A spacecraft autonomous astronomical navigation method based on cosmic particle detection

Abstract

The present invention relates to a spacecraft astronomical navigation method based on cosmic particle detection. First, a state model and a measurement model of a spacecraft astronomical navigation system based on cosmic particle detection are established, and the cosmic particle detector is used to obtain the arrival vector of cosmic particles relative to the cosmic particle detector as the quantity measurement of the astronomical navigation system; a state model of the astronomical navigation system is established, and the arrival vectors of cosmic particles emitted by three cosmic particle sources are combined as the measurement model of the astronomical navigation system, and the Unscented Kalman filter method is used to estimate the position and speed of the spacecraft. Aiming at the task requirements of high-precision autonomous navigation of deep space probes, the present invention studies a spacecraft astronomical navigation method based on cosmic particle detection, and provides theoretical and technical support for the upcoming Tianwen-2 Mars exploration, Jupiter system exploration, and solar system edge exploration tasks.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace navigation, and in particular relates to a spacecraft astronomical navigation method based on cosmic particle detection. Background Art

[0002] Spacecraft navigation currently uses radio measurement and control navigation, which measures the relative position relationship between the carrier and the measurement and control station through the reception, transmission and processing of radio waves, and thus realizes the positioning and navigation of the moving carrier. Its characteristics are that it needs to transmit and receive radio waves, so it is easy to be discovered and interfered with, and the measurement and control station is required to transmit and receive radio waves. Once the measurement and control station fails, the navigation system cannot be used. Therefore, spacecraft navigation urgently needs to realize autonomous navigation. Astronomical navigation is currently the most important autonomous navigation method for spacecraft. Astronomical navigation uses celestial bodies as navigation beacons, does not rely on other external information, and does not radiate energy to the outside. It passively receives light radiated or reflected by celestial bodies to obtain navigation information. It is a completely autonomous navigation method.

[0003] Cosmic particles are mainly divided into quarks and leptons, each of which has three generations. The first generation of quarks includes up quarks (muons) and down quarks (d-sons); the first generation of leptons includes electrons (e-sons) and neutrinos (Ve). The properties of the second and third generation quarks and leptons are the same as those of the first generation, but they are heavier. Among these cosmic particles, muons in the second generation of leptons and neutrinos (Ve) in the first generation of leptons have been used in navigation systems.

[0004] Cosmic particles such as muons and neutrinos have almost no mass and propagate at the speed of light. Cosmic particles propagate strictly in a straight line, and are not prone to reflection, refraction, and attenuation during propagation. They have extremely strong penetrating power. When protons or neutrons inside the nucleus decay, cosmic particles are produced. Natural celestial bodies (such as the sun) can produce abundant cosmic particles, and artificial nuclear reactors and particle accelerators can also produce cosmic particles. Different cosmic particles interact with each other with extremely weak forces and gravity. However, since the gravitational force is extremely weak and the action distance of other forces is also very short, its interaction scattering cross section with matter is extremely small, so dust, stars, etc. are transparent to it. Therefore, cosmic particles can propagate over ultra-long distances without being blocked by other substances, reaching areas that are difficult to cover even with radio signals. Using cosmic particles to navigate spacecraft can effectively solve the problems of large delay, easy interference, and limited coverage in the radio measurement, control and navigation of spacecraft. It is a new type of autonomous astronomical navigation method for spacecraft.

