Autonomous navigation method based on atmospheric absorption effect of X-ray source

Abstract

The invention discloses an autonomous navigation method based on the atmospheric absorption effect of an X-ray source, and belongs to the technical field of autonomous navigation of aircrafts. The method comprises the following steps: firstly, establishing a relation model of the tangency point height and the X-ray atmospheric transmittance in an occultation observation state, then calculating the X-ray atmospheric transmittance at the current moment to obtain the corresponding tangency point height, and combining the predicted speed and position information of the aircraft at the current moment, and carrying out information fusion through Kalman filtering to realize autonomous navigation of the aircraft. The X-ray pulsar navigation detector is used for detecting strong-flow X-ray sources including pulsar and direct-flow X-ray stars, the defect that the number of strong sources in X-ray pulsar navigation is insufficient is overcome, the number of navigation sources is increased, and the precision and real-time performance of X-ray pulsar navigation are improved.

Description

Technical Field

[0001] The invention relates to an autonomous navigation method based on the atmospheric absorption effect of an X-ray source, belonging to the technical field of autonomous navigation of aircraft. Background Art

[0002] X-ray pulsars have the advantages of absolute positioning, full autonomy, strong anti-interference ability, and a wide navigation range. They have important strategic research value and broad application prospects. Traditional X-ray pulsar navigation technology requires that the radiation source has a stable rotation period and a clear outline. In order to shorten the pulse integration time, the radiation source is also required to have a large flux. Except for Crab, the flux of other pulsars that meet the navigation requirements is very weak, 2 to 4 orders of magnitude lower than Crab. Therefore, the main bottleneck of X-ray pulsar navigation technology is that there are very few strong pulsar sources that meet the navigation requirements, resulting in too long an integration time required to observe high-precision pulse phases, making it difficult for navigation accuracy and real-time performance to meet application requirements. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, propose an autonomous navigation method based on the atmospheric absorption effect of an X-ray source, establish a relationship model between the tangent point height and the X-ray atmospheric transmittance under the occultation observation state, obtain the corresponding tangent point height according to the X-ray atmospheric transmittance at the current moment, combine the predicted aircraft speed and position information at the current moment, perform information fusion through Kalman filtering, and realize autonomous navigation of the aircraft.

[0004] The technical solution of the present invention is: An autonomous navigation method based on atmospheric absorption effect of an X-ray source, comprising: Obtain the flight history data of the aircraft under the occultation observation state and the positional relationship between each trajectory point and the X-ray source, respectively calculate the tangent point positions, obtain the X-ray atmospheric transmittance corresponding to each tangent point height, and establish a relationship model between the tangent point height and the X-ray atmospheric transmittance; the tangent point is the point closest to the ground surface on the line connecting the X-ray source line of sight and the aircraft trajectory point; The aircraft starts to fly, and in the state of occultation observation, calculates the photon transmittance at the current moment and substitutes it into the relationship model between the tangent point height and the X-ray atmospheric transmittance to obtain the tangent point height at the current moment; According to the speed and position of the aircraft at the previous moment, the orbital dynamics model is used to predict the position and speed of the aircraft at the current moment; Taking the position and velocity of the aircraft as the state quantity and the tangent point height as the observation quantity, based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent point height at the current moment, Kalman filtering is used for information fusion to correct the position and velocity of the aircraft at the current moment as the autonomous navigation information.

[0005] Furthermore, based on the obtained tangent point position, the method for calculating the X-ray atmospheric transmittance corresponding to the tangent point height is: Based on the tangent point height, the surface equations of the atmosphere layers above the tangent point are constructed; then combined with the ray equation from the aircraft to the X-ray source, the two intersection points of the surface of each atmospheric layer and the ray equation are solved; The coordinates of each intersection point are divided into two groups using the line connecting the tangent point and the center of the earth as the dividing line, and are arranged from small to large according to the distance to the tangent point. The distance between every two adjacent intersection points in each group is calculated to obtain the optical thickness on the left and right sides of the tangent point, and then the total optical thickness of the propagation path from the X-ray source to the aircraft is obtained; According to the total optical thickness of the propagation path from the X-ray source to the aircraft, the X-ray atmospheric transmittance corresponding to the tangent point height is calculated.

