An autonomous navigation method based on the atmospheric absorption effect of X-ray sources

Abstract

This invention discloses an autonomous navigation method based on the atmospheric absorption effect of X-ray sources, belonging to the field of autonomous navigation technology for aircraft. The method first establishes a model relating the tangent point altitude to the X-ray atmospheric transmittance under occultation observation conditions. Then, by calculating the current X-ray atmospheric transmittance, the corresponding tangent point altitude is obtained. Combined with the predicted current aircraft velocity and position information, information fusion is performed using Kalman filtering to achieve autonomous navigation. This invention utilizes an X-ray pulsar navigation detector to detect high-flow X-ray sources, including pulsars and direct-flow X-ray stars, compensating for the insufficient number of high-flow sources in X-ray pulsar navigation, expanding the number of navigation sources, and improving the accuracy and real-time performance of X-ray pulsar navigation.

Description

Technical Field

[0001] This invention relates to an autonomous navigation method based on the atmospheric absorption effect of an X-ray source, belonging to the field of autonomous navigation technology for aircraft. Background Technology

[0002] X-ray pulsars possess advantages such as absolute positioning, full autonomy, strong anti-interference capabilities, and a wide navigation range, making them promising for numerous applications. Traditional X-ray pulsar navigation technology requires the radiation source to have a stable rotation period and a clearly defined profile. To shorten the pulse integration time, a relatively high flux from the radiation source is also required. However, apart from Crab, the flux of other pulsars meeting these navigation requirements is extremely weak, 2-4 orders of magnitude lower than Crab's. Therefore, the main bottleneck of X-ray pulsar navigation technology is the extremely limited number of strong pulsar sources that meet navigation requirements. This results in excessively long integration times required for observing high-precision pulse phases, making it difficult to meet application demands in terms of navigation accuracy and real-time performance. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an autonomous navigation method based on the atmospheric absorption effect of X-ray sources. It establishes a relationship model between the tangent height and the X-ray atmospheric transmittance under occultation observation conditions. The corresponding tangent height is obtained based on the X-ray atmospheric transmittance at the current moment. Combined with the predicted velocity and position information of the spacecraft at the current moment, information fusion is performed through Kalman filtering to achieve autonomous navigation of the spacecraft.

[0004] The technical solution of this invention is:

[0005] An autonomous navigation method based on the atmospheric absorption effect of an X-ray source includes:

[0006] The flight history data of the spacecraft under occultation observation and the positional relationship between each trajectory point and the X-ray source were obtained. The tangent point position was calculated, and the X-ray atmospheric transmittance corresponding to the height of each tangent point was obtained. A relationship model between the height of the tangent point and the X-ray atmospheric transmittance was established. The tangent point is the point closest to the ground surface on the line connecting the line of sight of the X-ray source and the trajectory point of the spacecraft.

[0007] Once the spacecraft starts flying, under occultation observation conditions, it calculates the photon transmittance at the current moment and substitutes it into the relationship model between the tangent point altitude and the X-ray atmospheric transmittance to obtain the tangent point altitude at the current moment.

[0008] Based on the spacecraft’s velocity and position at the previous moment, an orbital dynamics model is used to predict the spacecraft’s position and velocity at the current moment.

[0009] Using the aircraft's position and velocity as state variables and the tangent height as an observation, Kalman filtering is used to fuse information based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent height at the current moment, and the corrected position and velocity of the aircraft at the current moment are used as autonomous navigation information.

[0010] Furthermore, based on the obtained tangent point location, the method for calculating the X-ray atmospheric transmittance corresponding to the tangent point height is as follows:

[0011] Based on the height of the tangent point, construct the surface equations of each atmospheric layer above the tangent point; then, combine the ray equations from the spacecraft to the X-ray source to solve for the two intersection points of the surface equations of each atmospheric layer and the ray equations.

[0012] The coordinates of the obtained intersection points are divided into two groups by using the line connecting the tangent point and the Earth's center as the dividing line. The groups are then arranged in ascending order of distance to the tangent point. The distance between any two adjacent intersection points in each group is calculated to obtain the optical thickness on the left and right sides of the tangent point. This leads to the total optical thickness of the X-ray source propagating along the spacecraft's path.

[0013] The atmospheric transmittance of X-rays at the tangent height is calculated based on the total optical thickness along the propagation path from the X-ray source to the spacecraft.

[0014] Furthermore, based on the height of the tangent point, the surface equations of each atmospheric layer above the tangent point are constructed, and the surface equation of the i-th atmospheric layer above the tangent point is Γ. i Represented as:

[0015]

[0016] In the formula, R a R is the semi-major axis of the reference ellipsoid. b The minor semi-axis of the reference ellipsoid is denoted by N; Δh is the height resolution. pL h represents the total number of atmospheric layers. tp The height of the tangent point.