[0005] Traditional astronomical navigation can be divided into astronomical angle measurement navigation, astronomical velocity measurement navigation and astronomical distance measurement navigation according to different measurement quantities. Astronomical angle measurement navigation is to use the angle between near celestial bodies such as the sun, planets, planetary satellites, comets and distant celestial bodies such as stars for autonomous navigation. Astronomical velocity measurement navigation uses the sun and stars as navigation celestial bodies. When the sun is used as a navigation celestial body, the navigation range is limited to the solar system. When the stars are used as navigation celestial bodies, velocity measurement navigation will be applicable to the entire space. The accuracy of astronomical velocity measurement navigation is related to the ephemeris error of the navigation celestial body. When the sun is used as a navigation celestial body, the accuracy of the solar vector direction is low, which will affect the navigation accuracy, while the ephemeris error of the star is small, and a higher accuracy of the navigation celestial body vector direction can be obtained. Astronomical distance measurement navigation refers to the comparison of the pulse arrival time of the X-ray pulsar relative to the detector with the standard pulse arrival time of the pulsar relative to the center of mass of the solar system. The projection length of the distance from the detector to the center of mass of the solar system in the direction of the X-ray pulsar can be obtained. By using appropriate filtering algorithms, navigation information such as the position, velocity, attitude and time of the detector can be obtained. The advantage of astronomical ranging navigation is that it can provide a time reference while providing navigation information. Its disadvantage is that there are currently few X-ray pulsars and the measurement accuracy cannot be guaranteed.

[0006] Traditional optical angle / velocity measurement autonomous astronomical navigation and X-ray pulsar ranging navigation are greatly affected by sunlight during observation and are easily blocked by other celestial bodies, making it difficult to meet the needs of all-day and all-weather autonomous navigation. Since cosmic particles strictly propagate in a straight line and have strong penetrability, the cosmic particle autonomous navigation method can overcome the problems of traditional astronomical navigation methods such as angle / velocity measurement and ranging being easily affected by celestial body blockage and easily contaminated by sunlight, and can provide spacecraft with high-precision autonomous navigation information.

[0007] At present, autonomous navigation methods based on various cosmic particles have begun to develop. Autonomous navigation based on neutrinos has been applied to positioning in hidden environments and underground. The principle of hidden environment positioning based on neutrino detection is: first, the projection of the heliocentric direction vector in the geographic coordinate system is obtained by using neutrino detectors and coordinate transformation, and then the projection of the heliocentric direction vector in the earth's fixed system is obtained by using solar ephemeris, clock and coordinate transformation. Finally, the longitude and latitude of the target are calculated based on the projection of the heliocentric direction vector in the geographic coordinate system and the earth's fixed system. The principle of the underground positioning method based on neutrino detection is: first, the positioning parameter information is received, and the time difference between the time when the underground positioning station receives the parameter information and the first time information is calculated based on the parameter information. According to the time difference and the GPS information of the base station, the position coordinates of the positioning station are solved by the spatial straight line equation. Since the underground positioning method lacks time synchronization information, other navigation and positioning systems such as GPS are required to provide auxiliary time information.

[0008] Muon navigation has been applied to underwater and underground positioning. At present, there is a laboratory positioning and navigation system based on muon measurement. Researchers have verified three-dimensional positioning with kilometer-level accuracy within 5 microseconds. The system mainly consists of multiple reference detectors and a receiving detector. The reference detector is used to define the system coordinates, and the receiving detector is used to define the relative position of the device within the coordinates. The position of the reference detector needs to be determined with the help of the GPS navigation system. The Cherenkov radiation generated by the reaction of muons with water is used. The experimental part uses lead plates instead of water to simulate the process of detecting muons for navigation. At the same time, through the application of Monte Carlo simulation, it is verified that the positioning and navigation system based on muon measurement can be used to detect plate tectonics or magma-driven seafloor movement and deformation. The limitations of the above-mentioned neutrino and muon navigation are mainly reflected in: ① A large number of detectors are required, including multiple reference detectors and one receiving detector; ② The lack of filtering links leads to low navigation accuracy; ③ Only position information can be obtained, but not velocity information; ④ It is mainly used for positioning on the surface and underground of the earth, and is not suitable for deep space exploration of spacecraft; ⑤ Other navigation and positioning systems such as GPS are required to provide auxiliary positioning information. Summary of the invention

