation of the time difference measurement model is based on the difference between the velocity measurement of the Doppler frequency shift of the pulsar system between adjacent filtering periods. The proposed time difference model is a linear model that does not require the calculation of large matrices. After discretizing the state model and the measurement model, the EKF filter is used to estimate the position and velocity of the spacecraft.

[0011] In order to achieve the above object, the present invention adopts the following technical scheme:

[0012] A time differential navigation method based on a pulsar system is proposed. According to the inherent spin phase and time propagation delay of the pulsar system, an observation pulse phase model on the spacecraft in the pulsar system, a linear position estimation model at the spacecraft, and a linear velocity estimation model based on Doppler frequency shift are established. In order to suppress the systematic errors of the position estimation model and the velocity estimation model, a time differential navigation method based on a pulsar system is proposed. The method includes the following steps:

[0013] Step 1: Establish a state model of the spacecraft navigation system;

[0014] Step 2: Establishing the observed pulse phase model at the spacecraft in the pulsar binary system;

[0015] Step 3: Use the observed pulse phase model to establish a position measurement model for the spacecraft in the pulsar binary system, and establish a linear position estimation model based on the position measurement model;

[0016] Step 4: Establish a velocity measurement model of the spacecraft in the pulsar binary system, and establish a linear velocity estimation model based on the velocity measurement model;

[0017] Step 5: Using the linear position estimation model and the linear velocity estimation model, a time difference measurement model based on the pulsar binary system is established;

[0018] Step 6: discretize the state model and the time difference component measurement model in step 1 and step 5 to obtain a discretized system model;

[0019] Step 7: Use the extended Kalman filter algorithm (EKF) to process the state and measurement information of the discretized system model to estimate the position and speed of the spacecraft.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) Using a binary pulsar system for navigation solves the problem of the scarcity of pulsars currently available for navigation and the large navigation error of the binary system;

[0022] (2) Establishing a position and velocity estimation model based on phase and Doppler frequency shift in a pulsar binary system, providing ideas for the application of pulsar navigation;

[0023] (3) The proposed measurement model suppresses the influence of system errors on navigation accuracy through time difference and can obtain high-precision position and velocity information. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A geometric principle diagram of the time differential navigation method based on a pulsar binary system of the present invention;

[0025] Figure 2 The present invention is a flow chart of the time difference navigation method based on the pulsar binary system. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] Take the Mars spacecraft as an example. Figure 1 The geometric principle diagram of the time difference navigation method based on the pulsar binary system is given. represents the initial position of the pulsar system's barycenter in the Solar System Barycenter Coordinate System (BCRS) ( ), represents the center of mass of the pulsar binary system ( ) in the barycentric coordinate system (BCRS), express Relative to The offset vector, represents the position vector of the Sun in the barycentric coordinate system (BCRS), represents the position vector of the pulsar in the binary barycentric coordinate system (BBCRS), represents the position vector of the pulsar relative to the spacecraft, represents the position vector of the spacecraft in BCRS, represents the position vector of Mars in BCRS, represents the position vector of the spacecraft relative to Mars, represents the position vector of Mars relative to the Sun, Represents the position vector of the spacecraft relative to the Sun. The signal from a binary pulsar passes through the binary pulsar system, interstellar space, and the solar system before reaching the detector. Relativistic delays as well as geometric propagation delays exist not only within the solar system but also in the binary system and interstellar space. However, in the absence of relativistic effects, the time delay of the pulse signal corresponds only to the geometric propagation delay, which is calculated as the distance divided by the speed of light. By incorporating various relativistic delays into the geometric propagation delay, a comprehensive pulse signal propagation delay can be determined.

[0028] The present invention is described in detail below with reference to specific embodiments.

[0029] like Figure 2 As shown, the navigation method based on the pulsar system of the present invention comprises the following steps:

[0030] Step (1) Establish the state model of the spacecraft navigation system:

[0031] For the Martian spacecraft, the coordinate system is the inertial coordinate system of the Martian center of mass at the epoch (J2000.0), and the factors such as the gravitational force of Mars on the Martian spacecraft, radiation pressure, rocket thrust during orbital maneuvers, and high-precision ephemeris are considered. The state model of the spacecraft navigation system is shown in formula (1):

[0032] (1)

[0033] The above formula can be simplified as:

[0034] (2)

[0035] In the formula, X ( t ) = [ x y z v x v y v z ] T is the state vector of the state model, for The differential of are the position and velocity of the Mars spacecraft in the X, Y, and Z directions respectively; is the nonlinear continuous state transfer function of the state model; is the vector from the center of mass of Mars to the spacecraft; Indicates the central gravity of Mars; , , , , , are system noise respectively; Indicates the current moment.