[0017] Furthermore, the model relating the tangent point height to X-ray atmospheric transmittance is as follows:

[0018]

[0019] in:

[0020]

[0021] In the formula, Q lc The pulsar flux under normal observation conditions; I(E,h) tp The intensity of the X-rays after atmospheric attenuation includes the photon count, energy, and tangent height h. tp The correspondence, E low Eup These represent the minimum and maximum energy levels at which an X-ray pulsar navigation detector can receive photons, respectively. lc For photon counting noise, η(h) tp () represents the height of the tangent point h. tp The corresponding X-ray atmospheric transmittance.

[0022] Furthermore, the intensity of X-rays after atmospheric attenuation, I(E,h) tp The calculation method for ) is as follows:

[0023]

[0024] In the formula, I0(E) is the reference energy spectrum, i.e., the energy spectrum without atmospheric attenuation, and E is the photon energy; τ(E,h) tp ) represents the total optical thickness of the X-ray propagation path from the X-ray source to the aircraft.

[0025] Furthermore, the method for calculating the total optical thickness along the propagation path from the X-ray source to the spacecraft is as follows:

[0026] Divide the coordinates of the obtained intersection points into two groups using the line connecting the tangent point and the Earth's center as the boundary. Arrange the groups in ascending order of distance to the tangent point, and calculate the distance between any two adjacent intersection points within each group:

[0027] In the group to the left of the dividing line, the distance between two adjacent intersection points is expressed as:

[0028]

[0029] In the group to the right of the dividing line, the distance between two adjacent intersection points is expressed as:

[0030]

[0031] Optical thickness τ on both sides of the tangent point L and τ R They are represented as follows:

[0032]

[0033] In the formula, Intersection Atmospheric density at that location Intersection Atmospheric density at that location; σ ζ (E) is the X-ray cross section, and ζ represents the atmospheric composition;

[0034] The total optical thickness τ(E,h) of the X-ray source propagation path to the spacecraft tp )for:

[0035] τ(E,h tp )=τ L(E,h tp )+τ R (E,h tp ).

[0036] Furthermore, the photon transmittance at the current moment is calculated as follows: using the sensor data on the X-ray pulsar navigation detector, the state of the detector at the time of photon recording is determined, X-ray photons are filtered, and the number of filtered X-ray photons per unit time is summed to obtain the photon count; the photon count is divided by the pulsar photon flux to obtain the photon transmittance at the current moment.

[0037] Furthermore, using the aircraft's position and velocity as state variables and the tangent altitude as the observation, based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent altitude 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:

[0038]

[0039] In the formula, v Po For tangent point height observation noise, observation matrix X j For the state variables containing the position and velocity of the aircraft, [h tp [This refers to the height observation at the tangent point;]

[0040]

[0041] In the formula, Re is the average radius of the Earth, and β tp The angle between the X-ray source direction vector and the spacecraft orbit point direction vector is the supplementary angle. This is the aircraft's position vector.

[0042] The advantages of this invention compared to the prior art are:

[0043] This invention constructs an X-ray atmospheric transmittance model based on Beer-Lambert's law and a filtered observation model based on tangent height, which solves the problem of insufficient number of strong sources for pulsar navigation, expands the number of navigation sources, and improves the accuracy and real-time performance of X-ray pulsar navigation. Attached Figure Description

[0044] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0045] Figure 1The first light curve measured by the Insight-HXMT LE telescope under the Crab occultation observation condition (observation number: P0111605008);

[0046] Figure 2 This is a schematic diagram showing the relationship between the X-ray source, tangent point, and spacecraft position during occultation observation.

[0047] Figure 3 This is a cross-sectional view of the X-ray source, tangent point, and spacecraft position under occultation observation conditions.

[0048] Figure 4 This is a flowchart illustrating the autonomous navigation process based on the atmospheric absorption effect of an X-ray source, as described in an embodiment of the present invention.

[0049] Figure 5 This is a schematic diagram showing the relationship between the X-ray source, tangent point, and spacecraft position during occultation observation. Detailed Implementation

[0050] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0051] According to astronomical observations, there are currently more than 10 known high-flow X-ray sources, including the Sun, black holes, and some neutron stars. The X-rays emitted by these celestial bodies have unstable or non-periodic periods, making them unsuitable for traditional pulsar navigation. However, the X-rays emitted by these objects will exhibit regular variations as they pass through different altitudes in the atmosphere, such as... Figure 1 As shown.