[0009] The technical problem to be solved by the present invention is: by utilizing the advantages that cosmic particles strictly propagate in a straight line and have extremely strong penetrating ability, strong anti-interference and shielding ability, etc., it can overcome the shortcomings of traditional radio navigation system signals being easily blocked by celestial bodies and astronomical navigation such as angle measurement / speed measurement / distance measurement being greatly affected by celestial body blockage and being easily polluted by sunlight, and it can also maintain the advantages of high accuracy and strong autonomy of astronomical navigation, so that when a spacecraft performs a space mission, the spacecraft can use the spacecraft autonomous navigation method based on cosmic particle detection to provide navigation information for the spacecraft.

[0010] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0011] A spacecraft astronomical navigation method based on cosmic particle detection, firstly, establishes the state model and measurement model of the astronomical navigation system, and uses the cosmic particle detector to obtain the arrival vector of cosmic particles as the measurement of the astronomical navigation system; secondly, considering multiple perturbation factors, establishes the state model of the astronomical navigation system, and uses the arrival vectors of cosmic particles emitted by three cosmic particle sources as the measurement model of the astronomical navigation system, and uses the Unscented Kalman filter method to estimate the position and velocity of the spacecraft.

[0012] The specific steps include:

[0013] 1. Establish the state model of the celestial navigation system:

[0014]

[0015]

[0016] It can be shortened to:

[0017]

[0018] In the formula, X = [xyzv x v y v z ] T is the state vector of the state model, is the differential of X(t), x, y, z, v x , v y , v z are the position and velocity of the three axes of the spacecraft in the equatorial inertial coordinate system centered on the Earth’s center of mass; R e is the radius of the earth; J2 is the second regional coefficient, its value is 0.0010826269; ΔF x , ΔF y , ΔF z are the perturbations of the three axes, including the non-spherical gravitational perturbation of the earth, the third body perturbation, the atmospheric drag perturbation, the solar light pressure perturbation and other perturbations; f(X, t) is the system nonlinear continuous state transfer function of the state model; μ is the gravitational constant; r is the satellite position parameter vector; w(t) is the state model error of the astronomical navigation system.

[0019] 2. Establish a measurement model for the astronomical navigation system:

[0020] Select three cosmic particle sources and measure the arrival vectors of the detected cosmic particles, which are recorded as l1, l2, and l3. Combining the known position coordinates of the two cosmic particle sources on the earth and the observed position coordinates of the sun relative to the earth, l1, l2, and l3 can be expressed as the result of subtracting the spacecraft's own coordinates from the position coordinates of the corresponding cosmic particle sources and normalizing them. The specific expression is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] Where x1=[x1 y1 z1] T 、x2=[x2 y2 z2] T、x3=[x3 y3 z3] T are the position coordinates of the three cosmic particle sources, x = [xyz] T is the position coordinate of the spacecraft, l 10 , l 20 , l 30 are the vectors obtained by subtracting the spacecraft's own coordinates from the position coordinates of the three cosmic particle sources, ||l 10 ||、||l 20 ||、||l 30 || indicates l 10 , l 20 , l 30 Modulo, l1, l2, l3 represent l 10 , l 20 , l 30 The normalized result.

[0028] Set l1, l2, l s A nine-dimensional vector Z is formed, which is the measurement of the spacecraft celestial navigation system established by the present invention. After adding the error term, the measurement model of the celestial navigation system based on cosmic particle detection can be written as follows:

[0029]

[0030] Where Z is the measurement of the established spacecraft astronomical navigation system, v is the error term, where [v 1x v 1y v 1z ] T is the projection of the error term corresponding to l1 calculated by the first cosmic particle source on the x, y, and z axes, [v 2x v 2y v 2z ] T is the projection of the error term corresponding to l2 on the x, y, and z axes, [v 3x v 3y v 3z ] T It is the projection of the error term corresponding to l3 in the x, y, and z axes.