[0036] Step (2) Establish the observed pulse phase model at the spacecraft in the pulsar binary system:

[0037] Using the pulse photon detector carried by the spacecraft itself, taking into account the pulse's solar system delay, interstellar delay and binary system delay, the phase tracking algorithm is used to obtain the observed pulse phase measurement value at the spacecraft. , and thus the observed pulse phase model is established:

[0038] (3)

[0039] In the formula, is the source frequency of the pulsar; are the zeroth, first, and second-order derivatives of the pulsar spin frequency with time, respectively. is the position vector of the spacecraft relative to the solar system barycenter (SSB); is the original phase of the pulsar; is the time delay experienced by the pulse photons of the pulsar system to the spacecraft; is the observed pulse phase The integer ambiguity of is the phase measurement error; are higher-order terms in the Taylor expansion.

[0040] Step (3) Establish a linear position estimation model for the spacecraft in a pulsar binary system:

[0041] Based on the observed pulse phase model at the spacecraft, a linearized position measurement model can be established. Considering the linearization error and the pulsar direction error, the spacecraft position measurement model can be obtained:

[0042] (4)

[0043] In the formula, represents the position vector of the spacecraft relative to the center of mass of the solar system; represents the actual direction vector of the pulsar; represents the system error, where , represents the direction error of the pulsar; , Indicates time delay error; represents the linearized position error; represents random position error.

[0044] If three navigation pulsars are selected, the position measurements are , , The error terms are , , , , , , then the position estimation model is:

[0045] z p = H 1 [ X ( t ) , t ] + x p + ψ p (5)

[0046] In the formula, z p = [ z ˜ p 1 , z ˜ p 2 , z ˜ p 3 ] T A measurement that represents the position of a spacecraft at a certain moment; x p = [ x p 1 , x p 2 , x p 3 ] T Represents the position measurement system error of the navigation system at the corresponding moment; ψ p = [ ψ p 1 , ψ p 2 , ψ p 3 ] T Represents the random error in position measurement of the navigation system at the corresponding moment. is the measurement transfer matrix of the position estimation model.

[0047] Step (4) Establish a velocity estimation model for the spacecraft in a pulsar binary system:

[0048] Using the pulse photon detector carried on the spacecraft, considering the pulse's solar system delay, interstellar delay and binary system delay, the estimated Doppler shift at the spacecraft is obtained using the traditional Doppler shift estimation algorithm. :

[0049] (6)

[0050] In the formula, Indicates the actual Doppler shift.

[0051] The derivative of the time delay term at a certain moment is:

[0052] (7)

[0053] In the formula, is the factor related to the gravitational potential produced by all solar system bodies except Mars; is the time derivative of the second-order Romer delay; is the second-order Romer delay of the solar system Derivative with respect to time; It is the double star Shapiro delay Derivative with respect to time; It is a binary Einstein delay Derivative with respect to time; and They are the radial components of the binary star Romer delay Angle of approach and the argument of periastron Time partial derivatives.

[0054] If the pulsar direction error is considered, the velocity measurement model can be obtained according to formula (6) and formula (7):

[0055] (8)

[0056] In the formula, represents the random error of the speed measurement system, where represents the estimation error of Doppler frequency shift; represents the estimated Doppler shift; represents the actual Doppler shift; represents the speed measurement system error, where , , Represents higher-order Doppler shift.

[0057] If three navigation pulsars are selected, the velocity measurements are , , The error terms are , , , , , , then the speed estimation model is:

[0058] z v = H 2 [ X ( t ) , t ] + x v + ψ v (9)

[0059] In the formula, z v = [ z ˜ v 1 , z ˜ v 2 , z ˜ v 3 ] T A measurement of the velocity of a spacecraft at a certain moment; x v = [ x v 1 , x v 2 , x v 3 ] T Indicates the speed measurement system error of the navigation system at the corresponding moment; ψ v = [ ψ v 1 , ψ v 2 , ψ v 3 ] T represents the random noise of the speed measurement of the navigation system at the corresponding moment, is the measurement transfer matrix of the velocity estimation model.

[0060] Step (5) Establish a time difference measurement model based on the pulsar binary system:

[0061] According to steps (3) and (4), if three pulsars are observed simultaneously, the navigation measurement model can be expressed as:

[0062] (10)

[0063] In the formula, Z ( t ) = [ z p , z v ] T It is navigation measurement information; is the linear measurement transfer matrix; is the state quantity of the spacecraft; is the systematic error of the measurement model; is the random noise of the measurement model; Indicates the current time; superscript Represents the transpose of a matrix.