[0052] This invention proposes an autonomous navigation method based on the atmospheric absorption effect of X-ray sources. Based on the changes and direction vectors of X-rays from these celestial bodies through the atmosphere, a measurement equation related to the spacecraft's position is established. Combined with filtering technology, navigation errors can be corrected, and the accuracy of autonomous navigation of the spacecraft can be improved.

[0053] This autonomous navigation method specifically includes:

[0054] I. Modeling of X-ray photon transmittance under occultation observation conditions

[0055] The process for modeling X-ray photon transmittance under occultation observation conditions is as follows, mainly including the following steps:

[0056] (1) Determining the location of the tangent point

[0057] Figure 2This diagram illustrates the positional relationship between the spacecraft, the tangent point, and the X-ray source. The tangent point is the point on the Earth's surface closest to the line connecting the X-ray source's line of sight and the spacecraft. When the spacecraft is in occultation observation mode, the tangent point is located within the Earth's atmosphere. Assume the tangent point's position vector in the J2000 mean equatorial geocentric coordinate system is... The aircraft's position vector is Pulsar direction vector is Based on the geometric characteristics of the positions of the tangent point, the spacecraft, and the X-ray source, we can conclude that:

[0058] 1) The line connecting the spacecraft's orbital point and the tangent point is parallel to the X-ray source direction vector;

[0059] 2) The line connecting the aircraft and the point of tangency is perpendicular to the direction vector of the point of tangency;

[0060] 3) The distance from the point of tangency to the Earth's center and the distance from the spacecraft to the Earth's center are within the same right triangle, such as... Figure 3 As shown, the included angle is the supplementary angle between the X-ray source direction vector and the spacecraft orbit point direction vector.

[0061] From the above three conditions, we can conclude that:

[0062]

[0063] In the formula, the included angle β tp It can be represented as:

[0064]

[0065] Since the coordinates of the spacecraft's orbital point and the direction vector of the X-ray source are known, only the coordinates of the tangent point are unknown in equation (1). The coordinates of the tangent point corresponding to the spacecraft's trajectory point can be directly solved, thus obtaining the tangent point height h. tp .

[0066] (2) Constructing the equations of atmospheric surfaces

[0067] The equation of the surface of the i-th atmospheric layer above the tangent point is Γ i It can be represented as:

[0068]

[0069] In the formula, R a R is the semi-major axis of the reference ellipsoid. b R is the minor semi-axis of the reference ellipsoid. In the reference ellipsoid model used in the WGS-84 coordinate system, R a =6378137m, R b =6356752m; Δh is the height resolution, N pL The total number of atmospheric layers is determined by the following formula:

[0070]

[0071] In the formula, h top To account for the maximum height at which the atmosphere absorbs X-rays, floor(·) is the floor function.

[0072] (3) Constructing the observation path ray equation

[0073] Since the X-ray source is extremely far from Earth, the X-rays it emits can be considered parallel light when they reach the vicinity of Earth. Therefore, according to the definition of the space ray equation, the ray equation Θ from the spacecraft to the X-ray source can be expressed as:

[0074]

[0075] (4) Calculate optical thickness

[0076] To find the intersection point of the ray and the atmospheric surface, we can combine equations (3) and (5) simultaneously, and by combining like terms, we can obtain a quadratic equation in t, namely:

[0077] at 2 +bt+c=0 (6)

[0078] In the formula:

[0079]

[0080] According to the quadratic formula, we can obtain:

[0081]

[0082] Substituting equation (8) into equation (5), the intersection points of each atmospheric layer and the ray equation can be obtained. Since the spacecraft is located outside the atmosphere, ray Θ has two intersection points with each surface equation, located on either side of the tangent point. The intersection point coordinates are divided into two groups by the line connecting the tangent point and the Earth's center, and arranged in ascending order of distance to the tangent point. The intersection point coordinates on the left side of the dividing line are marked as follows: The coordinates of the intersection point to the right of the dividing line are:

[0083] To the left of the dividing line, the distance between two adjacent intersection points can be expressed as:

[0084]

[0085] To the right of the dividing line, the distance between two adjacent intersection points can be expressed as:

[0086]

[0087] Optical thickness τ on both sides of the tangent point L and τR They can be represented as:

[0088]

[0089] In the formula, Intersection Atmospheric density at that location Intersection The atmospheric density at that location can be obtained using the NRLMSIS2.0 model; the X-ray cross-section σ ζ (E) can be obtained through the XCOM database, where ζ represents atmospheric components, including nitrogen molecules, oxygen molecules, nitrogen atoms, oxygen atoms, argon atoms, etc.