[0031] It can be shortened to:

[0032] Z(t)=h[X(t),t]+v(t) (11)

[0033] Where Z is the arrival vector of cosmic particles detected by the cosmic particle detector, that is, the quantity measured by the spacecraft astronomical navigation system; X(t) is the arrival vector of cosmic particles observed by the detector at a certain moment, and t is the moment when the spacecraft is in motion; v represents the directional measurement noise of the cosmic particle detector; x1, x2, and x3 are the coordinates of the position of the cosmic particle source, respectively, and x is the position coordinate of the spacecraft; h[X(t), t] is the nonlinear continuous measurement function of the astronomical navigation system.

[0034] 3. Measure the arrival direction vector of cosmic particles:

[0035] The arrival direction vector of cosmic particles is measured by the cosmic particle detector carried on the spacecraft;

[0036] 4. Discretize the state model and measurement model in step ① and step ②;

[0037] 5. Perform Unscented Kalman filtering on the celestial navigation system; obtain the position and velocity of the spacecraft expressed in the geocentric equatorial inertial coordinate system.

[0038] Compared with the prior art, the advantages of the present invention are: on the one hand, it maintains the advantages of high astronomical navigation accuracy, no error accumulation over time, and strong navigation autonomy, and on the other hand, it improves the problems of low data transmission efficiency and long information transmission time encountered by traditional radio navigation systems when spacecraft conduct deep space exploration. By taking advantage of the strict linear propagation and strong penetration of cosmic particles, the arrival vector of cosmic particles emitted by stars or nuclear power plants is used as a quantity measurement, and the position and speed of the spacecraft are estimated by using the Unscented Kalman filter method, high-precision navigation is achieved.

[0039] The advantages of the present invention over traditional autonomous navigation methods are mainly reflected in the following aspects: 1) it can effectively solve the problems of long information transmission time and low data transmission rate caused by the traditional radio navigation of spacecraft due to the fact that the signal is easily blocked by celestial bodies; 2) it can maintain the advantages of high astronomical navigation accuracy, no error accumulation over time, and strong autonomy, while overcoming the shortcomings of astronomical navigation such as angle measurement / speed measurement / distance measurement, which makes it difficult to observe celestial bodies during deep space exploration and is easily affected by celestial body blockage and sunlight, and can realize autonomous navigation of spacecraft around the clock and in all weather conditions.

[0040] At present, the navigation methods based on cosmic particle detection are mainly neutrino navigation and muon navigation. The advantages of the present invention over the above two navigation methods are mainly as follows: ① Three cosmic particle sources are required, which can be power stations on the surface of the earth or luminous stars. The site selection is more flexible, the number is relatively small, and the selection of natural cosmic particle sites is more reliable; ② The information of the target can be solved by the arrival vector of the cosmic particles, and both the position information and the speed information of the target can be obtained; ③ The obtained quantity measurement is subjected to Unscented Kalman filtering, and the result obtained is more accurate; ④ The information finally obtained is the position coordinates of the target, which can be applied to the navigation of earth satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of the measurement model of the cosmic particle astronomical navigation system of the present invention.

[0042] Figure 2 The present invention is a flow chart of the spacecraft astronomical navigation method based on cosmic particle detection. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions 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 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 the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0044] The invention discloses a spacecraft celestial navigation method based on cosmic particle detection, comprising the following steps: firstly, establishing a state model and a measurement model of a spacecraft celestial navigation system based on cosmic particle detection, and using the cosmic particle detector to obtain the arrival vector of cosmic particles as the measurement of the celestial navigation system; secondly, considering multiple perturbation factors, establishing a state model of the celestial navigation system, and using the arrival vectors of cosmic particles emitted by three cosmic particle sources as the measurement model of the celestial navigation system, and using the Unscented Kalman filter method to estimate the position and speed of the spacecraft.