[0006] Furthermore, based on the tangent point height, the surface equations of the atmospheric layers above the tangent point are constructed. Surface equation of the atmosphere It is expressed as:

[0007] In the formula, is the semi-major axis of the reference ellipsoid, is the minor semi-axis of the reference ellipsoid; is the height resolution, is the total number of atmospheric layers; is the tangent point height.

[0008] Furthermore, the relationship model between the tangent point height and the X-ray atmospheric transmittance is:

[0009] in:

[0010] In the formula, is the pulsar flux under normal observation conditions; is the X-ray intensity after atmospheric attenuation, including photon counts, energy, and tangent point height The corresponding relationship, , are the minimum and maximum energy levels of photons that the X-ray pulsar navigation detector can receive, is the photon counting noise, Height of tangent point The corresponding X-ray atmospheric transmittance.

[0011] Furthermore, the intensity of X-rays after atmospheric attenuation The calculation method is:

[0012] In the formula, is the reference energy spectrum, that is, the energy spectrum without atmospheric attenuation, is the photon energy; is the total optical thickness of the propagation path from the X-ray source to the spacecraft.

[0013] Furthermore, the method for calculating the total optical thickness of the X-ray source to the aircraft propagation path is: The coordinates of each intersection point are divided into two groups using the line connecting the tangent point and the center of the earth as the dividing line, and are arranged from small to large according to the distance to the tangent point. The distance between every two adjacent intersection points in each group is calculated: For the group on the left side of the dividing line, the distance between two adjacent intersection points is expressed as:

[0014] For the group on the right side of the dividing line, the distance between two adjacent intersection points is expressed as:

[0015] Optical thickness on both sides of the tangent point and Respectively expressed as:

[0016]

[0017] In the formula, For intersection The atmospheric density at For intersection The atmospheric density at is the X-ray cross section, represents the atmospheric composition; Total optical depth of the X-ray source to vehicle propagation path for: .

[0018] Furthermore, the photon transmittance at the current moment is calculated. The calculation method is: use the sensor data carried by the X-ray pulsar navigation detector to determine the state of the detector at the time of photon recording, filter the X-ray photons, and then sum the number of filtered X-ray photons per unit time to obtain the number of photons; divide the number of photons by the pulsar photon flow rate to obtain the photon transmittance at the current moment.

[0019] Furthermore, taking the position and velocity of the aircraft as the state quantity and the tangent point height as the observation quantity, based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent point height at the current moment, Kalman filtering is used for information fusion to form an observation model of autonomous navigation based on the atmospheric absorption effect of the X-ray source:

[0020] In the formula, is the tangent point height observation noise, the observation matrix , are state variables containing the position and velocity of the aircraft, is the observed height of the tangent point;

[0021] In the formula, is the average radius of the Earth, is the supplementary angle between the X-ray source direction vector and the spacecraft orbit point direction vector, is the aircraft position vector.

[0022] The advantages of the present invention compared with the prior art are: The present invention constructs an X-ray atmospheric transmittance model based on the Beer-Lambert law and a filtering observation model based on the tangent point height, which solves the problem of insufficient number of strong pulsar navigation sources, expands the number of navigation sources, and improves the accuracy and real-time performance of X-ray pulsar navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings: Figure 1 The first light curve of Crab occultation observed by Insight-HXMT LE telescope (observation number: P0111605008); Figure 2 This is a schematic diagram of the relationship between the X-ray source, tangent point and spacecraft position in the occultation observation state; Figure 3 It is a cross-sectional diagram of X-ray source, tangent point and spacecraft position under occultation observation state; Figure 4 This is a flowchart of autonomous navigation based on the atmospheric absorption effect of an X-ray source according to an embodiment of the present invention; Figure 5 Schematic diagram of the relationship between the X-ray source, intersection point and spacecraft position in the occultation observation state. DETAILED DESCRIPTION

[0024] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0025] According to astronomical observations, there are more than 10 known strong flux X-ray sources, including the sun, black holes and some neutron stars. The X-rays emitted by these celestial bodies are unstable or do not have periodic changes, so they are not suitable for traditional pulsar navigation. However, the X-rays they emit will produce regular changes when passing through different altitudes of the atmosphere, such as Figure 1 shown.