[0064] According to formula (10), the navigation measurement model performs time difference between adjacent filtering periods, and the time difference navigation measurement model based on pulsar can be obtained:

[0065] (11)

[0066] In the formula, Represents the navigation measurement information obtained using the difference model.

[0067] Step (6) discretizes the state model and time difference measurement model established in steps (1) and (5), and uses the posterior estimation Replace state quantity . We can get:

[0068] (12)

[0069] In the formula, ; express The discretization result; express The discretization result; is the discretized nonlinear state transfer function; is the state noise; is the measurement noise of the time difference navigation model; express The estimation error of and Respectively and The measurement random noise obtained after discretization; Indicates the current moment; express The measurement transfer matrix at time. ,in and Respectively and Equivalent system error obtained after discretization.

[0070] Step (7) uses the extended Kalman filter to process the state information and measurement information to estimate the position and velocity of the spacecraft, including:

[0071] Step (7.1) Initialize state and the state error variance matrix :

[0072] X ^ 0 = E [ X 0 ] P 0 = E [ ( X 0 − X ^ 0 ) ( X 0 − X ^ 0 ) T ] (13)

[0073] In the formula, Indicates the initial value of the state quantity; Represents the initial value of the state quantity with error; represents the mean function.

[0074] Step (7.2) performs time update:

[0075] (14)

[0076] In the formula, represents the prior state estimate; represents the covariance matrix; Represents the covariance matrix of the prior state estimation error; express Estimated value of state quantity at the moment; is the state transition function; represents the state transfer matrix; represents the process noise covariance.

[0077] Step (7.3) performs measurement update:

[0078] Calculate the measurement noise matrix :

[0079] (15)

[0080] In the formula, express The state gain matrix at time ; The measurement noise before time difference is The measurement noise matrix at time; The measurement noise before time difference is The measurement noise matrix at time;

[0081] calculate Status gain at the moment :

[0082] (16)

[0083] Calculate one-step-ahead measurements :

[0084] (17)

[0085] Calculate the posterior state estimate at time k :

[0086] (18)

[0087] In the formula, Indicates the actual quantity measured.

[0088] Compute the posterior state estimate error covariance :

[0089] (19)

[0090] In the formula, Represents the identity matrix.

[0091] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. It is easy for the technical personnel in the field to understand that the above description is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A time difference navigation method based on a pulsar binary system, characterized in that: The method comprises the following steps: Step 1: Establish a state model of the spacecraft navigation system; Step 2: Establishing the observed pulse phase model at the spacecraft in the pulsar binary system; Step 3: Use the observed pulse phase model to establish a position measurement model for the spacecraft in the pulsar binary system, and establish a linear position estimation model based on the position measurement model; Step 4: Establish a velocity measurement model of the spacecraft in the pulsar binary system, and establish a linear velocity estimation model based on the velocity measurement model; Step 5: Using the linear position estimation model and the linear velocity estimation model, a time difference measurement model based on the pulsar binary system is established; Step 6: discretize the state model and the time difference component measurement model in step 1 and step 5 to obtain a discretized system model; Step 7: Use the extended Kalman filter algorithm EKF to process the state and measurement information of the discretized system model to estimate the position and speed of the spacecraft; The second step includes: using the pulse photon detector carried by the spacecraft itself, taking into account the pulse's solar system delay, interstellar delay and binary system delay, and using a phase tracking algorithm to obtain the observed pulse phase at the spacecraft , and observe the pulse phase It is related to the position of the spacecraft relative to the solar system's barycenter coordinate system and establishes an observation pulse phase model: In the formula, is the source frequency of the pulsar; are the zeroth, first, and second-order derivatives of the pulsar spin frequency with time, respectively; is the position vector of the spacecraft relative to the solar system's center of mass; is the original phase of the pulsar; is the time delay experienced by the pulse photons of the pulsar system to the spacecraft; is the observed pulse phase The integer ambiguity of is the phase measurement error; is a higher-order term in Taylor expansion; The fourth step comprises: Using the pulse photon detector carried by the spacecraft itself, considering the pulse's solar system delay, interstellar delay and binary star system delay, the Doppler frequency shift estimation algorithm is used to obtain the Doppler frequency shift at the spacecraft: In the formula, is the source frequency of the pulsar; are the zeroth, first and second order derivatives of the pulsar spin frequency with time, is the position vector of the spacecraft relative to the solar system's center of mass; is the time delay experienced by the pulse photons of the pulsar system to the spacecraft; definition is the velocity vector of Mars relative to the mass center of the solar system; is the velocity vector of the spacecraft relative to Mars; then in the binary system: In the formula, c represents the speed of light, is the factor related to the gravitational potential produced by all solar system bodies except Mars; is the second-order Romer delay of the solar system Derivative with respect to time; It is the double star Shapiro delay Derivative with respect to time; It is a binary Einstein delay Derivative with respect to time; and They are the radial components of the binary star Romer delay Angle of approach and the argument of periastron The time partial derivative of ; According to the Doppler shift formula, the position of the spacecraft relative to the center of mass of the solar system is obtained from the estimated Doppler shift at the spacecraft. , considering the linearization error and pulsar direction error, the velocity measurement model of the spacecraft is obtained: In the formula, represents the actual direction vector of the pulsar; represents the random error of the speed measurement system, where represents the estimation error of Doppler frequency shift; represents the estimated Doppler shift; represents the actual Doppler frequency shift; c represents the speed of light; represents the speed measurement system error, where , , represents the higher-order Doppler shift; Three navigation pulsars were selected, and the speed measurements were , , The error terms are , , , , , , then the linear velocity estimation model is: In the formula, t represents the current time, A measurement of the velocity of a spacecraft at a certain moment; Indicates the speed measurement system error of the navigation system at the corresponding moment; represents the random noise of the speed measurement of the navigation system at the corresponding moment, is the measurement transfer matrix of the velocity estimation model.