[0045] The principle of the present invention is that because traditional celestial navigation is easily affected by celestial body obstruction and solar light pollution, traditional radio navigation is subject to signal obstruction, long signal transmission time, low data transmission rate and other limitations when applied. The most notable feature of cosmic particles is that they propagate strictly in a straight line, are not easily reflected or refracted during propagation, and have extremely strong penetrating power, and are not easily attenuated during propagation. Taking advantage of the outstanding advantages of cosmic particles in navigation, a new astronomical navigation method for spacecraft based on cosmic particle detection is studied, and a new astronomical navigation method for spacecraft based on cosmic particle detection is designed.

[0046] The present invention is described in detail below with reference to specific embodiments.

[0047] like Figure 1 As shown, the cosmic particle source involved in the present invention can be a nuclear power plant or a star on the earth. The following selects two nuclear power plants and the sun on the earth as cosmic particle navigation sources to illustrate the specific implementation process of the present invention:

[0048] 1. Establish the state model of the celestial navigation system

[0049]

[0050]

[0051] It can be shortened to:

[0052]

[0053] In the formula, X = [xyzv x v y v z ] T is the state vector of the state model, is the differential of X(t), x, y, z, v x , v y , v z are the position and velocity of the three axes of the spacecraft in the equatorial inertial coordinate system centered on the Earth’s center of mass; R e is the radius of the earth; J2 is the second regional coefficient, its value is 0.0010826269; ΔF x , ΔF y , ΔF z are the perturbations of the three axes, including the non-spherical gravitational perturbation of the earth, the third body perturbation, the atmospheric drag perturbation, the solar light pressure perturbation and other perturbations; f(X, t) is the system nonlinear continuous state transfer function of the state model; μ is the gravitational constant; r is the satellite position parameter vector; W(t) is the state model error of the astronomical navigation system.

[0054] 2. Establish a measurement model for the astronomical navigation system

[0055] Select three cosmic particle sources and measure the arrival vectors of the detected cosmic particles, which are recorded as l1, l2, and l3. Combining the known position coordinates of the two cosmic particle sources on the earth and the observed position coordinates of the sun relative to the earth, l1, l2, and l3 can be expressed as the result of subtracting the spacecraft's own coordinates from the position coordinates of the corresponding cosmic particle sources and normalizing them, which can be expressed as:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Where x1=[x1 y1 z1] T 、x2=[x2 y2 z2] T 、x3=[x3 y3 z3] T are the position coordinates of the three cosmic particle sources, x = [xyz] T is the position coordinate of the spacecraft, l 10 , l 20 , l 30 are the vectors obtained by subtracting the spacecraft's own coordinates from the position coordinates of the three cosmic particle sources, ||l 10 ||、||l 20 ||、||l 30 || indicates l 10 , l 20 , l 30 Modulo, l1, l2, l3 represent l 10 , l 20 , l 30 Normalized result. l1, l2, l3 form a nine-dimensional vector Z, which is the measurement of the spacecraft celestial navigation system established by the present invention. After adding the error term, the measurement model of the celestial navigation system based on cosmic particle detection can be written as follows:

[0063]

[0064] Where Z is the measurement of the established spacecraft astronomical navigation system, v is the error term, where [v 1x v 1y v 1z ] T is the projection of the error term corresponding to l1 calculated by the first cosmic particle source on the x, y, and z axes, [v 2x v 2y v 2z ] T is the projection of the error term corresponding to l2 on the x, y, and z axes, [v 3x v 3y v 3z ] T It is the projection of the error term corresponding to l3 in the x, y, and z axes.

[0065] It can be shortened to:

[0066] Z(t)=h[X(t),t]+v(t) (11)

[0067] Where Z is the arrival vector of cosmic particles detected by the cosmic particle detector, that is, the quantity measured by the spacecraft astronomical navigation system; X(t) is the arrival vector of cosmic particles observed by the detector at a certain moment, and t is the moment when the spacecraft is in motion; v represents the directional measurement noise of the cosmic particle detector; x1, x2, and x3 are the coordinates of the position of the cosmic particle source, respectively, and x is the position coordinate of the spacecraft; h[X(t), t] is the nonlinear continuous measurement function of the astronomical navigation system.