[0090] At this point, the total optical thickness τ(E,h) along the propagation path from the X-ray source to the spacecraft tp )for:

[0091] τ(E,h tp )=τ L (E,h tp )+τ R (E,h tp (13)

[0092] (5) Calculate the atmospheric transmittance of X-rays

[0093] The transmittance of X-ray photons in the atmosphere can be modeled using the Beer-Lambert law, that is:

[0094]

[0095] In the formula, I(E,h) tp I0(E) represents the intensity of X-rays after atmospheric attenuation; I0(E) represents the reference energy spectrum, i.e., the energy spectrum without atmospheric attenuation, and E represents the photon energy.

[0096] I(E,h tp This includes the correspondence between photon counts, energy, and tangent height, based on I(E,h) tp It can realize the construction of light curve models, that is

[0097]

[0098] In the formula, E low E up These are the minimum and maximum energy levels at which an X-ray pulsar navigation detector can receive photons; B lc This is photon counting noise.

[0099] At this point, the tangent height h tp The corresponding X-ray atmospheric transmittance η(h) tp )for:

[0100]

[0101] In the formula, Q lc This represents the pulsar flux under normal observation conditions.

[0102] By calculating the X-ray atmospheric transmittance at different tangent heights, the relationship between tangent height and photon transmittance can be established, resulting in an X-ray photon transmittance model under occultation observation conditions, which can be used to obtain subsequent tangent height observation values.

[0103] II. Autonomous Navigation Based on Atmospheric Absorption Effect of X-ray Sources

[0104] The autonomous navigation process based on the atmospheric absorption effect of X-ray sources is as follows: Figure 4 As shown, the main steps include:

[0105] (1) Photon Filtering

[0106] By using data from other sensors on the X-ray pulsar navigation detector, the state of the detector at the time of photon recording can be determined, thereby removing some noise; common X-ray detection satellites have corresponding photon filtering software, such as HXMTDAS and HEAsoft.

[0107] (2) Photon counting

[0108] The number of X-ray photons filtered per unit time is summed.

[0109] (3) Calculate photon transmittance

[0110] The photon transmittance can be obtained by dividing the photon count by the photon flux. The photon transmittance during occultation observation should be less than 1, while the transmittance during normal observation is close to 1. The photon flux of a pulsar can be obtained by taking the average of the photon counts during normal observation.

[0111] (4) Obtaining the tangent point height observation

[0112] The X-ray photon transmittance model under occultation observation state establishes the relationship between the tangent height and the photon transmittance. Based on the photon transmittance calculated in step (3), the corresponding tangent height observation value can be obtained by interpolation.

[0113] (5) Aircraft status prediction

[0114] Using an orbital dynamics model, given the velocity and position at the previous moment, the position and velocity at the current moment can be estimated.

[0115] (6) Information fusion

[0116] Using the aircraft's position and velocity as state variables and the tangent point altitude as the observation, a Kalman filter is employed for information fusion. The measurement model is as follows:

[0117] according to Figure 5 From the geometric constraints, we can see that:

[0118]

[0119] In the formula, Re is the average radius of the Earth.

[0120] The above equation establishes the relationship between the aircraft position vector and the tangent height. The tangent height can be predicted from the aircraft position and the X-ray source direction vector. At the same time, the tangent height can be observed through the X-ray atmospheric transmittance model. Therefore, the tangent height is selected as the filtered observation.

[0121] The measurement equation (17) is in Linearization yields:

[0122]

[0123] In the formula, For the tangent height pair The partial derivatives,

[0124]

[0125] When the position and velocity of the spacecraft 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 as follows:

[0126]

[0127] In the formula, v Po For the tangent point height observation noise, the observation matrix is:

[0128]