[0026] The present invention proposes an autonomous navigation method based on the atmospheric absorption effect of X-ray sources. According to the change amount and direction vector of these celestial X-rays passing through the atmosphere, a measurement equation related to the position of the aircraft is established. Combined with filtering technology, navigation errors can be corrected to improve the accuracy of autonomous navigation of the aircraft.

[0027] The autonomous navigation method specifically includes: 1. Modeling of X-ray photon transmittance under occultation observation The X-ray photon transmittance modeling process under occultation observation is as follows, which mainly includes the following steps: (1) Determination of the tangent point Figure 2 is a schematic diagram of the positional relationship between the aircraft, the tangent point and the X-ray source, where the tangent point is the point closest to the surface of the earth where the line of sight of the X-ray source and the aircraft is connected. When the aircraft is in the state of occultation observation, the tangent point is located in the earth's atmosphere. Assume that the tangent point position vector in the J2000 mean equatorial geocentric coordinate system is , the aircraft position vector is , the pulsar direction vector is According to the geometric characteristics of the positions of the tangent point, the aircraft, and the X-ray source, we can know that: 1) The line connecting the spacecraft's orbit point and the tangent point is parallel to the X-ray source direction vector; 2) The line connecting the aircraft and the tangent point is perpendicular to the tangent point direction vector; 3) The distance from the tangent point to the center of the earth and the distance from the aircraft to the center of the earth are in the same right triangle, such as Figure 3 As shown, the angle is the supplementary angle between the direction vector of the X-ray source and the direction vector of the spacecraft orbit point.

[0028] From the above three conditions we can get: (1) In the formula, the angle It can be expressed as: (2) Since the coordinates of the aircraft trajectory point and the direction vector of the X-ray source are known, there are only three unknown quantities in equation (1), namely, the coordinates of the tangent point. The coordinates of the tangent point corresponding to the aircraft trajectory point can be directly solved to obtain the tangent point height: .

[0029] (2) Constructing the atmospheric surface equation Above the tangent point Surface equation of the atmosphere It can be expressed as: (3) In the formula, is the semi-major axis of the reference ellipsoid, is the minor semi-axis of the reference ellipsoid. In the reference ellipsoid model used in the WGS-84 coordinate system, , ; is the height resolution, is the total number of atmospheric layers, determined by the following formula: (4) In the formula, To consider the maximum altitude of the atmosphere's absorption effect on X-rays, is the floor function.

[0030] (3) Constructing the observation path ray equation Since the X-ray source is very far away from the earth, it can be considered that the X-rays it radiates are parallel light when they reach the vicinity of the earth. At this time, according to the definition of the space ray equation, the ray equation from the aircraft to the X-ray source is It can be expressed as: (5) (4) Calculation of optical thickness In order to solve the intersection point of the ray and the atmospheric surface, we combine equations (3) and (5) and obtain the following equation by combining similar terms: The quadratic equation of , that is: (6) Where: (7) According to the root-finding formula of a quadratic equation, we can get: (8) Substituting equation (8) into equation (5), we can find the intersection of each layer of atmosphere and the ray equation. Since the aircraft is outside the atmosphere, the ray There are two intersection points with each surface equation, one on each side of the tangent point. The intersection coordinates are divided into two groups using the line connecting the tangent point and the center of the earth as the dividing line, and are arranged from small to large according to the distance to the tangent point. The intersection coordinates on the left side of the dividing line are marked as , the coordinates of the intersection point on the right side of the dividing line are .

[0031] On the left side of the dividing line, the distance between two adjacent intersection points can be expressed as: (9) On the right side of the dividing line, the distance between two adjacent intersection points can be expressed as: (10) Optical thickness on both sides of the tangent point and They can be expressed as: (11) (12) In the formula, For intersection The atmospheric density at For intersection The atmospheric density at , which can be obtained through the NRLMSIS 2.0 model; X-ray cross section Can be obtained through the XCOM database, Represents atmospheric components, including nitrogen molecules, oxygen molecules, nitrogen atoms, oxygen atoms, argon atoms, etc.