2. The time difference navigation method based on a pulsar system according to claim 1, characterized in that: The step 1 includes: for the Martian spacecraft, the coordinate system selects the Martian mass center inertial coordinate system of epoch J2000.0, considering the gravity of Mars on the spacecraft, radiation pressure, rocket thrust during orbital maneuvers, and high-precision ephemeris, and the state model of the spacecraft navigation system is written as follows: The above formula can be simplified as: In the formula, is the state vector of the state model, for The differential of are the position and velocity of the Mars spacecraft in the X, Y, and Z directions respectively; is the system nonlinear continuous state transfer function of the state model; is the spacecraft position vector relative to Mars; Indicates the central gravity of Mars; , , , , , They are the position system noise and velocity system noise in the three directions of X, Y and Z respectively; Indicates the current moment.

3. The time difference navigation method based on a pulsar system according to claim 2, characterized in that: The step three comprises: The observed pulse phase at the spacecraft Translated to the position of the spacecraft relative to the center of mass of the solar system , considering the linearization error and pulsar direction error, the spacecraft position measurement model is obtained: In the formula, represents the position vector of the spacecraft relative to the center of mass of the solar system; represents the actual direction vector of the pulsar; represents the system error, where , Represents the position error caused by the direction error of the pulsar; represents the direction vector error of the pulsar; , Indicates time delay error; represents the linearized position error; represents random position error; Three navigation pulsars are selected, and the position measurements are , , The error terms are , , , , , , then the linear position estimation model is: In the formula, A measurement that represents the position of a spacecraft at a certain moment; Represents the position measurement system error of the navigation system at the corresponding moment; Represents the random error of the position measurement of the navigation system at the corresponding moment; is the measurement transfer matrix of the position estimation model.

4. The time difference navigation method based on a pulsar system according to claim 3, characterized in that: The step five comprises: According to the formula of the position measurement model and the formula of the velocity measurement model, the navigation measurement model considering the system error while observing three pulsars is expressed as: In the formula, Navigation measurement information; is the linear measurement transfer matrix; is the state quantity of the spacecraft; is the systematic error of the measurement model; is the random noise of the measurement model; Indicates the current moment; the superscript T indicates the transpose of the matrix; According to the formula of the navigation measurement model, the navigation measurement model performs time difference between adjacent filtering cycles to obtain a time difference navigation measurement model based on pulsar binary stars: in, Represents navigation measurement information obtained using the time difference model.

5. The time difference navigation method based on a pulsar system according to claim 4, characterized in that: The step six comprises: The simplified formula of the state model and the formula of the differential navigation measurement model are discretized to obtain the discretized system model, and the a posteriori estimate is used Replace state quantity , the formula is as follows: In the formula, ; express The discretization result; express The discretization result; is the discretized nonlinear state transfer function; is the state noise; is the measurement noise of the time difference navigation model; express The estimation error of and Respectively and The measurement random noise obtained after discretization; Indicates the current moment; express The measurement transfer matrix at time, ,in and Respectively and Equivalent system error obtained after discretization.

6. The time difference navigation method based on a pulsar system according to claim 5, characterized in that: The step seven comprises: The formula of the discretized system model is obtained by filtering the extended Kalman filter algorithm EKF The a posteriori state estimate of the spacecraft at time and the posterior error covariance ;Will and Output and return the filter to obtain Output at the moment.

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