[0068] 3. Obtaining the direction vector of cosmic particles

[0069] The arrival direction vector of cosmic particles is measured by the cosmic particle detector carried on the spacecraft. The detector mainly uses the radiation generated by cosmic particles in weak interactions for detection. Cosmic particles and atomic nuclei react to produce leptons. Since the generated leptons have a very high speed, Cherenkov radiation will be generated in the medium. The detector can detect cosmic particles through radiation. For example, the Super-Kamiokande neutrino detector uses muon neutrinos to react with neutrons in water to produce muons and thus detect neutrinos.

[0070] 4. Discretize the state model and measurement model in steps 1 and 2

[0071] The results after discretization are as follows:

[0072] X(k)=F(X(k-1),k-1)+W(k-1) (12)

[0073] Z(k)=H(X(k),k)+V(k) (13)

[0074] Wherein, k=1, 2, …, X(k) and Z(k) are the discretized results of X(t) and Z(t), respectively; F(X(k-1), k-1) is the nonlinear state transfer function from the k-1th moment to the kth moment after the discretization of f(X(t), t); H(X(k), k) is the nonlinear measurement function at the kth moment after the discretization of h(X(t), t); W(k) and V(k) are the equivalent noises at the kth moment after the discretization of w(t) and v(t), and W(k) and V(k) are independent of each other.

[0075] 5. Unscented Kalman Filtering for Celestial Navigation Systems

[0076] Based on the state model of the astronomical navigation system, the measurement model of the astronomical navigation system, and the measurements obtained by the cosmic particle detector, the Unscented Kalman filter of the astronomical navigation system is performed to obtain the position and velocity of the spacecraft in the inertial coordinate system. A series of sample points are selected near, and the means and covariances of these sample points are and P k . Assume that the state variable is n×1 dimensional.

[0077] A. Initialization

[0078]

[0079]

[0080] B. In the formula, is the estimated value of the three-axis position and velocity of the spacecraft in the inertial coordinate system at the oth moment (initial moment), x0 is the true value of the three-axis position and velocity of the spacecraft in the inertial coordinate system at the oth moment (initial moment), and P0 is the initial mean square error matrix of the state vector.

[0081] Calculate the sampling points:

[0082] At the k-1th moment, the state vector of the celestial navigation system A series of sample points are selected near the vicinity, and the mean and mean square error matrix of these sample points are respectively and P k-1 . Assuming the state vector is n×1 dimensional, the 2n+1 sample points and their weights are:

[0083]

[0084] Where x i are sampling points, and their distribution is The Gaussian distribution is approximated; τ is the scale adjustment parameter, and its size change will affect the filtering effect; A is the system state transfer matrix. When P k =A T When A Take the i-th row of A; when P k =AA T hour, Take the i-th column of A.

[0085] Time update:

[0086] One-step prediction of the state vector of celestial navigation system for:

[0087]

[0088] One-step prediction weighted result of the state vector of all sampling points of the celestial navigation system for:

[0089]

[0090] Where W i is the weight of the i-th sampling point;

[0091] One-step prediction of the mean square error matrix of the state vector of the celestial navigation system for:

[0092]

[0093] In the formula, Q k is the state model error covariance matrix of the celestial navigation system at time k;

[0094] The measurement estimation vector corresponding to the sampling point of the celestial navigation system

[0095]

[0096] The weighted vector of all sampling points of the celestial navigation system

[0097]

[0098] The measurements are updated as follows:

[0099] Celestial Navigation System Measurement Mean Square Error Matrix for:

[0100]

[0101] In the formula, R k is the measurement noise covariance matrix of the celestial navigation system at time k;

[0102] The mean square error matrix of state vector measurement of celestial navigation system

[0103]

[0104] Celestial navigation system filter gain K k for:

[0105]

[0106] Estimated state vector of celestial navigation system and the estimated mean square error matrix P k for

[0107]

[0108]

[0109] After the Unscented Kalman filter of the astronomical navigation system, the position and velocity of the spacecraft are obtained in the inertial coordinate system.