[0129] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within 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: The flight history data of the spacecraft under occultation observation and the positional relationship between each trajectory point and the X-ray source were obtained. The tangent point position was calculated, and the X-ray atmospheric transmittance corresponding to the height of each tangent point was obtained. A relationship model between the height of the tangent point and the X-ray atmospheric transmittance was established. The tangent point is the point closest to the ground surface on the line connecting the line of sight of the X-ray source and the trajectory point of the spacecraft. Once the spacecraft starts flying, under occultation observation conditions, it calculates the photon transmittance at the current moment and substitutes it into the relationship model between the tangent point altitude and the X-ray atmospheric transmittance to obtain the tangent point altitude at the current moment. Based on the spacecraft’s velocity and position at the previous moment, an orbital dynamics model is used to predict the spacecraft’s position and velocity at the current moment. Using the aircraft's position and velocity as state variables and the tangent height as an observation, Kalman filtering is used to fuse information based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent height at the current moment, and the corrected position and velocity of the aircraft at the current moment are used as autonomous navigation information. The model relating the tangent height to X-ray atmospheric transmittance is as follows: in: In the formula, Q lc The pulsar flux under normal observation conditions; I(E,h) tp The intensity of the X-rays after atmospheric attenuation includes the photon count, energy, and tangent height h. tp The correspondence, E low 、E up These represent the minimum and maximum energy levels at which an X-ray pulsar navigation detector can receive photons, respectively. lc For photon counting noise, η(h) tp (h) represents the height of the tangent point. tp The corresponding X-ray atmospheric transmittance; X-ray intensity I(E,h) after atmospheric attenuation tp The calculation method for ) is as follows: In the formula, I0(E) is the reference energy spectrum, i.e., the energy spectrum without atmospheric attenuation, and E is the photon energy; τ(E,h) tp The total optical thickness along the X-ray propagation path from the X-ray source to the spacecraft is calculated as follows: Divide the coordinates of the obtained intersection points into two groups using the line connecting the tangent point and the Earth's center as the boundary. Arrange the groups in ascending order of distance to the tangent point, and calculate the distance between any two adjacent intersection points within each group: In the group to the left of the dividing line, the distance between two adjacent intersection points is expressed as: In the group to the right of the dividing line, the distance between two adjacent intersection points is expressed as: Optical thickness τ on both sides of the tangent point L and τ R They are represented as follows: In the formula, Intersection Atmospheric density at that location Intersection Atmospheric density at that location; σ ζ (E) is the X-ray cross section, ζ represents the atmospheric composition; N pL This represents the total number of atmospheric layers. The total optical thickness τ(E,h) of the X-ray source propagation path to the spacecraft tp )for: τ(E,h tp )=τ L (E,h tp )+τ R (E,h tp )。 2. The autonomous navigation method based on the atmospheric absorption effect of an X-ray source according to claim 1, characterized in that, Based on the obtained tangent point location, the method for calculating the X-ray atmospheric transmittance corresponding to the tangent point height is as follows: Based on the height of the tangent point, construct the surface equations of each atmospheric layer above the tangent point; then, combine the ray equations from the spacecraft to the X-ray source to solve for the two intersection points of the surface equations of each atmospheric layer and the ray equations. The coordinates of the obtained intersection points are divided into two groups by using the line connecting the tangent point and the Earth's center as the dividing line. The groups are then arranged in ascending order of distance to the tangent point. The distance between any two adjacent intersection points in each group is calculated to obtain the optical thickness on the left and right sides of the tangent point. This leads to the total optical thickness of the X-ray source propagating along the spacecraft's path. The atmospheric transmittance of X-rays at the tangent height is calculated based on the total optical thickness along the propagation path from the X-ray source to the spacecraft.

3. The autonomous navigation method based on the atmospheric absorption effect of an X-ray source according to claim 2, characterized in that, Based on the height of the tangent point, construct the surface equations of each atmospheric layer above the tangent point, and the surface equation of the i-th atmospheric layer above the tangent point is Γ. i Expressed as: Where R a R is the semi-major axis of the reference ellipsoid. b The minor semi-axis of the reference ellipsoid is denoted by N; Δh is the height resolution. pL h represents the total number of atmospheric layers. tp The height of the tangent point.

4. The autonomous navigation method based on the atmospheric absorption effect of an X-ray source according to claim 1, characterized in that, The photon transmittance at the current moment is calculated as follows: using sensor data on the X-ray pulsar navigation detector, the state of the detector at the time of photon recording is determined, X-ray photons are filtered, and the number of filtered X-ray photons per unit time is summed to obtain the photon count; the photon count is divided by the pulsar photon flux to obtain the photon transmittance at the current moment.

5. The autonomous navigation method based on the atmospheric absorption effect of an X-ray source according to claim 1, characterized in that, Using the aircraft's position and velocity as state variables and the tangent altitude as an observation, a Kalman filter is used to fuse information based on the predicted position and velocity of the aircraft at the current moment and the calculated tangent altitude at the current moment, forming an observation model for autonomous navigation based on the atmospheric absorption effect of the X-ray source. Where, v Po For tangent point height observation noise, observation matrix For the tangent height pair The partial derivatives, X is the aircraft's position vector; j For state variables containing the position and velocity of the aircraft; [h tp [This refers to the height observation at the tangent point.] Re is the average radius of the Earth, β tp It is the supplementary angle between the X-ray source direction vector and the spacecraft orbit point direction vector.

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