[0032] At this time, the total optical thickness of the X-ray source to the spacecraft propagation path is for: (13) (5) Calculation of X-ray atmospheric transmittance The transmittance of X-ray photons in the atmosphere can be modeled using the Beer-Lambert law, namely: (14) In the formula, is the intensity of X-rays after atmospheric attenuation; is the reference energy spectrum, that is, the energy spectrum without atmospheric attenuation, is the photon energy.

[0033] Contains the correspondence between photon counts, energy, and tangent point height, based on The construction of the light curve model can be realized, that is, (15) In the formula, , are the minimum and maximum energy levels of photons that can be received by the X-ray pulsar navigation detector; is the photon counting noise.

[0034] At this time, the tangent point height Corresponding X-ray atmospheric transmittance for: (16) In the formula, is the pulsar flux under normal observation conditions.

[0035] By obtaining the X-ray atmospheric transmittance corresponding to different tangent point heights, the relationship between the tangent point height and the photon transmittance can be established, and the X-ray photon transmittance model under the occultation observation state can be obtained for the subsequent acquisition of tangent point height observation values.

[0036] 2. Autonomous navigation based on the atmospheric absorption effect of X-ray sources The autonomous navigation process based on the atmospheric absorption effect of X-ray source is as follows Figure 4 As shown, it mainly includes the following steps: (1) Photon screening Data from other sensors on the X-ray pulsar navigation detector are used to determine the state of the detector at the time the photon is recorded, thereby removing some noise; common X-ray detection satellites have corresponding photon screening software, such as HXMTDAS and HEAsoft.

[0037] (2) Photon counting The number of X-ray photons screened per unit time is summed.

[0038] (3) Calculation of photon transmittance The photon count divided by the photon flow rate can give the photon transmittance at this time. The photon transmittance in the occultation observation state should be less than 1, and the transmittance in the normal observation state is close to 1; the pulsar photon flow rate can be obtained by taking the average of the photon counts during normal observation.

[0039] (4) Obtaining the tangent point height observation The X-ray photon transmittance model under occultation observation establishes the relationship between the tangent point height and the photon transmittance. According to the photon transmittance calculated in step (3), the corresponding tangent point height observation value can be obtained by interpolation.

[0040] (5) Aircraft status prediction Using the orbital dynamics model, the current position and speed can be estimated given the speed and position at the previous moment.

[0041] (6) Information Fusion The position and velocity of the aircraft are used as state variables, the tangent point height is used as the observation variable, and the Kalman filter is used for information fusion. The measurement model is as follows: according to Figure 5 From the geometric constraints in, we can see that: (17) In the formula, is the average radius of the Earth.

[0042] The above formula establishes the relationship between the aircraft position vector and the tangent point height. The tangent point height can be predicted by the aircraft position and the X-ray source direction vector. At the same time, the tangent point height can be observed through the X-ray atmospheric transmittance model, so the tangent point height is selected as the filtered observation.

[0043] The measurement equation (17) is Linearization gives: (18) In the formula, The tangent point height The partial derivative of (19) When the position and velocity of the aircraft in the J2000 flat equatorial geocentric coordinate system are selected as state variables, the observation model of the autonomous navigation method based on the atmospheric absorption effect of the X-ray source is: (20) In the formula, is the tangent point height observation noise, and the observation matrix is: (twenty one) The above-described embodiments are only preferred specific implementations of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

1. An autonomous navigation method based on the atmospheric absorption effect of an X-ray source, characterized in that: include: Obtain the flight history data of the aircraft under the occultation observation state and the positional relationship between each trajectory point and the X-ray source, respectively calculate the tangent point positions, obtain the X-ray atmospheric transmittance corresponding to each tangent point height, and establish a relationship model between the tangent point height and the X-ray atmospheric transmittance; the tangent point is the point closest to the ground surface on the line connecting the X-ray source line of sight and the aircraft trajectory point; The aircraft starts to fly, and in the state of occultation observation, calculates the photon transmittance at the current moment and substitutes it into the relationship model between the tangent point height and the X-ray atmospheric transmittance to obtain the tangent point height at the current moment; According to the speed and position of the aircraft at the previous moment, the orbital dynamics model is used to predict the position and speed of the aircraft at the current moment; Taking the position and velocity of the aircraft as the state quantity and the tangent point height as the observation quantity, based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent point height at the current moment, Kalman filtering is used for information fusion to correct the position and velocity of the aircraft at the current moment as the autonomous navigation information.

2. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 1, characterized in that: Based on the obtained tangent point position, the method for calculating the X-ray atmospheric transmittance corresponding to the tangent point height is: Based on the tangent point height, the surface equations of the atmosphere layers above the tangent point are constructed; then combined with the ray equation from the aircraft to the X-ray source, the two intersection points of the surface of each atmospheric layer and the ray equation are solved; The coordinates of each intersection point are divided into two groups using the line connecting the tangent point and the center of the earth as the dividing line, and are arranged from small to large according to the distance to the tangent point. The distance between every two adjacent intersection points in each group is calculated to obtain the optical thickness on the left and right sides of the tangent point, and then the total optical thickness of the propagation path from the X-ray source to the aircraft is obtained; According to the total optical thickness of the propagation path from the X-ray source to the aircraft, the X-ray atmospheric transmittance corresponding to the tangent point height is calculated.

3. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 2, characterized in that: Based on the tangent point height, the surface equations of the atmospheric layers above the tangent point are constructed. Atmospheric surface equation It is expressed as: In the formula, is the semi-major axis of the reference ellipsoid, is the minor semi-axis of the reference ellipsoid; is the height resolution, is the total number of atmospheric layers; is the tangent point height.

4. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 1, characterized in that: The relationship model between the tangent point height and the X-ray atmospheric transmittance is: in: In the formula, is the pulsar flux under normal observation conditions; is the X-ray intensity after atmospheric attenuation, including photon counts, energy, and tangent point height The corresponding relationship, , are the minimum and maximum energy levels of photons that the X-ray pulsar navigation detector can receive, is the photon counting noise, Height of tangent point The corresponding X-ray atmospheric transmittance.

5. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 4, characterized in that: X-ray intensity after atmospheric attenuation The calculation method is: In the formula, is the reference energy spectrum, that is, the energy spectrum without atmospheric attenuation, is the photon energy; is the total optical thickness of the propagation path from the X-ray source to the spacecraft.

6. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 2 or 5, characterized in that: The method for calculating the total optical depth of the X-ray source to the spacecraft propagation path is: The coordinates of each intersection point are divided into two groups using the line connecting the tangent point and the center of the earth as the dividing line, and are arranged from small to large according to the distance to the tangent point. The distance between every two adjacent intersection points in each group is calculated: For the group on the left side of the dividing line, the distance between two adjacent intersection points is expressed as: For the group on the right side of the dividing line, the distance between two adjacent intersection points is expressed as: Optical thickness on both sides of the tangent point and Respectively expressed as: In the formula, For intersection The atmospheric density at For intersection The atmospheric density at is the X-ray cross section, represents the atmospheric composition; Total optical depth of the X-ray source to vehicle propagation path for: 。 7. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 1, characterized in that: Calculate the photon transmittance at the current moment. The calculation method is: use the sensor data carried by the X-ray pulsar navigation detector to determine the state of the detector at the time of photon recording, filter the X-ray photons, and then sum the number of filtered X-ray photons per unit time to obtain the number of photons; divide the number of photons by the pulsar photon flow rate to obtain the photon transmittance at the current moment.

8. The autonomous navigation method based on the atmospheric absorption effect of the X-ray source according to claim 1, characterized in that: Taking the position and speed of the aircraft as the state quantity and the tangent point height as the observation quantity, based on the predicted position and speed of the aircraft at the current moment and the calculated tangent point height at the current moment, Kalman filtering is used for information fusion to form an observation model for autonomous navigation based on the atmospheric absorption effect of the X-ray source: In the formula, is the tangent point height observation noise, the observation matrix , are state variables containing the position and velocity of the aircraft; is the observed height of the tangent point, , is the average radius of the Earth, is the supplementary angle between the X-ray source direction vector and the spacecraft orbit point direction vector, is the aircraft position vector.

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