[0110] 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 spacecraft astronomical navigation method based on cosmic particle detection, characterized in that: The state model and measurement model of the spacecraft astronomical navigation system based on cosmic particle detection are established, and the arrival vector of cosmic particles is obtained by using the cosmic particle detector as the measurement of the astronomical navigation system; considering multiple perturbation factors, the state model of the astronomical navigation system is established, and the arrival vectors of cosmic particles emitted by three cosmic particle sources are combined as the measurement model of the astronomical navigation system, and the unscented Kalman filter method is used to estimate the position and speed of the spacecraft; the specific steps include: Step 1: Establish the state model of the celestial navigation system: (1) (2) Its abbreviation is: (3) In the formula, is the state vector of the state model, for The differential of x, y, z, are the position and velocity of the three axes of the spacecraft in the equatorial inertial coordinate system centered on the Earth’s center of mass; is the radius of the Earth; is the second area coefficient, and its value is 0.0010826269; , , The perturbations of the three axes include the non-spherical gravitational perturbation of the Earth, the third body perturbation, the atmospheric drag perturbation, the solar light pressure perturbation and other perturbations; is the system nonlinear continuous state transfer function of the state model; is the gravitational constant; is the satellite position parameter vector; is the state model error of the celestial navigation system; Step 2: Establish a measurement model for the celestial navigation system: Select three cosmic particle source locations, namely two cosmic particle sources on the earth and the sun, and measure the arrival vector of the detected cosmic particles, denoted as , , , combining the known position coordinates of the two cosmic particle sources on Earth and the observed position coordinates of the Sun relative to the Earth, , , It is expressed as the result of deducting the spacecraft's own coordinates from the position coordinates of the corresponding cosmic particle source and normalizing them, expressed as: (4) (5) (6) (7) (8) (9) in, , , are the position coordinates of three cosmic particle sources, is the position coordinate of the spacecraft, , , are the vectors obtained by subtracting the spacecraft's own coordinates from the position coordinates of the three cosmic particle sources, , , Express , , To take the model, , , express , , The normalized result; Will , , Form a nine-dimensional vector , which is the measurement of the established spacecraft astronomical navigation system. After adding the error term, the measurement model of the astronomical navigation system based on cosmic particle detection is written as follows: (10) in, To establish the measurement of spacecraft astronomical navigation system, is the error term, where is calculated from the first cosmic particle source The corresponding error term is projected on the x, y, and z axes. for The corresponding error term is projected on the x, y, and z axes. for The corresponding error term is projected on the x, y, and z axes; Its abbreviation is: (11) In the formula, The arrival vector of cosmic particles detected by cosmic particle detectors, i.e., the quantity measurement of the spacecraft astronomical navigation system; is the arrival vector of cosmic particles observed by the detector at a certain moment, and t is the moment when the spacecraft is moving; represents the directional measurement noise of cosmic particle detectors; , , are the coordinates of the cosmic particle source positions, is the position coordinate of the spacecraft; It is a nonlinear continuous measurement function of the celestial navigation system; Step 3: Measure and obtain the arrival direction vector of cosmic particles: The arrival direction vector of cosmic particles is measured by the cosmic particle detector carried on the spacecraft; Step 4: discretize the state model and measurement model in step 1 and step 2; Step 5: Perform unscented Kalman filtering on the celestial navigation system to obtain the position and velocity of the spacecraft expressed in the geocentric equatorial inertial coordinate system.

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